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229.68 Tm <6F6E20> Tj 1 0 0 1 287.52 229.68 Tm <626F7468> Tj 0.72 Tc 1 0 0 1 72.24 216.96 Tm <62696F2D20> Tj 1 0 0 1 96.72 216.96 Tm <616E6420> Tj 1 0 0 1 120.96 216.96 Tm <73796E74686574696320> Tj 1 0 0 1 174.96 216.96 Tm <6D6163726F6D6F6C6563756C617220> Tj 1 0 0 1 266.64 216.96 Tm <73797374656D73> Tj 0.72 Tc 1 0 0 1 71.76 204.24 Tm <7468617420> Tj 1 0 0 1 94.80 204.24 Tm <61726520> Tj 1 0 0 1 114.24 204.24 Tm <6E6F7720> Tj 1 0 0 1 138.96 204.96 Tm <706F737369626C6520> Tj 1 0 0 1 186.96 204.00 Tm <7769746820> Tj 1 0 0 1 210.96 204.00 Tm <74686520> Tj 1 0 0 1 230.16 204.00 Tm <616E616C79746963616C20> Tj 1 0 0 1 283.68 204.24 Tm <756C7472612D> Tj 0.72 Tc 1 0 0 1 72.00 191.28 Tm <63656E74726966756765> Tj 0.96 Tc 1 0 0 1 72.48 150.00 Tm <312E20> Tj 1 0 0 1 88.80 150.00 Tm <6C6E74726F64756374696F6E> Tj 0.48 Tc 1 0 0 1 84.00 122.88 Tm <41626F757420> Tj 1 0 0 1 117.84 122.88 Tm <6120> Tj 1 0 0 1 126.96 122.88 Tm <64656361646520> Tj 1 0 0 1 164.16 122.88 Tm <61676F20> Tj 1 0 0 1 185.28 122.64 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85.20 Tm <6A6F75726E616C2E20> Tj 1 0 0 1 279.60 84.00 Tm <497420> Tj 1 0 0 1 293.04 84.24 Tm <776173> Tj 0.72 Tc 1 0 0 1 71.52 71.52 Tm <717569636B6C7920> Tj 1 0 0 1 113.52 71.28 Tm <72657475726E656420> Tj 1 0 0 1 158.88 71.04 Tm <627920> Tj 1 0 0 1 176.40 71.04 Tm <616E20> Tj 1 0 0 1 193.20 71.04 Tm <456469746F7220> Tj 1 0 0 1 228.48 71.28 Tm <7769746820> Tj 1 0 0 1 254.88 71.04 Tm <74686520> Tj 1 0 0 1 274.80 71.04 Tm <6661746865726C79> Tj 0.72 Tc 1 0 0 1 71.76 58.32 Tm <61647669636520> Tj 1 0 0 1 108.48 58.32 Tm <746F20> Tj 1 0 0 1 123.12 58.32 Tm <7468697320> Tj 1 0 0 1 145.68 58.56 Tm <706F73742D646F6320> Tj 1 0 0 1 192.48 58.08 Tm <7468617420> Tj 1 0 0 1 215.52 58.08 Tm <686520> Tj 1 0 0 1 231.84 58.08 Tm <73686F756C6420> Tj 1 0 0 1 268.80 58.08 Tm <736572696F75736C79> Tj 0.48 Tc 1 0 0 1 71.52 45.60 Tm <636F6E736964657220> Tj 1 0 0 1 117.36 45.60 Tm <6D6F76696E6720> Tj 1 0 0 1 158.64 45.36 Tm <6177617920> Tj 1 0 0 1 188.88 45.36 Tm <66726F6D20> Tj 1 0 0 1 216.72 45.36 Tm 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573.12 437.76 Tm <41> Tj 0.48 Tc 1 0 0 1 342.48 425.52 Tm <64656361646520> Tj 1 0 0 1 378.72 425.52 Tm <697320> Tj 1 0 0 1 389.04 425.28 Tm <6120> Tj 1 0 0 1 397.44 425.52 Tm <6C6F6E6720> Tj 1 0 0 1 420.72 425.52 Tm <74696D6520> Tj 1 0 0 1 444.72 425.28 Tm <696E20> Tj 1 0 0 1 456.24 425.28 Tm <6D6F6465726E20> Tj 1 0 0 1 495.36 425.04 Tm <736369656E636520> Tj 1 0 0 1 533.04 424.80 Tm <616E6420> Tj 1 0 0 1 553.20 424.80 Tm <696E20> Tj 1 0 0 1 564.72 424.80 Tm <74686973> Tj 0.48 Tc 1 0 0 1 342.72 412.80 Tm <706572696F6420> Tj 1 0 0 1 375.84 412.32 Tm <746865726520> Tj 1 0 0 1 402.48 412.32 Tm <68617320> Tj 1 0 0 1 420.72 412.32 Tm <6265656E20> Tj 1 0 0 1 445.68 412.32 Tm <6120> Tj 1 0 0 1 453.36 412.56 Tm <717569746520> Tj 1 0 0 1 480.00 412.08 Tm <72656D61726B61626C6520> Tj 1 0 0 1 536.16 411.84 Tm <7475726E61626F7574> Tj 0.72 Tc 1 0 0 1 342.96 399.36 Tm <696E20> Tj 1 0 0 1 354.48 399.36 Tm <74686520> Tj 1 0 0 1 371.76 399.36 Tm <666F7274756E657320> Tj 1 0 0 1 413.28 399.36 Tm <6F6620> 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0 1 556.32 151.68 Tm <67726F7373> Tj 0.96 Tc 1 0 0 1 365.52 138.24 Tm <636F6E666F726D6174696F6E293B> Tj 0.72 Tc 1 0 0 1 341.52 126.48 Tm <2E20> Tj 1 0 0 1 365.76 125.04 Tm <74686520> Tj 1 0 0 1 382.56 125.28 Tm <70757269747920> Tj 1 0 0 1 413.04 125.04 Tm <6F6620> Tj 1 0 0 1 425.52 125.04 Tm <6120> Tj 1 0 0 1 433.44 125.04 Tm <6D6163726F6D6F6C6563756C61727072657061726174696F6E20> Tj 1 0 0 1 570.72 125.76 Tm <2861> Tj 0.72 Tc 1 0 0 1 365.76 111.84 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 436.80 112.32 Tm <76656C6F6369747920> Tj 1 0 0 1 479.28 111.84 Tm <6469616772616D20> Tj 1 0 0 1 522.72 111.84 Tm <6F7220> Tj 1 0 0 1 537.36 111.84 Tm <6120> Tj 1 0 0 1 546.96 112.08 Tm <64656E73697479> Tj 0.72 Tc 1 0 0 1 365.76 98.88 Tm <737065637472756D20> Tj 1 0 0 1 410.64 97.44 Tm <2920> Tj 1 0 0 1 415.92 97.68 Tm <3B> Tj 0.72 Tc 1 0 0 1 341.52 87.12 Tm <6F20> Tj 1 0 0 1 365.76 85.44 Tm <74686520> Tj 1 0 0 1 384.00 85.44 Tm <746865726D6F64796E616D696320> Tj 1 0 0 1 462.72 85.44 Tm <6E6F6E2D696465616C69747920> Tj 1 0 0 1 524.16 85.44 Tm <6F6620> Tj 1 0 0 1 538.32 85.44 Tm <6120> Tj 1 0 0 1 547.92 85.44 Tm <6D6163726F2D> Tj 0.72 Tc 1 0 0 1 366.00 72.48 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 421.44 72.48 Tm <736F6C7574696F6E20> Tj 1 0 0 1 468.96 74.40 Tm <2820> Tj 1 0 0 1 474.48 72.48 Tm <76697269616C20> Tj 1 0 0 1 507.36 72.24 Tm <636F656666696369656E747320> Tj 1 0 0 1 570.96 72.24 Tm <6F72> Tj 0.72 Tc 1 0 0 1 365.76 59.28 Tm <6163746920> Tj 1 0 0 1 383.28 59.52 Tm <7669747920> Tj 1 0 0 1 403.92 59.28 Tm <636F6566666920> Tj 1 0 0 1 431.04 59.28 Tm <6369656E747320> Tj 1 0 0 1 460.08 57.36 Tm <2920> Tj 1 0 0 1 465.60 57.84 Tm <3B> Tj 0.72 Tc 1 0 0 1 341.52 47.76 Tm <6F20> Tj 1 0 0 1 365.76 46.08 Tm <74686520> Tj 1 0 0 1 389.52 46.08 Tm <696E746572616374696F6E7320> Tj 1 0 0 1 453.84 46.08 Tm <6265747765656E20> Tj 1 0 0 1 502.80 46.08 Tm <6D6163726F6D6F6C6563756C6573> Tj 0.72 Tc 1 0 0 1 366.48 33.84 Tm <2820> Tj 1 0 0 1 372.00 33.12 Tm <696E636C7564696E6720> Tj 1 0 0 1 421.44 33.12 Tm <73656C662D6173736F63696174696F6E20> Tj 1 0 0 1 500.64 32.88 Tm <6265686176696F75722C20> Tj 1 0 0 1 556.32 32.88 Tm <636F6D2D> Tj 0.72 Tc 1 0 0 1 365.76 20.40 Tm <706C657820> Tj 1 0 0 1 389.28 20.16 Tm <666F726D6174696F6E20> Tj 1 0 0 1 438.72 20.16 Tm <616E6420> Tj 1 0 0 1 459.36 20.16 Tm <6C6967616E6420> Tj 1 0 0 1 491.76 19.92 Tm <62696E64696E67292E> Tj ET endstream endobj 5 0 obj 25590 endobj 6 0 obj << /Type /Font /Subtype /Type1 /Name /F3 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 7 0 obj << /Length 8 0 R >> stream trends in analytical chemistry, vol. 13, no. 10, 1994[40] I. Marle, C. Pettersson and T. Arvidsson, ./.Chromatogr., 456 (1988) 323.[41] J. Stihlberg, S. Jcinsson and G. Pettersson, in P.Suominen and T. Reinikainen Editors),Proceedings of the 2nd TRICEL symposium onTrichoderma cellulases and other hydrolases,Espoo, Finland 1993, Foundation forBiotechnical and lndustrial FermentationResearch, Helsinki, Vol. 8, 1993, pp. 273-280.Roland Isaksson, Curt Pettersson and StefanJonsson are at the Department of PharmaceuticalChemistry, Analytical Pharmaceutical Chemistry, 439Uppsala University, BiomedicalCenter, p. O. Box574, 5-751 23 Uppsala, Sweden.Goran Pettersson /b at the Department ofBiochemistry, Uppsala University, BiomedicalCenter, P. O. Box 576, 5-751 23 Uppsala, Sweden.Ingrid Marle is at Pharmaceutical and AnalyticalR&D, Astra Pain ControlAB, S-151 85 Sodertdlje,Sweden.Jerry Stdlberg is at the Department of MolecularBiology, Uppsala University, Biomedical Center, P.O. Box 590, 3-751 24 Uppsala, Sweden.Jorgen Hermansson is at ChromTech AB, P. O.Box 6056, S-129 06 Hdgersten, Sweden. The analytical ultracentrifuge spins again Stephen E. HardingSutton Bonington, UKSince its inception by T. Svedberg and co-workers in the 1920's the technique of ana-lytical ultracentrifugation has undergone anextraordinary evolution, peaking in popular-ity in the 1950's and 1960's followed by asteady decline untilthe last few years with arenewalof interest culminating in the launchof a new commercially available instrument.The technique is worthy of consideration byany analyticalchemist interested in the char-acterisation of the physical behaviour ofmacromolecules in solution. This articleattempts to indicate the breadth of the rangeof different types of measurements on bothbio- and synthetic macromolecular systemsthat are now possible with the analytical ultra-centrifuge1. lntroductionAbout a decade ago a young post-doctoral sci-entist submitted a manuscript on a topic concerningthe analytical ultracentrifugation of macromole-cules to a leading biochemical journal. It wasquickly returned by an Editor with the fatherlyadvice to this post-doc that he should seriouslyconsider moving away from such an out-of-datetechnique and turn instead towards more modernand informative techniques - such as nuclear magnetic resonance (advice politely declined!). Adecade is a long time in modern science and in thisperiod there has been a quite remarkable turnaboutin the fortunes of this technique which is now over70 years old and whose climax of popularity wasprobably over three decades ago. After many yearsof decline since that time (largely because of theadvance of gel electrophoresis and gel filtrationmethods for molecular weight determination andthe advent of high resolution structural methods inprotein biochemistry) it has now reemerged. Thereis a growing recognition across the chemical andbiochemical communities that this technique stillhas a leading role to play in the characterisation of,and understanding the behaviour of, polymers,macromolecules and macromolecular assemblies- whether they be biological in origin or not -in terms ofo the size (either the molecular weight ordimensions);. the size distribution (for a polydisperse solu-tion of macromolecules) ;o solution conformation (the overall or grossconformation);. the purity of a macromolecularpreparation (asedimentation velocity diagram or a densityspectrum ) ;o the thermodynamic non-ideality of a macro-molecular solution ( virial coefficients oracti vity coeffi cients ) ;o the interactions between macromolecules( including self-association behaviour, com-plex formation and ligand binding). endstream endobj 8 0 obj 3680 endobj 9 0 obj << /Length 10 0 R >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj3 Do Q endstream endobj 10 0 obj 44 endobj 12 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 6 0 R >> /XObject << /Obj3 3 0 R >> /Subtype 7 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 2 0 R 9 0 R 4 0 R ] >> endobj 11 0 obj << /Kids [ 12 0 R ] /Count 1 /Type /Pages >> endobj 13 0 obj << /Pages 11 0 R /Type /Catalog >> endobj xref 0 14 0000000000 65535 f 0000000015 00000 n 0000000110 00000 n 0000000188 00000 n 0000082010 00000 n 0000107653 00000 n 0000107675 00000 n 0000107789 00000 n 0000111522 00000 n 0000111543 00000 n 0000111641 00000 n 0000111910 00000 n 0000111661 00000 n 0000111976 00000 n trailer << /Size 14 /Info 1 0 R /Root 13 0 R >> startxref 112031 %%EOF 14 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 15 0 obj << /Type /XObject /Subtype /Image /Name /Obj15 /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 92340 >> stream &ɲW?__>@tIG :*R`H@p<4  Bx2 x-/$ (ܱ R M2:#莉/tf0hOxE̎tJ 4ʌ)c3f|1E|f>ٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٶٲ⳾+#p<6xd #Dg`A tGЈ Dq:#DlP@ 8tܧ" XMBAQ(uZ[JYT4 q9lTAy2uUuVZ>,:&=iKa$ zK`D0Ši jI*AI46J/x$D.+)J(唺; L0M0PL*`0<*&UBd'  ~wݧw\ݭz|v;5\NYN#_?-׽u__%2$DTy!D^^8s4<ٚ4 S!_8GȐ)PG|2\Bv\L?* @΂$,^ fkqHdjD%)r"zOdUr|GJf 3C4<& ݄L"pohLv A!٦LidK"(`0@  < f<36B92F`Fl`55&40!\ZhlApZ*' .MZM Ƃtpz` P!dOӋXP Sa Aaw1L2:_"vHp}A< mto}&otE zwa{XVJb-4[ `l0Hh9}DTEmS]t\5"xv AA[m;եpӆ}&T]AvVmEhiDa0.4z6 otm 7M'm^'ۯ~޻z~I.'D{zM;7OMVim_iշth}}׿Z}~]Kwz[o^L5 oM|[zHX?կm}N._{߿{ջw??_T_}z{[[n_z_% ɕP/8o7\wWIKWic?Ub>@}ԈPmWbƬ?ד JXpJMOOVO6 \:ҫzo5=,%^xl0zW Obo]phõFw})ko]{޻it/X?K4a+K}az;H z:Wv|cK)b*Wئ:y#{ul?צnl!C_ׇ_Km~_m+[JUWH-uߟ]jZKmmon[ ;K]--NuMG+Jw^݆k0 %c]uuUg}j }kO %Wi{ % };Xاb4% m+[^ݭ%uk*TWk &vON/mVaZMUl+6OvBaSQV)+au{;ݍ5U5V]1[m-N"BMI&ailL&xU{ A)!&j.{~Pj M]h7IOv4S ;U*AqLSXaZm0[Mj0LEћ` '`B"#'I""2vat#AZիWzwAµ"<0 ا`{ &)D0B"""""""""""88"""""i<LBd[mDD!`Չ!:b" ЈDC$TDDD `킈#C?%$'%Z8uh2/##"̮JLnɹJ,\ ")"ޢb2 jxdU;¸Lʻ qjaץ^WvU}w}B)Wݭ+fHȟ-Wģ|acfEk靧]W\Io]Uu]zWYC$*A DBh[2KB)93_0`qLTv:UMA&FI<)LjuGYȔAdHS|fˊK0P &d;40N0 L& 10Bٙ3":8~:CϲJt"]R34y[3PB`333A!H.%0A !C!|2FlˊfAI d9@0 qh }A/{,&8qpH %:'n"o  v Dj &~ @΂\A$;F e4vZAa0!L !t VAZ !ŷiۢpA>t-I;% JR GҦ6M8` L5MT"nN&cN&аBiyޕNDXO8ö B*v̄ wNn&xս4j?;h-*F^NV=i6ȷ4N: ޶M싄K <"Jr ~$JTK}RUV޿ץ/~ak*UUU~ӯ]Vw{#Yp7wDhBT^IT*J_K_U}-w~]RTJJ/K {i6޿ԋ|~4ꫭ~ZZ~_apo_괿U%IVt} ߶/}l7tkG_Iu~:k_}K~I_k~]*T-t}edKO>wOuK'/WKru]{iܨK?7^fmKJ\ZViыKU#kv}׵>Zں_=~N?m.B 'eviZz:UÎ=-%׫[VEi:]okwoՄ}va/u +JJ)U!{iZ}N`.M%\Vl$ZVmvw$V)د){l ^8*[V.n0NNcMNj&'LBjmTBꫴTSl/TCJI.I?iW-WdKMZiݾիl0": $aEvbl(+0 aa4aja1 馡1 UXi|0B=0i4LUUwLPiޛ!ȐQ hC h0vjB"Q"$""""""""""""" V4 a5Aix؅ 0LS쥋@L 0 'paArx0X`FS"""8ЈɸAˆDDDDG)uۯ_KbjL_].XOt`tQł-~"?#H/[eFd" i(ذʡxTP4̫;]oPj4^.\7``p;BmJ?ſIDX뤦DqQ{m#"̑S_mvWR$22΄AS32&DDI aȕ) STp!38P)GA ʳ30ALق ie `3D&L )H! 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364.56 Tm <73697A657320> Tj 1 0 0 1 173.52 365.04 Tm <7468617420> Tj 1 0 0 1 193.68 365.04 Tm <63616E20> Tj 1 0 0 1 212.88 364.80 Tm <626520> Tj 1 0 0 1 226.80 365.04 Tm <737475646965642E20> Tj 1 0 0 1 266.88 365.28 Tm <697420> Tj 1 0 0 1 275.52 365.28 Tm <63616E20> Tj 1 0 0 1 294.96 365.04 Tm <6265> Tj 0.48 Tc 1 0 0 1 67.20 351.36 Tm <7573656420> Tj 1 0 0 1 95.04 351.60 Tm <746F20> Tj 1 0 0 1 110.16 351.60 Tm <63686172616374657269736520> Tj 1 0 0 1 173.28 351.84 Tm <74686520> Tj 1 0 0 1 193.92 351.84 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 246.96 352.32 Tm <77656967687420> Tj 1 0 0 1 285.12 352.08 Tm <6F6620> Tj 1 0 0 1 300.96 352.08 Tm <61> Tj 0.72 Tc 1 0 0 1 67.20 338.40 Tm <737563726F736520> Tj 1 0 0 1 108.48 338.64 Tm <6D6F6C6563756C6520> Tj 1 0 0 1 158.64 339.60 Tm <284D573A3334322920> Tj 1 0 0 1 226.80 339.12 Tm <726967687420> Tj 1 0 0 1 254.40 339.12 Tm <7468726F75676820> Tj 1 0 0 1 296.88 339.12 Tm <746F> Tj 0.48 Tc 1 0 0 1 67.44 325.68 Tm <6C6F6F6B696E6720> Tj 1 0 0 1 108.00 325.68 Tm <617420> Tj 1 0 0 1 120.48 325.68 Tm <74686520> Tj 1 0 0 1 139.44 325.68 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 210.24 325.92 Tm <636F656666696369656E747320> Tj 1 0 0 1 268.80 326.16 Tm <6F6620> Tj 1 0 0 1 282.96 326.16 Tm <68756765> Tj 0.48 Tc 1 0 0 1 67.20 312.48 Tm <6D6163726F6D6F6C6563756C6172636F6D706C6578657320> Tj 1 0 0 1 200.16 312.96 Tm <7573656420> Tj 1 0 0 1 224.16 312.96 Tm <666F7220> Tj 1 0 0 1 240.00 313.20 Tm <6472756720> Tj 1 0 0 1 264.00 313.20 Tm <746172676574696E67> Tj 0.72 Tc /F3 13.0 Tf 1 0 0 1 68.64 297.84 Tm <4932742E> Tj 0.96 Tc 1 0 0 1 66.96 260.64 Tm <332E20> Tj 1 0 0 1 84.24 260.88 Tm <44696C75746520> Tj 1 0 0 1 119.76 260.88 Tm <736F6C7574696F6E732C20> Tj 1 0 0 1 179.28 261.36 Tm <636F6E63656E747261746564> Tj 0.96 Tc 1 0 0 1 67.20 247.92 Tm <736F6C7574696F6E7320> Tj 1 0 0 1 122.88 248.16 Tm <616E6420> Tj 1 0 0 1 147.60 248.88 Tm <67656C73> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 78.72 222.24 Tm <54686520> Tj 1 0 0 1 99.36 222.48 Tm <616E616C79746963616C20> Tj 1 0 0 1 148.08 222.48 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 220.08 222.72 Tm <697320> Tj 1 0 0 1 229.44 223.20 Tm <7072696D6172696C7920> Tj 1 0 0 1 275.28 222.96 Tm <6120> Tj 1 0 0 1 282.24 222.96 Tm <746563682D> Tj 0.72 Tc 1 0 0 1 67.20 209.28 Tm <6E6971756520> Tj 1 0 0 1 96.48 209.52 Tm <666F7220> Tj 1 0 0 1 113.52 209.52 Tm <6C6F6F6B696E6720> Tj 1 0 0 1 152.88 209.76 Tm <617420> Tj 1 0 0 1 164.40 209.76 Tm <74686520> Tj 1 0 0 1 181.68 209.76 Tm <73747275637475726520> Tj 1 0 0 1 225.84 210.00 Tm <616E6420> Tj 1 0 0 1 245.76 210.00 Tm <6265686176696F757220> Tj 1 0 0 1 295.92 210.00 Tm <6F66> Tj 0.72 Tc 1 0 0 1 66.72 196.32 Tm <6120> Tj 1 0 0 1 75.12 196.32 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 152.16 196.80 Tm <696E20> Tj 1 0 0 1 163.92 196.80 Tm <64696C75746520> Tj 1 0 0 1 193.92 196.80 Tm <736F6C7574696F6E20> Tj 1 0 0 1 235.68 197.52 Tm <28692E652E20> Tj 1 0 0 1 260.40 197.28 Tm <3C20> Tj 1 0 0 1 271.20 197.04 Tm <6C3020> Tj 1 0 0 1 284.88 197.04 Tm <6D672F> Tj 0.72 Tc 1 0 0 1 66.96 183.36 Tm <6D6C292E20> Tj 1 0 0 1 92.88 183.36 Tm <497420> Tj 1 0 0 1 104.64 183.60 Tm <697320> Tj 1 0 0 1 116.40 183.60 Tm <686F776576657220> Tj 1 0 0 1 162.48 183.84 Tm <66696E64696E6720> Tj 1 0 0 1 200.64 184.08 Tm <696E6372656173696E6720> Tj 1 0 0 1 253.20 184.08 Tm <75736520> Tj 1 0 0 1 273.36 184.08 Tm <666F7220> Tj 1 0 0 1 291.36 184.32 Tm <746865> Tj 0.72 Tc 1 0 0 1 66.96 170.40 Tm <696E7665737469676174696F6E20> Tj 1 0 0 1 132.00 170.64 Tm <6F6620> Tj 1 0 0 1 145.68 170.64 Tm <74686520> Tj 1 0 0 1 164.16 170.88 Tm <6265686176696F757220> Tj 1 0 0 1 214.80 170.88 Tm <6F6620> Tj 1 0 0 1 228.48 171.12 Tm <6D6163726F6D6F6C6563756C6573> Tj 0.48 Tc 1 0 0 1 67.20 157.44 Tm <696E20> Tj 1 0 0 1 82.08 157.44 Tm <636F6E63656E74726174656420> Tj 1 0 0 1 150.00 157.92 Tm <736F6C7574696F6E20> Tj 1 0 0 1 194.40 158.16 Tm <666F726D2E20> Tj 1 0 0 1 226.56 158.16 Tm <74686520> Tj 1 0 0 1 246.96 158.16 Tm <646966667573696F6E20> Tj 1 0 0 1 295.92 158.40 Tm <6F66> Tj 0.72 Tc 1 0 0 1 66.96 144.48 Tm <736D616C6C20> Tj 1 0 0 1 96.96 144.72 Tm <6D6F6C6563756C657320> Tj 1 0 0 1 149.76 144.96 Tm <7468726F75676820> Tj 1 0 0 1 190.80 144.96 Tm <636F6E63656E74726174656420> Tj 1 0 0 1 255.60 145.68 Tm <706861736520> Tj 1 0 0 1 287.04 145.44 Tm <7379732D> Tj 0.48 Tc 1 0 0 1 66.96 131.52 Tm <74656D7320> Tj 1 0 0 1 91.92 131.76 Tm <616E6420> Tj 1 0 0 1 111.60 131.76 Tm <74686520> Tj 1 0 0 1 128.88 131.76 Tm <746865726D6F64796E616D696320> Tj 1 0 0 1 206.16 132.24 Tm <616E6420> Tj 1 0 0 1 225.60 132.24 Tm <656C617374696320> Tj 1 0 0 1 258.48 132.72 Tm <70726F70657274696573> Tj 0.72 Tc 1 0 0 1 66.72 118.80 Tm <6F6620> Tj 1 0 0 1 79.92 119.28 Tm <67656C732E> Tj 0.72 Tc /F3 13.0 Tf 1 0 0 1 66.72 80.40 Tm <342E20> Tj 1 0 0 1 83.28 80.40 Tm <547970657320> Tj 1 0 0 1 121.20 80.64 Tm <6F6620> Tj 1 0 0 1 135.36 80.64 Tm <616E616C79746963616C20> Tj 1 0 0 1 193.20 80.88 Tm <756C74726163656E74726966756765> Tj 0.72 Tc 1 0 0 1 67.20 67.44 Tm <6D6561737572656D656E74> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 78.96 42.00 Tm <5768617420> Tj 1 0 0 1 108.24 42.00 Tm <736F727420> Tj 1 0 0 1 129.12 42.00 Tm <6F6620> Tj 1 0 0 1 143.04 42.24 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 202.08 42.48 Tm <63616E20> Tj 1 0 0 1 222.24 42.72 Tm <776520> Tj 1 0 0 1 239.04 42.96 Tm <67657420> Tj 1 0 0 1 256.80 42.72 Tm <66726F6D20> Tj 1 0 0 1 283.20 42.72 Tm <736564692D> Tj 0.72 Tc 1 0 0 1 67.20 29.04 Tm <6D656E746174696F6E20> Tj 1 0 0 1 120.96 29.28 Tm <616E616C7973697320> Tj 1 0 0 1 166.08 29.52 Tm <696E20> Tj 1 0 0 1 180.96 29.52 Tm <74686520> Tj 1 0 0 1 201.60 29.52 Tm <616E616C79746963616C20> Tj 1 0 0 1 253.44 29.76 Tm <756C74726163656E7472692D> Tj 0.48 Tc 1 0 0 1 67.20 16.08 Tm <667567653F20> Tj 1 0 0 1 99.36 16.32 Tm <497420> Tj 1 0 0 1 112.08 16.32 Tm <646570656E647320> Tj 1 0 0 1 157.20 16.56 Tm <6F6E20> Tj 1 0 0 1 174.96 16.56 Tm <74686520> Tj 1 0 0 1 195.12 16.80 Tm <7479706520> Tj 1 0 0 1 221.04 16.56 Tm <6F6620> Tj 1 0 0 1 236.40 16.80 Tm <756C74726163656E74726966756765> Tj 0.24 Tc /F3 8.0 Tf 1 0 0 1 400.56 725.28 Tm <7472656E647320> Tj 1 0 0 1 424.08 725.28 Tm <696E20> Tj 1 0 0 1 432.24 725.28 Tm <616E616C79746963616C20> Tj 1 0 0 1 466.80 725.04 Tm <6368656D69737472792C20> Tj 1 0 0 1 504.96 724.80 Tm <766F6C2E20> Tj 1 0 0 1 520.32 724.80 Tm <31392C20> Tj 1 0 0 1 531.60 724.56 Tm <6E6F2E20> Tj 1 0 0 1 546.24 724.32 Tm <74302C20> Tj 1 0 0 1 559.20 724.32 Tm <6C396734> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 336.72 688.80 Tm <746563686E6971756520> Tj 1 0 0 1 386.88 689.04 Tm <776520> Tj 1 0 0 1 404.16 689.04 Tm <6170706C7920> Tj 1 0 0 1 433.92 691.44 Tm <2D20> Tj 1 0 0 1 449.76 689.04 Tm <616C6C20> Tj 1 0 0 1 465.12 689.28 Tm <706F737369626C6520> Tj 1 0 0 1 507.84 688.80 Tm <7769746820> Tj 1 0 0 1 532.32 688.56 Tm <74686520> Tj 1 0 0 1 550.80 688.32 Tm <73616D65> Tj 0.48 Tc 1 0 0 1 336.96 676.08 Tm <696E737472756D656E746174696F6E2E20> Tj 1 0 0 1 419.04 676.08 Tm <536564696D656E746174696F6E20> Tj 1 0 0 1 492.00 676.08 Tm <75656C6F6369747920> Tj 1 0 0 1 533.52 675.84 Tm <63616E20> Tj 1 0 0 1 555.36 675.84 Tm <70726F2D> Tj 0.48 Tc 1 0 0 1 336.96 663.12 Tm <7669646520> Tj 1 0 0 1 360.96 663.12 Tm <757320> Tj 1 0 0 1 375.36 663.36 Tm <7769746820> Tj 1 0 0 1 400.08 663.12 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 459.36 663.12 Tm <6F6E20> Tj 1 0 0 1 474.96 663.12 Tm <74686520> Tj 1 0 0 1 493.20 663.12 Tm <73616D706C6520> Tj 1 0 0 1 530.16 662.88 Tm <68657465726F67652D> Tj 0.48 Tc 1 0 0 1 336.72 650.16 Tm <6E656974792C20> Tj 1 0 0 1 370.56 649.92 Tm <736861706520> Tj 1 0 0 1 404.64 650.16 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 466.80 652.56 Tm <2D20> Tj 1 0 0 1 486.24 650.16 Tm <696E20> Tj 1 0 0 1 502.08 649.92 Tm <736F6D6520> Tj 1 0 0 1 533.52 649.92 Tm <636173657320> Tj 1 0 0 1 565.92 649.92 Tm <746F> Tj 0.48 Tc 1 0 0 1 336.48 636.96 Tm <73757270726973696E6720> Tj 1 0 0 1 388.08 637.20 Tm <64657461696C20> Tj 1 0 0 1 418.32 639.60 Tm <2D20> Tj 1 0 0 1 434.64 637.20 Tm <616E6420> Tj 1 0 0 1 455.76 637.20 Tm <616C736F20> Tj 1 0 0 1 479.04 636.96 Tm <696E746572616374696F6E20> Tj 1 0 0 1 534.00 636.96 Tm <696E666F726D612D> Tj 0.72 Tc 1 0 0 1 336.48 624.24 Tm <74696F6E20> Tj 1 0 0 1 358.08 624.00 Tm <627920> Tj 1 0 0 1 372.96 624.24 Tm <666F7220> Tj 1 0 0 1 389.52 624.24 Tm <6578616D706C6520> Tj 1 0 0 1 432.96 624.24 Tm <6173736179696E6720> Tj 1 0 0 1 476.64 624.24 Tm <666F7220> Tj 1 0 0 1 493.44 624.48 Tm <7768617420> Tj 1 0 0 1 519.36 624.24 Tm <776520> Tj 1 0 0 1 535.92 624.00 Tm <63616C6C20> Tj 1 0 0 1 557.04 629.28 Tm <27636F2D> Tj 0.72 Tc 1 0 0 1 336.48 611.04 Tm <736564696D656E746174696F6E2720> Tj 1 0 0 1 425.76 611.52 Tm <7068656E6F6D656E6120> Tj 1 0 0 1 499.68 612.00 Tm <2820> Tj 1 0 0 1 504.96 611.28 Tm <692E652E2C20> Tj 1 0 0 1 541.20 611.04 Tm <73706563696573> Tj 0.72 Tc 1 0 0 1 336.48 598.32 Tm <736564696D656E74696E6720> Tj 1 0 0 1 401.04 598.32 Tm <617420> Tj 1 0 0 1 415.92 598.32 Tm <74686520> Tj 1 0 0 1 436.80 598.32 Tm <73616D6520> Tj 1 0 0 1 467.28 598.32 Tm <72617465292E20> Tj 1 0 0 1 500.40 598.32 Tm <417420> Tj 1 0 0 1 519.12 598.08 Tm <6C6F77657220> Tj 1 0 0 1 552.48 598.32 Tm <726F746F72> Tj 0.48 Tc 1 0 0 1 336.24 585.36 Tm <7370656564732C20> Tj 1 0 0 1 378.24 585.36 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 452.16 585.60 Tm <657175696C69627269756D20> Tj 1 0 0 1 515.76 585.36 Tm <63616E20> Tj 1 0 0 1 539.04 585.60 Tm <70726F76696465> Tj 0.72 Tc 1 0 0 1 336.24 572.40 Tm <6162736F6C75746520> Tj 1 0 0 1 379.92 572.40 Tm <73697A6520> Tj 1 0 0 1 402.00 572.40 Tm <616E6420> Tj 1 0 0 1 422.88 572.40 Tm <73697A6520> Tj 1 0 0 1 444.72 572.64 Tm <646973747269627574696F6E20> Tj 1 0 0 1 503.52 572.64 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 563.04 574.80 Tm <2D> Tj 0.48 Tc 1 0 0 1 336.48 559.44 Tm <696E20> Tj 1 0 0 1 348.96 559.44 Tm <7465726D7320> Tj 1 0 0 1 378.24 559.44 Tm <6F6620> Tj 1 0 0 1 391.20 559.44 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 441.84 559.92 Tm <77656967687420> Tj 1 0 0 1 476.88 559.68 Tm <617665726167657320> Tj 1 0 0 1 521.76 559.44 Tm <616E6420> Tj 1 0 0 1 542.40 559.44 Tm <6D6F6C65632D> Tj 0.72 Tc 1 0 0 1 336.24 546.48 Tm <756C617220> Tj 1 0 0 1 361.92 546.72 Tm <77656967687420> Tj 1 0 0 1 400.80 546.72 Tm <646973747269627574696F6E732E20> Tj 1 0 0 1 469.68 546.96 Tm <546865726520> Tj 1 0 0 1 504.72 546.72 Tm <61726520> Tj 1 0 0 1 526.08 546.72 Tm <74776F20> Tj 1 0 0 1 550.80 546.48 Tm <6F74686572> Tj 0.72 Tc 1 0 0 1 336.48 533.76 Tm <696D706F7274616E7420> Tj 1 0 0 1 385.20 533.76 Tm <747970657320> Tj 1 0 0 1 412.80 533.76 Tm <6F6620> Tj 1 0 0 1 425.76 534.00 Tm <616E616C79746963616C20> Tj 1 0 0 1 474.00 534.00 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 547.20 533.76 Tm <6D6561732D> Tj 0.72 Tc 1 0 0 1 336.24 520.80 Tm <7572656D656E7420> Tj 1 0 0 1 378.72 523.20 Tm <2D20> Tj 1 0 0 1 394.80 521.04 Tm <6E616D656C7920> Tj 1 0 0 1 433.68 521.04 Tm <69736F7079636E696320> Tj 1 0 0 1 483.12 521.76 Tm <2820> Tj 1 0 0 1 488.88 521.04 Tm <692E652E20> Tj 1 0 0 1 507.36 526.32 Tm <27636F6E7374616E7420> Tj 1 0 0 1 553.92 520.80 Tm <64656E2D> Tj 0.48 Tc 1 0 0 1 336.24 507.84 Tm <73697479272920> Tj 1 0 0 1 370.32 507.84 Tm <64656E7369747920> Tj 1 0 0 1 410.88 508.56 Tm <6772616469656E7420> Tj 1 0 0 1 458.16 508.32 Tm <616E616C797369732C20> Tj 1 0 0 1 508.08 508.08 Tm <696D706F7274616E7420> Tj 1 0 0 1 561.36 508.08 Tm <666F72> Tj 0.72 Tc 1 0 0 1 336.00 494.88 Tm <6173736179696E6720> Tj 1 0 0 1 380.88 495.12 Tm <74686520> Tj 1 0 0 1 398.40 495.12 Tm <636F6D706F736974696F6E20> Tj 1 0 0 1 461.52 496.08 Tm <28616E6420> Tj 1 0 0 1 487.44 495.36 Tm <68656E636520> Tj 1 0 0 1 518.40 495.60 Tm <7075726974792920> Tj 1 0 0 1 556.56 495.12 Tm <6F6620> Tj 1 0 0 1 570.00 495.12 Tm <61> Tj 0.48 Tc 1 0 0 1 336.00 481.92 Tm <6D6163726F6D6F6C6563756C617220> Tj 1 0 0 1 417.84 482.40 Tm <7072657061726174696F6E20> Tj 1 0 0 1 476.40 482.16 Tm <616E6420> Tj 1 0 0 1 498.48 482.16 Tm <66696E616C6C7920> Tj 1 0 0 1 533.04 482.16 Tm <6466666973696F6E> Tj 0.48 Tc 1 0 0 1 335.76 468.72 Tm <616E616C797369733B20> Tj 1 0 0 1 381.60 468.96 Tm <616C74686F75676820> Tj 1 0 0 1 425.76 468.96 Tm <64796E616D696320> Tj 1 0 0 1 469.68 469.20 Tm <6C6967687420> Tj 1 0 0 1 494.40 469.20 Tm <73636174746572696E6720> Tj 1 0 0 1 543.84 469.20 Tm <697320> Tj 1 0 0 1 554.64 469.20 Tm <6E6F77> Tj 0.48 Tc 1 0 0 1 336.00 455.76 Tm <74686520> Tj 1 0 0 1 353.28 455.76 Tm <6D6574686F6420> Tj 1 0 0 1 391.20 455.76 Tm <6F6620> Tj 1 0 0 1 403.20 456.00 Tm <63686F69636520> Tj 1 0 0 1 437.04 456.00 Tm <666F7220> Tj 1 0 0 1 453.12 456.24 Tm <74686520> Tj 1 0 0 1 469.92 456.24 Tm <6D6561737572656D656E7420> Tj 1 0 0 1 535.44 456.00 Tm <6F6620> Tj 1 0 0 1 548.16 456.24 Tm <7472616E732D> Tj 0.48 Tc 1 0 0 1 336.24 442.80 Tm <6C6174696F6E616C20> Tj 1 0 0 1 376.32 442.80 Tm <646966667573696F6E20> Tj 1 0 0 1 423.60 443.04 Tm <636F656666696369656E74732C20> Tj 1 0 0 1 485.76 443.04 Tm <74686520> Tj 1 0 0 1 504.72 443.04 Tm <6F70746963616C20> Tj 1 0 0 1 542.16 443.04 Tm <73797374656D> Tj 0.72 Tc 1 0 0 1 335.76 429.84 Tm <6F6E20> Tj 1 0 0 1 353.04 429.84 Tm <74686520> Tj 1 0 0 1 372.96 429.84 Tm <616E616C79746963616C20> Tj 1 0 0 1 423.84 430.08 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 498.96 430.08 Tm <697320> Tj 1 0 0 1 511.44 430.32 Tm <70726F76696E6720> Tj 1 0 0 1 554.16 430.32 Tm <76657279> Tj 0.72 Tc 1 0 0 1 336.00 416.88 Tm <75736566756C20> Tj 1 0 0 1 368.40 416.88 Tm <666F7220> Tj 1 0 0 1 385.92 416.88 Tm <696E7665737469676174696E6720> Tj 1 0 0 1 449.76 417.36 Tm <74686520> Tj 1 0 0 1 467.28 417.12 Tm <646966667573696F6E20> Tj 1 0 0 1 513.60 417.12 Tm <6F6620> Tj 1 0 0 1 526.80 417.12 Tm <6D6F6C6563756C6573> Tj 0.48 Tc 1 0 0 1 336.00 403.92 Tm <7468726F75676820> Tj 1 0 0 1 378.00 404.16 Tm <6D6174726963657320> Tj 1 0 0 1 422.40 404.16 Tm <616E6420> Tj 1 0 0 1 444.00 404.40 Tm <746F776172647320> Tj 1 0 0 1 485.76 404.40 Tm <616E6420> Tj 1 0 0 1 507.60 404.40 Tm <7468726F75676820> Tj 1 0 0 1 549.84 404.40 Tm <696E7465722D> Tj 0.48 Tc 1 0 0 1 336.00 390.96 Tm <666163657320> Tj 1 0 0 1 363.60 390.96 Tm <6265747765656E20> Tj 1 0 0 1 406.08 391.20 Tm <74776F20> Tj 1 0 0 1 427.20 391.68 Tm <706861736520> Tj 1 0 0 1 457.20 391.44 Tm <73797374656D732E> Tj 0.72 Tc /F3 13.0 Tf 1 0 0 1 335.76 352.32 Tm <352E20> Tj 1 0 0 1 352.80 352.56 Tm <496E737472756D656E746174696F6E3A20> Tj 1 0 0 1 449.04 352.80 Tm <7768617420> Tj 1 0 0 1 479.28 352.80 Tm <697320> Tj 1 0 0 1 492.00 352.56 Tm <616E20> Tj 1 0 0 1 509.04 352.56 Tm <616E616C79746963616C> Tj 0.72 Tc 1 0 0 1 336.24 339.36 Tm <756C74726163656E747269667567653F> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 348.00 313.68 Tm <416E20> Tj 1 0 0 1 365.76 313.68 Tm <616E616C79746963616C20> Tj 1 0 0 1 414.96 313.68 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 488.16 313.68 Tm <697320> Tj 1 0 0 1 499.20 313.68 Tm <73696D706C7920> Tj 1 0 0 1 534.96 313.92 Tm <616E20> Tj 1 0 0 1 549.36 313.92 Tm <756C7472612D> Tj 0.72 Tc 1 0 0 1 335.52 300.72 Tm <63656E7472696675676520> Tj 1 0 0 1 390.48 301.68 Tm <28692E652E2C20> Tj 1 0 0 1 418.32 300.96 Tm <6869676820> Tj 1 0 0 1 444.96 300.96 Tm 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0 1 542.40 30.96 Tm <4520> Tj 1 0 0 1 556.80 31.20 Tm <776173> Tj 0.72 Tc 1 0 0 1 336.00 17.28 Tm <6C61756E6368656420> Tj 1 0 0 1 381.60 17.28 Tm <627920> Tj 1 0 0 1 395.76 17.52 Tm <4265636B6D616E20> Tj 1 0 0 1 443.04 20.16 Tm <2D20> Tj 1 0 0 1 457.44 17.76 Tm <74686520> Tj 1 0 0 1 474.00 17.76 Tm <4F7074696D6120> Tj 1 0 0 1 512.64 17.76 Tm <584C4120> Tj 1 0 0 1 539.28 20.40 Tm <2D20> Tj 1 0 0 1 554.40 18.48 Tm <77697468> Tj ET endstream endobj 17 0 obj 29486 endobj 18 0 obj << /Length 19 0 R >> stream 440The technique is, however, most powerful whenused with complementary techniques, such as: (forconformation analysis) X-ray scattering, viscom-etry, rotational diffusional techniques and electronmicroscopy, or (for e.g., protein subunit compo-sition work) gel electrophoresis, or ( for molecularweight distribution studies) gel filtration and lightscattering.This article is intended to give the reader animpression of the range of measurements and anal-yses that are possible with the modern analyticalultracentrifuge. For more details on any of theapplications mentioned here, see Ref. I I ], or thereferences cited therei n.2. Types of macromolecule or polymerAlthough the main emphasis of the technique inthe past has been in the fields of biochemistry andmolecular biology (focusing on proteins andnucleic acids) it is of increasing importance inpolysaccharide chemistry and the general field ofpolymer science ( including the characterisation ofsynthetic macromolecules ). Insofar as the range ofmacromolecular sizes that can be studied. it can beused to characterise the molecular weight of asucrose molecule (MW:342) right through tolooking at the sedimentation coefficients of hugemacromolecularcomplexes used for drug targetingI2t.3. Dilute solutions, concentratedsolutions and gelsThe analytical ultracentrifuge is primarily a tech-nique for looking at the structure and behaviour ofa macromolecule in dilute solution (i.e. < l0 mg/ml). It is however finding increasing use for theinvestigation of the behaviour of macromoleculesin concentrated solution form. the diffusion ofsmall molecules through concentrated phase sys-tems and the thermodynamic and elastic propertiesof gels.4. Types of analytical ultracentrifugemeasurementWhat sort of information can we get from sedi-mentation analysis in the analytical ultracentri-fuge? It depends on the type of ultracentrifuge trends in analytical chemistry, vol. 19, no. t0, l9g4technique we apply - all possible with the sameinstrumentation. Sedimentation uelocity can pro-vide us with information on the sample heteroge-neity, shape information - in some cases tosurprising detail - and also interaction informa-tion by for example assaying for what we call 'co-sedimentation' phenomena ( i.e., speciessedimenting at the same rate). At lower rotorspeeds, sedimentation equilibrium can provideabsolute size and size distribution information -in terms of molecular weight averages and molec-ular weight distributions. There are two otherimportant types of analytical ultracentrifuge meas-urement - namely isopycnic ( i.e. 'constant den-sity') density gradient analysis, important forassaying the composition (and hence purity) of amacromolecular preparation and finally dffisionanalysis; although dynamic light scattering is nowthe method of choice for the measurement of trans-lational diffusion coefficients, the optical systemon the analytical ultracentrifuge is proving veryuseful for investigating the diffusion of moleculesthrough matrices and towards and through inter-faces between two phase systems.5. Instrumentation: what is an analyticalultracentrifuge?An analytical ultracentrifuge is simply an ultra-centrifuge (i.e., high speed centrifuge - up to60 000 rev/min) with an appropriate optical sys-tem for observing and recording solute distribu-tions during and at the end of the sedimentationprocess. The technique of analytical ultracentrifu-gation is not new - Svedberg's inception of thetechnique dates from the early 1920's. The boomperiod of the technique was in the period 1950-1970 with several commercially produced analyt-ical ultracentrifuges available, most notably thefamous Beckman Model E (then present in virtu-ally every biochemistry and chemistry department)but for the last 20 years until very recently therehas been no commercially available instrument,apart from second hand Model E's. Concentrationdistributions of the macromolecular solution dur-ing ultracentrifugation were recorded using eitherrefractive index optics (Schlieren and interfer-ence) or absorption optics for those particular mac-romolecules such as proteins and nucleic acidspossessing a suitable chromophore. 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0 0 1 86.64 307.20 Tm <666F7220> Tj 1 0 0 1 104.64 306.96 Tm <6120> Tj 1 0 0 1 113.76 307.20 Tm <70726F7465696E20> Tj 1 0 0 1 151.44 306.72 Tm <7072657061726174696F6E20> Tj 1 0 0 1 210.00 306.00 Tm <636F6E7461696E696E6720> Tj 1 0 0 1 264.72 305.76 Tm <74776F20> Tj 1 0 0 1 286.08 305.52 Tm <636F6D2D> Tj 0.48 Tc 1 0 0 1 70.32 294.48 Tm <706F6E656E747320> Tj 1 0 0 1 110.40 294.00 Tm <616E6420> Tj 1 0 0 1 130.32 293.76 Tm <4669672E20> Tj 1 0 0 1 153.60 293.76 Tm <4920> Tj 1 0 0 1 157.92 293.52 Tm <6320> Tj 1 0 0 1 166.32 293.52 Tm <666F7220> Tj 1 0 0 1 182.88 293.52 Tm <6120> Tj 1 0 0 1 190.80 293.76 Tm <706F6C79646973706572736520> Tj 1 0 0 1 253.68 293.04 Tm <706F6C797361636368612D> Tj 0.72 Tc 1 0 0 1 70.56 281.28 Tm <726964652E> Tj 0.72 Tc 1 0 0 1 82.08 268.32 Tm <54686520> Tj 1 0 0 1 104.40 268.08 Tm <7261746520> Tj 1 0 0 1 125.52 267.84 Tm <6F6620> Tj 1 0 0 1 138.96 267.60 Tm <6D6F76656D656E7420> Tj 1 0 0 1 192.72 267.36 Tm <6F6620> Tj 1 0 0 1 206.40 267.12 Tm <6120> Tj 1 0 0 1 215.04 267.12 Tm <736564696D656E74696E6720> Tj 1 0 0 1 276.72 266.64 Tm <626F756E642D> Tj 0.48 Tc 1 0 0 1 69.84 255.12 Tm <61727920> Tj 1 0 0 1 90.24 255.12 Tm <66726F6D20> Tj 1 0 0 1 117.84 254.88 Tm <746865736520> Tj 1 0 0 1 147.12 254.88 Tm <7061747465726E7320> Tj 1 0 0 1 189.60 254.64 Tm <70657220> Tj 1 0 0 1 209.76 254.16 Tm <756E697420> Tj 1 0 0 1 232.56 253.92 Tm <63656E747269667567616C20> Tj 1 0 0 1 288.96 253.68 Tm <6669656C64> Tj 0.72 Tc 1 0 0 1 69.60 242.64 Tm <676976657320> Tj 1 0 0 1 97.92 242.16 Tm <74686520> Tj 1 0 0 1 114.96 241.92 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 184.32 241.44 Tm <636F656666696369656E742C20> Tj 1 0 0 1 240.24 240.96 Tm <732C20> Tj 1 0 0 1 250.80 241.20 Tm <776869636820> Tj 1 0 0 1 282.48 240.72 Tm <697320> Tj 1 0 0 1 292.56 240.72 Tm <6F6E65> Tj 0.72 Tc 1 0 0 1 69.36 229.20 Tm <6F6620> Tj 1 0 0 1 84.00 229.20 Tm <6F757220> Tj 1 0 0 1 104.64 228.96 Tm <736861706520> Tj 1 0 0 1 136.08 228.96 Tm <706172616D65746572732E20> Tj 1 0 0 1 196.08 228.24 Tm <427920> Tj 1 0 0 1 214.56 228.24 Tm <61646A757374696E6720> Tj 1 0 0 1 262.56 227.76 Tm <7468697320> Tj 1 0 0 1 283.92 227.76 Tm <7573696E67> Tj 0.72 Tc 1 0 0 1 69.60 216.24 Tm <73696D706C6520> Tj 1 0 0 1 105.60 216.24 Tm <666F726D756C616520> Tj 1 0 0 1 152.16 215.76 Tm <746F20> Tj 1 0 0 1 165.60 215.52 Tm <7374616E6461726420> Tj 1 0 0 1 209.76 215.28 Tm <636F6E646974696F6E7320> Tj 1 0 0 1 264.48 216.00 Tm <28776174657220> Tj 1 0 0 1 299.52 214.80 Tm <6173> Tj 0.72 Tc 1 0 0 1 69.36 203.28 Tm <736F6C76656E7420> Tj 1 0 0 1 109.68 203.28 Tm <617420> Tj 1 0 0 1 123.84 203.04 Tm <323022432920> Tj 1 0 0 1 159.36 202.80 Tm <616E6420> Tj 1 0 0 1 181.92 202.56 Tm <6578747261706F6C6174696E6720> Tj 1 0 0 1 250.80 202.08 Tm <7468697320> Tj 1 0 0 1 274.32 202.56 Tm <286F7220> Tj 1 0 0 1 294.96 201.84 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.36 190.56 Tm <7265636970726F63616C20> Tj 1 0 0 1 121.68 190.08 Tm <74686572656F662920> Tj 1 0 0 1 166.08 189.84 Tm <746F20> Tj 1 0 0 1 180.00 189.84 Tm <7A65726F20> Tj 1 0 0 1 204.96 189.60 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 274.56 189.12 Tm <776520> Tj 1 0 0 1 292.56 188.88 Tm <63616E> Tj 0.48 Tc 1 0 0 1 68.88 177.84 Tm <67657420> Tj 1 0 0 1 87.36 177.60 Tm <66726F6D20> Tj 1 0 0 1 113.76 177.36 Tm <74686520> Tj 1 0 0 1 131.76 177.12 Tm <696E7465726365707420> Tj 1 0 0 1 176.88 176.88 Tm <74686520> Tj 1 0 0 1 194.64 176.64 Tm <636F7272656374656420> Tj 1 0 0 1 242.40 176.16 Tm <736564696D656E746174696F6E> Tj 0.72 Tc 1 0 0 1 68.64 164.64 Tm <636F656666696369656E742C20> Tj 1 0 0 1 125.04 164.16 Tm <4A6F32302E72222D20> Tj 1 0 0 1 154.32 164.64 Tm <28756E69743A20> Tj 1 0 0 1 190.32 163.68 Tm <7365636F6E647320> Tj 1 0 0 1 230.88 163.44 Tm <6F7220> Tj 1 0 0 1 243.84 163.20 Tm <5376656462657267732C20> Tj 1 0 0 1 299.28 162.96 Tm <532C> Tj 0.72 Tc 1 0 0 1 69.12 151.92 Tm <776865726520> Tj 1 0 0 1 102.72 151.68 Tm <4920> Tj 1 0 0 1 109.44 151.44 Tm <533A20> Tj 1 0 0 1 129.36 151.44 Tm <6C302D723320> Tj 1 0 0 1 155.28 150.96 Tm <732920> Tj 1 0 0 1 168.48 150.96 Tm <616E6420> Tj 1 0 0 1 188.64 150.96 Tm <66726F6D20> Tj 1 0 0 1 214.32 150.72 Tm <74686520> Tj 1 0 0 1 231.12 150.48 Tm <736C6F706520> Tj 1 0 0 1 259.20 150.72 Tm <776520> Tj 1 0 0 1 275.04 150.24 Tm <63616E20> Tj 1 0 0 1 294.24 150.48 Tm <676574> Tj 0.72 Tc 1 0 0 1 68.88 138.72 Tm <74686520> Tj 1 0 0 1 86.64 138.72 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 156.96 138.00 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 225.84 137.76 Tm <72656772657373696F6E20> Tj 1 0 0 1 277.68 137.28 Tm <636F656666692D> Tj 0.96 Tc 1 0 0 1 68.16 126.00 Tm <6369656E742C20> Tj 1 0 0 1 98.88 126.00 Tm <6B2E20> Tj 1 0 0 1 112.56 126.48 Tm <28756E69743A6D6C2F672920> Tj 1 0 0 1 183.12 125.28 Tm <616E6420> Tj 1 0 0 1 204.96 125.04 Tm <7468656E20> Tj 1 0 0 1 230.40 125.04 Tm <66726F6D20> Tj 1 0 0 1 256.80 124.80 Tm <626F746820> Tj 1 0 0 1 281.04 125.04 Tm <706172612D> Tj 0.48 Tc 1 0 0 1 68.16 113.04 Tm <6D657465727320> Tj 1 0 0 1 103.20 112.80 Tm <6F757220> Tj 1 0 0 1 122.40 112.80 Tm <736861706520> Tj 1 0 0 1 152.64 112.56 Tm <696E666F726D6174696F6E> Tj 0.72 Tc 1 0 0 1 80.16 100.08 Tm <54686520> Tj 1 0 0 1 103.92 99.84 Tm <75736566756C6E65737320> Tj 1 0 0 1 158.40 99.36 Tm <6F6620> Tj 1 0 0 1 173.52 99.36 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 245.52 99.12 Tm <76656C6F6369747920> Tj 1 0 0 1 288.24 98.64 Tm <617320> Tj 1 0 0 1 303.12 98.64 Tm <61> Tj 0.72 Tc 1 0 0 1 68.40 87.12 Tm <726170696420> Tj 1 0 0 1 96.72 86.88 Tm <636865636B20> Tj 1 0 0 1 129.36 86.88 Tm <666F7220> Tj 1 0 0 1 147.60 86.40 Tm <73616D706C6520> Tj 1 0 0 1 186.00 86.40 Tm <686F6D6F67656E6569747920> Tj 1 0 0 1 252.48 85.92 Tm <63616E20> Tj 1 0 0 1 273.60 85.68 Tm <616C736F20> Tj 1 0 0 1 296.88 85.44 Tm <6265> Tj 0.72 Tc 1 0 0 1 67.92 74.16 Tm <7365656E20> Tj 1 0 0 1 93.36 74.16 Tm <6469726563746C7920> Tj 1 0 0 1 134.40 73.92 Tm <66726F6D20> Tj 1 0 0 1 162.00 73.68 Tm <4669672E20> Tj 1 0 0 1 187.20 73.44 Tm <6C2C20> Tj 1 0 0 1 198.96 73.44 Tm <66726F6D20> Tj 1 0 0 1 226.56 73.20 Tm <696E7370656374696F6E20> Tj 1 0 0 1 279.12 72.72 Tm <6F6620> Tj 1 0 0 1 293.52 72.72 Tm <746865> Tj 0.72 Tc 1 0 0 1 67.92 61.44 Tm <6E756D62657220> Tj 1 0 0 1 107.52 61.20 Tm <6F6620> Tj 1 0 0 1 121.20 60.96 Tm <626F756E64617269657320> Tj 1 0 0 1 176.88 60.72 Tm <616E6420> Tj 1 0 0 1 197.76 60.48 Tm <736861706520> Tj 1 0 0 1 228.24 60.24 Tm <666F7220> Tj 1 0 0 1 245.04 60.24 Tm <6561636820> Tj 1 0 0 1 270.72 60.00 Tm <696E64697669642D> Tj 0.72 Tc 1 0 0 1 67.68 48.48 Tm <75616C20> Tj 1 0 0 1 84.48 48.48 Tm <7363616E3A20> Tj 1 0 0 1 112.32 49.20 Tm <28612920> Tj 1 0 0 1 131.28 48.24 Tm <697320> Tj 1 0 0 1 141.12 48.00 Tm <6120> Tj 1 0 0 1 148.80 48.00 Tm <6D6F6E6F646973706572736520> Tj 1 0 0 1 217.68 48.00 Tm <70726F7465696E20> Tj 1 0 0 1 253.68 47.76 Tm <7072657061726174696F6E> Tj 0.72 Tc 1 0 0 1 68.16 36.48 Tm <286F6E6520> Tj 1 0 0 1 96.48 35.76 Tm <73796D6D6574726963616C20> Tj 1 0 0 1 161.28 35.04 Tm <626F756E6461727920> Tj 1 0 0 1 212.16 35.28 Tm <70657220> Tj 1 0 0 1 233.04 34.80 Tm <7363616E292C20> Tj 1 0 0 1 269.04 34.56 Tm <77686572656173> Tj 0.72 Tc 1 0 0 1 68.16 23.76 Tm <28622920> Tj 1 0 0 1 87.36 22.80 Tm <636C6561726C7920> Tj 1 0 0 1 122.16 22.80 Tm <73686F777320> Tj 1 0 0 1 154.32 22.32 Tm <74776F20> Tj 1 0 0 1 174.48 22.32 Tm <636F6D706F6E656E74732C20> Tj 1 0 0 1 238.08 22.08 Tm <7769746820> Tj 1 0 0 1 261.12 21.60 Tm <61626F757420> Tj 1 0 0 1 289.68 21.60 Tm <74776F> Tj 0.24 Tc /F3 10.0 Tf 1 0 0 1 569.76 726.00 Tm <3434270031> Tj 2.88 Tc /F3 17.0 Tf 1 0 0 1 346.08 676.80 Tm <286129> Tj 2.64 Tc 1 0 0 1 343.92 583.68 Tm <286229> Tj 3.12 Tc 1 0 0 1 343.68 506.88 Tm <286329> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 342.72 406.80 Tm <4669672E20> Tj 1 0 0 1 365.04 406.80 Tm <312E20> Tj 1 0 0 1 377.52 406.56 Tm <4578616D706C657320> Tj 1 0 0 1 426.96 406.08 Tm <6F6620> Tj 1 0 0 1 440.16 405.84 Tm <616E616C79746963616C20> Tj 1 0 0 1 488.40 405.36 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 559.20 404.40 Tm <736564692D> Tj 0.48 Tc 1 0 0 1 342.00 393.84 Tm <6D656E746174696F6E20> Tj 1 0 0 1 389.52 393.36 Tm <76656C6F6369747920> Tj 1 0 0 1 426.48 393.84 Tm <7061747465726E7320> Tj 1 0 0 1 466.08 393.36 Tm <287265636F7264656420> Tj 1 0 0 1 512.64 392.16 Tm <7573696E6720> Tj 1 0 0 1 539.76 391.68 Tm <7363616E6E696E67> Tj 0.48 Tc 1 0 0 1 341.52 380.88 Tm <6F7074696373292E20> Tj 1 0 0 1 378.48 381.12 Tm <28612920> Tj 1 0 0 1 393.36 380.40 Tm <4162736F727074696F6E20> Tj 1 0 0 1 445.92 379.92 Tm <6F707469637320> Tj 1 0 0 1 475.92 379.44 Tm <7363616E7320> Tj 1 0 0 1 506.40 379.68 Tm <28657665727920> Tj 1 0 0 1 538.32 378.72 Tm <333020> Tj 1 0 0 1 553.20 378.72 Tm <6D696E20> Tj 1 0 0 1 572.64 378.48 Tm <6174> Tj 0.48 Tc 1 0 0 1 341.52 367.92 Tm <343920> Tj 1 0 0 1 356.16 367.68 Tm <30303020> Tj 1 0 0 1 377.76 367.68 Tm <7265762F6D696E2920> Tj 1 0 0 1 418.56 367.20 Tm <617420> Tj 1 0 0 1 431.28 366.96 Tm <6120> Tj 1 0 0 1 440.64 366.96 Tm <776176656C656E67746820> Tj 1 0 0 1 497.52 366.24 Tm <6F6620> Tj 1 0 0 1 510.24 366.24 Tm <32393520> Tj 1 0 0 1 532.08 366.00 Tm <6E6D20> Tj 1 0 0 1 550.56 365.76 Tm <666F7220> Tj 1 0 0 1 566.64 365.52 Tm <746865> Tj 0.96 Tc 1 0 0 1 341.52 354.72 Tm <656E7A796D6520> Tj 1 0 0 1 385.68 354.48 Tm <6D657468796C6D616C6F6E796C20> Tj 1 0 0 1 461.52 353.76 Tm <6D75746173652E20> Tj 1 0 0 1 506.64 353.04 Tm <52656620> Tj 1 0 0 1 525.36 354.96 Tm <3A7265666572656E6365> Tj 0.72 Tc 1 0 0 1 341.52 342.00 Tm <6D61726B20> Tj 1 0 0 1 366.96 341.76 Tm <616C6C6F77696E6720> Tj 1 0 0 1 406.80 341.28 Tm <63616C6962726174696F6E20> Tj 1 0 0 1 456.72 340.80 Tm <6F6620> Tj 1 0 0 1 468.48 340.80 Tm <72616469616C20> Tj 1 0 0 1 496.32 341.28 Tm <706F736974696F6E733B20> Tj 1 0 0 1 543.36 339.84 Tm <533A20> Tj 1 0 0 1 560.88 339.60 Tm <7374617274> Tj 0.96 Tc 1 0 0 1 341.04 329.04 Tm <6F6620> Tj 1 0 0 1 354.96 328.80 Tm <63656C6C3B20> Tj 1 0 0 1 378.96 328.80 Tm <4D736F6C763A736F6C76656E7420> Tj 1 0 0 1 454.08 328.08 Tm <6D656E69736375733B20> Tj 1 0 0 1 506.16 327.36 Tm <4D736F6C6E3A736F6C7574696F6E> Tj 0.72 Tc 1 0 0 1 341.04 316.08 Tm <6D656E69736375733B20> Tj 1 0 0 1 391.20 315.60 Tm <423A20> Tj 1 0 0 1 408.00 315.36 Tm <63656C6C20> Tj 1 0 0 1 426.72 315.36 Tm <626173652E20> Tj 1 0 0 1 454.80 315.12 Tm <4172726F7720> Tj 1 0 0 1 485.28 314.88 Tm <696E6469636174657320> Tj 1 0 0 1 529.44 314.16 Tm <646972656374696F6E20> Tj 1 0 0 1 572.16 313.92 Tm <6F66> Tj 0.48 Tc 1 0 0 1 340.80 303.12 Tm <736564696D656E746174696F6E2E20> Tj 1 0 0 1 411.84 303.36 Tm <28622920> Tj 1 0 0 1 427.44 302.64 Tm <4162736F727074696F6E20> Tj 1 0 0 1 480.48 301.92 Tm <6F707469637320> Tj 1 0 0 1 511.20 301.44 Tm <7363616E7320> Tj 1 0 0 1 542.40 301.68 Tm <28657665727920> Tj 1 0 0 1 574.80 303.60 Tm <67> Tj 0.72 Tc 1 0 0 1 340.80 290.40 Tm <6D696E20> Tj 1 0 0 1 361.20 290.16 Tm <617420> Tj 1 0 0 1 373.92 290.16 Tm <343020> Tj 1 0 0 1 388.32 289.92 Tm <30303020> Tj 1 0 0 1 409.68 289.68 Tm <7265762F6D696E2920> Tj 1 0 0 1 450.72 289.44 Tm <616C32373820> Tj 1 0 0 1 484.80 288.96 Tm <6E6D20> Tj 1 0 0 1 503.04 288.72 Tm <666F7220> Tj 1 0 0 1 519.12 288.48 Tm <74686520> Tj 1 0 0 1 538.08 293.28 Tm <2C2C47656E6520> Tj 1 0 0 1 571.20 288.24 Tm <352C2C> Tj 0.72 Tc 1 0 0 1 340.80 277.20 Tm <444E4120> Tj 1 0 0 1 366.24 276.96 Tm <62696E64696E6720> Tj 1 0 0 1 402.72 277.44 Tm <70726F7465696E2E20> Tj 1 0 0 1 441.12 276.96 Tm <28632920> Tj 1 0 0 1 456.48 276.24 Tm <5363686C696572656E20> Tj 1 0 0 1 503.04 275.76 Tm <6F707469637320> Tj 1 0 0 1 534.24 275.28 Tm <7363616E7320> Tj 1 0 0 1 565.44 276.00 Tm <283330> Tj 0.48 Tc 1 0 0 1 340.56 264.24 Tm <6D696E2C20> Tj 1 0 0 1 362.64 264.00 Tm <343920> Tj 1 0 0 1 377.04 263.76 Tm <30303020> Tj 1 0 0 1 397.20 263.76 Tm <7265762F6D696E2920> Tj 1 0 0 1 436.80 263.52 Tm <666F7220> Tj 1 0 0 1 451.44 263.28 Tm <616E20> Tj 1 0 0 1 465.60 263.04 Tm <616C67696E61746520> Tj 1 0 0 1 504.72 263.52 Tm <706F6C79736163636861726964652E> Tj 0.72 Tc 1 0 0 1 339.84 229.20 Tm <74686972647320> Tj 1 0 0 1 369.36 228.72 Tm <6F6620> Tj 1 0 0 1 381.60 228.72 Tm <74686520> Tj 1 0 0 1 398.16 228.72 Tm <6D6174657269616C20> Tj 1 0 0 1 439.20 228.24 Tm <6120> Tj 1 0 0 1 446.64 228.24 Tm <6D6163726F6D6F6C6563756C6172636F6D706F6E656E74> Tj 0.72 Tc 1 0 0 1 339.84 216.00 Tm <736564696D656E74696E6720> Tj 1 0 0 1 402.96 215.52 Tm <617420> Tj 1 0 0 1 416.64 215.52 Tm <322E3620> Tj 1 0 0 1 436.80 215.28 Tm <532C20> Tj 1 0 0 1 451.20 215.28 Tm <74686520> Tj 1 0 0 1 470.88 215.28 Tm <7265737420> Tj 1 0 0 1 493.20 214.80 Tm <6120> Tj 1 0 0 1 504.00 214.80 Tm <6C6172676520> Tj 1 0 0 1 532.80 214.32 Tm <616767726567617465> Tj 0.96 Tc 1 0 0 1 339.60 203.28 Tm <736564696D656E74696E6720> Tj 1 0 0 1 401.28 202.80 Tm <617420> Tj 1 0 0 1 413.28 202.56 Tm <33352E3520> Tj 1 0 0 1 437.52 202.32 Tm <532E20> Tj 1 0 0 1 450.48 202.32 Tm <496E20> Tj 1 0 0 1 463.44 202.32 Tm <4669672E20> Tj 1 0 0 1 487.44 202.08 Tm <6C6320> Tj 1 0 0 1 500.88 201.84 Tm <697420> Tj 1 0 0 1 510.96 201.84 Tm <697320> Tj 1 0 0 1 522.48 201.60 Tm <6E6F7420> Tj 1 0 0 1 540.96 201.60 Tm <717569746520> Tj 1 0 0 1 568.56 201.36 Tm <736F> Tj 0.72 Tc 1 0 0 1 339.36 190.08 Tm <6170706172656E7420> Tj 1 0 0 1 385.20 189.84 Tm <7468617420> Tj 1 0 0 1 407.04 189.60 Tm <74686520> Tj 1 0 0 1 426.48 189.36 Tm <73616D706C6520> Tj 1 0 0 1 464.64 189.12 Tm <697320> Tj 1 0 0 1 476.88 189.12 Tm <706F6C7964697370657273652E20> Tj 1 0 0 1 545.04 188.16 Tm <5468697320> Tj 1 0 0 1 571.20 188.40 Tm <6973> Tj 0.72 Tc 1 0 0 1 339.36 176.88 Tm <6265636175736520> Tj 1 0 0 1 382.56 176.64 Tm <74686520> Tj 1 0 0 1 402.48 176.64 Tm <706F6C797361636368617269646520> Tj 1 0 0 1 479.28 175.92 Tm <697320> Tj 1 0 0 1 492.48 175.92 Tm <706F6C79646973706572736520> Tj 1 0 0 1 558.96 175.20 Tm <696E20> Tj 1 0 0 1 573.36 175.20 Tm <61> Tj 0.72 Tc 1 0 0 1 340.08 169.20 Tm <2771756173692D636F6E74696E756F75732720> Tj 1 0 0 1 432.48 163.20 Tm <73656E736520> Tj 1 0 0 1 462.96 163.92 Tm <28692E652E2C20> Tj 1 0 0 1 490.08 162.72 Tm <6D616E7920> Tj 1 0 0 1 520.56 162.48 Tm <636F6D706F6E656E7473> Tj 0.72 Tc 1 0 0 1 339.36 151.44 Tm <7769746820> Tj 1 0 0 1 364.08 150.96 Tm <6120> Tj 1 0 0 1 372.72 151.20 Tm <71756173692D636F6E74696E756F757320> Tj 1 0 0 1 457.92 150.24 Tm <646973747269627574696F6E20> Tj 1 0 0 1 516.72 149.52 Tm <6F6620> Tj 1 0 0 1 531.12 149.52 Tm <6D6F6C6563756C6172> Tj 0.48 Tc 1 0 0 1 339.12 138.48 Tm <776569676874732920> Tj 1 0 0 1 385.92 137.76 Tm <617320> Tj 1 0 0 1 399.36 137.52 Tm <6F70706F73656420> Tj 1 0 0 1 443.04 137.28 Tm <746F20> Tj 1 0 0 1 456.24 137.28 Tm <74686520> Tj 1 0 0 1 474.48 137.04 Tm <646973637265746520> Tj 1 0 0 1 516.96 141.84 Tm <2774776F2D636F6D706F2D> Tj 0.72 Tc 1 0 0 1 338.88 125.28 Tm <6E656E74732720> Tj 1 0 0 1 372.24 125.04 Tm <6361736520> Tj 1 0 0 1 397.20 124.80 Tm <6F6620> Tj 1 0 0 1 411.60 124.80 Tm <4669672E20> Tj 1 0 0 1 436.32 124.56 Tm <6C622E20> Tj 1 0 0 1 454.08 124.56 Tm <4E6F6E657468656C65737320> Tj 1 0 0 1 517.44 123.84 Tm <66726F6D20> Tj 1 0 0 1 545.52 123.60 Tm <6D617468652D> Tj 0.72 Tc 1 0 0 1 338.88 112.32 Tm <6D61746963616C20> Tj 1 0 0 1 376.56 112.08 Tm <616E616C7973697320> Tj 1 0 0 1 417.36 111.60 Tm <6F6620> Tj 1 0 0 1 430.32 111.60 Tm <74686520> Tj 1 0 0 1 447.84 111.36 Tm <626F756E6461727920> Tj 1 0 0 1 495.84 110.88 Tm <736861706520> Tj 1 0 0 1 526.08 110.64 Tm <616E6420> Tj 1 0 0 1 546.72 110.64 Tm <69747320> Tj 1 0 0 1 560.40 110.64 Tm <72617465> Tj 0.72 Tc 1 0 0 1 338.16 99.12 Tm <6F6620> Tj 1 0 0 1 352.08 98.88 Tm <6D6F76656D656E7420> Tj 1 0 0 1 405.84 98.64 Tm <697420> Tj 1 0 0 1 415.68 98.64 Tm <697320> Tj 1 0 0 1 426.72 98.88 Tm <706F737369626C6520> Tj 1 0 0 1 469.44 98.40 Tm <746F20> Tj 1 0 0 1 481.68 98.16 Tm <657374696D61746520> Tj 1 0 0 1 525.36 97.68 Tm <6120> Tj 1 0 0 1 534.48 97.68 Tm <736564696D656E2D> Tj 0.96 Tc 1 0 0 1 338.40 86.16 Tm <746174696F6E20> Tj 1 0 0 1 368.40 85.92 Tm <636F656666696369656E7420> Tj 1 0 0 1 421.44 85.68 Tm <646973747269627574696F6E20> Tj 1 0 0 1 480.72 83.28 Tm <5B335D2E> Tj 0.48 Tc 1 0 0 1 350.40 73.20 Tm <466F7220> Tj 1 0 0 1 369.12 72.96 Tm <736861706520> Tj 1 0 0 1 398.64 72.72 Tm <616E616C7973697320> Tj 1 0 0 1 439.44 72.48 Tm <746865726520> Tj 1 0 0 1 465.36 72.24 Tm <61726520> Tj 1 0 0 1 482.64 72.24 Tm <746872656520> Tj 1 0 0 1 509.04 71.76 Tm <6C696E657320> Tj 1 0 0 1 533.76 71.52 Tm <6F6620> Tj 1 0 0 1 546.48 71.76 Tm <61747461636B2E> Tj 0.72 Tc 1 0 0 1 338.16 60.24 Tm <496620> Tj 1 0 0 1 348.00 60.24 Tm <74686520> Tj 1 0 0 1 364.80 60.00 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 439.92 59.52 Tm <697320> Tj 1 0 0 1 449.76 59.52 Tm <666169726C7920> Tj 1 0 0 1 477.36 59.28 Tm <726967696420> Tj 1 0 0 1 502.08 59.04 Tm <776520> Tj 1 0 0 1 517.68 58.80 Tm <63616E20> Tj 1 0 0 1 536.40 58.80 Tm <636F6D62696E65> Tj 0.72 Tc 1 0 0 1 337.92 47.28 Tm <74686520> Tj 1 0 0 1 354.72 47.04 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 423.36 46.56 Tm <636F656666696369656E7420> Tj 1 0 0 1 475.92 46.56 Tm <7769746820> Tj 1 0 0 1 499.44 45.84 Tm <6F7468657220> Tj 1 0 0 1 526.56 45.84 Tm <746563686E6971756573> Tj 0.72 Tc 1 0 0 1 337.68 34.56 Tm <7375636820> Tj 1 0 0 1 366.48 34.32 Tm <617320> Tj 1 0 0 1 383.76 34.32 Tm <696E7472696E73696320> Tj 1 0 0 1 429.36 34.08 Tm <766973636F736974792C20> Tj 1 0 0 1 481.20 33.60 Tm <726F746174696F6E616C20> Tj 1 0 0 1 534.24 33.12 Tm <646966667573696F6E> Tj 0.72 Tc 1 0 0 1 338.40 22.32 Tm <2866726F6D20> Tj 1 0 0 1 370.32 21.12 Tm <666C756F72657363656E636520> Tj 1 0 0 1 432.24 20.64 Tm <6465706F6C617269736174696F6E20> Tj 1 0 0 1 503.04 20.16 Tm <6F7220> Tj 1 0 0 1 516.24 20.16 Tm <656C65637472696320> Tj 1 0 0 1 555.12 20.64 Tm <626972652D> Tj 0.00 Tc /F3 6.0 Tf 1 0 0 1 417.60 630.96 Tm <7474626F74> Tj 0.00 Tc /F3 9.0 Tf 1 0 0 1 420.96 618.96 Tm <74> Tj ET endstream endobj 26 0 obj 27233 endobj 27 0 obj << /Length 28 0 R >> stream . trends in analytical chemistty, vol. 13, no. lO, lgg4full on-line computer data capture and analysisfacilities, superb drive stability (even at 1000 revlmin) and absorption optics reliable even in the farultraviolet (down to a wavelength of ca. 210 nm).The aim of the rest of this article is to give a briefoverview of the four types of ultracentrifuge tech-niques mentioned above and then very briefly indi-cate their potential for the characterisation ofproteins, polysaccharides, nucleic acids and syn-thetic macromolecu les.6. Sedimentation velocity: shape analysisand homogeneityA typical analytical ultracentrifuge cell containstwo sector shape channels (one for the solution,one for the reference solvent) which can takebetween 0.I to 0.8 ml. With an analytical ultracen-trifuge, using the appropriate optical system youcan record the position and rate of movement ofthe sedimenting boundary within the solution chan-nel. For a macromolecule with an absorbing chro-mophore (such as a protein or nucleic acid) wecan use the absorption optical system. Otherwisewe can use a special type of refractive index (gra-dient) optics called Schlieren optics which recordsthe boundary on photographic film or chart paperas a peak. Fig. I compares some of these patterns:Fig. I a for a monodisperse protein preparation, Fig.I b for a protein preparation containing two com-ponents and Fig. I c for a polydisperse polysaccha-ride.The rate of movement of a sedimenting bound-ary from these patterns per unit centrifugal fieldgives the sedimentation coefficient, s, which is oneof our shape parameters. By adjusting this usingsimple formulae to standard conditions (water assolvent at 20"C) and extrapolating this (or thereciprocal thereof) to zero concentration we canget from the intercept the corrected sedimentationcoefficient, Jo20.r"- (unit: seconds or Svedbergs, S,where I S: l0-r3 s) and from the slope we can getthe sedimentation concentration regression coeffi-cient, k. (unit:ml/g) and then from both para-meters our shape informationThe usefulness of sedimentation velocity as arapid check for sample homogeneity can also beseen directly from Fig. l, from inspection of thenumber of boundaries and shape for each individ-ual scan: (a) is a monodisperse protein preparation(one symmetrical boundary per scan), whereas(b) clearly shows two components, with about two 44' (a) (b) (c) Fig. 1. Examples of analytical ultracentrifuge sedi-mentation velocity patterns (recorded using scanningoptics). (a) Absorption optics scans (every 30 min at49 000 rev/min) at a wavelength of 295 nm for theenzyme methylmalonyl mutase. Ref :referencemark allowing calibration of radial positions; S: startof cell; Msolv:solvent meniscus; Msoln:solutionmeniscus; B: cell base. Arrow indicates direction ofsedimentation. (b) Absorption optics scans (every gmin at 40 000 rev/min) al278 nm for the ,,Gene 5,,DNA binding protein. (c) Schlieren optics scans (30min, 49 000 rev/min) for an alginate polysaccharide.thirds of the material a macromolecularcomponentsedimenting at 2.6 S, the rest a large aggregatesedimenting at 35.5 S. In Fig. lc it is not quite soapparent that the sample is polydisperse. This isbecause the polysaccharide is polydisperse in a'quasi-continuous' sense (i.e., many componentswith a quasi-continuous distribution of molecularweights) as opposed to the discrete 'two-compo-nents' case of Fig. lb. Nonetheless from mathe-matical analysis of the boundary shape and its rateof movement it is possible to estimate a sedimen-tation coefficient distribution [3].For shape analysis there are three lines of attack.If the macromolecule is fairly rigid we can combinethe sedimentation coefficient with other techniquessuch as intrinsic viscosity, rotational diffusion(from fluorescence depolarisation or electric bire- ttbott endstream endobj 28 0 obj 3825 endobj 29 0 obj << /Length 30 0 R >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj24 Do Q endstream endobj 30 0 obj 45 endobj 31 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 6 0 R >> /XObject << /Obj24 24 0 R >> /Subtype 27 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 23 0 R 29 0 R 25 0 R ] >> endobj 11 0 obj << /Kids [ 12 0 R 22 0 R 31 0 R ] /Count 3 /Type /Pages >> endobj xref 0 1 0000000000 65535 f 11 1 0000358042 00000 n 23 9 0000239735 00000 n 0000239814 00000 n 0000326454 00000 n 0000353742 00000 n 0000353765 00000 n 0000357645 00000 n 0000357667 00000 n 0000357767 00000 n 0000357787 00000 n trailer << /Size 32 /Info 1 0 R /Root 13 0 R /Prev 239406 >> startxref 358122 %%EOF 32 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 33 0 obj << /Type /XObject /Subtype /Image /Name /Obj33 /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 77020 >> stream &o}kz8z?@p@],r<Ɇ@Yr dTdG .D  @iP Du (Qd(^#F_.||Dddp<˂X GhF@a^GDp<#.Z6ayt`!K#pV#xM͆Xdp2>_HM""#fɸNM":.̎!֑#GÈp?#Ȑ 膄f@#20Dp#D\KŲ>}hDb9cEKbF@X$P(Md:;QƩe4M Dҵ AҐ5 TIT]XMtPA$$dU,,|'U׮dGzX?K*SDҡ厺ܱʺʲճ83B3<|;De'^ISuF1fODnMBz޺-!W-/먾'%ti(OUXZZЙƕx`7)@y|U ֩(~֪Ti:OYJWK~֗Z/U/'ZEz%NIZG*+S]B%}$33)䶧/lNUu~TVf]=[_z4鴴1JWM4?_ZUikiWkPX_뤫K&) DDzԘ_L__auE֑u/ B 5_[J/ ! kޞEc`R]5ZCid)%hD$1JW%΂5+c'U@MZ@LjWu=zZt֖XAkK V]4 XH+GR\ g70 C7 04dpN|WW-خV[ـ2¨s``My;x2Yp0HS"a&dnS PM>͡9L  mPO-ZpICwǿP"QDڻ}_kiAoaXtv|V'?a:C׊pZ״c<J7`!Uo_sjNgx`>{FT/_Vp4 ozx^h)|v;n vj4L߭[mSҮӈէ3ӶAND/9i.tGVIB#\6,>hDy70f?_O_zWdäHX5)!^ըj2v̉04wr(a:| S ?YAWj5楐wrT Szd \çBwX :!$"^a.pA0W\"+ z A_{5[=ma/@.@ڷ k=@ւ (" l{uPWA0Ӓp'A Q tJCVaBi0z 8b-AL'i7mi] 0{pnI 6i7AMMt WIMH6 II6nڽ&6jڶInt7I=:۫M'm'7[I7O.~.o7ZWo]='[MڶWK޿W]_^WV?7_M~o߫׵I7}[j_W{S{~KWw%I7}7}tJ:߾{i+}+뷺J߫ToniW[7[vI/ukM[I_i6w&D6Roj Ri{IHCm$; -7n ]ҶKnڶI*ti$mI'aUI %nMK{i0 J0Jl0I/L0A*Ma'a %{i6aUvM VdL$a݆A MIl._ elF`$vl K{ $4JJ0 i.I%W  d8%na+4$haӥ0`i$݃ ].*AI'J*n  !&$ ceknnT p0$oISޒC oҦI};wMmI%j7݆I/)*o+ui%oT܋gh!ﶓi$6uVN=}am-$$.Ov}n$JoVֈmiMڤvRۺoI% WmI-?mToUz & ׵hƒMpMմOUWۧ|4o{auW֭m[4jtBO#;վzwܳHOJbm_j?!:KBnNNoI}CoIM?:NNztikMH:Ʈ_an֪~D_WAkoa&?ҽҺޯKD'{~!$tJoV nW $v֩ja$|%v#I;ID-o#;K7ªw4}?|" `nI;+tB~ݺH4{ZuWMIױ][O+tA~@Z@~t~n . 7]&^7It~ޯuUnn7I_WmnZ}+uJȣպ#}0_n+6I/n[t&{nl:INK}u WA^Kna*l0M· @[IҽҷIҲn Z %OAnH=MWKt&m^Vm&{ai]&O 6ML$7Ia2V a7 `v8P􅴮am[JO 7&: =&IOOIMmni<$æڷIA7MmzM tjXut^utV7'!vCْAQh)>3B ["!z;t._ڧ>W.m&޵՗}[!/4?O]RT N!K vp^dhp<5O i m[(%u;,Dp<»|VDx1Ai/?/j ¿nXHH&rc͆4m+bA%9L bүdUi[8"0L!a}Z; 3j"qE-J & kZ<8,jd^'EwH?š\ %ظv3NvƐTl -'[V< {Kkl7V+i;wVՆ_ _F wm@u6ߥ#pDuݼMI":5W3) 5nݭ.lD4LvꝮInMA9cIWZpvn%ZmƒZڷmn/VRmRң?gM8V R_ڱ;c;m&kC1__m!A&~u/+ױ!:],4nJ5I'օy9^k63_jK qS/|~-*tni4!xJʙmA ko-#ab+t!H=V>=%n$I-[ $ #S"%@;OAN,}.8bkA7d0>MZ[ꚑ7-2Kɲuq5gaf?奮u+Lr+A'"AIɠ -5;y ސk1zUK#A4٥פ? 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1 57.36 390.00 Tm <2C6E7522726F6D6F692263756C657320> Tj 1 0 0 1 138.24 391.92 Tm <7375636820> Tj 1 0 0 1 162.96 392.64 Tm <617320> Tj 1 0 0 1 175.20 392.88 Tm <6D616E7920> Tj 1 0 0 1 204.00 393.84 Tm <70726F7465696E7320> Tj 1 0 0 1 246.00 392.88 Tm <4947385D20> Tj 1 0 0 1 275.04 395.52 Tm <2720> Tj 1 0 0 1 279.84 395.76 Tm <466F72> Tj 0.48 Tc 1 0 0 1 57.84 377.04 Tm <6E6F742D736F2D726967696420> Tj 1 0 0 1 121.44 378.72 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 207.60 380.64 Tm <7375636820> Tj 1 0 0 1 236.40 381.60 Tm <617320> Tj 1 0 0 1 253.92 382.08 Tm <73796E746865746963> Tj 0.48 Tc 1 0 0 1 58.08 365.52 Tm <706F6C796D65724A616E6420> Tj 1 0 0 1 124.08 366.24 Tm <706F6C79736163636861726964657320> Tj 1 0 0 1 203.04 367.92 Tm <776520> Tj 1 0 0 1 218.88 368.16 Tm <6861766520> Tj 1 0 0 1 243.36 368.88 Tm <746F20> Tj 1 0 0 1 254.64 369.12 Tm <75736520> Tj 1 0 0 1 272.64 369.60 Tm <6D6F7265> Tj 0.48 Tc 1 0 0 1 58.08 350.88 Tm <212222272272226620> Tj 1 0 0 1 96.72 352.08 Tm <73686170656920> Tj 1 0 0 1 131.76 353.04 Tm <7574696E6720> Tj 1 0 0 1 161.28 353.76 Tm <74686520> Tj 1 0 0 1 180.24 359.52 Tm <2757616C65732F76616E20> Tj 1 0 0 1 239.28 355.92 Tm <486F6C64652720> Tj 1 0 0 1 275.52 356.64 Tm <726174696F> Tj 0.72 Tc 1 0 0 1 58.08 338.16 Tm <336920> Tj 1 0 0 1 72.00 338.64 Tm <72722E20> Tj 1 0 0 1 84.48 338.88 Tm <692220> Tj 1 0 0 1 97.92 339.36 Tm <7468655E696E7472696E7369632D766973636F736974792C20> Tj 1 0 0 1 210.24 336.96 Tm <4C6C6C2D6F7220> Tj 1 0 0 1 245.52 343.20 Tm <74686520> Tj 1 0 0 1 264.48 348.72 Tm <274D61726B2D> Tj 0.48 Tc 1 0 0 1 58.80 325.44 Tm <486F752A696E742D6675686E2D73616B75726164612720> Tj 1 0 0 1 190.32 329.52 Tm <284D484B532920> Tj 1 0 0 1 238.80 329.76 Tm <6220> Tj 1 0 0 1 247.68 330.48 Tm <636F656666696369656E74> Tj 0.48 Tc 1 0 0 1 59.04 312.72 Tm <2A7420> Tj 1 0 0 1 73.68 312.72 Tm <6922747420> Tj 1 0 0 1 91.20 313.20 Tm <636F6D657320> Tj 1 0 0 1 125.28 314.16 Tm <66726F6D20> Tj 1 0 0 1 151.92 314.88 Tm <74686520> Tj 1 0 0 1 170.16 315.12 Tm <72656C6174696F6E20> Tj 1 0 0 1 209.76 316.08 Tm <6265747765656E20> Tj 1 0 0 1 252.48 317.28 Tm <73223236272A20> Tj 1 0 0 1 281.04 318.00 Tm <266F64> Tj 0.48 Tc 1 0 0 1 59.28 299.52 Tm <74686520> Tj 1 0 0 1 76.80 299.76 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 127.44 301.44 Tm <7765696768742C20> Tj 1 0 0 1 165.84 302.16 Tm <4D3A> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 59.52 280.32 Tm <536F326F2E2A20> Tj 1 0 0 1 86.88 283.68 Tm <3A20> Tj 1 0 0 1 96.48 281.52 Tm <434F6E53742E20> Tj 1 0 0 1 127.68 282.24 Tm <4D62> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 60.96 262.08 Tm <2873696D696C617220> Tj 1 0 0 1 102.48 262.56 Tm <636F656666696369656E747320> Tj 1 0 0 1 161.52 264.00 Tm <657869737420> Tj 1 0 0 1 187.92 264.72 Tm <666F7220> Tj 1 0 0 1 205.44 265.20 Tm <74686520> Tj 1 0 0 1 223.68 265.68 Tm <696E7472696E73696320> Tj 1 0 0 1 265.92 266.88 Tm <766973636F732D> Tj 0.48 Tc 1 0 0 1 60.72 248.64 Tm <692C792C20> Tj 1 0 0 1 78.48 249.12 Tm <7274742220> Tj 1 0 0 1 95.28 249.60 Tm <646966667573696F6E20> Tj 1 0 0 1 140.88 250.56 Tm <636F656666696369656E742C20> Tj 1 0 0 1 197.04 252.24 Tm <616E6420> Tj 1 0 0 1 216.72 252.72 Tm <72616469757320> Tj 1 0 0 1 247.68 253.44 Tm <6F6620> Tj 1 0 0 1 260.16 254.16 Tm <6779726174696F2E6E> Tj 0.72 Tc 1 0 0 1 60.72 235.92 Tm <2C6969746E20> Tj 1 0 0 1 84.48 236.40 Tm <552C73656520> Tj 1 0 0 1 118.56 237.12 Tm <5265662E20> Tj 1 0 0 1 143.04 235.68 Tm <4920> Tj 1 0 0 1 149.28 238.08 Tm <4920> Tj 1 0 0 1 155.04 236.16 Tm <5D20> Tj 1 0 0 1 161.04 236.40 Tm <292E20> Tj 1 0 0 1 171.60 238.56 Tm <54686520> Tj 1 0 0 1 193.20 239.04 Tm <4D484B5320> Tj 1 0 0 1 230.40 240.00 Tm <6220> Tj 1 0 0 1 239.04 240.24 Tm <636F656666696369656E7420> Tj 1 0 0 1 292.08 241.68 Tm <6973> Tj 0.72 Tc 1 0 0 1 60.96 222.72 Tm <752E2A66667920> Tj 1 0 0 1 102.24 223.92 Tm <6F627461696E656420> Tj 1 0 0 1 150.48 225.12 Tm <627920> Tj 1 0 0 1 169.20 225.84 Tm <707265706172696C6720> Tj 1 0 0 1 221.76 226.80 Tm <612E2E27686F6D6F6C6F676F757327> Tj 0.72 Tc 1 0 0 1 61.20 210.00 Tm <73657269657369692E652E2C20> Tj 1 0 0 1 117.84 211.44 Tm <74686520> Tj 1 0 0 1 135.60 211.92 Tm <73616D6520> Tj 1 0 0 1 163.20 212.88 Tm <706F6C796D657220> Tj 1 0 0 1 205.92 213.60 Tm <62757420> Tj 1 0 0 1 223.92 214.08 Tm <646966666572656E7420> Tj 1 0 0 1 267.60 215.28 Tm <6D6F6C65632D> Tj 0.72 Tc 1 0 0 1 61.44 197.04 Tm <756C617220> Tj 1 0 0 1 83.76 197.76 Tm <776569676874732920> Tj 1 0 0 1 130.56 198.72 Tm <6F6620> Tj 1 0 0 1 144.72 199.20 Tm <74686520> Tj 1 0 0 1 162.72 199.92 Tm <706F6C796D657220> Tj 1 0 0 1 207.36 201.60 Tm <2862792E20> Tj 1 0 0 1 228.00 201.36 Tm <6527672220> Tj 1 0 0 1 251.76 202.08 Tm <6368726F6D61746F2D> Tj 0.48 Tc 1 0 0 1 62.16 183.84 Tm <7372617068696320> Tj 1 0 0 1 101.04 185.04 Tm <69657061726174696F6E20> Tj 1 0 0 1 155.04 186.48 Tm <6F6920> Tj 1 0 0 1 169.20 186.96 Tm <6865617420> Tj 1 0 0 1 193.20 187.44 Tm <6465677261646174696F6E2920> Tj 1 0 0 1 259.44 189.36 Tm <616E6420> Tj 1 0 0 1 280.32 189.84 Tm <7468656E> Tj 0.48 Tc 1 0 0 1 61.68 171.12 Tm <6922666922676974742220> Tj 1 0 0 1 111.84 172.32 Tm <696C6F706520> Tj 1 0 0 1 139.68 173.04 Tm <6F6620> Tj 1 0 0 1 152.40 173.52 Tm <6120> Tj 1 0 0 1 160.08 173.76 Tm <646F75626C6520> Tj 1 0 0 1 195.60 174.72 Tm <6C6F6761726974686D696320> Tj 1 0 0 1 252.48 176.40 Tm <706C6F7420> Tj 1 0 0 1 273.36 176.64 Tm <6F6620> Tj 1 0 0 1 286.32 177.12 Tm <6C6F67> Tj 0.72 Tc 1 0 0 1 62.16 158.16 Tm <736F32362C2A20> Tj 1 0 0 1 90.48 159.12 Tm <56807253557320> Tj 1 0 0 1 124.08 159.84 Tm <6C6F6720> Tj 1 0 0 1 142.08 160.32 Tm <4D20> Tj 1 0 0 1 156.72 158.64 Tm <5B395D2E> Tj 0.72 Tc 1 0 0 1 74.40 145.68 Tm <66696C74747420> Tj 1 0 0 1 100.08 146.16 Tm <6B2E2F20> Tj 1 0 0 1 116.16 144.72 Tm <5B372C5D696E6420> Tj 1 0 0 1 156.48 147.60 Tm <74686520> Tj 1 0 0 1 173.28 148.08 Tm <4D484B5320> Tj 1 0 0 1 210.24 149.04 Tm <6220> Tj 1 0 0 1 218.40 149.28 Tm <636F656666696369656E7420> Tj 1 0 0 1 270.96 150.96 Tm <7065726D7274> Tj 0.48 Tc 1 0 0 1 62.88 132.48 Tm <7474726520> Tj 1 0 0 1 79.92 132.96 Tm <6D6F4F656966696E6720> Tj 1 0 0 1 131.28 134.16 Tm <6F6620> Tj 1 0 0 1 144.00 134.64 Tm <7474726520> Tj 1 0 0 1 161.04 134.88 Tm <636F6E666F726D6174696F6E20> Tj 1 0 0 1 228.24 136.80 Tm <696E20> Tj 1 0 0 1 239.76 137.04 Tm <7465726D7320> Tj 1 0 0 1 268.32 137.76 Tm <6F6620> Tj 1 0 0 1 281.04 138.48 Tm <67656E2D> Tj 0.48 Tc 1 0 0 1 62.88 119.52 Tm <6572616C20> Tj 1 0 0 1 83.28 120.00 Tm <7368617065732C20> Tj 1 0 0 1 120.24 120.96 Tm <626C747765656E20> Tj 1 0 0 1 162.48 122.16 Tm <74686520> Tj 1 0 0 1 179.52 122.64 Tm <746872656520> Tj 1 0 0 1 205.20 123.36 Tm <65787472656D657320> Tj 1 0 0 1 250.08 124.56 Tm <6F6620> Tj 1 0 0 1 262.08 124.80 Tm <636F6D70616374> Tj 0.48 Tc 1 0 0 1 63.60 106.56 Tm <747074742274222C2D6974676C4F20> Tj 1 0 0 1 126.24 108.48 Tm <726F6420> Tj 1 0 0 1 145.44 108.96 Tm <616E6420> Tj 1 0 0 1 165.60 109.44 Tm <72616E646F6D20> Tj 1 0 0 1 204.72 110.40 Tm <636F696C2720> Tj 1 0 0 1 228.72 111.36 Tm <466F7220> Tj 1 0 0 1 247.92 111.84 Tm <7468697320> Tj 1 0 0 1 268.08 112.56 Tm <67656E6572616C> Tj 0.48 Tc 1 0 0 1 63.60 93.84 Tm <3B69703B20> Tj 1 0 0 1 88.32 94.32 Tm <226920> Tj 1 0 0 1 102.96 94.80 Tm <7474696F61227474696E6720> Tj 1 0 0 1 156.00 96.48 Tm <776520> Tj 1 0 0 1 174.00 96.72 Tm <656D706C6F7920> Tj 1 0 0 1 214.32 97.68 Tm <6120> Tj 1 0 0 1 223.92 98.16 Tm <7665727920> Tj 1 0 0 1 248.88 99.12 Tm <75736566756C20> Tj 1 0 0 1 282.00 99.60 Tm <636F6E2D> Tj 0.72 Tc 1 0 0 1 64.32 80.64 Tm <736972756374696F6E20> Tj 1 0 0 1 107.76 82.08 Tm <6B6E6F776E20> Tj 1 0 0 1 142.56 83.04 Tm <617320> Tj 1 0 0 1 154.32 83.28 Tm <74686520> Tj 1 0 0 1 170.64 83.76 Tm <4861756720> Tj 1 0 0 1 198.48 84.48 Tm <747269616E676C6520> Tj 1 0 0 1 237.36 86.40 Tm <2820> Tj 1 0 0 1 242.40 85.68 Tm <4669672720> Tj 1 0 0 1 263.28 86.16 Tm <3320> Tj 1 0 0 1 269.76 84.72 Tm <2920> Tj 1 0 0 1 277.92 84.72 Tm <5B20> Tj 1 0 0 1 284.16 86.88 Tm <6C305D20> Tj 1 0 0 1 300.96 87.36 Tm <27> Tj 0.48 Tc 1 0 0 1 64.32 68.16 Tm <4561636820> Tj 1 0 0 1 93.12 68.88 Tm <6F6620> Tj 1 0 0 1 108.00 69.36 Tm <74686520> Tj 1 0 0 1 127.44 69.84 Tm <746872656520> Tj 1 0 0 1 156.48 70.56 Tm <65787472656D657320> Tj 1 0 0 1 204.48 71.76 Tm <6F6620> Tj 1 0 0 1 219.12 72.24 Tm <636F6E666F726D6174696F6E20> Tj 1 0 0 1 288.00 74.16 Tm <686173> Tj 0.48 Tc 1 0 0 1 64.80 55.20 Tm <72702222696E2E20> Tj 1 0 0 1 104.88 56.64 Tm <76616C75657320> Tj 1 0 0 1 138.96 57.36 Tm <666F7220> Tj 1 0 0 1 156.24 57.60 Tm <6B2E2F20> Tj 1 0 0 1 172.32 56.16 Tm <5B20> Tj 1 0 0 1 177.60 55.92 Tm <345D20> Tj 1 0 0 1 193.92 58.56 Tm <616E642E20> Tj 1 0 0 1 214.56 59.04 Tm <7468652E20> Tj 1 0 0 1 232.56 59.52 Tm <4D484B5320> Tj 1 0 0 1 270.24 60.48 Tm <6220> Tj 1 0 0 1 279.36 60.96 Tm <636F65662D> Tj 0.48 Tc 1 0 0 1 65.04 42.72 Tm <66696369656E7420> Tj 1 0 0 1 96.96 43.44 Tm <616E6420> Tj 1 0 0 1 116.16 43.92 Tm <7468697320> Tj 1 0 0 1 135.36 44.40 Tm <7479706520> Tj 1 0 0 1 157.92 44.88 Tm <6F66696E616C7973697320> Tj 1 0 0 1 210.48 46.32 Tm <68617320> Tj 1 0 0 1 228.24 46.80 Tm <6265656E20> Tj 1 0 0 1 252.72 47.76 Tm <7665727920> Tj 1 0 0 1 275.28 48.00 Tm <75736566756C> Tj 0.48 Tc 1 0 0 1 65.52 29.76 Tm <696E2C20> Tj 1 0 0 1 79.68 30.24 Tm <666F2C20> Tj 1 0 0 1 95.52 30.72 Tm <222A752A706C652C20> Tj 1 0 0 1 141.36 32.16 Tm <70626C20> Tj 1 0 0 1 156.96 32.64 Tm <797361636368697269646520> Tj 1 0 0 1 215.04 33.60 Tm <636F6E666F726D6174696F6E20> Tj 1 0 0 1 281.04 35.52 Tm <616E616C2D> Tj 0.72 Tc 1 0 0 1 65.52 18.24 Tm <7973697320> Tj 1 0 0 1 88.08 18.48 Tm <285461626C6520> Tj 1 0 0 1 125.04 18.48 Tm <4920> Tj 1 0 0 1 130.56 17.04 Tm <29> Tj 0.24 Tc /F3 8.0 Tf 1 0 0 1 383.28 732.96 Tm <7472656E647320> Tj 1 0 0 1 406.56 733.92 Tm <696E20> Tj 1 0 0 1 414.48 733.92 Tm <616E617479746963616C20> Tj 1 0 0 1 449.52 734.40 Tm <6368656D69737472792C20> Tj 1 0 0 1 487.92 735.12 Tm <766F6C2E20> Tj 1 0 0 1 502.80 735.12 Tm <31332C20> Tj 1 0 0 1 514.56 735.36 Tm <6E6F2E20> Tj 1 0 0 1 528.96 735.36 Tm <4C4F2720> Tj 1 0 0 1 541.92 735.60 Tm <31393934> Tj 0.00 Tc /F3 6.0 Tf 1 0 0 1 455.28 707.28 Tm <613D4F> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 359.52 700.56 Tm <636F4D5041637220> Tj 1 0 0 1 397.92 701.52 Tm <53504845524520> Tj 1 0 0 1 435.60 693.60 Tm <4F20> Tj 1 0 0 1 455.28 693.60 Tm <486F6C> Tj 0.72 Tc /F3 7.0 Tf 1 0 0 1 511.68 591.12 Tm <524947544420> Tj 1 0 0 1 535.68 591.36 Tm <524F44> Tj 0.72 Tc 1 0 0 1 323.04 585.12 Tm <52414E444F4D20> Tj 1 0 0 1 358.08 586.08 Tm <434F494C> Tj 0.48 Tc 1 0 0 1 321.84 569.52 Tm <613D4F2E3520> Tj 1 0 0 1 341.04 571.44 Tm <2D20> Tj 1 0 0 1 345.12 570.24 Tm <302E38> Tj 0.24 Tc 1 0 0 1 322.08 560.40 Tm <623D6F2E3420> Tj 1 0 0 1 341.52 562.32 Tm <2D20> Tj 1 0 0 1 346.08 561.12 Tm <302E35> Tj 0.72 Tc 1 0 0 1 322.32 551.52 Tm <6B732F5B716C2D20> Tj 1 0 0 1 347.04 552.24 Tm <312E36> Tj 0.96 Tc 1 0 0 1 530.16 563.28 Tm <613D312E38> Tj 0.96 Tc 1 0 0 1 530.64 554.40 Tm <627B2E3135> Tj 0.72 Tc 1 0 0 1 530.88 545.28 Tm <6B732F5B716C2D2E33> Tj 0.96 Tc /F3 11.0 Tf 1 0 0 1 323.76 522.48 Tm <4669672E20> Tj 1 0 0 1 344.40 522.72 Tm <332E20> Tj 1 0 0 1 356.64 523.20 Tm <54686520> Tj 1 0 0 1 378.48 523.68 Tm <4861756720> Tj 1 0 0 1 406.32 524.16 Tm <747269616E676C6520> Tj 1 0 0 1 444.24 525.84 Tm <287365652C20> Tj 1 0 0 1 470.64 525.60 Tm <652767272C20> Tj 1 0 0 1 494.88 526.32 Tm <5265662720> Tj 1 0 0 1 517.20 524.40 Tm <5B31305D292720> Tj 1 0 0 1 544.08 527.28 Tm <546865> Tj 0.48 Tc 1 0 0 1 323.52 509.52 Tm <636F6E666F726D6174696F6E20> Tj 1 0 0 1 386.88 510.96 Tm <6F6620> Tj 1 0 0 1 398.88 511.20 Tm <6120> Tj 1 0 0 1 407.52 512.16 Tm <676976656E20> Tj 1 0 0 1 435.84 512.16 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 509.28 513.36 Tm <63616E20> Tj 1 0 0 1 529.44 513.84 Tm <626520> Tj 1 0 0 1 544.32 514.08 Tm <7265702D> Tj 0.72 Tc 1 0 0 1 324.24 496.80 Tm <726573656E74656420> Tj 1 0 0 1 368.40 497.52 Tm <627920> Tj 1 0 0 1 382.80 498.00 Tm <6120> Tj 1 0 0 1 392.64 498.24 Tm <6C6F63757320> Tj 1 0 0 1 420.00 498.96 Tm <616C6F6E6720> Tj 1 0 0 1 448.80 499.44 Tm <74686520> Tj 1 0 0 1 467.28 499.68 Tm <736964657320> Tj 1 0 0 1 495.36 500.40 Tm <6F6620> Tj 1 0 0 1 507.60 500.64 Tm <74686520> Tj 1 0 0 1 525.84 500.88 Tm <747269616E676C6527> Tj 0.72 Tc 1 0 0 1 324.00 483.36 Tm <652E672E2C20> Tj 1 0 0 1 346.32 484.56 Tm <676C6F62756C697270726F7465696E736F6E20> Tj 1 0 0 1 436.80 486.24 Tm <7369646520> Tj 1 0 0 1 457.68 486.72 Tm <412C20> Tj 1 0 0 1 469.44 487.68 Tm <706F6C797361636368617269646573616E64> Tj 0.72 Tc 1 0 0 1 324.48 470.64 Tm <74696E6C6169706F6C796D65727320> Tj 1 0 0 1 396.24 472.32 Tm <6F6E20> Tj 1 0 0 1 409.92 472.56 Tm <7369646520> Tj 1 0 0 1 431.04 473.28 Tm <422C20> Tj 1 0 0 1 442.80 473.52 Tm <64656E61747572656420> Tj 1 0 0 1 491.76 475.20 Tm <70726F7465696E7320> Tj 1 0 0 1 530.88 475.20 Tm <6F6E20> Tj 1 0 0 1 544.56 475.20 Tm <73696465> Tj 0.72 Tc 1 0 0 1 324.72 457.44 Tm <432E20> Tj 1 0 0 1 337.92 457.68 Tm <612C7472667234696C665320> Tj 1 0 0 1 390.48 459.12 Tm <6578706F6E656E747320> Tj 1 0 0 1 440.16 460.32 Tm <66726F6D20> Tj 1 0 0 1 464.16 460.80 Tm <726573706563746976656C792C20> Tj 1 0 0 1 524.16 462.00 Tm <766973636F73697479> Tj 0.72 Tc 1 0 0 1 324.96 444.48 Tm <616E6420> Tj 1 0 0 1 345.12 444.96 Tm <736564696D656E746174696F6E2C20> Tj 1 0 0 1 415.20 446.64 Tm <6F7468657220> Tj 1 0 0 1 441.12 447.36 Tm <73796D626F6C7320> Tj 1 0 0 1 481.92 448.32 Tm <617320> Tj 1 0 0 1 495.84 448.56 Tm <696E20> Tj 1 0 0 1 506.16 448.56 Tm <74686520> Tj 1 0 0 1 523.20 449.04 Tm <7465787427> Tj 0.48 Tc 1 0 0 1 337.68 420.96 Tm <536564696D656E746174696F6E20> Tj 1 0 0 1 408.96 423.12 Tm <76656C6F6369747920> Tj 1 0 0 1 448.80 423.84 Tm <63616E20> Tj 1 0 0 1 468.00 424.08 Tm <616C736F20> Tj 1 0 0 1 489.60 424.56 Tm <626520> Tj 1 0 0 1 503.04 424.80 Tm <7573656420> Tj 1 0 0 1 527.28 425.28 Tm <746F20> Tj 1 0 0 1 539.04 425.76 Tm <6173736179> Tj 0.72 Tc 1 0 0 1 325.92 408.00 Tm <666F7220> Tj 1 0 0 1 342.96 408.48 Tm <696E746572616374696F6E20> Tj 1 0 0 1 396.00 409.68 Tm <696E20> Tj 1 0 0 1 407.76 409.92 Tm <6120> Tj 1 0 0 1 415.44 410.16 Tm <6D6978656420> Tj 1 0 0 1 447.84 410.88 Tm <736F6C75746520> Tj 1 0 0 1 478.80 411.60 Tm <73797374656D2C20> Tj 1 0 0 1 517.20 412.32 Tm <657370656369616C6C79> Tj 0.48 Tc 1 0 0 1 326.40 395.04 Tm <696620> Tj 1 0 0 1 337.44 395.28 Tm <74686520> Tj 1 0 0 1 355.92 395.76 Tm <646966666572656E7420> Tj 1 0 0 1 401.04 396.72 Tm <7370656369657320> Tj 1 0 0 1 439.20 398.16 Tm <706F737365737320> Tj 1 0 0 1 479.04 398.64 Tm <646966666572696E6720> Tj 1 0 0 1 524.64 399.60 Tm <6368726F6D6F2D> Tj 0.48 Tc 1 0 0 1 326.40 379.68 Tm <666E6F74227420> Tj 1 0 0 1 362.16 383.04 Tm <6162736F7262696E6720> Tj 1 0 0 1 413.04 384.48 Tm <696E20> Tj 1 0 0 1 425.76 384.72 Tm <74686F20> Tj 1 0 0 1 444.48 385.20 Tm <76697369626C6520> Tj 1 0 0 1 479.76 385.68 Tm <6F7220> Tj 1 0 0 1 493.44 386.16 Tm <75736561626C6520> Tj 1 0 0 1 533.28 387.36 Tm <7061727420> Tj 1 0 0 1 555.36 387.60 Tm <6F66> Tj 0.48 Tc 1 0 0 1 326.64 369.36 Tm <69686520> Tj 1 0 0 1 344.16 369.60 Tm <756C74726176696F6C657420> Tj 1 0 0 1 396.00 371.04 Tm <737065637472756D20> Tj 1 0 0 1 442.80 372.96 Tm <28666F7220> Tj 1 0 0 1 464.64 372.72 Tm <6120> Tj 1 0 0 1 472.56 372.72 Tm <6D6F6465726E20> Tj 1 0 0 1 512.16 373.68 Tm <696E737472756D656E7427> Tj 0.72 Tc 1 0 0 1 327.12 356.64 Tm <776176656C656E6774687320> Tj 1 0 0 1 390.00 357.84 Tm <6265697765656E20> Tj 1 0 0 1 432.96 359.04 Tm <32313020> Tj 1 0 0 1 454.56 359.52 Tm <616E6420> Tj 1 0 0 1 475.44 359.76 Tm <38303020> Tj 1 0 0 1 497.04 360.24 Tm <6E6D292720> Tj 1 0 0 1 524.88 360.96 Tm <627920> Tj 1 0 0 1 540.48 361.44 Tm <7573696E67> Tj 0.48 Tc 1 0 0 1 327.12 343.44 Tm <74686520> Tj 1 0 0 1 344.88 343.92 Tm <7072696E636C706C6520> Tj 1 0 0 1 390.24 344.88 Tm <6F6620> Tj 1 0 0 1 402.96 345.12 Tm <636F2D736564696D656E746174696F6E2720> Tj 1 0 0 1 490.80 347.04 Tm <4669672720> Tj 1 0 0 1 512.64 348.24 Tm <6120> Tj 1 0 0 1 522.48 348.24 Tm <73686F777320> Tj 1 0 0 1 555.12 348.72 Tm <616E> Tj 0.48 Tc 1 0 0 1 327.12 330.48 Tm <6578616D706C6520> Tj 1 0 0 1 370.32 331.44 Tm <66627220> Tj 1 0 0 1 386.16 331.92 Tm <74686520> Tj 1 0 0 1 402.72 332.40 Tm <656E7A796D6520> Tj 1 0 0 1 442.08 333.36 Tm <6D657468796C6D616C6F6E796C20> Tj 1 0 0 1 516.72 335.04 Tm <6D75746173652720> Tj 1 0 0 1 555.36 335.76 Tm <616E> Tj 0.48 Tc 1 0 0 1 328.08 317.52 Tm <696D706F7274616E7420> Tj 1 0 0 1 383.28 318.96 Tm <656E7A796D6520> Tj 1 0 0 1 429.84 320.16 Tm <696E20> Tj 1 0 0 1 448.08 320.64 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 504.96 321.84 Tm <62696F73796E7468657369732D27> Tj 0.48 Tc 1 0 0 1 328.08 304.80 Tm <77686C726520> Tj 1 0 0 1 363.12 305.52 Tm <66726F6D20> Tj 1 0 0 1 391.44 306.24 Tm <636F2D736564696D656E746174696F6E20> Tj 1 0 0 1 479.04 308.16 Tm <6578706572696D656E747320> Tj 1 0 0 1 544.56 307.92 Tm <4920> Tj 1 0 0 1 550.80 310.08 Tm <4920> Tj 1 0 0 1 556.56 310.08 Tm <4920> Tj 1 0 0 1 562.08 308.40 Tm <5D> Tj 0.48 Tc 1 0 0 1 328.32 291.60 Tm <74683B20> Tj 1 0 0 1 346.08 292.08 Tm <4220> Tj 1 0 0 1 355.20 290.16 Tm <313220> Tj 1 0 0 1 365.28 292.56 Tm <636F2D666163746F7220> Tj 1 0 0 1 411.12 294.00 Tm <77617320> Tj 1 0 0 1 432.48 294.24 Tm <73686F776E20> Tj 1 0 0 1 466.56 294.96 Tm <746F20> Tj 1 0 0 1 478.80 295.20 Tm <626520> Tj 1 0 0 1 493.44 295.68 Tm <6669726D6C7920> Tj 1 0 0 1 525.36 296.40 Tm <626F756E6420> Tj 1 0 0 1 558.00 297.36 Tm <746F> Tj 0.48 Tc 1 0 0 1 328.56 278.64 Tm <74686520> Tj 1 0 0 1 346.32 279.36 Tm <70726F7465696E2E> Tj 0.96 Tc 1 0 0 1 328.80 252.96 Tm <372E20> Tj 1 0 0 1 346.08 253.20 Tm <536564696D656E746174696F6E20> Tj 1 0 0 1 430.32 255.36 Tm <657175696C69627269756D3A20> Tj 1 0 0 1 501.84 257.04 Tm <6D6F6C6563756C6172> Tj 0.96 Tc /F3 13.0 Tf 1 0 0 1 329.28 240.00 Tm <2A226967682C20> Tj 1 0 0 1 370.32 240.96 Tm <616E6420> Tj 1 0 0 1 394.80 241.44 Tm <6D6F6C6563756C697220> Tj 1 0 0 1 453.12 243.12 Tm <77656967687420> Tj 1 0 0 1 494.16 243.84 Tm <646973747269627574696F6E> Tj 0.96 Tc 1 0 0 1 329.76 227.04 Tm <616E616C59736973> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 342.48 208.08 Tm <6C6E20> Tj 1 0 0 1 355.92 208.56 Tm <6120> Tj 1 0 0 1 365.28 208.56 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 435.60 210.72 Tm <76656C6F6369747920> Tj 1 0 0 1 477.36 211.20 Tm <6578706572696D656E7420> Tj 1 0 0 1 535.44 212.88 Tm <617420> Tj 1 0 0 1 547.92 213.36 Tm <72656C612D> Tj 0.72 Tc 1 0 0 1 330.48 194.88 Tm <746976656C7920> Tj 1 0 0 1 361.20 195.60 Tm <6869676820> Tj 1 0 0 1 385.92 196.32 Tm <726F746F7220> Tj 1 0 0 1 412.32 196.80 Tm <73706565647320> Tj 1 0 0 1 448.08 198.48 Tm <28666F7220> Tj 1 0 0 1 470.64 198.24 Tm <6120> Tj 1 0 0 1 479.28 198.72 Tm <676C6F62756C617220> Tj 1 0 0 1 522.72 199.92 Tm <70726F7465696E20> Tj 1 0 0 1 559.44 200.64 Tm <6F72> Tj 0.72 Tc /F3 9.0 Tf 1 0 0 1 330.72 173.28 Tm <5461626C6520> Tj 1 0 0 1 356.40 173.76 Tm <31> Tj 0.96 Tc 1 0 0 1 330.96 162.24 Tm <436F6E666F726D6174696F6E74797065736F7C74687265656D6163726F6D6F6C6563757C65732874776F706F7C797361632E> Tj 0.48 Tc 1 0 0 1 331.20 151.20 Tm <636861726964657320> Tj 1 0 0 1 367.92 152.16 Tm <616E6420> Tj 1 0 0 1 384.96 152.64 Tm <6120> Tj 1 0 0 1 392.16 152.88 Tm <6D7563696E2920> Tj 1 0 0 1 420.72 153.60 Tm <6C726F6D20> Tj 1 0 0 1 440.64 154.08 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 498.48 155.52 Tm <76656C6F63697479> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 447.60 133.68 Tm <7463746C6E6C20> Tj 1 0 0 1 479.52 134.16 Tm <62> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 514.32 135.36 Tm <436F6E666F726D6174696F6E> Tj 0.72 Tc 1 0 0 1 332.64 110.16 Tm <50756C6C756C616E73> Tj 0.48 Tc 1 0 0 1 332.64 98.88 Tm <43697472757320> Tj 1 0 0 1 358.32 98.16 Tm <50656374696E73> Tj 0.48 Tc 1 0 0 1 333.12 88.32 Tm <42726F6E636869616C20> Tj 1 0 0 1 372.72 89.28 Tm <6D7563696E20> Tj 1 0 0 1 398.88 90.48 Tm <28435973746963> Tj 0.48 Tc 1 0 0 1 332.88 77.52 Tm <666962726F74696329> Tj 0.72 Tc 1 0 0 1 479.76 114.00 Tm <302E343520> Tj 1 0 0 1 515.04 114.96 Tm <52616E646F6D20> Tj 1 0 0 1 550.80 115.68 Tm <636F696C> Tj 0.96 Tc 1 0 0 1 480.00 102.72 Tm <302E313720> Tj 1 0 0 1 515.28 103.92 Tm <52696769642D726F64> Tj 0.72 Tc 1 0 0 1 480.24 91.92 Tm <302E3420> Tj 1 0 0 1 515.52 92.88 Tm <52616E646F6D20> Tj 1 0 0 1 551.52 93.60 Tm <636F696C> Tj 1.44 Tc 1 0 0 1 447.36 113.28 Tm <312E34> Tj 0.96 Tc /F3 11.0 Tf 1 0 0 1 446.88 102.00 Tm <6F2E32> Tj 1.68 Tc /F3 9.0 Tf 1 0 0 1 448.08 91.44 Tm <312E35> Tj 0.48 Tc 1 0 0 1 333.36 56.64 Tm <54686520> Tj 1 0 0 1 352.08 56.88 Tm <4D484B5320> Tj 1 0 0 1 380.88 57.60 Tm <6220> Tj 1 0 0 1 387.84 57.84 Tm <636F656666696369656E7420> Tj 1 0 0 1 430.56 59.28 Tm <63616E20> Tj 1 0 0 1 447.84 59.52 Tm <616C736F20> Tj 1 0 0 1 466.80 60.00 Tm <626520> Tj 1 0 0 1 479.52 60.24 Tm <7573656420> Tj 1 0 0 1 501.36 60.72 Tm <746F20> Tj 1 0 0 1 511.92 60.96 Tm <6D6F64656C20> Tj 1 0 0 1 538.80 61.44 Tm <74686520> Tj 1 0 0 1 554.16 61.92 Tm <666C6578692D> Tj 0.48 Tc 1 0 0 1 333.84 45.84 Tm <6F697269697920> Tj 1 0 0 1 354.48 46.08 Tm <6F6620> Tj 1 0 0 1 364.56 46.56 Tm <6120> Tj 1 0 0 1 372.48 47.52 Tm <706F6C796D657220> Tj 1 0 0 1 406.80 47.76 Tm <696E20> Tj 1 0 0 1 415.68 48.00 Tm <6C65726D7320> Tj 1 0 0 1 440.64 48.72 Tm <6F7427776F726D6C696B6520> Tj 1 0 0 1 490.56 49.68 Tm <636F696C2720> Tj 1 0 0 1 508.80 50.16 Tm <6D6F64656C7320> Tj 1 0 0 1 540.24 50.88 Tm <66726F6D20> Tj 1 0 0 1 560.88 51.36 Tm <746865> Tj 0.48 Tc 1 0 0 1 334.32 35.04 Tm <726174696F20> Tj 1 0 0 1 354.24 35.52 Tm <6F6620> Tj 1 0 0 1 364.08 35.76 Tm <74686520> Tj 1 0 0 1 378.96 36.24 Tm <636F6E746F757220> Tj 1 0 0 1 411.60 37.20 Tm <6C656E67746820> Tj 1 0 0 1 438.48 37.92 Tm <4C20> Tj 1 0 0 1 445.20 37.92 Tm <746F20> Tj 1 0 0 1 455.28 38.16 Tm <74686520> Tj 1 0 0 1 470.64 39.36 Tm <70657273697374656E636520> Tj 1 0 0 1 519.36 39.60 Tm <6C656E67746820> Tj 1 0 0 1 546.72 40.08 Tm <6120> Tj 1 0 0 1 553.92 40.80 Tm <2873656527> Tj 0.72 Tc 1 0 0 1 334.32 24.00 Tm <652E672E20> Tj 1 0 0 1 352.08 24.48 Tm <5265662E20> Tj 1 0 0 1 370.80 23.28 Tm <5B395D292E> Tj ET endstream endobj 35 0 obj 25426 endobj 36 0 obj << /Length 37 0 R >> stream 442 ??0f Fig. 2.Hydrodynamic bead model for a bacteriophageviirs in islow'-and 'fast' moving forms (d2o'' 710 Sand 1020 S, respectively) (Reproduced with permis-sion from Ref. [6].)fringence measurements), or the radius of gyration(frJm 'static' light scattering or low angle x-ray^ri"r*i"gl to *6d"1 the conformation in terms of;t.pl" eiiipsoids of revolution, general triaxial"ifiisoiAs 1+1 or sophisticate.d. but beautiful bead*oi"ft tSi tiee Fig. z;, but this approach is really;; f"; i"iay rigio 1in a time-averaged-s9n1e),nu"romoi"cules such as many proteins IG8] ' Fornot-so-rigid macromolecules such as syntheticpolymerJand polysaccharides we have to use more!""'"r"f shapei uting the 'Wales/van Holde' ratio3i rr. i" the^intrinsic-viscosity, Lll-or the 'Mark-Hou*int-fuhn-sakurada' (MHKS) b coefficient*t i"tt comes from the relation between s"26'* &odthe molecular weight, M:So2o.* : COnSt. Mb(similar coefficients exist for the intrinsic viscos-i,y, rtt" diffusion coefficient, and radius of gyratio.n,iitn U,see Ref. I I ] ). The MHKS b coefficient isu.*ffy obtained by preparilg a..'homologous'seriesii.e., the same polymer but different molec-ular weights) of the polymer (by. e'g" chromato-sraphic ieparation oi heat degradation) and theni"fi"gitt" ilope of a double logarithmic plot of logso26,* VrSUs log M [9].filttt k./ [7,]ind the MHKS b coefficient permrtttre moOeifing of ttre conformation in terms of gen-eral shapes, bltween the three extremes of compacttptt"t",-itglO rod and random coil' For this general;ip; "i ttioa"tting we employ a very useful con-siruction known as the Haug triangle ( Fig' 3 ) [ l0] 'Each of the three extremes of conformation hasrp""in. values for k./ [ 4] and. the. MHKS b coef-ficient and this type ofinalysis has been very usefulin, fo, "*u*ple, pbl ysacchiride conformation anal-ysis (Table I ) trends in anatytical chemistry, vol. 13, no. LO' 1994 a=OcoMPAcr SPHERE O Hol RIGTD ROD RANDOM COIL a=O.5 - 0.8b=o.4 - 0.5ks/[ql- 1.6 a=1.8b{.15ks/[ql-.3 Fig. 3. The Haug triangle (see, e'g', Ref' [10])' Theconformation of a given macromolecule can be rep-resented by a locus along the sides of the triangle'e.g., globulirproteinson side A, polysaccharidesandtinlaipolymers on side B, denatured proteins on sideC. a,trfr4ilfS exponents from respectively, viscosityand sedimentation, other symbols as in the text'Sedimentation velocity can also be used to assayfor interaction in a mixed solute system, especiallyif the different species possess differing chromo-fnot"t absorbing in tho visible or useable part ofihe ultraviolet spectrum (for a modern instrument'wavelengths beiween 210 and 800 nm)' by usingthe princlple of co-sedimentation' Fig' a shows anexample fbr the enzyme methylmalonyl mutase' animportant enzyme in molecular biosynthesis-'whlre from co-sedimentation experiments I I I ]th; B 12 co-factor was shown to be firmly bound tothe protein.7. Sedimentation equilibrium: molecular*"igh, and moleculir weight distributionanalYsisln a sedimentation velocity experiment at rela-tively high rotor speeds (for a globular protein orTable 1Conformationtypeso|threemacromolecu|es(twopo|ysac.charides and a mucin) lrom sedimentation velocity tctlnl b Conformation PullulansCitrus PectinsBronchial mucin (CYsticfibrotic) 0.45 Random coil0.17 Rigid-rod0.4 Random coil 1.4o.21.5 The MHKS b coefficient can also be used to model the flexi-oiriiy of a polymer in lerms ot'wormlike coil' models from theratio of the contour length L to the persistence length a (see'e.g. Ref. 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0.72 Tc 1 0 0 1 71.52 452.88 Tm <6C696E656172706F6C797361636368617269646520> Tj 1 0 0 1 173.76 451.68 Tm <73617920> Tj 1 0 0 1 191.28 451.68 Tm <343020> Tj 1 0 0 1 206.40 451.20 Tm <3030302D353020> Tj 1 0 0 1 245.28 450.72 Tm <30303020> Tj 1 0 0 1 265.20 450.72 Tm <7265766C6D696E29> Tj 0.48 Tc 1 0 0 1 71.04 439.92 Tm <74686520> Tj 1 0 0 1 91.44 439.44 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 164.16 438.72 Tm <7261746520> Tj 1 0 0 1 187.44 438.48 Tm <616E6420> Tj 1 0 0 1 210.48 438.24 Tm <68656E636520> Tj 1 0 0 1 243.84 437.76 Tm <736564696D656E746174696F6E> Tj 0.48 Tc 1 0 0 1 70.56 426.72 Tm <636F656666696369656E7420> Tj 1 0 0 1 124.08 426.24 Tm <697320> Tj 1 0 0 1 134.16 426.00 Tm <6120> Tj 1 0 0 1 142.08 426.00 Tm <6D65617375726520> Tj 1 0 0 1 183.84 425.28 Tm <6F6620> Tj 1 0 0 1 196.56 425.28 Tm <74686520> Tj 1 0 0 1 213.60 425.04 Tm <73697A6520> Tj 1 0 0 1 234.24 424.80 Tm <616E6420> Tj 1 0 0 1 254.16 424.56 Tm <736861706520> Tj 1 0 0 1 283.44 424.32 Tm <6F6620> Tj 1 0 0 1 295.92 424.32 Tm <746865> Tj 0.72 Tc 1 0 0 1 70.80 413.52 Tm <6D6F6C6563756C652E20> Tj 1 0 0 1 120.48 413.28 Tm <417420> Tj 1 0 0 1 135.36 413.04 Tm <6D75636820> Tj 1 0 0 1 164.64 412.80 Tm <6C6F77657220> Tj 1 0 0 1 194.40 412.08 Tm <73706565647320> Tj 1 0 0 1 229.68 412.56 Tm <2873617920> Tj 1 0 0 1 254.88 411.60 Tm <6C3020> Tj 1 0 0 1 268.08 411.36 Tm <30303020> Tj 1 0 0 1 289.20 411.36 Tm <7265766C> Tj 0.72 Tc 1 0 0 1 70.56 400.56 Tm <6D696E20> Tj 1 0 0 1 91.68 400.32 Tm <6F7220> Tj 1 0 0 1 105.12 400.32 Tm <6C6573732920> Tj 1 0 0 1 131.76 399.84 Tm <696E20> Tj 1 0 0 1 143.52 399.84 Tm <6120> Tj 1 0 0 1 151.44 399.60 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 221.28 398.64 Tm <657175696C69627269756D65787065722D> Tj 0.48 Tc 1 0 0 1 70.32 387.60 Tm <696D656E7420> Tj 1 0 0 1 100.32 387.36 Tm <74686520> Tj 1 0 0 1 117.84 387.12 Tm <666F7263657320> Tj 1 0 0 1 149.52 386.64 Tm <6F6620> Tj 1 0 0 1 162.48 386.40 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 232.08 385.68 Tm <616E6420> Tj 1 0 0 1 252.00 385.44 Tm <646966667573696F6E20> Tj 1 0 0 1 297.84 384.96 Tm <6F6E> Tj 0.48 Tc 1 0 0 1 70.08 374.40 Tm <74686520> Tj 1 0 0 1 95.04 374.16 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 179.04 372.96 Tm <6265636F6D6520> Tj 1 0 0 1 226.32 372.72 Tm <636F6D70617261626C6520> Tj 1 0 0 1 292.32 372.00 Tm <616E64> Tj 0.72 Tc 1 0 0 1 69.84 361.20 Tm <696E737465616420> Tj 1 0 0 1 106.32 360.72 Tm <6F6620> Tj 1 0 0 1 119.04 360.96 Tm <67657474696E6720> Tj 1 0 0 1 154.80 360.24 Tm <6120> Tj 1 0 0 1 162.72 360.00 Tm <736564696D656E74696E6720> Tj 1 0 0 1 223.92 359.28 Tm <626F756E6461727920> Tj 1 0 0 1 271.20 359.28 Tm <796F7520> Tj 1 0 0 1 291.84 359.04 Tm <6765742C> Tj 0.48 Tc 1 0 0 1 69.60 348.00 Tm <616674657220> Tj 1 0 0 1 95.04 347.76 Tm <6120> Tj 1 0 0 1 103.92 348.00 Tm <706572696F6420> Tj 1 0 0 1 138.00 347.28 Tm <6F6620> Tj 1 0 0 1 151.68 347.04 Tm <74696D6520> Tj 1 0 0 1 177.36 347.52 Tm <2866726F6D20> Tj 1 0 0 1 209.28 346.56 Tm <6120> Tj 1 0 0 1 218.40 346.32 Tm <66657720> Tj 1 0 0 1 239.76 346.08 Tm <686F75727320> Tj 1 0 0 1 269.52 345.84 Tm <746F20> Tj 1 0 0 1 282.48 345.60 Tm <6120> Tj 1 0 0 1 291.60 345.60 Tm <666577> Tj 0.72 Tc 1 0 0 1 69.12 335.04 Tm <6461797320> Tj 1 0 0 1 96.72 334.80 Tm <646570656E64696E6720> Tj 1 0 0 1 152.16 334.08 Tm <6F6E20> Tj 1 0 0 1 170.16 334.08 Tm <74686520> Tj 1 0 0 1 190.32 333.84 Tm <6E617475726520> Tj 1 0 0 1 225.36 333.36 Tm <6F6620> Tj 1 0 0 1 240.96 333.36 Tm <74686520> Tj 1 0 0 1 260.88 332.88 Tm <736F6C757465292C20> Tj 1 0 0 1 303.84 332.64 Tm <61> Tj 0.72 Tc 1 0 0 1 69.12 321.84 Tm <7374656164792D737461746520> Tj 1 0 0 1 128.16 321.36 Tm <65717520> Tj 1 0 0 1 145.92 321.36 Tm <696C20> Tj 1 0 0 1 152.64 321.12 Tm <69627269756D20> Tj 1 0 0 1 186.24 320.64 Tm <646973747269627574696F6E20> Tj 1 0 0 1 244.08 319.92 Tm <6F6620> Tj 1 0 0 1 256.80 319.92 Tm <6D6163726F6D6F6C2D> Tj 0.72 Tc 1 0 0 1 68.64 308.88 Tm <6563756C657320> Tj 1 0 0 1 103.92 308.64 Tm <7769746820> Tj 1 0 0 1 129.60 308.16 Tm <6120> Tj 1 0 0 1 139.92 308.16 Tm <6C6F7720> Tj 1 0 0 1 162.00 307.92 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 231.84 307.20 Tm <617420> Tj 1 0 0 1 245.04 306.96 Tm <74686520> Tj 1 0 0 1 264.24 306.72 Tm <6D656E6973637573> Tj 0.72 Tc 1 0 0 1 68.64 295.68 Tm <6275696C64696E6720> Tj 1 0 0 1 111.36 295.44 Tm <757020> Tj 1 0 0 1 125.76 295.44 Tm <746F20> Tj 1 0 0 1 137.76 295.20 Tm <6120> Tj 1 0 0 1 145.44 294.96 Tm <6869676820> Tj 1 0 0 1 168.96 294.72 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 236.64 294.00 Tm <617420> Tj 1 0 0 1 247.68 294.00 Tm <74686520> Tj 1 0 0 1 264.48 293.76 Tm <63656C6C20> Tj 1 0 0 1 284.16 293.52 Tm <626173652E> Tj 0.72 Tc 1 0 0 1 68.16 282.72 Tm <5468697320> Tj 1 0 0 1 93.12 282.48 Tm <66696E616C20> Tj 1 0 0 1 117.36 282.24 Tm <7374656164792D737461746520> Tj 1 0 0 1 176.64 281.76 Tm <7061747465726E20> Tj 1 0 0 1 213.12 281.28 Tm <697320> Tj 1 0 0 1 223.68 281.04 Tm <6120> Tj 1 0 0 1 232.32 281.04 Tm <66756E6374696F6E20> Tj 1 0 0 1 274.32 280.56 Tm <6F6E6C7920> Tj 1 0 0 1 298.32 280.32 Tm <6F66> Tj 0.72 Tc 1 0 0 1 68.40 269.52 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 121.92 269.52 Tm <77656967687420> Tj 1 0 0 1 159.36 268.56 Tm <616E6420> Tj 1 0 0 1 182.16 268.32 Tm <72656C6174656420> Tj 1 0 0 1 219.60 268.08 Tm <706172616D657465727320> Tj 1 0 0 1 277.92 268.08 Tm <2876697269616C> Tj 0.72 Tc 1 0 0 1 67.92 256.56 Tm <636F656666696369656E747320> Tj 1 0 0 1 125.28 256.08 Tm <616E6420> Tj 1 0 0 1 144.72 255.84 Tm <6173736F63696174696F6E20> Tj 1 0 0 1 199.44 255.12 Tm <636F6E7374616E747320> Tj 1 0 0 1 246.24 254.88 Tm <776865726520> Tj 1 0 0 1 276.72 254.40 Tm <617070726F2D> Tj 0.72 Tc 1 0 0 1 67.92 243.84 Tm <7072696174652920> Tj 1 0 0 1 103.68 243.12 Tm <616E6420> Tj 1 0 0 1 123.84 242.88 Tm <6E6F7420> Tj 1 0 0 1 141.12 242.64 Tm <6F6620> Tj 1 0 0 1 153.60 242.64 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 203.76 241.92 Tm <736861706520> Tj 1 0 0 1 233.04 241.68 Tm <73696E636520> Tj 1 0 0 1 259.68 241.44 Tm <617420> Tj 1 0 0 1 270.48 241.44 Tm <657175696C69622D> Tj 0.48 Tc 1 0 0 1 67.92 230.40 Tm <7269756D20> Tj 1 0 0 1 100.08 230.16 Tm <746865726520> Tj 1 0 0 1 133.92 229.92 Tm <697320> Tj 1 0 0 1 150.96 229.68 Tm <6E6F20> Tj 1 0 0 1 172.32 229.20 Tm <6675727468657220> Tj 1 0 0 1 214.32 228.96 Tm <6D6F76656D656E7420> Tj 1 0 0 1 273.36 228.24 Tm <6F6620> Tj 1 0 0 1 293.04 228.24 Tm <746865> Tj 0.72 Tc 1 0 0 1 67.68 217.44 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 152.88 216.72 Tm <616E6420> Tj 1 0 0 1 181.68 216.48 Tm <68656E636520> Tj 1 0 0 1 221.04 216.00 Tm <6672696374696F6E616C20> Tj 1 0 0 1 275.52 215.28 Tm <65666665637473> Tj 0.72 Tc 1 0 0 1 67.44 204.72 Tm <7468726F75676820> Tj 1 0 0 1 107.76 204.24 Tm <736861706520> Tj 1 0 0 1 138.24 204.24 Tm <766172696174696F6E20> Tj 1 0 0 1 183.12 203.28 Tm <646F6E20> Tj 1 0 0 1 204.24 203.28 Tm <6E6F7420> Tj 1 0 0 1 221.76 203.04 Tm <636F6D6520> Tj 1 0 0 1 251.04 202.80 Tm <696E746F20> Tj 1 0 0 1 271.92 202.80 Tm <706C617920> Tj 1 0 0 1 294.72 204.72 Tm <2D> Tj 0.72 Tc 1 0 0 1 67.20 191.52 Tm <736F20> Tj 1 0 0 1 83.28 191.28 Tm <6C696B6520> Tj 1 0 0 1 107.28 196.56 Tm <277374617469632720> Tj 1 0 0 1 145.44 191.28 Tm <28617320> Tj 1 0 0 1 165.60 190.32 Tm <6F70706F73656420> Tj 1 0 0 1 210.96 190.08 Tm <746F20> Tj 1 0 0 1 226.08 195.12 Tm <2764796E616D6963272920> Tj 1 0 0 1 285.60 189.36 Tm <6C69676874> Tj 0.72 Tc 1 0 0 1 66.96 178.56 Tm <73636174746572696E6720> Tj 1 0 0 1 116.88 178.08 Tm <697420> Tj 1 0 0 1 126.48 178.08 Tm <697320> Tj 1 0 0 1 136.80 177.84 Tm <616E20> Tj 1 0 0 1 150.72 177.60 Tm <6162736F6C75746520> Tj 1 0 0 1 193.68 177.36 Tm <77617920> Tj 1 0 0 1 216.00 176.88 Tm <6F6620> Tj 1 0 0 1 228.72 177.12 Tm <67657474696E6720> Tj 1 0 0 1 265.44 177.12 Tm <287765696768742D> Tj 0.72 Tc 1 0 0 1 66.96 165.60 Tm <6176657261676520> Tj 1 0 0 1 105.84 163.68 Tm <2920> Tj 1 0 0 1 113.52 165.12 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 164.40 164.64 Tm <7765696768742E> Tj 0.72 Tc 1 0 0 1 78.72 152.40 Tm <54686520> Tj 1 0 0 1 101.52 152.16 Tm <6D6F737420> Tj 1 0 0 1 127.92 151.92 Tm <616363757261746520> Tj 1 0 0 1 171.36 151.44 Tm <77617920> Tj 1 0 0 1 194.88 150.96 Tm <6F6620> Tj 1 0 0 1 208.56 150.96 Tm <7265636F7264696E6720> Tj 1 0 0 1 257.52 150.48 Tm <746865736520> Tj 1 0 0 1 285.60 150.24 Tm <66696E616C> Tj 0.72 Tc 1 0 0 1 66.48 139.44 Tm <7374656164792D737461746520> Tj 1 0 0 1 126.96 138.72 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 196.08 138.00 Tm <646973747269627574696F6E7320> Tj 1 0 0 1 259.92 137.52 Tm <697320> Tj 1 0 0 1 271.20 137.28 Tm <7573696E6720> Tj 1 0 0 1 301.20 137.04 Tm <61> Tj 0.48 Tc 1 0 0 1 66.24 126.48 Tm <7370656369616C20> Tj 1 0 0 1 104.64 126.24 Tm <7479706520> Tj 1 0 0 1 129.84 125.76 Tm <6F6620> Tj 1 0 0 1 144.72 125.76 Tm <7265667261637469766520> Tj 1 0 0 1 195.12 125.04 Tm <696E64657820> Tj 1 0 0 1 225.84 124.80 Tm <6F707469637320> Tj 1 0 0 1 259.20 124.56 Tm <6B6E6F776E20> Tj 1 0 0 1 296.16 124.08 Tm <6173> Tj 0.72 Tc 1 0 0 1 66.24 113.52 Tm <5261796C6569676820> Tj 1 0 0 1 114.24 113.28 Tm <696E746572666572656E636520> Tj 1 0 0 1 175.20 112.32 Tm <6F707469637320> Tj 1 0 0 1 209.04 112.80 Tm <284669672E20> Tj 1 0 0 1 237.36 111.84 Tm <354127292E20> Tj 1 0 0 1 265.20 111.60 Tm <466F7220> Tj 1 0 0 1 286.08 111.60 Tm <70726F2D> Tj 0.72 Tc 1 0 0 1 66.00 100.32 Tm <7465696E732C20> Tj 1 0 0 1 94.32 100.32 Tm <6E75636C65696320> Tj 1 0 0 1 131.28 99.84 Tm <616369647320> Tj 1 0 0 1 157.92 99.60 Tm <616E6420> Tj 1 0 0 1 177.60 99.12 Tm <6F7468657220> Tj 1 0 0 1 204.72 99.12 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 284.88 98.40 Tm <77697468> Tj 0.72 Tc 1 0 0 1 65.76 87.36 Tm <616E20> Tj 1 0 0 1 81.84 87.36 Tm <6162736F7262696E6720> Tj 1 0 0 1 133.44 86.88 Tm <6368726F6D6F70686F726520> Tj 1 0 0 1 202.56 86.40 Tm <776520> Tj 1 0 0 1 220.56 85.92 Tm <63616E20> Tj 1 0 0 1 241.68 85.68 Tm <75736520> Tj 1 0 0 1 262.32 85.44 Tm <74686520> Tj 1 0 0 1 281.52 85.20 Tm <6D6F7265> Tj 0.72 Tc 1 0 0 1 65.28 74.40 Tm <636F6E76656E69656E7420> Tj 1 0 0 1 124.08 74.64 Tm <2862757420> Tj 1 0 0 1 149.52 73.68 Tm <6C65737320> Tj 1 0 0 1 171.84 73.44 Tm <61636375726174652920> Tj 1 0 0 1 222.24 72.72 Tm <6162736F727074696F6E20> Tj 1 0 0 1 277.20 72.24 Tm <6F7074696373> Tj 0.96 Tc 1 0 0 1 66.24 61.92 Tm <284669672E20> Tj 1 0 0 1 94.80 60.96 Tm <35382920> Tj 1 0 0 1 120.24 61.44 Tm <28646F776E20> Tj 1 0 0 1 156.72 60.48 Tm <746F20> Tj 1 0 0 1 170.16 60.24 Tm <6120> Tj 1 0 0 1 180.00 60.48 Tm <776176656C656E67726820> Tj 1 0 0 1 239.04 59.52 Tm <6F6620> Tj 1 0 0 1 253.68 59.52 Tm <5A6C3020> Tj 1 0 0 1 276.00 59.28 Tm <6E6D20> Tj 1 0 0 1 295.20 59.04 Tm <6F72> Tj 0.72 Tc 1 0 0 1 65.28 48.48 Tm <706F737369626C7920> Tj 1 0 0 1 109.44 48.00 Tm <6C65737320> Tj 1 0 0 1 131.52 47.76 Tm <7769746820> Tj 1 0 0 1 156.48 47.52 Tm <74686520> Tj 1 0 0 1 175.20 47.28 Tm <4265636B6D616E20> Tj 1 0 0 1 224.16 46.56 Tm <584C4120> Tj 1 0 0 1 252.72 46.56 Tm <756C74726163656E7472692D> Tj 0.72 Tc 1 0 0 1 65.04 35.28 Tm <66756765292E20> Tj 1 0 0 1 100.32 35.04 Tm <5768656E20> Tj 1 0 0 1 133.44 34.56 Tm <6162736F727074696F6E20> Tj 1 0 0 1 188.64 34.08 Tm <6F707469637320> Tj 1 0 0 1 221.76 33.84 Tm <61726520> Tj 1 0 0 1 241.20 33.60 Tm <7573656420> Tj 1 0 0 1 267.36 33.84 Tm <7061747465726E73> Tj 0.72 Tc 1 0 0 1 64.80 22.32 Tm <63616E20> Tj 1 0 0 1 83.76 21.84 Tm <626520> Tj 1 0 0 1 97.20 22.08 Tm <726F7574696E656C7920> Tj 1 0 0 1 141.84 21.36 Tm <636170747572656420> Tj 1 0 0 1 185.28 20.88 Tm <6175746F6D61746963616C6C7920> Tj 1 0 0 1 252.00 20.40 Tm <6F6E2D6C696E6520> Tj 1 0 0 1 287.52 19.92 Tm <616E64> Tj 0.72 Tc 1 0 0 1 342.72 536.64 Tm <4669672E20> Tj 1 0 0 1 362.64 536.16 Tm <352E20> Tj 1 0 0 1 374.16 536.16 Tm <4F70746963616C20> Tj 1 0 0 1 409.44 535.92 Tm <7265636F72647320> Tj 1 0 0 1 446.40 535.20 Tm <6F6620> Tj 1 0 0 1 457.92 535.20 Tm <736F6C75746520> Tj 1 0 0 1 488.40 534.72 Tm <646973747269627574696F6E7320> Tj 1 0 0 1 547.44 533.52 Tm <617420> Tj 1 0 0 1 558.96 533.52 Tm <736564692D> Tj 0.72 Tc 1 0 0 1 342.00 523.44 Tm <6D656E746174696F6E20> Tj 1 0 0 1 389.76 522.96 Tm <657175696C69627269756D2E20> Tj 1 0 0 1 444.48 522.48 Tm <54686520> Tj 1 0 0 1 464.40 522.00 Tm <646972656374696F6E20> Tj 1 0 0 1 505.68 521.28 Tm <6F6620> Tj 1 0 0 1 516.48 521.04 Tm <74686520> Tj 1 0 0 1 533.28 520.80 Tm <63656E747269667567616C> Tj 0.48 Tc 1 0 0 1 341.52 510.48 Tm <6669656C6420> Tj 1 0 0 1 365.76 510.24 Tm <697320> Tj 1 0 0 1 377.52 510.24 Tm <66726F6D20> Tj 1 0 0 1 403.44 510.00 Tm <6C65667420> Tj 1 0 0 1 421.20 509.76 Tm <746F20> Tj 1 0 0 1 435.12 509.52 Tm <72696768742E20> Tj 1 0 0 1 462.48 509.76 Tm <28412920> Tj 1 0 0 1 481.20 508.80 Tm <5261796C6569676820> Tj 1 0 0 1 526.32 508.08 Tm <696E7465646572656E6365> Tj 0.72 Tc 1 0 0 1 341.52 498.24 Tm <70726F66696C657320> Tj 1 0 0 1 378.24 497.28 Tm <666F7220> Tj 1 0 0 1 393.60 497.04 Tm <68756D616E20> Tj 1 0 0 1 428.40 496.80 Tm <6C67633B20> Tj 1 0 0 1 450.72 497.04 Tm <28422920> Tj 1 0 0 1 467.28 496.08 Tm <6162736F727074696F6E20> Tj 1 0 0 1 519.12 495.12 Tm <6F70746963616C70726F66696C65> Tj 0.72 Tc 1 0 0 1 341.52 485.28 Tm <28617420> Tj 1 0 0 1 356.88 484.32 Tm <32383020> Tj 1 0 0 1 378.24 484.32 Tm <6E6D2920> Tj 1 0 0 1 399.12 484.08 Tm <666F7220> Tj 1 0 0 1 414.72 483.84 Tm <74686520> Tj 1 0 0 1 432.96 483.60 Tm <6D7573636C6520> Tj 1 0 0 1 468.96 483.84 Tm <70726F7465696E20> Tj 1 0 0 1 504.48 482.64 Tm <746974696E2E20> Tj 1 0 0 1 527.52 482.16 Tm <533A20> Tj 1 0 0 1 545.04 481.92 Tm <736F6C7574696F6E> Tj 0.72 Tc 1 0 0 1 341.52 471.84 Tm <7265636F72643B20> Tj 1 0 0 1 376.32 471.36 Tm <4F3A20> Tj 1 0 0 1 394.56 471.12 Tm <6F70746963616C20> Tj 1 0 0 1 427.20 470.88 Tm <626173656C696E652E> Tj 0.72 Tc 1 0 0 1 340.80 445.20 Tm <616E616C797365642C20> Tj 1 0 0 1 389.76 444.96 Tm <7768696C6520> Tj 1 0 0 1 420.00 444.72 Tm <7769746820> Tj 1 0 0 1 444.96 444.24 Tm <74686520> Tj 1 0 0 1 463.68 444.00 Tm <696E746572666572656E636520> Tj 1 0 0 1 524.40 442.80 Tm <73767374656D20> Tj 1 0 0 1 561.84 442.56 Tm <697420> Tj 1 0 0 1 572.40 442.32 Tm <6973> Tj 0.48 Tc 1 0 0 1 340.56 426.96 Tm <543131635F6820> Tj 1 0 0 1 373.68 432.00 Tm <6D6F726520> Tj 1 0 0 1 404.64 431.76 Tm <636F6D706C69636174656420> Tj 1 0 0 1 469.44 430.80 Tm <616E6420> Tj 1 0 0 1 493.68 430.56 Tm <696E6465656420> Tj 1 0 0 1 532.08 429.84 Tm <657870656E73697665> Tj 0.72 Tc 1 0 0 1 341.76 417.60 Tm <4920> Tj 1 0 0 1 347.76 419.28 Tm <6C325D2E20> Tj 1 0 0 1 370.08 419.28 Tm <576861746576657220> Tj 1 0 0 1 418.80 418.56 Tm <74686520> Tj 1 0 0 1 435.84 418.32 Tm <73797374656D2C20> Tj 1 0 0 1 474.48 417.84 Tm <746865736520> Tj 1 0 0 1 501.60 417.84 Tm <7061747465726E7320> Tj 1 0 0 1 542.40 416.88 Tm <61726520> Tj 1 0 0 1 559.44 416.64 Tm <6E6F77> Tj 0.72 Tc 1 0 0 1 340.08 406.56 Tm <757375616C6C7920> Tj 1 0 0 1 380.64 406.08 Tm <636170747572656420> Tj 1 0 0 1 428.16 405.60 Tm <616E6420> Tj 1 0 0 1 451.44 405.36 Tm <7265616420> Tj 1 0 0 1 478.08 404.88 Tm <6175746F6D61746963616C6C792C20> Tj 1 0 0 1 552.24 403.68 Tm <656974686572> Tj 0.48 Tc 1 0 0 1 339.60 393.36 Tm <6469726563746C7920> Tj 1 0 0 1 379.20 393.12 Tm <696E746F20> Tj 1 0 0 1 399.84 392.88 Tm <6120> Tj 1 0 0 1 407.04 392.88 Tm <636F6D707574657220> Tj 1 0 0 1 454.32 392.16 Tm <6F7220> Tj 1 0 0 1 467.04 392.16 Tm <76696120> Tj 1 0 0 1 483.60 391.92 Tm <6120> Tj 1 0 0 1 491.52 391.68 Tm <62697420> Tj 1 0 0 1 506.40 391.44 Tm <6F6620> Tj 1 0 0 1 519.12 391.68 Tm <70686F746F677261706879> Tj 0.48 Tc 1 0 0 1 339.60 380.40 Tm <6F7220> Tj 1 0 0 1 352.32 380.40 Tm <636861727420> Tj 1 0 0 1 379.68 380.16 Tm <7265636F7264657220> Tj 1 0 0 1 421.92 379.68 Tm <6F757470757420> Tj 1 0 0 1 455.52 379.20 Tm <66697273742E> Tj 0.72 Tc 1 0 0 1 351.60 367.20 Tm <486F7720> Tj 1 0 0 1 378.48 366.96 Tm <646F20> Tj 1 0 0 1 394.32 367.20 Tm <776520> Tj 1 0 0 1 411.60 367.20 Tm <67657420> Tj 1 0 0 1 430.08 366.48 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 481.20 366.24 Tm <77656967687420> Tj 1 0 0 1 517.68 365.28 Tm <696E666F726D6174696F6E3F> Tj 0.72 Tc 1 0 0 1 339.12 354.24 Tm <54686520> Tj 1 0 0 1 360.72 354.00 Tm <636F6D707574657220> Tj 1 0 0 1 409.20 353.76 Tm <757375616C6C7920> Tj 1 0 0 1 446.16 353.28 Tm <636F6E766572747320> Tj 1 0 0 1 489.60 352.80 Tm <74686520> Tj 1 0 0 1 507.36 352.32 Tm <64696769746973656420> Tj 1 0 0 1 552.00 351.84 Tm <696E666F722D> Tj 0.72 Tc 1 0 0 1 339.36 341.52 Tm <6D6174696F6E20> Tj 1 0 0 1 375.36 341.04 Tm <6F6620> Tj 1 0 0 1 388.32 341.04 Tm <4669672E20> Tj 1 0 0 1 409.92 340.80 Tm <3520> Tj 1 0 0 1 419.52 340.80 Tm <696E746F20> Tj 1 0 0 1 440.40 340.32 Tm <6120> Tj 1 0 0 1 449.04 340.32 Tm <7265636F726420> Tj 1 0 0 1 481.92 339.84 Tm <6F6620> Tj 1 0 0 1 495.60 339.84 Tm <6C6F6720> Tj 1 0 0 1 513.36 339.36 Tm <636F6E63656E74726174696F6E> Tj 0.72 Tc 1 0 0 1 339.84 329.28 Tm <2865787072657373656420> Tj 1 0 0 1 398.40 328.08 Tm <696E20> Tj 1 0 0 1 412.80 327.84 Tm <7465726D7320> Tj 1 0 0 1 444.72 327.36 Tm <6F6620> Tj 1 0 0 1 460.56 327.36 Tm <6162736F7262616E636520> Tj 1 0 0 1 520.56 326.40 Tm <756E6974732C20> Tj 1 0 0 1 551.76 326.16 Tm <412C20> Tj 1 0 0 1 568.32 325.92 Tm <6F72> Tj 0.72 Tc 1 0 0 1 338.88 315.84 Tm <6672696E676520> Tj 1 0 0 1 374.64 315.36 Tm <646973706C6163656D656E742C20> Tj 1 0 0 1 447.12 314.64 Tm <222F2920> Tj 1 0 0 1 466.56 314.64 Tm <76657273757320> Tj 1 0 0 1 504.72 313.92 Tm <72616469616C20> Tj 1 0 0 1 539.28 313.20 Tm <64697374616E6365> Tj 0.72 Tc 1 0 0 1 338.64 302.64 Tm <737175617265642E20> Tj 1 0 0 1 384.96 302.40 Tm <466F7220> Tj 1 0 0 1 407.52 302.16 Tm <666169726C7920> Tj 1 0 0 1 439.20 301.92 Tm <696465616C20> Tj 1 0 0 1 467.76 301.44 Tm <6D6F6E6F646973706572736520> Tj 1 0 0 1 540.72 300.24 Tm <73797374656D73> Tj 0.96 Tc 1 0 0 1 339.12 290.64 Tm <28652E672E20> Tj 1 0 0 1 364.56 289.68 Tm <64696C75746520> Tj 1 0 0 1 394.32 289.44 Tm <736F6C7574696F6E7320> Tj 1 0 0 1 439.68 288.96 Tm <6F6620> Tj 1 0 0 1 452.40 288.72 Tm <736F6D6520> Tj 1 0 0 1 480.24 288.24 Tm <736D616C6C20> Tj 1 0 0 1 509.04 288.00 Tm <70726F7465696E732920> Tj 1 0 0 1 556.32 287.28 Tm <73756368> Tj 0.72 Tc 1 0 0 1 338.16 276.96 Tm <706C6F747320> Tj 1 0 0 1 364.32 276.72 Tm <61726520> Tj 1 0 0 1 381.84 276.48 Tm <49696E6561722C20> Tj 1 0 0 1 414.24 276.00 Tm <62757420> Tj 1 0 0 1 432.00 276.00 Tm <666F7220> Tj 1 0 0 1 448.56 275.76 Tm <6E6F6E2D696465616C20> Tj 1 0 0 1 495.84 275.04 Tm <6F7220> Tj 1 0 0 1 508.80 274.80 Tm <68657465726F67656E656F7573> Tj 0.72 Tc 1 0 0 1 337.92 263.76 Tm <73797374656D7320> Tj 1 0 0 1 379.92 263.52 Tm <7468657920> Tj 1 0 0 1 403.92 263.28 Tm <61726520> Tj 1 0 0 1 422.64 263.04 Tm <6E6F7420> Tj 1 0 0 1 442.08 263.52 Tm <284669672E20> Tj 1 0 0 1 469.92 262.32 Tm <36292E20> Tj 1 0 0 1 488.64 262.08 Tm <54686520> Tj 1 0 0 1 511.44 261.84 Tm <6176657261676520> Tj 1 0 0 1 552.96 261.12 Tm <736C6F7065> Tj 0.72 Tc 1 0 0 1 337.68 250.80 Tm <6F6620> Tj 1 0 0 1 355.44 250.56 Tm <746865736520> Tj 1 0 0 1 387.60 250.80 Tm <706C6F74732C20> Tj 1 0 0 1 421.68 250.32 Tm <6C696E65617220> Tj 1 0 0 1 455.28 249.60 Tm <6F7220> Tj 1 0 0 1 472.80 249.36 Tm <6F74686572776973652C20> Tj 1 0 0 1 530.16 249.84 Tm <676976657320> Tj 1 0 0 1 563.28 248.16 Tm <746865> Tj 0.00 Tc /F3 7.0 Tf 1 0 0 1 359.04 228.00 Tm <6C> Tj 0.00 Tc /F3 4.0 Tf 1 0 0 1 358.32 213.12 Tm <49> Tj 0.00 Tc /F3 7.0 Tf 1 0 0 1 358.32 197.76 Tm <7A> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 365.28 228.00 Tm <30> Tj 0.00 Tc /F3 10.0 Tf 1 0 0 1 365.52 213.12 Tm <29> Tj 0.00 Tc /F3 6.0 Tf 1 0 0 1 364.80 199.44 Tm <67> Tj 0.00 Tc /F3 18.0 Tf 1 0 0 1 351.84 92.40 Tm <2D2C20> Tj 1 0 0 1 362.16 85.44 Tm <612E62> Tj 1.20 Tc /F3 8.0 Tf 1 0 0 1 417.84 84.96 Tm <6F2E34> Tj 6.72 Tc /F3 6.0 Tf 1 0 0 1 337.44 168.24 Tm <467274> Tj 12.00 Tc /F3 8.0 Tf 1 0 0 1 337.68 153.84 Tm <294F> Tj 1.68 Tc 1 0 0 1 362.16 151.44 Tm <2E35> Tj 0.96 Tc /F3 11.0 Tf 1 0 0 1 356.64 136.32 Tm <6F2E73> Tj 0.96 Tc /F3 9.0 Tf 1 0 0 1 352.32 107.76 Tm <2D742E6F> Tj 1.68 Tc /F3 8.0 Tf 1 0 0 1 502.32 84.00 Tm <742E6F> Tj 1.44 Tc 1 0 0 1 390.24 85.20 Tm <392E32> Tj 1.44 Tc /F3 7.0 Tf 1 0 0 1 445.68 84.96 Tm <392E36> Tj 1.44 Tc 1 0 0 1 473.52 84.72 Tm <302E38> Tj 0.00 Tc /F3 9.0 Tf 1 0 0 1 436.08 70.32 Tm <63> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 335.52 58.08 Tm <4669672E20> Tj 1 0 0 1 358.32 57.60 Tm <362E20> Tj 1 0 0 1 372.96 57.60 Tm <4C6F6720> Tj 1 0 0 1 395.52 57.36 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 463.44 57.36 Tm <2865787072657373656420> Tj 1 0 0 1 521.04 56.16 Tm <696E20> Tj 1 0 0 1 534.96 55.92 Tm <5261796C65696768> Tj 0.72 Tc 1 0 0 1 334.80 45.36 Tm <6672696E676520> Tj 1 0 0 1 363.12 44.88 Tm <646973706C6163656D656E7420> Tj 1 0 0 1 426.24 44.40 Tm <756E6974732C20> Tj 1 0 0 1 452.88 43.92 Tm <222F2920> Tj 1 0 0 1 463.20 43.92 Tm <76657273757320> Tj 1 0 0 1 495.84 43.44 Tm <64697374616E636520> Tj 1 0 0 1 537.36 42.96 Tm <73717561726564> Tj 0.72 Tc 1 0 0 1 335.04 32.88 Tm <2865787072657373656420> Tj 1 0 0 1 390.00 31.92 Tm <696E20> Tj 1 0 0 1 400.56 31.68 Tm <7465726D7320> Tj 1 0 0 1 429.60 31.44 Tm <6F6620> Tj 1 0 0 1 441.12 31.20 Tm <74686520> Tj 1 0 0 1 458.88 31.20 Tm <6E6F726D616C6973656420> Tj 1 0 0 1 513.12 30.96 Tm <706172616D6574657220> Tj 1 0 0 1 564.24 28.08 Tm <7B292C> Tj 0.72 Tc 1 0 0 1 334.56 19.44 Tm <666F7220> Tj 1 0 0 1 349.44 19.20 Tm <6120> Tj 1 0 0 1 358.32 19.20 Tm <68657465726F67656E656F757320> Tj 1 0 0 1 430.08 18.48 Tm <6D7563757320> Tj 1 0 0 1 462.96 18.72 Tm <676C79636F70726F7465696E2E> Tj ET endstream endobj 44 0 obj 24036 endobj 45 0 obj << /Length 46 0 R >> stream trends ip analytical chemistry, vol. 13, no. lO, lgg4 443 B Fig. 4. Co-sedimentation diagram (at 44 OOO rev/min)for an enzyme (methyl-malonylmutase), scanned at295 nm and (top) its 812 co-factor, scanned 2 minlater at 608 nm. The centre of the sedimenting bound-ary is virtually the same for both, with no residualabsorbance, confirming complete binding of the co-factorto the enzyme.linearpolysaccharide say 40 000-50 000 revlmin)the sedimentation rate and hence sedimentationcoefficient is a measure of the size and shape of themolecule. At much lower speeds (say l0 000 revlmin or less) in a sedimentation equilibriumexper-iment the forces of sedimentation and diffusion onthe macromolecule become comparable andinstead of getting a sedimenting boundary you get,after a period of time (from a few hours to a fewdays depending on the nature of the solute), asteady-state equ il ibrium distribution of macromol-ecules with a low concentration at the meniscusbuilding up to a high concentration at the cell base.This final steady-state pattern is a function only ofmolecular weight and related parameters (virialcoefficients and association constants where appro-priate) and not of molecular shape since at equilib-rium there is no further movement of themacromolecule and hence frictional effectsthrough shape variation don not come into play -so like 'static' (as opposed to 'dynamic') lightscattering it is an absolute way of getting (weight-average ) molecular weight.The most accurate way of recording these finalsteady-state concentration distributions is using aspecial type of refractive index optics known asRayleigh interference optics (Fig. 5A'). For pro-teins, nucleic acids and other macromolecules withan absorbing chromophore we can use the moreconvenient (but less accurate) absorption optics(Fig. 58) (down to a wavelengrh of Zl0 nm orpossibly less with the Beckman XLA ultracentri-fuge). When absorption optics are used patternscan be routinely captured automatically on-line and Fig. 5. Optical records of solute distributions at sedi-mentation equilibrium. The direction of the centrifugalfield is from left to right. (A) Rayleigh intederenceprofiles for human lgc; (B) absorption opticalprofile(at 280 nm) for the muscle protein titin. S: solutionrecord; O: optical baseline.analysed, while with the interference svstem it isT11c_h more complicated and indeed expensiveI l2]. Whatever the system, these patterns are nowusually captured and read automatically, eitherdirectly into a computer or via a bit of photographyor chart recorder output first.How do we get molecular weight information?The computer usually converts the digitised infor-mation of Fig. 5 into a record of log concentration(expressed in terms of absorbance units, A, orfringe displacement, "/) versus radial distancesquared. For fairly ideal monodisperse systems(e.g. dilute solutions of some small proteins) suchplots are Iinear, but for non-ideal or heterogeneoussystems they are not (Fig. 6). The average slopeof these plots, linear or otherwise, gives the lIz 0)g -, a.b o.4 Frt)O .5 o.s -t.o t.o 9.2 9.6 0.8 cFig. 6. Log concentration (expressed in Rayleighfringe displacement units, "/) versus distance squared(expressed in terms of the normalised parameter {),for a heterogeneous mucus glycoprotein. endstream endobj 46 0 obj 3298 endobj 47 0 obj << /Length 48 0 R >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj42 Do Q endstream endobj 48 0 obj 45 endobj 49 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 6 0 R >> /XObject << /Obj42 42 0 R >> /Subtype 45 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 41 0 R 47 0 R 43 0 R ] >> endobj 11 0 obj << /Kids [ 12 0 R 22 0 R 31 0 R 40 0 R 49 0 R ] /Count 5 /Type /Pages >> endobj xref 0 1 0000000000 65535 f 11 1 0000568146 00000 n 41 9 0000465687 00000 n 0000465766 00000 n 0000540282 00000 n 0000564373 00000 n 0000564396 00000 n 0000567749 00000 n 0000567771 00000 n 0000567871 00000 n 0000567891 00000 n trailer << /Size 50 /Info 1 0 R /Root 13 0 R /Prev 465358 >> startxref 568240 %%EOF 50 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 51 0 obj << /Type /XObject /Subtype /Image /Name /Obj51 /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 95270 >> stream &ɲW?\\q_޿D0<  Bx2 Dtm̏Dp<H ѼGˆH|؄\yt]8GB]r(s܅¸:F l DDDDDDDDF"""#f2Quqˢ:.徠x,]F)],2r>]Ј @V#:#>F!&"#i "8VP v@tGbd_Dt!oXSby8Ģ&2imԃM:yzSFwK*,C ,|iRv"$ ٯ5 ִN# f: N).G 5 Mdݢ┷Uȉ3Hh5<)6a 顦\'gAˊiBI8JlNmeF4gN=:1&;OTa= Jvf̈́& aRzvI䢉zah ܼ'y,ƉA_n֗UKHd◚pz&K'V`5j /.IZޒIKIDZý$vqWפzZ^S.Z|%zZW]T}I.-U.R@KC`ֵ_*IVKZ*Xaդ7ZkjYcLJ%uK;dW/-izA~\Uy-k_K馕kKK4vkXe Ny/{KUҥO_CH]-.RWK.iX]Kj\k}ZU6/J:S3D3vWnz {OE_MV=5֩U/ ݅Mldq} 2x"M[LB:VTSMi~UvMPdB 2B""" !ivBA ^**ka"""#B)PaST; i0A1_D0Bb !vUVHR4T&E9¡#ZT% j) m#A!o,*#G0k!l:# C6S5<` rˁ*Xn_-t떰ق||…^"l!,ra] 'U6)D].26DV)υor\3laPw\N) &, wBmy"JAǓvDy$ " 9;}> Wh'WjqDC3X `D5 p,]h4Nza&veKDa4a &`InZD+2] 2 3xM]w HAnZ^߿OOc#͒!H b $ASMwn%mzӿMT:R>3f!~kh?A(rcn¾KM.ڷM0`B-DA5H4 'm_^ޛ]D~ծ}Z'ޘIm4_nz}^avjEM;KUץ*Mwo]I V޻{ +Im7}/گkI ݬ7߷]%OҏuK^wpUn8﮾ #O ޗKEKa/E?uKH^G }w/6:]?d'xA5ivխiO~^aM}zbki}i=ܑZ_J}V]c݊Kbh붕SkkޝIb&0+^˭k0%m&8`TbdAi}vl%aw ; ǽlSR$$ج0!;kc:uu☻{ 4I F&G)a{T Iծ&4`DDT4OW&WKj&i m&-fhDD !!&6M6A !hAHB"Dp>la zd[M0 !0oM`E*ݦ@ʎ"*")O,IgWIJ>kիl$ ЈZ *mIB4Cxm *pEs'^ E>8OkZzoOWj}[ax.YdvAUg 5@6KC-B w~ ;Od}Z࿂xdTpN(/]N^NzA @uf` N|P 0D/]Ke9fa4^hժEi~) "$ " ; * o]DB -D;l 7t놻G3H i &Nމwhp_M_a-L#Q! ٙzN< ܋_MO:~Я)Qȍȡ2♐ a п O#zNp{zK׵ 'aAa֪׈21vK AfUbI`0_b/jRi*aVZQ^Z j RGz4]ߖw*,[4Xa~(C'fa!O CՐaH/KkU.QO庳5fA2r20 a4\+!"A\p]2) zVA¸zd3"".: 'җ횆LD 0A\W_yt"q3HфD]&5xRL4Ztˢ  0 DݭAo.H C5t#Q ̙BPh\QwDZȑIdxlDH@` $H 2#fFG `蛆MMo[OL Hh pU$B$!>G .G8zLzWA~^C$APA&;vVȨ2 D"   pp POV.2X I<줎:"(` A` (*'Ii[IKƭy $+! t``0D L!r%:M6zmw9 (hk &0A'}[wׄ;z=دZuE2a 1Et]u[M.5, IC 0+Pp<,pm- 6Ni;=>>a_ZF Wm/y aC "ʼn<oMׇ[KvǼ} ׿ׄL{ ź9NS"$C \  <5i5_h{upC*a KUȺ/d(! dHa;_$m/v!y yA& @5U!x_'m/acwe:#V`5a}(KaOiv= ?b"t Z}߻Kr  0aDK>Emu}WvC$0*"&;l/߭!,RdBӦ K/K<׿ۯy˻ 8a!\t7rK!C{;V 2H(f`2 l#jW[a$'{kmjAi 0Y U)a 2>?[]-{ᄭ{ L]lZȐ!0T3Q@q  @Rjci_ޭ/ثk|jrv & !hC A%r2 } 6%i0>Bݦ-{ZiB+8Ad 9/l6Fxk_%0TCJ*҈imHGIGt !DDER*R^')`տcmXڵN!a0LEmaui4xv0p `!,ؕ`m0U`Aᑌ I `&l0a%x>Za!-dHVNGD 4l0d@ `DGTf!A 3dpBFBm %F (% C4rQ Z, \ta d) AAp`d$!- ) #p pa dTV ep`E@l! 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<746865736520> Tj 1 0 0 1 93.36 635.28 Tm <63616E20> Tj 1 0 0 1 113.52 635.52 Tm <626520> Tj 1 0 0 1 127.92 636.00 Tm <706172746963756C61726C7920> Tj 1 0 0 1 186.00 636.24 Tm <75736566756C20> Tj 1 0 0 1 218.16 636.48 Tm <666F7220> Tj 1 0 0 1 235.20 636.72 Tm <6173736179696E6720> Tj 1 0 0 1 279.36 637.20 Tm <696E7465722D> Tj 0.48 Tc 1 0 0 1 66.00 622.08 Tm <616374696E6720> Tj 1 0 0 1 97.92 622.56 Tm <73797374656D732E20> Tj 1 0 0 1 141.12 623.04 Tm <467572746865722C20> Tj 1 0 0 1 181.92 623.28 Tm <6120> Tj 1 0 0 1 189.60 623.28 Tm <646966666572656E7420> Tj 1 0 0 1 232.80 623.76 Tm <7479706520> Tj 1 0 0 1 255.60 624.00 Tm <6F6620> Tj 1 0 0 1 268.08 624.24 Tm <61766572616765> Tj 0.48 Tc 1 0 0 1 65.76 609.12 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 118.08 609.84 Tm <7765696768742C20> Tj 1 0 0 1 158.64 610.08 Tm <74686520> Tj 1 0 0 1 176.40 609.36 Tm <7A2D6175657261676520> Tj 1 0 0 1 228.72 610.80 Tm <63616E20> Tj 1 0 0 1 248.64 610.80 Tm <626520> Tj 1 0 0 1 264.00 611.04 Tm <6F627461696E6564> Tj 0.48 Tc 1 0 0 1 65.76 596.16 Tm <65697468657220> Tj 1 0 0 1 96.00 596.40 Tm <627920> Tj 1 0 0 1 110.88 596.64 Tm <6675727468657220> Tj 1 0 0 1 145.92 596.88 Tm <6D617468656D61746963616C20> Tj 1 0 0 1 212.88 597.60 Tm <6D616E6970756C6174696F6E20> Tj 1 0 0 1 277.92 598.32 Tm <6F6620> Tj 1 0 0 1 290.64 598.56 Tm <746865> Tj 0.72 Tc 1 0 0 1 65.76 583.20 Tm <6461746120> Tj 1 0 0 1 88.80 583.44 Tm <6F7220> Tj 1 0 0 1 101.76 583.68 Tm <6469726563746C7920> Tj 1 0 0 1 141.36 583.92 Tm <627920> Tj 1 0 0 1 156.48 584.16 Tm <7573696E6720> Tj 1 0 0 1 185.28 584.64 Tm <74686520> Tj 1 0 0 1 203.04 584.64 Tm <5363686C696572656E20> Tj 1 0 0 1 250.80 585.12 Tm <6F70746963616C20> Tj 1 0 0 1 286.08 585.60 Tm <7379732D> Tj 0.48 Tc 1 0 0 1 66.00 570.24 Tm <74656D20> Tj 1 0 0 1 88.08 570.48 Tm <6D656E74696F6E656420> Tj 1 0 0 1 142.32 570.96 Tm <6561726C69657220> Tj 1 0 0 1 177.12 571.44 Tm <696E20> Tj 1 0 0 1 190.32 571.68 Tm <74686520> Tj 1 0 0 1 208.80 571.68 Tm <636F6E7465787420> Tj 1 0 0 1 247.68 572.16 Tm <6F6620> Tj 1 0 0 1 261.84 572.16 Tm <736564696D656E2D> Tj 0.72 Tc 1 0 0 1 66.00 557.04 Tm <746174696F6E20> Tj 1 0 0 1 96.72 557.76 Tm <76656C6F636974792E20> Tj 1 0 0 1 141.60 558.48 Tm <28496E20> Tj 1 0 0 1 159.84 558.00 Tm <736F6D6520> Tj 1 0 0 1 187.92 558.24 Tm <7370656369616C636173657320> Tj 1 0 0 1 251.76 558.96 Tm <74686520> Tj 1 0 0 1 269.28 559.20 Tm <6E756D626572> Tj 0.48 Tc 1 0 0 1 66.24 544.08 Tm <6176657261676520> Tj 1 0 0 1 106.80 544.56 Tm <6D6F6C6574756C617220> Tj 1 0 0 1 157.44 545.28 Tm <77656967687420> Tj 1 0 0 1 192.48 545.52 Tm <69616E20> Tj 1 0 0 1 212.16 545.76 Tm <616C736F20> Tj 1 0 0 1 234.00 545.76 Tm <626520> Tj 1 0 0 1 248.16 546.00 Tm <6F627461696E65642920> Tj 1 0 0 1 299.04 551.28 Tm <272E> Tj 0.48 Tc 1 0 0 1 66.00 531.12 Tm <54686520> Tj 1 0 0 1 89.52 531.36 Tm <726174696F20> Tj 1 0 0 1 115.44 531.60 Tm <6F6620> Tj 1 0 0 1 129.84 531.84 Tm <74686520> Tj 1 0 0 1 149.76 531.84 Tm <7A2D6176657261676520> Tj 1 0 0 1 199.44 532.56 Tm <746F20> Tj 1 0 0 1 213.12 532.56 Tm <74686520> Tj 1 0 0 1 231.84 533.04 Tm <77656967687420> Tj 1 0 0 1 268.56 533.28 Tm <61766572616765> Tj 0.48 Tc 1 0 0 1 66.48 518.16 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 116.40 518.88 Tm <77656967687420> Tj 1 0 0 1 150.96 519.12 Tm <697320> Tj 1 0 0 1 160.80 519.12 Tm <6F6674656E20> Tj 1 0 0 1 187.44 519.36 Tm <7573656420> Tj 1 0 0 1 211.44 519.84 Tm <617320> Tj 1 0 0 1 223.20 519.84 Tm <616E20> Tj 1 0 0 1 237.12 525.12 Tm <27696E64657820> Tj 1 0 0 1 268.56 520.32 Tm <6F6620> Tj 1 0 0 1 280.56 520.80 Tm <706F6C792D> Tj 0.48 Tc 1 0 0 1 66.48 505.20 Tm <646973706572736974792720> Tj 1 0 0 1 124.32 505.68 Tm <6F6620> Tj 1 0 0 1 141.84 506.16 Tm <706F6C796D6572696320> Tj 1 0 0 1 197.52 506.40 Tm <73616D706C65732C20> Tj 1 0 0 1 246.00 506.88 Tm <616E6420> Tj 1 0 0 1 270.48 507.36 Tm <63616E20> Tj 1 0 0 1 294.48 507.60 Tm <6265> Tj 0.48 Tc 1 0 0 1 66.48 492.24 Tm <72656C6174656420> Tj 1 0 0 1 102.00 492.48 Tm <746F20> Tj 1 0 0 1 114.24 492.72 Tm <74686520> Tj 1 0 0 1 132.00 492.72 Tm <6272656164746820> Tj 1 0 0 1 170.88 493.20 Tm <6F6620> Tj 1 0 0 1 183.84 493.44 Tm <6120> Tj 1 0 0 1 191.76 493.44 Tm <646973747269627574696F6E2E> Tj 0.48 Tc 1 0 0 1 78.24 479.04 Tm <546865726520> Tj 1 0 0 1 112.32 479.52 Tm <61726520> Tj 1 0 0 1 132.00 479.52 Tm <6F7468657220> Tj 1 0 0 1 162.48 480.24 Tm <7761797320> Tj 1 0 0 1 192.48 480.24 Tm <6F6620> Tj 1 0 0 1 207.84 480.48 Tm <7573696E6720> Tj 1 0 0 1 239.28 480.72 Tm <736564696D656E746174696F6E> Tj 0.72 Tc 1 0 0 1 66.48 465.84 Tm <657175696C69627269756D20> Tj 1 0 0 1 125.76 466.56 Tm <6461746120> Tj 1 0 0 1 149.04 466.80 Tm <746F20> Tj 1 0 0 1 161.52 467.28 Tm <67657420> Tj 1 0 0 1 179.52 467.04 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 230.16 467.76 Tm <77656967687420> Tj 1 0 0 1 265.68 468.24 Tm <64697374726962752D> Tj 0.72 Tc 1 0 0 1 66.72 452.88 Tm <74696F6E732E20> Tj 1 0 0 1 97.44 453.36 Tm <5065726861707320> Tj 1 0 0 1 139.20 453.60 Tm <74686520> Tj 1 0 0 1 158.16 453.84 Tm <73696D706C65737420> Tj 1 0 0 1 202.08 454.32 Tm <696E20> Tj 1 0 0 1 215.28 454.80 Tm <7072696E6369706C6520> Tj 1 0 0 1 261.60 455.04 Tm <616E6420> Tj 1 0 0 1 282.96 455.28 Tm <6D6F7374> Tj 0.72 Tc 1 0 0 1 66.96 439.68 Tm <75736566756C20> Tj 1 0 0 1 100.08 440.16 Tm <697320> Tj 1 0 0 1 110.88 440.16 Tm <746F20> Tj 1 0 0 1 123.36 440.40 Tm <636F6D62696E6520> Tj 1 0 0 1 168.48 441.12 Tm <7769746820> Tj 1 0 0 1 192.72 441.36 Tm <67656C20> Tj 1 0 0 1 210.96 441.36 Tm <66696C74726174696F6E2C20> Tj 1 0 0 1 258.00 442.08 Tm <676976696E6720> Tj 1 0 0 1 291.60 442.08 Tm <746865> Tj 0.72 Tc 1 0 0 1 67.20 426.48 Tm <6C617474657220> Tj 1 0 0 1 98.88 426.96 Tm <616E20> Tj 1 0 0 1 118.08 432.48 Tm <276162736F6C7574652720> Tj 1 0 0 1 172.32 427.68 Tm <626173697320> Tj 1 0 0 1 204.00 428.88 Tm <28692E652E2C20> Tj 1 0 0 1 233.76 428.40 Tm <6E6F7420> Tj 1 0 0 1 256.32 428.40 Tm <7375626A65637420> Tj 1 0 0 1 296.88 429.12 Tm <746F> Tj 0.48 Tc 1 0 0 1 67.20 413.52 Tm <617373756D7074696F6E7320> Tj 1 0 0 1 129.60 414.24 Tm <636F6E6365726E696E6720> Tj 1 0 0 1 186.48 414.72 Tm <74686520> Tj 1 0 0 1 204.24 414.96 Tm <636F6E666F726D6174696F6E20> Tj 1 0 0 1 271.68 415.68 Tm <6F6620> Tj 1 0 0 1 285.12 415.92 Tm <63616C692D> Tj 0.72 Tc 1 0 0 1 66.96 400.56 Tm <62726174696F6E20> Tj 1 0 0 1 105.12 401.04 Tm <7374616E6461726473292E20> Tj 1 0 0 1 162.96 401.52 Tm <47656C20> Tj 1 0 0 1 184.32 402.00 Tm <66696C74726174696F6E20> Tj 1 0 0 1 229.20 402.24 Tm <697320> Tj 1 0 0 1 240.72 402.48 Tm <6120> Tj 1 0 0 1 250.08 402.72 Tm <7665727920> Tj 1 0 0 1 274.80 402.72 Tm <73696D706C65> Tj 0.48 Tc 1 0 0 1 67.20 387.36 Tm <62757420> Tj 1 0 0 1 84.96 387.84 Tm <706F77657266756C20> Tj 1 0 0 1 130.56 388.32 Tm <77617920> Tj 1 0 0 1 152.88 388.32 Tm <6F6620> Tj 1 0 0 1 165.36 388.32 Tm <73657061726174696E6720> Tj 1 0 0 1 216.48 389.04 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 296.40 389.76 Tm <6F66> Tj 0.72 Tc 1 0 0 1 67.20 374.16 Tm <646966666572656E7420> Tj 1 0 0 1 110.64 374.64 Tm <73697A657320> Tj 1 0 0 1 135.84 375.12 Tm <696E20> Tj 1 0 0 1 147.12 375.12 Tm <6120> Tj 1 0 0 1 154.32 375.60 Tm <706F6C79646973706572736520> Tj 1 0 0 1 216.72 375.84 Tm <736F6C7574696F6E2E20> Tj 1 0 0 1 260.16 376.56 Tm <497420> Tj 1 0 0 1 268.80 376.56 Tm <63616E20> Tj 1 0 0 1 287.52 376.80 Tm <616C736F> Tj 0.72 Tc 1 0 0 1 67.20 361.44 Tm <6769766520> Tj 1 0 0 1 91.20 361.44 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 142.32 362.16 Tm <77656967687420> Tj 1 0 0 1 177.84 362.40 Tm <646973747269627574696F6E7320> Tj 1 0 0 1 240.48 362.88 Tm <627920> Tj 1 0 0 1 255.60 363.36 Tm <636F6D706172696E67> Tj 0.72 Tc 1 0 0 1 67.20 348.00 Tm <656C7574696F6E20> Tj 1 0 0 1 104.88 348.96 Tm <70726F66696C657320> Tj 1 0 0 1 145.20 349.20 Tm <7769746820> Tj 1 0 0 1 170.40 349.20 Tm <74686F736520> Tj 1 0 0 1 199.92 349.44 Tm <6F6620> Tj 1 0 0 1 214.08 349.68 Tm <7374616E6461726420> Tj 1 0 0 1 258.72 350.40 Tm <6D6F6C6563756C6573> Tj 0.48 Tc 1 0 0 1 67.20 335.04 Tm <6F6620> Tj 1 0 0 1 81.12 335.28 Tm <6B6E6F776E20> Tj 1 0 0 1 117.36 335.76 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 168.72 336.48 Tm <77656967687420> Tj 1 0 0 1 204.48 336.72 Tm <616E6420> Tj 1 0 0 1 226.56 336.96 Tm <74686520> Tj 1 0 0 1 244.08 336.96 Tm <73616D6520> Tj 1 0 0 1 271.68 337.44 Tm <636F6E666F722D> Tj 0.72 Tc 1 0 0 1 67.68 322.08 Tm <6D6174696F6E20> Tj 1 0 0 1 104.88 322.56 Tm <617320> Tj 1 0 0 1 118.80 322.56 Tm <74686520> Tj 1 0 0 1 137.76 322.80 Tm <6D6F6C6563756C657320> Tj 1 0 0 1 190.08 323.52 Tm <6265696E6720> Tj 1 0 0 1 220.80 323.76 Tm <737475646965642E20> Tj 1 0 0 1 262.08 324.24 Tm <416C74686F756768> Tj 0.72 Tc 1 0 0 1 67.68 309.12 Tm <74686520> Tj 1 0 0 1 87.84 309.36 Tm <6C617474657220> Tj 1 0 0 1 117.36 309.60 Tm <726571756972656D656E7420> Tj 1 0 0 1 180.48 310.32 Tm <697320> Tj 1 0 0 1 193.20 310.56 Tm <757375616C6C7920> Tj 1 0 0 1 232.80 310.80 Tm <4F4B20> Tj 1 0 0 1 255.36 311.28 Tm <696620> Tj 1 0 0 1 267.60 311.52 Tm <676C6F62756C6172> Tj 0.72 Tc 1 0 0 1 67.68 296.40 Tm <70726F7465696E7320> Tj 1 0 0 1 112.32 296.64 Tm <61726520> Tj 1 0 0 1 132.48 296.88 Tm <6265696E6720> Tj 1 0 0 1 165.12 297.12 Tm <7374756469656420> Tj 1 0 0 1 205.44 297.84 Tm <616E6420> Tj 1 0 0 1 228.00 298.32 Tm <676C6F62756C617220> Tj 1 0 0 1 273.60 298.80 Tm <70726F7465696E> Tj 0.48 Tc 1 0 0 1 67.92 282.96 Tm <7374616E646172647320> Tj 1 0 0 1 117.84 283.68 Tm <61726520> Tj 1 0 0 1 136.32 283.92 Tm <757365642C20> Tj 1 0 0 1 166.32 284.40 Tm <697420> Tj 1 0 0 1 177.12 284.64 Tm <6661696C7320> Tj 1 0 0 1 202.08 284.64 Tm <666F7220> Tj 1 0 0 1 220.32 284.88 Tm <73796E74686574696320> Tj 1 0 0 1 267.84 285.60 Tm <706F6C796D6572> Tj 0.72 Tc 1 0 0 1 67.92 270.00 Tm <616E6420> Tj 1 0 0 1 88.80 270.72 Tm <706F6C797361636368617269646520> Tj 1 0 0 1 164.40 271.20 Tm <73797374656D7320> Tj 1 0 0 1 205.68 271.92 Tm <7765726520> Tj 1 0 0 1 232.08 271.92 Tm <736F2D63616C6C656420> Tj 1 0 0 1 279.36 277.92 Tm <27706F6C792D> Tj 0.48 Tc 1 0 0 1 67.92 256.80 Tm <73747972656E652720> Tj 1 0 0 1 109.44 257.52 Tm <7374616E646172647320> Tj 1 0 0 1 156.96 258.00 Tm <6F7220> Tj 1 0 0 1 170.40 263.52 Tm <2770756C6C756C616E2720> Tj 1 0 0 1 218.88 258.72 Tm <7374616E646172647320> Tj 1 0 0 1 266.16 259.44 Tm <61726520> Tj 1 0 0 1 282.96 259.44 Tm <6F6674656E> Tj 0.72 Tc 1 0 0 1 68.16 244.08 Tm <757365642E20> Tj 1 0 0 1 97.92 244.56 Tm <546865736520> Tj 1 0 0 1 131.52 245.28 Tm <70726F626C656D7320> Tj 1 0 0 1 180.72 245.52 Tm <63616E20> Tj 1 0 0 1 202.56 245.76 Tm <626520> Tj 1 0 0 1 218.64 246.00 Tm <61766F6964656420> Tj 1 0 0 1 261.12 246.24 Tm <627920> Tj 1 0 0 1 277.92 246.48 Tm <74616B696E67> Tj 0.72 Tc 1 0 0 1 68.40 231.12 Tm <6672616374696F6E7320> Tj 1 0 0 1 114.72 231.60 Tm <66726F6D20> Tj 1 0 0 1 142.56 231.84 Tm <74686520> Tj 1 0 0 1 161.76 232.08 Tm <636F6C756D6E20> Tj 1 0 0 1 202.32 232.56 Tm <616E6420> Tj 1 0 0 1 223.68 232.80 Tm <64657465726D696E696E6720> Tj 1 0 0 1 286.08 233.52 Tm <7468656972> Tj 0.72 Tc 1 0 0 1 68.40 217.92 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 121.44 218.88 Tm <7765696768747320> Tj 1 0 0 1 163.68 219.12 Tm <627920> Tj 1 0 0 1 180.72 219.36 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 252.00 220.08 Tm <657175696C69627269756D> Tj 2.16 Tc /F3 15.0 Tf 1 0 0 1 69.84 203.28 Tm <74656C2E> Tj 0.72 Tc /F3 9.0 Tf 1 0 0 1 67.92 178.32 Tm <542D6F2E2A757474792C20> Tj 1 0 0 1 130.32 178.80 Tm <756E6C65737320> Tj 1 0 0 1 161.04 179.52 Tm <796F7520> Tj 1 0 0 1 180.96 179.52 Tm <61726520> Tj 1 0 0 1 198.00 179.76 Tm <776F726B696E6720> Tj 1 0 0 1 236.88 180.48 Tm <7769746820> Tj 1 0 0 1 259.68 180.24 Tm <73617920> Tj 1 0 0 1 277.92 180.48 Tm <6120> Tj 1 0 0 1 286.80 180.72 Tm <77656C6C2D> Tj 0.48 Tc 1 0 0 1 68.64 167.04 Tm <6265686176656420> Tj 1 0 0 1 107.76 167.52 Tm <736F6C7574696F6E20> Tj 1 0 0 1 145.20 168.00 Tm <6F6620> Tj 1 0 0 1 157.92 168.24 Tm <6120> Tj 1 0 0 1 166.56 168.24 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 234.48 168.96 Tm <6F6620> Tj 1 0 0 1 247.20 169.20 Tm <6C6F7720> Tj 1 0 0 1 266.88 169.44 Tm <6D6F6C6563756C6172> Tj 0.72 Tc 1 0 0 1 69.12 156.48 Tm <77656967687420> Tj 1 0 0 1 99.84 157.44 Tm <2820> Tj 1 0 0 1 106.56 157.20 Tm <3C20> Tj 1 0 0 1 114.96 156.96 Tm <35303030302920> Tj 1 0 0 1 148.56 157.20 Tm <617420> Tj 1 0 0 1 158.16 157.44 Tm <6C6F7720> Tj 1 0 0 1 175.68 157.68 Tm <6C6F6164696E6720> Tj 1 0 0 1 208.32 157.92 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 267.60 159.12 Tm <2820> Tj 1 0 0 1 274.32 160.80 Tm <2820> Tj 1 0 0 1 284.16 158.88 Tm <4920> Tj 1 0 0 1 289.92 158.88 Tm <6D672F> Tj 0.72 Tc 1 0 0 1 69.12 145.20 Tm <6D6C2931686520> Tj 1 0 0 1 104.16 145.92 Tm <7765696768742C20> Tj 1 0 0 1 139.20 146.16 Tm <7A2D6176657261676520> Tj 1 0 0 1 181.68 146.64 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 226.32 147.60 Tm <7765696768747320> Tj 1 0 0 1 261.36 147.60 Tm <6F627461696E656420> Tj 1 0 0 1 300.48 148.08 Tm <696E> Tj 0.72 Tc 1 0 0 1 69.12 134.40 Tm <7468697320> Tj 1 0 0 1 89.52 135.12 Tm <77617920> Tj 1 0 0 1 112.56 135.84 Tm <28616E6420> Tj 1 0 0 1 137.28 135.36 Tm <74686520> Tj 1 0 0 1 155.28 135.60 Tm <6E756D62657220> Tj 1 0 0 1 192.24 136.08 Tm <617665726167652920> Tj 1 0 0 1 234.96 136.80 Tm <77696C6C20> Tj 1 0 0 1 256.08 136.80 Tm <626520> Tj 1 0 0 1 270.72 136.80 Tm <6170706172656E74> Tj 0.72 Tc 1 0 0 1 69.36 123.60 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 116.16 124.56 Tm <7765696768747320> Tj 1 0 0 1 153.60 124.56 Tm <64756520> Tj 1 0 0 1 174.00 125.04 Tm <746F20> Tj 1 0 0 1 187.20 125.04 Tm <736F6C7574696F6E20> Tj 1 0 0 1 225.84 125.52 Tm <6E6F6E2D696465616C69747920> Tj 1 0 0 1 280.80 126.24 Tm <65666665637473> Tj 0.72 Tc 1 0 0 1 70.08 113.28 Tm <287265616C20> Tj 1 0 0 1 93.12 112.80 Tm <736F6C7574696F6E7320> Tj 1 0 0 1 133.20 113.52 Tm <6F6620> Tj 1 0 0 1 145.20 113.52 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 216.00 114.24 Tm <64696666657220> Tj 1 0 0 1 242.40 114.96 Tm <66726F6D20> Tj 1 0 0 1 265.20 115.20 Tm <696465616C20> Tj 1 0 0 1 288.00 115.20 Tm <736F6C752D> Tj 0.48 Tc 1 0 0 1 69.36 101.52 Tm <74696F6E7320> Tj 1 0 0 1 92.16 102.00 Tm <696E20> Tj 1 0 0 1 102.96 102.00 Tm <6D75636820> Tj 1 0 0 1 128.40 102.48 Tm <74686520> Tj 1 0 0 1 143.52 102.48 Tm <73616D6520> Tj 1 0 0 1 167.52 103.20 Tm <77617920> Tj 1 0 0 1 187.20 103.20 Tm <617320> Tj 1 0 0 1 198.24 103.20 Tm <7265616C20> Tj 1 0 0 1 216.00 103.92 Tm <676173657320> Tj 1 0 0 1 240.48 103.68 Tm <64696666657220> Tj 1 0 0 1 266.40 104.16 Tm <66726F6D20> Tj 1 0 0 1 288.72 104.40 Tm <696465616C> Tj 0.72 Tc 1 0 0 1 69.36 90.96 Tm <6761736573292E20> Tj 1 0 0 1 102.96 91.20 Tm <546865726520> Tj 1 0 0 1 130.80 91.44 Tm <61726520> Tj 1 0 0 1 146.88 91.68 Tm <6120> Tj 1 0 0 1 154.80 91.92 Tm <6E756D62657220> Tj 1 0 0 1 189.60 92.16 Tm <6F6620> Tj 1 0 0 1 202.08 92.64 Tm <7761797320> Tj 1 0 0 1 226.32 92.64 Tm <6F6620> Tj 1 0 0 1 238.08 92.64 Tm <6F766572636F6D696E6720> Tj 1 0 0 1 291.36 93.60 Tm <7468697327> Tj 0.72 Tc 1 0 0 1 69.36 79.68 Tm <69686520> Tj 1 0 0 1 85.44 79.92 Tm <6D6F737420> Tj 1 0 0 1 108.24 80.16 Tm <73696D706C6520> Tj 1 0 0 1 138.96 80.64 Tm <6265696E6720> Tj 1 0 0 1 165.12 80.88 Tm <746F20> Tj 1 0 0 1 175.92 81.12 Tm <6D65617375726520> Tj 1 0 0 1 213.36 81.36 Tm <74686520> Tj 1 0 0 1 228.72 81.60 Tm <6170706172656E7420> Tj 1 0 0 1 267.60 82.08 Tm <6D6F6C6563756C6172> Tj 0.48 Tc 1 0 0 1 69.84 68.88 Tm <77656967687420> Tj 1 0 0 1 101.28 69.12 Tm <617420> Tj 1 0 0 1 111.84 69.36 Tm <6120> Tj 1 0 0 1 119.52 69.36 Tm <73657269657320> Tj 1 0 0 1 146.16 69.84 Tm <6F6620> Tj 1 0 0 1 157.92 69.84 Tm <636F6E63656E74726174696F6E7320> Tj 1 0 0 1 222.24 70.56 Tm <616E6420> Tj 1 0 0 1 240.00 70.80 Tm <6578747261706F6C61746520> Tj 1 0 0 1 289.44 71.52 Tm <6261636B> Tj 0.48 Tc 1 0 0 1 69.84 57.84 Tm <746865732D6520> Tj 1 0 0 1 94.56 58.56 Tm <76616C75657320> Tj 1 0 0 1 125.04 59.52 Tm <286F7220> Tj 1 0 0 1 141.36 58.80 Tm <74686520> Tj 1 0 0 1 157.44 59.04 Tm <7265636970726F63616C7320> Tj 1 0 0 1 206.40 59.52 Tm <74686572656F662920> Tj 1 0 0 1 243.84 60.00 Tm <746F20> Tj 1 0 0 1 255.36 60.24 Tm <7A65726F20> Tj 1 0 0 1 276.00 60.48 Tm <636F6E63656E2D> Tj 0.48 Tc 1 0 0 1 69.84 47.04 Tm <74726174696F6E20> Tj 1 0 0 1 98.88 47.52 Tm <746F20> Tj 1 0 0 1 108.48 48.00 Tm <6769766520> Tj 1 0 0 1 128.16 47.76 Tm <74686520> Tj 1 0 0 1 142.32 52.80 Tm <22696465616C2220> Tj 1 0 0 1 171.60 48.72 Tm <76616C75652E20> Tj 1 0 0 1 198.00 48.72 Tm <54686520> Tj 1 0 0 1 216.24 48.96 Tm <6E6F6E2D696465616C69747920> Tj 1 0 0 1 267.84 49.68 Tm <706172616D65746572> Tj 0.72 Tc 1 0 0 1 70.08 36.24 Tm <697473656C6620> Tj 1 0 0 1 93.60 37.92 Tm <286361696C656420> Tj 1 0 0 1 126.00 41.76 Tm <27422720> Tj 1 0 0 1 141.36 37.20 Tm <6F7220> Tj 1 0 0 1 152.88 42.00 Tm <274172272920> Tj 1 0 0 1 177.60 37.92 Tm <776869636820> Tj 1 0 0 1 204.96 37.92 Tm <636F6D657320> Tj 1 0 0 1 234.00 38.40 Tm <66726F6D20> Tj 1 0 0 1 256.08 38.64 Tm <74686520> Tj 1 0 0 1 270.96 38.64 Tm <736C6F706520> Tj 1 0 0 1 294.72 39.12 Tm <63616E> Tj 0.48 Tc 1 0 0 1 70.08 25.44 Tm <616C736F20> Tj 1 0 0 1 90.48 26.16 Tm <6769766520> Tj 1 0 0 1 111.84 26.16 Tm <75736566756C20> Tj 1 0 0 1 140.88 26.40 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 193.68 27.12 Tm <61626F757420> Tj 1 0 0 1 220.08 27.60 Tm <6D6163726F6D6F6C6563756C617220> Tj 1 0 0 1 290.88 28.08 Tm <636F6E2D> Tj 0.48 Tc 1 0 0 1 70.32 14.64 Tm <666F726D6174696F6E2E> Tj 0.24 Tc /F3 8.0 Tf 1 0 0 1 398.16 726.24 Tm <7472656E647320> Tj 1 0 0 1 421.92 726.48 Tm <696E20> Tj 1 0 0 1 429.84 726.48 Tm <616E616C79746963616C20> Tj 1 0 0 1 464.40 726.72 Tm <6368656D69737472792C20> Tj 1 0 0 1 503.04 726.72 Tm <766F6C2E20> Tj 1 0 0 1 518.40 726.48 Tm <31332C20> Tj 1 0 0 1 529.92 726.24 Tm <6E6F2E20> Tj 1 0 0 1 544.32 726.00 Tm <37302C20> Tj 1 0 0 1 557.28 726.24 Tm <31393934> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 335.28 582.24 Tm <4669672E372E20> Tj 1 0 0 1 365.52 582.96 Tm <28612920> Tj 1 0 0 1 380.64 582.48 Tm <5261796C6569676820> Tj 1 0 0 1 422.88 582.96 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 489.60 583.20 Tm <657175696C69627269756D20> Tj 1 0 0 1 542.16 584.16 Tm <7061747465726E> Tj 0.72 Tc 1 0 0 1 334.32 569.28 Tm <666F7220> Tj 1 0 0 1 350.40 570.00 Tm <706F6C795B2869736F7072656E65292D702D28657468796C656E6520> Tj 1 0 0 1 477.60 570.24 Tm <6F78696465295D20> Tj 1 0 0 1 512.64 570.48 Tm <626C6F636B20> Tj 1 0 0 1 540.48 570.48 Tm <636F706F6C792D> Tj 0.72 Tc 1 0 0 1 335.04 556.32 Tm <6D657220> Tj 1 0 0 1 356.64 556.32 Tm <6D6963656C6C657320> Tj 1 0 0 1 397.92 556.80 Tm <696E20> Tj 1 0 0 1 408.96 556.80 Tm <77617465722E20> Tj 1 0 0 1 441.12 557.76 Tm <28622920> Tj 1 0 0 1 457.44 557.28 Tm <5261796C6569676820> Tj 1 0 0 1 500.64 557.52 Tm <666C6F746174696F6E20> Tj 1 0 0 1 541.20 557.52 Tm <657175696C69622D> Tj 0.72 Tc 1 0 0 1 335.28 543.36 Tm <7269756D20> Tj 1 0 0 1 359.76 544.32 Tm <7061747465726E2C20> Tj 1 0 0 1 399.60 543.84 Tm <73616D6520> Tj 1 0 0 1 429.60 544.80 Tm <706F6C796D657220> Tj 1 0 0 1 470.64 544.56 Tm <62757420> Tj 1 0 0 1 489.60 544.80 Tm <696E20> Tj 1 0 0 1 502.08 544.56 Tm <756E696D657220> Tj 1 0 0 1 538.32 544.80 Tm <666F726D2C20> Tj 1 0 0 1 566.64 545.04 Tm <696E> Tj 0.72 Tc 1 0 0 1 335.04 530.40 Tm <63686C6F726F666F726D2E20> Tj 1 0 0 1 392.40 530.88 Tm <526570726F647563656420> Tj 1 0 0 1 452.40 531.60 Tm <7769746820> Tj 1 0 0 1 475.68 532.32 Tm <7065726D697373696F6E20> Tj 1 0 0 1 530.16 531.84 Tm <66726F6D20> Tj 1 0 0 1 556.08 532.08 Tm <5265662E> Tj 1.20 Tc /F3 13.0 Tf 1 0 0 1 335.28 515.52 Tm <743133312E29> Tj 0.96 Tc 1 0 0 1 335.28 491.76 Tm <382E20> Tj 1 0 0 1 352.56 492.00 Tm <466C6F746174696F6E20> Tj 1 0 0 1 405.36 492.48 Tm <76656C6F6369747920> Tj 1 0 0 1 452.40 492.72 Tm <616E6420> Tj 1 0 0 1 476.40 492.96 Tm <657175696C69627269756D> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 347.76 463.44 Tm <556E64657220> Tj 1 0 0 1 381.60 463.68 Tm <74686520> Tj 1 0 0 1 400.08 463.92 Tm <696E666C75656E636520> Tj 1 0 0 1 447.12 464.40 Tm <6F6620> Tj 1 0 0 1 461.28 464.40 Tm <6120> Tj 1 0 0 1 469.92 464.40 Tm <63656E747269667567616C20> Tj 1 0 0 1 526.32 464.88 Tm <6669656C642C20> Tj 1 0 0 1 553.92 465.12 Tm <636F6E2D> Tj 0.48 Tc 1 0 0 1 335.76 450.72 Tm <76656E74696F6E616C20> Tj 1 0 0 1 384.24 450.72 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 454.32 451.68 Tm <74616B657320> Tj 1 0 0 1 482.16 452.16 Tm <706C61636520> Tj 1 0 0 1 511.20 452.16 Tm <70726F766964656420> Tj 1 0 0 1 557.76 452.40 Tm <74686174> Tj 0.72 Tc 1 0 0 1 335.76 437.52 Tm <74686520> Tj 1 0 0 1 352.32 437.52 Tm <64656E7369747920> Tj 1 0 0 1 389.04 438.00 Tm <6F6620> Tj 1 0 0 1 401.04 438.00 Tm <74686520> Tj 1 0 0 1 417.60 438.24 Tm <736564696D656E74696E6720> Tj 1 0 0 1 477.36 438.96 Tm <7061727469636C6520> Tj 1 0 0 1 515.52 438.96 Tm <697320> Tj 1 0 0 1 525.60 438.96 Tm <6C617267657220> Tj 1 0 0 1 555.12 439.44 Tm <7468616E> Tj 0.72 Tc 1 0 0 1 335.76 424.56 Tm <7468617420> Tj 1 0 0 1 357.12 424.80 Tm <6F6620> Tj 1 0 0 1 370.80 424.80 Tm <74686520> Tj 1 0 0 1 388.80 424.80 Tm <736F6C76656E7420> Tj 1 0 0 1 426.72 425.28 Tm <697420> Tj 1 0 0 1 436.56 425.52 Tm <697320> Tj 1 0 0 1 447.36 425.52 Tm <64697370657273656420> Tj 1 0 0 1 496.32 425.76 Tm <696E2E20> Tj 1 0 0 1 511.92 426.00 Tm <496620> Tj 1 0 0 1 523.20 426.00 Tm <74686520> Tj 1 0 0 1 540.96 426.24 Tm <64656E73697479> Tj 0.72 Tc 1 0 0 1 336.24 411.60 Tm <697320> Tj 1 0 0 1 348.48 411.84 Tm <6C6573732C20> Tj 1 0 0 1 373.20 412.08 Tm <7468656E20> Tj 1 0 0 1 397.92 412.32 Tm <74686520> Tj 1 0 0 1 416.16 412.80 Tm <7061727469636C6520> Tj 1 0 0 1 456.00 413.04 Tm <77696C6C20> Tj 1 0 0 1 478.56 413.04 Tm <6D6F766520> Tj 1 0 0 1 509.28 413.04 Tm <696E20> Tj 1 0 0 1 522.72 413.28 Tm <74686520> Tj 1 0 0 1 541.44 413.28 Tm <72657665727365> Tj 0.72 Tc 1 0 0 1 335.76 398.64 Tm <646972656374696F6E2E20> Tj 1 0 0 1 384.24 399.12 Tm <5468697320> Tj 1 0 0 1 408.72 399.12 Tm <736974756174696F6E20> Tj 1 0 0 1 452.40 399.60 Tm <68617070656E7320> Tj 1 0 0 1 494.64 400.32 Tm <7769746820> Tj 1 0 0 1 518.88 400.08 Tm <6C69706F70726F7465696E73> Tj 0.72 Tc 1 0 0 1 336.24 385.68 Tm <696E20> Tj 1 0 0 1 349.20 385.92 Tm <617175656F757320> Tj 1 0 0 1 392.16 386.16 Tm <736F6C76656E747320> Tj 1 0 0 1 434.88 386.64 Tm <616E6420> Tj 1 0 0 1 455.52 386.88 Tm <736F6D6520> Tj 1 0 0 1 484.56 387.12 Tm <73796E74686574696320> Tj 1 0 0 1 531.60 387.60 Tm <706F6C796D657273> Tj 0.72 Tc 1 0 0 1 336.48 372.72 Tm <696E20> Tj 1 0 0 1 351.12 372.96 Tm <7665727920> Tj 1 0 0 1 377.04 372.96 Tm <64656E736520> Tj 1 0 0 1 409.44 373.44 Tm <736F6C76656E747320> Tj 1 0 0 1 453.36 373.92 Tm <7375636820> Tj 1 0 0 1 480.48 374.16 Tm <617320> Tj 1 0 0 1 495.12 374.16 Tm <63686C6F726F666F726D2E20> Tj 1 0 0 1 557.04 374.64 Tm <546865> Tj 0.72 Tc 1 0 0 1 336.24 359.52 Tm <626173696320> Tj 1 0 0 1 362.88 360.00 Tm <7468656F727920> Tj 1 0 0 1 395.52 360.24 Tm <617320> Tj 1 0 0 1 407.28 360.48 Tm <666F72736564696D656E746174696F6E20> Tj 1 0 0 1 492.00 361.44 Tm <76656C6F6369747920> Tj 1 0 0 1 532.32 361.44 Tm <616E64657175692D> Tj 0.72 Tc 1 0 0 1 336.48 346.80 Tm <6C69627269756D20> Tj 1 0 0 1 375.84 347.04 Tm <697320> Tj 1 0 0 1 386.88 347.28 Tm <74686520> Tj 1 0 0 1 405.36 347.28 Tm <73616D652C20> Tj 1 0 0 1 436.08 347.76 Tm <74686520> Tj 1 0 0 1 454.08 347.76 Tm <6F6E6C7920> Tj 1 0 0 1 479.04 348.00 Tm <646966666572656E636520> Tj 1 0 0 1 531.36 348.24 Tm <6265696E6720> Tj 1 0 0 1 561.84 348.72 Tm <746865> Tj 0.48 Tc 1 0 0 1 336.24 333.84 Tm <646972656374696F6E20> Tj 1 0 0 1 381.84 334.32 Tm <6F6620> Tj 1 0 0 1 394.56 334.32 Tm <6D6F76656D656E742E20> Tj 1 0 0 1 450.48 335.04 Tm <436F6E666F726D6174696F6E7320> Tj 1 0 0 1 525.12 335.52 Tm <616E6420> Tj 1 0 0 1 545.28 335.76 Tm <686F6D6F2D> Tj 0.48 Tc 1 0 0 1 336.48 321.36 Tm <67656E6569747920> Tj 1 0 0 1 375.12 321.36 Tm <696E666F726D6174696F6E20> Tj 1 0 0 1 433.92 321.84 Tm <63616E20> Tj 1 0 0 1 453.36 322.08 Tm <626520> Tj 1 0 0 1 467.28 322.32 Tm <6465647563656420> Tj 1 0 0 1 510.48 322.56 Tm <66726F6D20> Tj 1 0 0 1 536.88 322.80 Tm <666C6F746174696F6E> Tj 0.72 Tc 1 0 0 1 336.96 308.16 Tm <76656C6F636974792C20> Tj 1 0 0 1 384.96 308.40 Tm <616E6420> Tj 1 0 0 1 408.96 308.88 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 462.96 309.60 Tm <7765696768747320> Tj 1 0 0 1 506.64 309.60 Tm <66726F6D20> Tj 1 0 0 1 537.12 309.84 Tm <666C6F746174696F6E> Tj 0.72 Tc 1 0 0 1 336.48 295.20 Tm <657175696C69627269756D20> Tj 1 0 0 1 397.44 295.92 Tm <6578706572696D656E747320> Tj 1 0 0 1 461.28 296.40 Tm <696E20> Tj 1 0 0 1 475.44 296.64 Tm <6D75636820> Tj 1 0 0 1 507.12 296.64 Tm <74686520> Tj 1 0 0 1 527.04 296.88 Tm <73616D6520> Tj 1 0 0 1 557.04 297.60 Tm <776179> Tj 0.96 Tc 1 0 0 1 338.16 280.32 Tm <5B332C31345D2E20> Tj 1 0 0 1 384.72 282.72 Tm <416E20> Tj 1 0 0 1 404.40 282.96 Tm <6578616D706C6520> Tj 1 0 0 1 450.72 283.44 Tm <697320> Tj 1 0 0 1 463.92 283.44 Tm <73686F776E20> Tj 1 0 0 1 501.12 283.68 Tm <696E20> Tj 1 0 0 1 515.52 283.92 Tm <4669672E20> Tj 1 0 0 1 540.48 284.16 Tm <3720> Tj 1 0 0 1 552.24 284.40 Tm <666F7220> Tj 1 0 0 1 571.44 284.64 Tm <61> Tj 0.72 Tc 1 0 0 1 336.72 269.52 Tm <636F706F6C796D657220> Tj 1 0 0 1 390.96 270.00 Tm <73797374656D20> Tj 1 0 0 1 427.20 270.96 Tm <286120> Tj 1 0 0 1 440.16 270.48 Tm <6D6F64656C20> Tj 1 0 0 1 472.32 270.72 Tm <73797374656D20> Tj 1 0 0 1 508.08 270.96 Tm <666F7220> Tj 1 0 0 1 524.40 271.20 Tm <6472756720> Tj 1 0 0 1 549.12 271.44 Tm <64656C69762D> Tj 0.72 Tc 1 0 0 1 336.96 256.56 Tm <657279292C20> Tj 1 0 0 1 366.72 257.04 Tm <776869636820> Tj 1 0 0 1 400.80 257.04 Tm <696E20> Tj 1 0 0 1 414.72 257.28 Tm <617175656F757320> Tj 1 0 0 1 458.64 257.76 Tm <736F6C76656E7420> Tj 1 0 0 1 497.76 258.24 Tm <676976657320> Tj 1 0 0 1 528.24 258.24 Tm <6120> Tj 1 0 0 1 538.08 258.24 Tm <636F6E76656E2D> Tj 0.72 Tc 1 0 0 1 337.20 243.60 Tm <74696F6E616C20> Tj 1 0 0 1 368.40 243.84 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 438.48 244.56 Tm <657175696C69627269756D20> Tj 1 0 0 1 497.76 245.28 Tm <7061747465726E20> Tj 1 0 0 1 534.96 245.52 Tm <696E20> Tj 1 0 0 1 547.92 246.00 Tm <7768696368> Tj 0.72 Tc 1 0 0 1 337.20 230.88 Tm <74686520> Tj 1 0 0 1 356.16 231.12 Tm <706F6C796D657220> Tj 1 0 0 1 400.32 231.36 Tm <666F726D7320> Tj 1 0 0 1 432.48 231.60 Tm <6D6963656C6C65732C20> Tj 1 0 0 1 479.04 232.08 Tm <62757420> Tj 1 0 0 1 499.20 232.08 Tm <696E20> Tj 1 0 0 1 512.16 232.32 Tm <63686C6F726F666F726D20> Tj 1 0 0 1 570.72 233.04 Tm <6974> Tj 0.72 Tc 1 0 0 1 337.20 218.16 Tm <676976657320> Tj 1 0 0 1 365.28 218.16 Tm <6120> Tj 1 0 0 1 373.44 218.16 Tm <666C6F746174696F6E20> Tj 1 0 0 1 414.96 218.40 Tm <657175696C69627269756D20> Tj 1 0 0 1 472.80 219.36 Tm <7061747465726E20> Tj 1 0 0 1 508.32 219.36 Tm <636F72726573706F6E64696E67> Tj 0.48 Tc 1 0 0 1 337.44 204.96 Tm <746F20> Tj 1 0 0 1 353.52 204.96 Tm <74686520> Tj 1 0 0 1 375.12 205.68 Tm <706F6C796D657220> Tj 1 0 0 1 421.44 205.68 Tm <617320> Tj 1 0 0 1 437.76 205.92 Tm <646973637265746520> Tj 1 0 0 1 481.68 206.40 Tm <756E696D6572732E20> Tj 1 0 0 1 530.16 206.88 Tm <46726F6D20> Tj 1 0 0 1 562.56 207.36 Tm <746865> Tj 0.72 Tc 1 0 0 1 337.68 192.00 Tm <7265737065637469766520> Tj 1 0 0 1 389.76 192.48 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 440.64 193.20 Tm <7765696768747320> Tj 1 0 0 1 481.20 193.44 Tm <666F7220> Tj 1 0 0 1 498.72 193.68 Tm <6D6963656C6C6520> Tj 1 0 0 1 537.36 193.92 Tm <616E6420> Tj 1 0 0 1 558.00 194.40 Tm <756E692D> Tj 0.72 Tc 1 0 0 1 337.92 179.04 Tm <6D657220> Tj 1 0 0 1 359.28 179.28 Tm <697420> Tj 1 0 0 1 368.40 179.28 Tm <697320> Tj 1 0 0 1 378.48 179.76 Tm <706F737369626C6520> Tj 1 0 0 1 419.76 179.76 Tm <746F20> Tj 1 0 0 1 431.28 180.00 Tm <6F627461696E20> Tj 1 0 0 1 463.44 180.48 Tm <616E20> Tj 1 0 0 1 477.12 180.48 Tm <657374696D61746520> Tj 1 0 0 1 519.60 180.96 Tm <666F7220> Tj 1 0 0 1 535.92 180.96 Tm <74686520> Tj 1 0 0 1 552.96 181.20 Tm <6173736F2D> Tj 0.72 Tc 1 0 0 1 337.44 166.08 Tm <63696174696F6E20> Tj 1 0 0 1 373.68 166.56 Tm <6E756D62657220> Tj 1 0 0 1 412.80 166.80 Tm <6F6620> Tj 1 0 0 1 425.76 167.04 Tm <74686520> Tj 1 0 0 1 443.28 167.28 Tm <6D6963656C6C652E> Tj 0.72 Tc 1 0 0 1 338.16 123.12 Tm <392E20> Tj 1 0 0 1 354.96 123.60 Tm <416E616C79746963616C20> Tj 1 0 0 1 414.00 124.08 Tm <64656E7369745920> Tj 1 0 0 1 458.64 125.28 Tm <6772616469656E74> Tj 0.96 Tc /F3 13.0 Tf 1 0 0 1 338.40 110.40 Tm 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weight. Local slopesalong curves as in Fig. 6 can also be taken to givepoint or 'local' average molecular weights at agiven radial position in the ultracentrifuge cell, andthese can be particularly useful for assaying inter-acting systems. Further, a different type of averagemolecular weight, the z-auerage can be obtainedeither by further mathematical manipulation of thedata or directly by using the Schlieren optical sys-tem mentioned earlier in the context of sedimen-tation velocity. (In some specialcases the numberaverage moletular weight ian also be obtained) '.The ratio of the z-average to the weight averagemolecular weight is often used as an 'index of poly-dispersity' of polymeric samples, and can berelated to the breadth of a distribution.There are other ways of using sedimentationequilibrium data to get molecular weight distribu-tions. Perhaps the simplest in principle and mostuseful is to combine with gel filtration, giving thelatter an 'absolute' basis (i.e., not subject toassumptions concerning the conformation of cali-bration standards). Gel filtration is a very simplebut powerful way of separating macromolecules ofdifferent sizes in a polydisperse solution. It can alsogive molecular weight distributions by comparingelution profiles with those of standard moleculesof known molecular weight and the same confor-mation as the molecules being studied. Althoughthe latter requirement is usually OK if globularproteins are being studied and globular proteinstandards are used, it fails for synthetic polymerand polysaccharide systems were so-called 'poly-styrene' standards or 'pullulan' standards are oftenused. These problems can be avoided by takingfractions from the column and determining theirmolecular weights by sedimentation equilibriumtel.T-o.*utty, unless you are working with say a well-behaved solution of a macromolecule of low molecularweight ( < 50000) at low loading concentration ( ( I mg/ml)1he weight, z-average molecular weights obtained inthis way (and the number average) will be apparentmolecular weights due to solution non-ideality effects(real solutions of macromolecules differ from ideal solu-tions in much the same way as real gases differ from idealgases). There are a number of ways of overcoming this'ihe most simple being to measure the apparent molecularweight at a series of concentrations and extrapolate backthes-e values (or the reciprocals thereof) to zero concen-tration to give the "ideal" value. The non-ideality parameteritself (cailed 'B' or 'Ar') which comes from the slope canalso give useful information about macromolecular con-formation. trends in analytical chemistry, vol. 13, no. 70, 1994 Fig.7. (a) Rayleigh sedimentation equilibrium patternfor poly[(isoprene)-p-(ethylene oxide)] block copoly-mer micelles in water. (b) Rayleigh flotation equilib-rium pattern, same polymer but in unimer form, inchloroform. Reproduced with permission from Ref.t131.)8. Flotation velocity and equilibriumUnder the influence of a centrifugal field, con-ventional sedimentation takes place provided thatthe density of the sedimenting particle is larger thanthat of the solvent it is dispersed in. If the densityis less, then the particle will move in the reversedirection. This situation happens with lipoproteinsin aqueous solvents and some synthetic polymersin very dense solvents such as chloroform. Thebasic theory as forsedimentation velocity andequi-librium is the same, the only difference being thedirection of movement. Conformations and homo-geneity information can be deduced from flotationvelocity, and molecular weights from flotationequilibrium experiments in much the same way[3,14]. An example is shown in Fig. 7 for acopolymer system (a model system for drug deliv-ery), which in aqueous solvent gives a conven-tional sedimentation equilibrium pattern in whichthe polymer forms micelles, but in chloroform itgives a flotation equilibrium pattern correspondingto the polymer as discrete unimers. From therespective molecular weights for micelle and uni-mer it is possible to obtain an estimate for the asso-ciation number of the micelle.9. Analytical densitY gradientsedimentation equilibrium : compositionanalysisDensity gradient sedimentation equi I ibriu m pro-cedures using preparatiue ultracentrifuges are rou-tinely used in biochemical science for purifyingmacromolecular systems on the basis of their den-sity - the method is sometimes called isopycnic endstream endobj 55 0 obj 4470 endobj 56 0 obj << /Length 57 0 R >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj51 Do Q endstream endobj 57 0 obj 45 endobj 58 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 6 0 R >> /XObject << /Obj51 51 0 R >> /Subtype 54 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 50 0 R 56 0 R 52 0 R ] >> endobj 11 0 obj << /Kids [ 12 0 R 22 0 R 31 0 R 40 0 R 49 0 R 58 0 R ] /Count 6 /Type /Pages >> endobj xref 0 1 0000000000 65535 f 11 1 0000700445 00000 n 50 9 0000568569 00000 n 0000568648 00000 n 0000664150 00000 n 0000695500 00000 n 0000695523 00000 n 0000700048 00000 n 0000700070 00000 n 0000700170 00000 n 0000700190 00000 n trailer << /Size 59 /Info 1 0 R /Root 13 0 R /Prev 568240 >> startxref 700546 %%EOF 59 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 60 0 obj << /Type /XObject /Subtype /Image /Name /Obj60 /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 91534 >> stream &ɲW}}_ _ ҁ`H H 5EB=Ι73LDtGet\4J AtYFqLMd3\7i!A$ zPq6,(ለ( /2|ЙDD75-ta27t% LLTҾء3%!;i !MbnO Q@OM3S;ȉgC:%}0a|S1R5تO5<-*W+UBa<rzŗ1IiO'^~[SM3g fIO 8TNֽzIah N/ \͑t`'EA֗c]=i$OwFSjPqvKzkJ- ’儈╪j !aZM/&HSA]!I駪~H}SPtZGZ}ak8 %R_^=`;oU^F^=pTjC%MA=~-kM-0>%T/֓i/N^uM/~#Wikz/V_kk#%׷^VJjo8>_E_'Ɨz-./K^34,?ߥ__v40-V/ b}(3ZJIA z~*/i/ZҮc:؆_!i¯ՎׯEDDia2(b }Zե*"! &0^rG5UR'BA au\R|0NI! 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642.00 Tm <444E4120> Tj 1 0 0 1 243.12 641.76 Tm <77617320> Tj 1 0 0 1 265.92 641.28 Tm <73656D692D636F6E2D> Tj 0.72 Tc 1 0 0 1 72.72 630.24 Tm <7365727661746976652E2920> Tj 1 0 0 1 127.68 630.00 Tm <54686520> Tj 1 0 0 1 149.52 629.76 Tm <6964656120> Tj 1 0 0 1 172.56 629.28 Tm <697320> Tj 1 0 0 1 182.88 629.28 Tm <746F20> Tj 1 0 0 1 194.88 629.28 Tm <6861766520> Tj 1 0 0 1 220.08 628.80 Tm <617320> Tj 1 0 0 1 232.80 628.80 Tm <6120> Tj 1 0 0 1 240.72 628.56 Tm <736F6C76656E7420> Tj 1 0 0 1 278.16 628.56 Tm <6120> Tj 1 0 0 1 286.08 628.32 Tm <64656E7365> Tj 0.48 Tc 1 0 0 1 72.72 617.52 Tm <6D6174657269616C20> Tj 1 0 0 1 115.68 617.28 Tm <776869636820> Tj 1 0 0 1 148.56 616.80 Tm <7265646973747269627574657320> Tj 1 0 0 1 211.44 616.08 Tm <736F20> Tj 1 0 0 1 225.36 615.84 Tm <7468617420> Tj 1 0 0 1 247.20 615.84 Tm <746865726520> Tj 1 0 0 1 275.04 615.60 Tm <697320> Tj 1 0 0 1 286.32 615.60 Tm <6120> Tj 1 0 0 1 294.96 615.36 Tm <6469732D> Tj 0.48 Tc 1 0 0 1 72.72 604.56 Tm <747269627574696F6E20> Tj 1 0 0 1 117.84 604.08 Tm <6F6620> Tj 1 0 0 1 131.76 603.84 Tm <64656E7369747920> Tj 1 0 0 1 170.64 603.60 Tm <7468726F7567686F757420> Tj 1 0 0 1 227.28 602.88 Tm <74686520> Tj 1 0 0 1 246.00 602.64 Tm <736564696D656E746174696F6E> Tj 0.72 Tc 1 0 0 1 72.00 591.36 Tm <63656C6C2E20> Tj 1 0 0 1 95.04 591.36 Tm <416E7920> Tj 1 0 0 1 117.84 591.12 Tm <646973736F6C76656420> Tj 1 0 0 1 165.60 590.64 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 241.20 589.92 Tm <77696C6C20> Tj 1 0 0 1 262.32 589.68 Tm <6D6F766520> Tj 1 0 0 1 290.88 589.44 Tm <756E74696C> Tj 0.72 Tc 1 0 0 1 72.00 578.40 Tm <617420> Tj 1 0 0 1 84.72 578.40 Tm <657175696C69627269756D20> Tj 1 0 0 1 144.96 577.92 Tm <697420> Tj 1 0 0 1 155.52 577.68 Tm <7265616368657320> Tj 1 0 0 1 195.84 577.44 Tm <69747320> Tj 1 0 0 1 210.96 577.44 Tm <69736F64656E7369747920> Tj 1 0 0 1 263.28 576.96 Tm <706F696E742C20> Tj 1 0 0 1 295.20 576.48 Tm <692E652E2C> Tj 0.72 Tc 1 0 0 1 72.00 565.44 Tm <74686520> Tj 1 0 0 1 92.64 565.68 Tm <706F736974696F6E20> Tj 1 0 0 1 138.00 564.96 Tm <696E20> Tj 1 0 0 1 153.36 564.72 Tm <74686520> Tj 1 0 0 1 174.24 564.48 Tm <63656C6C20> Tj 1 0 0 1 198.24 564.48 Tm <776865726520> Tj 1 0 0 1 233.52 564.00 Tm <69747320> Tj 1 0 0 1 250.80 563.76 Tm <6F776E20> Tj 1 0 0 1 277.68 563.52 Tm <64656E73697479> Tj 0.48 Tc 1 0 0 1 72.00 552.48 Tm <6D61746368657320> Tj 1 0 0 1 115.92 552.24 Tm <7468617420> Tj 1 0 0 1 138.24 552.00 Tm <6F6620> Tj 1 0 0 1 152.88 552.00 Tm <74686520> Tj 1 0 0 1 172.56 551.76 Tm <736F6C76656E742E20> Tj 1 0 0 1 214.56 551.28 Tm <496E20> Tj 1 0 0 1 229.20 551.04 Tm <617175656F757320> Tj 1 0 0 1 273.12 550.80 Tm <736F6C76656E7473> Tj 0.48 Tc 1 0 0 1 71.28 539.52 Tm <6361657369756D20> Tj 1 0 0 1 113.28 539.28 Tm <73616C747320> Tj 1 0 0 1 136.56 539.04 Tm <61726520> Tj 1 0 0 1 153.12 538.80 Tm <6F6674656E20> Tj 1 0 0 1 180.24 538.56 Tm <7573656420> Tj 1 0 0 1 204.24 538.32 Tm <746F20> Tj 1 0 0 1 215.52 538.56 Tm <70726F6475636520> Tj 1 0 0 1 256.32 537.84 Tm <74686520> Tj 1 0 0 1 272.88 538.08 Tm <6772616469656E74> Tj 0.96 Tc 1 0 0 1 72.24 527.28 Tm <28696E20> Tj 1 0 0 1 90.48 526.56 Tm <74686520> Tj 1 0 0 1 108.96 526.32 Tm <72616E676520> Tj 1 0 0 1 140.40 526.08 Tm <6C2E32746F20> Tj 1 0 0 1 172.08 525.60 Tm <312E3720> Tj 1 0 0 1 188.88 525.84 Tm <672F6D6C292E20> Tj 1 0 0 1 225.84 525.12 Tm <50726F7465696E732C20> Tj 1 0 0 1 271.44 525.12 Tm <706F6C797361632D> Tj 0.72 Tc 1 0 0 1 71.04 513.60 Tm <636861726964657320> Tj 1 0 0 1 116.64 513.12 Tm <616E6420> Tj 1 0 0 1 139.20 512.88 Tm <6E75636C65696320> Tj 1 0 0 1 178.80 512.64 Tm <616369647320> Tj 1 0 0 1 208.80 512.40 Tm <6861766520> Tj 1 0 0 1 236.16 511.92 Tm <746865697220> Tj 1 0 0 1 263.52 511.68 Tm <69736F64656E73697479> Tj 0.96 Tc 1 0 0 1 71.04 500.88 Tm <706F696E747320> Tj 1 0 0 1 106.56 500.40 Tm <617420> Tj 1 0 0 1 120.72 500.16 Tm <617070726F78696D6174656C7920> Tj 1 0 0 1 197.52 499.44 Tm <312E332C20> Tj 1 0 0 1 221.04 499.20 Tm <312E3620> Tj 1 0 0 1 240.00 498.96 Tm <616E6420> Tj 1 0 0 1 264.72 498.96 Tm <312E3720> Tj 1 0 0 1 283.68 498.96 Tm <676C6D6C2C> Tj 0.48 Tc 1 0 0 1 70.80 487.68 Tm <726573706563746976656C792E20> Tj 1 0 0 1 138.00 486.96 Tm <466F7220> Tj 1 0 0 1 161.04 486.72 Tm <6E6F6E2D617175656F757320> Tj 1 0 0 1 228.24 486.00 Tm <73797374656D7320> Tj 1 0 0 1 272.16 485.76 Tm <736F6C76656E7473> Tj 0.48 Tc 1 0 0 1 70.80 474.48 Tm <6C696B6520> Tj 1 0 0 1 96.24 474.24 Tm <6D6978656420> Tj 1 0 0 1 133.20 474.00 Tm <6469696F646F6D657468616E652D7465747261687964726F667572616E20> Tj 1 0 0 1 292.08 472.56 Tm <7379732D> Tj 0.48 Tc 1 0 0 1 70.56 461.52 Tm <74656D7320> Tj 1 0 0 1 95.52 461.28 Tm <63616E20> Tj 1 0 0 1 114.96 461.04 Tm <626520> Tj 1 0 0 1 128.64 461.04 Tm <7573656420> Tj 1 0 0 1 154.32 458.88 Tm <4920> Tj 1 0 0 1 160.56 460.80 Tm <4920> Tj 1 0 0 1 165.12 460.56 Tm <3620> Tj 1 0 0 1 172.32 458.88 Tm <5D20> Tj 1 0 0 1 177.36 460.80 Tm <2E20> Tj 1 0 0 1 182.64 460.56 Tm <466F7220> Tj 1 0 0 1 201.60 460.32 Tm <6120> Tj 1 0 0 1 209.28 460.32 Tm <6D6F6E6F646973706572736520> Tj 1 0 0 1 277.92 459.84 Tm <73797374656D> Tj 0.72 Tc 1 0 0 1 71.04 449.04 Tm <287375636820> Tj 1 0 0 1 102.48 448.32 Tm <617320> Tj 1 0 0 1 116.16 448.08 Tm <6120> Tj 1 0 0 1 125.52 448.32 Tm <77656C6C20> Tj 1 0 0 1 149.76 447.84 Tm <6672616374696F6E6174656420> Tj 1 0 0 1 210.48 447.60 Tm <706F6C7973747972656E652920> Tj 1 0 0 1 276.24 446.64 Tm <64656E73697479> Tj 0.48 Tc 1 0 0 1 70.08 435.84 Tm <6772616469656E7420> Tj 1 0 0 1 113.52 435.12 Tm <616E616C7973697320> Tj 1 0 0 1 155.28 434.64 Tm <63616E20> Tj 1 0 0 1 176.16 434.40 Tm <616C736F20> Tj 1 0 0 1 199.20 434.16 Tm <626520> Tj 1 0 0 1 214.08 434.16 Tm <7573656420> Tj 1 0 0 1 239.76 433.92 Tm <746F20> Tj 1 0 0 1 252.48 433.92 Tm <657374696D61746520> Tj 1 0 0 1 296.16 433.44 Tm <746865> Tj 0.72 Tc 1 0 0 1 69.84 422.40 Tm <646966667573696F6E20> Tj 1 0 0 1 116.40 422.16 Tm <636F656666696369656E7420> Tj 1 0 0 1 171.60 419.76 Tm <4920> Tj 1 0 0 1 177.84 421.44 Tm <6C3520> Tj 1 0 0 1 189.36 419.52 Tm <5D20> Tj 1 0 0 1 194.64 421.44 Tm <2E> Tj 1.20 Tc /F3 13.0 Tf 1 0 0 1 69.84 383.52 Tm <31302E20> Tj 1 0 0 1 93.12 383.28 Tm <47656C73> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 81.12 357.60 Tm <54686520> Tj 1 0 0 1 102.96 357.36 Tm <746563686E6971756520> Tj 1 0 0 1 152.16 356.88 Tm <6F6620> Tj 1 0 0 1 165.12 356.88 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 234.48 356.40 Tm <657175696C69627269756D20> Tj 1 0 0 1 293.04 355.92 Tm <63616E> Tj 0.48 Tc 1 0 0 1 68.88 344.64 Tm <616C736F20> Tj 1 0 0 1 91.20 344.40 Tm <626520> Tj 1 0 0 1 105.12 344.40 Tm <6170706C69656420> Tj 1 0 0 1 143.04 344.16 Tm <746F20> Tj 1 0 0 1 155.04 344.16 Tm <74686520> Tj 1 0 0 1 172.56 343.92 Tm <737475647920> Tj 1 0 0 1 200.88 343.68 Tm <6F6620> Tj 1 0 0 1 213.60 343.68 Tm <74686520> Tj 1 0 0 1 230.64 343.44 Tm <73747275637475726520> Tj 1 0 0 1 274.80 343.20 Tm <6F6620> Tj 1 0 0 1 287.28 343.68 Tm <67656C732C> Tj 0.72 Tc 1 0 0 1 68.64 331.68 Tm <657370656369616C6C7920> Tj 1 0 0 1 121.68 331.68 Tm <696620> Tj 1 0 0 1 132.96 331.44 Tm <74686520> Tj 1 0 0 1 151.68 331.20 Tm <5363686C696572656E20> Tj 1 0 0 1 201.12 330.72 Tm <6F70746963616C20> Tj 1 0 0 1 237.84 330.48 Tm <73797374656D20> Tj 1 0 0 1 275.76 330.24 Tm <697320> Tj 1 0 0 1 287.52 330.24 Tm <75736564> Tj 0.72 Tc 1 0 0 1 70.08 316.80 Tm <5B20> Tj 1 0 0 1 76.08 318.72 Tm <31375D2C20> Tj 1 0 0 1 98.40 318.72 Tm <616E6420> Tj 1 0 0 1 118.08 318.48 Tm <63616E20> Tj 1 0 0 1 137.28 318.48 Tm <70726F7669646520> Tj 1 0 0 1 176.16 318.00 Tm <636F6D706C656D656E7461727920> Tj 1 0 0 1 253.44 317.52 Tm <696E666F726D6174696F6E> Tj 0.72 Tc 1 0 0 1 68.40 305.76 Tm <746F20> Tj 1 0 0 1 79.92 305.76 Tm <636F6E76656E74696F6E616C20> Tj 1 0 0 1 144.72 305.28 Tm <7268656F6C6F676963616C20> Tj 1 0 0 1 201.12 304.80 Tm <6D6574686F64732E20> Tj 1 0 0 1 246.72 304.56 Tm <466F7220> Tj 1 0 0 1 265.44 304.32 Tm <6578616D706C652C> Tj 0.72 Tc 1 0 0 1 68.40 292.80 Tm <6265636175736520> Tj 1 0 0 1 109.44 292.56 Tm <74686520> Tj 1 0 0 1 127.20 292.56 Tm <6E6574776F726B20> Tj 1 0 0 1 168.96 292.08 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 236.88 291.84 Tm <77696C6C20> Tj 1 0 0 1 258.48 291.60 Tm <7661727920> Tj 1 0 0 1 282.48 291.36 Tm <696E20> Tj 1 0 0 1 294.24 291.36 Tm <746865> Tj 0.72 Tc 1 0 0 1 67.92 280.08 Tm <67656C20> Tj 1 0 0 1 86.16 279.60 Tm <617320> Tj 1 0 0 1 99.36 279.60 Tm <6120> Tj 1 0 0 1 108.24 279.60 Tm <66756E6374696F6E20> Tj 1 0 0 1 150.96 279.12 Tm <6F6620> Tj 1 0 0 1 164.40 279.12 Tm <72616469616C20> Tj 1 0 0 1 194.64 279.12 Tm <706F736974696F6E20> Tj 1 0 0 1 236.40 278.64 Tm <697420> Tj 1 0 0 1 246.24 278.64 Tm <697320> Tj 1 0 0 1 257.28 278.64 Tm <706F737369626C6520> Tj 1 0 0 1 299.52 278.16 Tm <746F> Tj 0.72 Tc 1 0 0 1 68.16 266.64 Tm <6D6F6E69746F7220> Tj 1 0 0 1 110.88 266.64 Tm <74686520> Tj 1 0 0 1 130.32 266.16 Tm <7377656C6C696E6720> Tj 1 0 0 1 175.44 266.40 Tm <707265737375726520> Tj 1 0 0 1 219.84 265.68 Tm <616E6420> Tj 1 0 0 1 241.68 265.44 Tm <6F7468657220> Tj 1 0 0 1 271.20 265.20 Tm <746865726D6F2D> Tj 0.72 Tc 1 0 0 1 67.68 253.68 Tm <64796E616D696320> Tj 1 0 0 1 112.56 253.92 Tm <70726F7065727469657320> Tj 1 0 0 1 163.20 252.96 Tm <6F6620> Tj 1 0 0 1 176.40 252.96 Tm <74686520> Tj 1 0 0 1 193.68 253.20 Tm <67656C20> Tj 1 0 0 1 211.20 252.72 Tm <617320> Tj 1 0 0 1 223.68 252.72 Tm <6120> Tj 1 0 0 1 232.08 252.48 Tm <66756E6374696F6E20> Tj 1 0 0 1 274.56 252.48 Tm <6F6620> Tj 1 0 0 1 287.04 252.48 Tm <636F6E2D> Tj 0.72 Tc 1 0 0 1 67.44 240.96 Tm <63656E74726174696F6E20> Tj 1 0 0 1 125.28 238.56 Tm <4920> Tj 1 0 0 1 131.52 240.48 Tm <6C3720> Tj 1 0 0 1 143.04 238.56 Tm <5D20> Tj 1 0 0 1 148.56 240.48 Tm <2E20> Tj 1 0 0 1 158.88 240.24 Tm <5573696E6720> Tj 1 0 0 1 195.36 240.00 Tm <74686520> Tj 1 0 0 1 217.68 239.76 Tm <6162736F727074696F6E20> Tj 1 0 0 1 276.00 239.28 Tm <6F70726963616C> Tj 0.48 Tc 1 0 0 1 67.44 227.76 Tm <73797374656D20> Tj 1 0 0 1 104.16 227.76 Tm <616E6420> Tj 1 0 0 1 124.56 227.52 Tm <616674657220> Tj 1 0 0 1 149.52 227.28 Tm <73656C656374696F6E20> Tj 1 0 0 1 194.88 226.80 Tm <6F6620> Tj 1 0 0 1 207.60 226.80 Tm <616E20> Tj 1 0 0 1 222.00 226.80 Tm <617070726F70726961746520> Tj 1 0 0 1 279.36 226.56 Tm <776176652D> Tj 0.96 Tc 1 0 0 1 67.68 215.04 Tm <6C656E67746820> Tj 1 0 0 1 101.52 215.52 Tm <28692E652E2C20> Tj 1 0 0 1 127.68 214.80 Tm <696E20> Tj 1 0 0 1 139.68 214.80 Tm <776869636820> Tj 1 0 0 1 172.08 214.32 Tm <74686520> Tj 1 0 0 1 189.36 214.56 Tm <67656C20> Tj 1 0 0 1 207.12 214.08 Tm <6D617472697820> Tj 1 0 0 1 240.96 213.84 Tm <697320> Tj 1 0 0 1 252.00 213.84 Tm <696E76697369626C652920> Tj 1 0 0 1 301.68 213.36 Tm <6974> Tj 0.72 Tc 1 0 0 1 67.44 202.08 Tm <697320> Tj 1 0 0 1 79.20 202.32 Tm <706F737369626C6520> Tj 1 0 0 1 123.60 201.84 Tm <696E20> Tj 1 0 0 1 136.56 201.84 Tm <7072696E6369706C6520> Tj 1 0 0 1 183.36 201.36 Tm <746F20> Tj 1 0 0 1 196.80 201.12 Tm <666F6C6C6F7720> Tj 1 0 0 1 232.08 200.88 Tm <74686520> Tj 1 0 0 1 250.56 200.64 Tm <646966667573696F6E20> Tj 1 0 0 1 297.84 200.40 Tm <6F66> Tj 0.96 Tc 1 0 0 1 66.96 189.12 Tm <736D616C6C20> Tj 1 0 0 1 104.64 188.88 Tm <6D6F6C6563756C657320> Tj 1 0 0 1 165.12 189.12 Tm <28696E636C7564696E6720> Tj 1 0 0 1 226.56 187.92 Tm <736D616C6C20> Tj 1 0 0 1 263.28 187.92 Tm <70726F7465696E7329> Tj 0.48 Tc 1 0 0 1 66.96 176.16 Tm <7468726F75676820> Tj 1 0 0 1 107.76 175.92 Tm <74686520> Tj 1 0 0 1 125.52 176.16 Tm <67656C2C20> Tj 1 0 0 1 146.16 175.44 Tm <617320> Tj 1 0 0 1 159.12 175.44 Tm <6120> Tj 1 0 0 1 167.52 175.68 Tm <70726F626520> Tj 1 0 0 1 198.00 175.20 Tm <696E746F20> Tj 1 0 0 1 219.12 175.44 Tm <67656C20> Tj 1 0 0 1 236.88 174.96 Tm <7374727563747572652E> Tj 0.96 Tc 1 0 0 1 67.20 137.28 Tm <31312E20> Tj 1 0 0 1 90.72 137.28 Tm <446966667573696F6E20> Tj 1 0 0 1 145.20 136.80 Tm <616E616C79736973> Tj 0.72 Tc 1 0 0 1 78.72 111.84 Tm <486973746F726963616C6C7920> Tj 1 0 0 1 140.64 111.36 Tm <74686520> Tj 1 0 0 1 160.56 111.12 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 235.92 110.88 Tm <77617320> Tj 1 0 0 1 259.68 110.40 Tm <7573656420> Tj 1 0 0 1 286.80 110.40 Tm <617320> Tj 1 0 0 1 301.92 110.16 Tm <61> Tj 0.48 Tc 1 0 0 1 66.24 98.88 Tm <746F6F6C20> Tj 1 0 0 1 91.20 98.64 Tm <666F7220> Tj 1 0 0 1 111.12 98.64 Tm <6D6561737572696E6720> Tj 1 0 0 1 167.04 98.16 Tm <74686520> Tj 1 0 0 1 187.20 98.16 Tm <646966667573696F6E20> Tj 1 0 0 1 235.92 97.68 Tm <636F656666696369656E747320> Tj 1 0 0 1 296.88 97.20 Tm <6F66> Tj 0.72 Tc 1 0 0 1 66.24 86.16 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 152.40 85.44 Tm <696E20> Tj 1 0 0 1 168.72 85.20 Tm <736F6C7574696F6E20> Tj 1 0 0 1 213.84 84.96 Tm <7573696E6720> Tj 1 0 0 1 246.96 84.96 Tm <6120> Tj 1 0 0 1 259.20 85.20 Tm <70726F636564757265> Tj 0.72 Tc 1 0 0 1 66.00 73.20 Tm <6B6E6F776E20> Tj 1 0 0 1 102.72 72.96 Tm <617320> Tj 1 0 0 1 117.36 78.24 Tm <27626F756E6461727920> Tj 1 0 0 1 169.68 72.48 Tm <737072656164696E67272E20> Tj 1 0 0 1 226.80 72.00 Tm <486F7720> Tj 1 0 0 1 253.92 72.00 Tm <6661737420> Tj 1 0 0 1 274.80 71.76 Tm <6120> Tj 1 0 0 1 283.68 71.76 Tm <736564692D> Tj 0.48 Tc 1 0 0 1 66.24 60.48 Tm <6D656E74696E6720> Tj 1 0 0 1 108.00 60.00 Tm <626F756E6461727920> Tj 1 0 0 1 156.00 59.76 Tm <62726F6164656E656420> Tj 1 0 0 1 208.32 59.28 Tm <6F757420> Tj 1 0 0 1 226.08 59.28 Tm <77617320> Tj 1 0 0 1 246.96 59.04 Tm <6120> Tj 1 0 0 1 254.88 59.28 Tm <66756E6374696F6E20> Tj 1 0 0 1 296.64 58.80 Tm <6F66> Tj 0.72 Tc 1 0 0 1 65.76 47.52 Tm <74686520> Tj 1 0 0 1 84.96 47.52 Tm <646966667573696F6E20> Tj 1 0 0 1 132.96 47.28 Tm <636F656666696369656E7420> Tj 1 0 0 1 189.36 47.52 Tm <287468656E20> Tj 1 0 0 1 219.60 46.32 Tm <627920> Tj 1 0 0 1 235.92 46.32 Tm <636F6D62696E696E6720> Tj 1 0 0 1 292.08 46.08 Tm <746865> Tj 0.48 Tc 1 0 0 1 65.52 34.80 Tm <646966667573696F6E20> Tj 1 0 0 1 113.04 34.56 Tm <636F656666696369656E7420> Tj 1 0 0 1 168.00 34.32 Tm <7769746820> Tj 1 0 0 1 192.72 34.08 Tm <74686520> Tj 1 0 0 1 211.20 33.84 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 281.76 33.36 Tm <636F65662D> Tj 0.72 Tc 1 0 0 1 65.76 22.08 Tm <66696369656E7420> Tj 1 0 0 1 98.88 21.84 Tm <74686520> Tj 1 0 0 1 116.88 21.60 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 168.00 21.60 Tm <77656967687420> Tj 1 0 0 1 203.28 20.88 Tm <636F756C6420> Tj 1 0 0 1 233.28 20.64 Tm <626520> Tj 1 0 0 1 247.44 20.64 Tm <6F627461696E656420> Tj 1 0 0 1 292.08 20.64 Tm <766961> Tj 0.24 Tc 1 0 0 1 568.08 724.32 Tm <343435> Tj 0.72 Tc 1 0 0 1 344.16 692.40 Tm <6120> Tj 1 0 0 1 355.92 692.40 Tm <72656C6174696F6E20> Tj 1 0 0 1 398.40 691.92 Tm <6B6E6F776E20> Tj 1 0 0 1 437.04 691.44 Tm <617320> Tj 1 0 0 1 453.12 691.44 Tm <74686520> Tj 1 0 0 1 474.72 696.48 Tm <27737665646265726720> Tj 1 0 0 1 529.20 689.76 Tm <6571756174696F6E2C292E> Tj 0.48 Tc 1 0 0 1 343.92 679.68 Tm <4E6F77616461797320> Tj 1 0 0 1 399.12 678.96 Tm <74686520> Tj 1 0 0 1 418.32 678.96 Tm <6D6F726520> Tj 1 0 0 1 447.36 678.48 Tm <726170696420> Tj 1 0 0 1 476.40 678.24 Tm <746563686E6971756520> Tj 1 0 0 1 527.52 676.80 Tm <6F6620> Tj 1 0 0 1 541.92 676.32 Tm <64796E752A692E> Tj 0.72 Tc 1 0 0 1 344.16 666.72 Tm <6C6967687420> Tj 1 0 0 1 367.68 666.48 Tm <73636174746572696E6720> Tj 1 0 0 1 415.92 666.00 Tm <697320> Tj 1 0 0 1 425.52 666.00 Tm <74686520> Tj 1 0 0 1 442.08 665.76 Tm <6D6574686F6420> Tj 1 0 0 1 479.28 665.28 Tm <6F6620> Tj 1 0 0 1 491.04 665.04 Tm <63686F69636520> Tj 1 0 0 1 524.16 664.32 Tm <666F7220> Tj 1 0 0 1 540.00 663.84 Tm <646966667573696F6E> Tj 0.48 Tc 1 0 0 1 343.68 653.52 Tm <6D6561737572656D656E74732C20> Tj 1 0 0 1 417.84 652.80 Tm <62757420> Tj 1 0 0 1 435.84 652.80 Tm <666F7220> Tj 1 0 0 1 452.40 652.56 Tm <6365727461696E20> Tj 1 0 0 1 487.92 652.08 Tm <73797374656D7320> Tj 1 0 0 1 528.96 651.12 Tm <74686520> Tj 1 0 0 1 546.48 650.64 Tm <616E616C7674695F> Tj 0.48 Tc 1 0 0 1 343.20 640.56 Tm <63616C20> Tj 1 0 0 1 362.64 640.56 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 437.52 639.84 Tm <68617320> Tj 1 0 0 1 458.16 639.60 Tm <636C65617220> Tj 1 0 0 1 486.48 639.12 Tm <616476616E74616765732E20> Tj 1 0 0 1 547.92 637.68 Tm <4F6E6520> Tj 1 0 0 1 572.88 636.96 Tm <6F66> Tj 0.48 Tc 1 0 0 1 343.44 627.84 Tm <746865736520> Tj 1 0 0 1 371.76 627.60 Tm <697320> Tj 1 0 0 1 383.52 627.36 Tm <666F7220> Tj 1 0 0 1 401.28 627.12 Tm <74686520> Tj 1 0 0 1 419.52 627.12 Tm <616E616C7973697320> Tj 1 0 0 1 461.52 626.64 Tm <6F6620> Tj 1 0 0 1 475.44 626.64 Tm <74686520> Tj 1 0 0 1 493.68 626.16 Tm <646966667573696F6E20> Tj 1 0 0 1 540.96 625.20 Tm <6F6620> Tj 1 0 0 1 555.12 624.72 Tm <6D6F6C655F> Tj 0.48 Tc 1 0 0 1 342.72 614.88 Tm <63756C657320> Tj 1 0 0 1 374.64 614.64 Tm <6F7220> Tj 1 0 0 1 392.16 614.40 Tm <6D6163726F6D6F6C6563756C657320> Tj 1 0 0 1 477.12 613.68 Tm <7468726F75676820> Tj 1 0 0 1 521.28 612.96 Tm <636F6E63656E747261746564> Tj 0.72 Tc 1 0 0 1 342.96 601.92 Tm <6D656469612C20> Tj 1 0 0 1 377.52 601.68 Tm <696E636C7564696E6720> Tj 1 0 0 1 423.84 601.44 Tm <67656C7320> Tj 1 0 0 1 445.20 600.96 Tm <616E6420> Tj 1 0 0 1 464.40 600.96 Tm <74776F2D706861736520> Tj 1 0 0 1 515.52 600.00 Tm <73797374656D732E20> Tj 1 0 0 1 558.72 599.28 Tm <57697468> Tj 0.48 Tc 1 0 0 1 342.72 588.96 Tm <74686520> Tj 1 0 0 1 359.52 588.96 Tm <6C617474657220> Tj 1 0 0 1 385.68 588.72 Tm <697420> Tj 1 0 0 1 394.32 588.48 Tm <697320> Tj 1 0 0 1 403.68 588.72 Tm <706F737369626C6520> Tj 1 0 0 1 444.48 588.00 Tm <746F20> Tj 1 0 0 1 455.76 588.00 Tm <6D6F64656C20> Tj 1 0 0 1 487.44 587.52 Tm <6D656D6272616E6520> Tj 1 0 0 1 539.28 587.04 Tm <7068656E6F6D5F> Tj 0.48 Tc 1 0 0 1 342.24 576.00 Tm <656E612E20> Tj 1 0 0 1 365.04 575.76 Tm <4170706C69656420> Tj 1 0 0 1 406.80 575.52 Tm <696E20> Tj 1 0 0 1 418.56 575.28 Tm <7468697320> Tj 1 0 0 1 438.96 575.28 Tm <7761792C20> Tj 1 0 0 1 464.64 575.04 Tm <74686520> Tj 1 0 0 1 482.40 574.80 Tm <756C74726163656E7472696675676520> Tj 1 0 0 1 556.08 573.60 Tm <697320> Tj 1 0 0 1 566.88 573.12 Tm <6E6F74> Tj 0.72 Tc 1 0 0 1 342.24 562.80 Tm <6265696E6720> Tj 1 0 0 1 374.16 562.80 Tm <7573656420> Tj 1 0 0 1 400.56 562.56 Tm <617320> Tj 1 0 0 1 415.68 562.32 Tm <6120> Tj 1 0 0 1 426.00 562.08 Tm <736564696D656E746174696F6E20> Tj 1 0 0 1 497.76 561.36 Tm <746F6F6C20> Tj 1 0 0 1 521.52 561.12 Tm <617320> Tj 1 0 0 1 536.40 560.88 Tm <737563682C20> Tj 1 0 0 1 566.64 560.16 Tm <627574> Tj 0.48 Tc 1 0 0 1 342.24 550.08 Tm <72617468657274686520> Tj 1 0 0 1 388.80 549.60 Tm <6F70746963616C20> Tj 1 0 0 1 423.60 549.36 Tm <73797374656D20> Tj 1 0 0 1 458.40 549.12 Tm <616C6F6E6520> Tj 1 0 0 1 486.72 548.88 Tm <697320> Tj 1 0 0 1 496.80 548.64 Tm <6265696E6720> Tj 1 0 0 1 525.60 548.16 Tm <757365642E20> Tj 1 0 0 1 552.72 547.68 Tm <4120> Tj 1 0 0 1 564.00 547.44 Tm <6C6F77> Tj 0.72 Tc 1 0 0 1 342.00 537.12 Tm <726F746F7220> Tj 1 0 0 1 368.88 536.88 Tm <737065656420> Tj 1 0 0 1 399.60 536.64 Tm <697320> Tj 1 0 0 1 410.40 536.64 Tm <63686F73656E20> Tj 1 0 0 1 447.12 536.16 Tm <73696D706C7920> Tj 1 0 0 1 482.88 535.92 Tm <746F20> Tj 1 0 0 1 495.84 535.68 Tm <6D696E696D69736520> Tj 1 0 0 1 543.36 534.96 Tm <636F6E7665635F> Tj 0.72 Tc 1 0 0 1 342.00 524.16 Tm <74696F6E20> Tj 1 0 0 1 363.12 523.92 Tm <6566666563747320> Tj 1 0 0 1 399.36 521.76 Tm <4920> Tj 1 0 0 1 405.60 523.68 Tm <6C3820> Tj 1 0 0 1 417.12 521.52 Tm <5D20> Tj 1 0 0 1 422.40 523.44 Tm <2E> Tj 0.96 Tc /F3 13.0 Tf 1 0 0 1 341.52 478.32 Tm <31322E20> Tj 1 0 0 1 364.32 478.08 Tm <54686520> Tj 1 0 0 1 388.56 477.84 Tm <667574757265> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 352.80 448.56 Tm <417320> Tj 1 0 0 1 370.32 448.32 Tm <6C6F6E6720> Tj 1 0 0 1 395.04 448.08 Tm <617320> Tj 1 0 0 1 408.72 448.08 Tm <746865726520> Tj 1 0 0 1 436.56 447.84 Tm <697320> Tj 1 0 0 1 448.08 447.60 Tm <6120> Tj 1 0 0 1 457.20 447.60 Tm <6E65656420> Tj 1 0 0 1 483.60 447.36 Tm <746F20> Tj 1 0 0 1 496.80 447.12 Tm <6D65617375726520> Tj 1 0 0 1 540.48 446.64 Tm <74686520> Tj 1 0 0 1 558.96 446.40 Tm <73697A652C> Tj 0.48 Tc 1 0 0 1 340.80 435.60 Tm <736861706520> Tj 1 0 0 1 373.92 435.36 Tm <616E6420> Tj 1 0 0 1 397.20 435.12 Tm <696E746572616374696F6E20> Tj 1 0 0 1 453.12 434.88 Tm <70726F7065727469657320> Tj 1 0 0 1 506.64 433.92 Tm <6F6620> Tj 1 0 0 1 522.72 433.92 Tm <6D6163726F6D6F6C652D> Tj 0.72 Tc 1 0 0 1 340.32 422.64 Tm <63756C657320> Tj 1 0 0 1 367.92 422.40 Tm <696E20> Tj 1 0 0 1 379.44 422.16 Tm <736F6C7574696F6E20> Tj 1 0 0 1 420.00 422.16 Tm <746865726520> Tj 1 0 0 1 446.40 422.16 Tm <77696C6C20> Tj 1 0 0 1 467.28 421.68 Tm <616C7761797320> Tj 1 0 0 1 502.80 421.20 Tm <626520> Tj 1 0 0 1 516.48 420.96 Tm <6120> Tj 1 0 0 1 524.40 420.96 Tm <6E65656420> Tj 1 0 0 1 549.36 420.72 Tm <666F7220> Tj 1 0 0 1 565.68 420.72 Tm <746865> Tj 0.48 Tc 1 0 0 1 340.32 409.68 Tm <616E616C79746963616C20> Tj 1 0 0 1 389.04 409.44 Tm <756C74726163656E747269667567652E20> Tj 1 0 0 1 463.68 408.72 Tm <547275652C20> Tj 1 0 0 1 491.52 408.48 Tm <666F7220> Tj 1 0 0 1 507.12 408.24 Tm <6365727461696E20> Tj 1 0 0 1 542.16 407.76 Tm <73797374656D73> Tj 0.48 Tc 1 0 0 1 340.08 396.96 Tm <746865726520> Tj 1 0 0 1 367.20 396.72 Tm <61726520> Tj 1 0 0 1 385.44 396.48 Tm <6D6F726520> Tj 1 0 0 1 412.56 396.48 Tm <706F77657266756C20> Tj 1 0 0 1 458.88 396.00 Tm <6D6574686F647320> Tj 1 0 0 1 502.56 395.52 Tm <666F7220> Tj 1 0 0 1 520.08 395.52 Tm <7765696768742C20> Tj 1 0 0 1 558.48 394.80 Tm <636F6E2D> Tj 0.72 Tc 1 0 0 1 340.32 383.76 Tm <666F726D6174696F6E20> Tj 1 0 0 1 390.48 383.52 Tm <6F7220> Tj 1 0 0 1 403.92 383.52 Tm <696E746572616374696F6E20> Tj 1 0 0 1 457.92 383.04 Tm <616E616C7973697320> Tj 1 0 0 1 499.68 382.56 Tm <62757420> Tj 1 0 0 1 518.16 382.32 Tm <6561636820> Tj 1 0 0 1 543.84 382.08 Tm <6D6574686F64> Tj 0.72 Tc 1 0 0 1 339.84 370.80 Tm <68617320> Tj 1 0 0 1 360.72 370.80 Tm <69747320> Tj 1 0 0 1 375.60 370.56 Tm <6F776E20> Tj 1 0 0 1 400.80 370.56 Tm <6C696D69746174696F6E732C20> Tj 1 0 0 1 458.40 370.08 Tm <757375616C6C7920> Tj 1 0 0 1 497.28 369.60 Tm <72656C6174696E6720> Tj 1 0 0 1 538.08 369.36 Tm <746F20> Tj 1 0 0 1 552.00 369.12 Tm <6D6178692D> Tj 0.72 Tc 1 0 0 1 339.84 357.84 Tm <6D756D20> Tj 1 0 0 1 367.68 357.84 Tm <6F7220> Tj 1 0 0 1 381.60 357.60 Tm <6D696E696D756D20> Tj 1 0 0 1 431.04 357.36 Tm <73697A6520> Tj 1 0 0 1 452.64 357.12 Tm <6F6620> Tj 1 0 0 1 466.32 357.12 Tm <74686520> Tj 1 0 0 1 484.56 356.88 Tm <6D6163726F6D6F6C6563756C6520> Tj 1 0 0 1 561.60 356.16 Tm <74686174> Tj 0.72 Tc 1 0 0 1 339.36 345.12 Tm <63616E20> Tj 1 0 0 1 358.32 344.88 Tm <626520> Tj 1 0 0 1 371.76 344.88 Tm <737475646965642C20> Tj 1 0 0 1 411.36 344.88 Tm <7768657468657220> Tj 1 0 0 1 451.20 344.16 Tm <6F7220> Tj 1 0 0 1 463.44 344.16 Tm <6E6F7420> Tj 1 0 0 1 481.20 344.16 Tm <697420> Tj 1 0 0 1 488.88 343.92 Tm <63616E20> Tj 1 0 0 1 507.84 343.68 Tm <626520> Tj 1 0 0 1 521.04 343.68 Tm <6372797374616C6C697A65642C> Tj 0.72 Tc 1 0 0 1 339.36 332.16 Tm <74686520> Tj 1 0 0 1 358.80 332.16 Tm <6D696E696D756D20> Tj 1 0 0 1 409.44 331.68 Tm <636F6E63656E74726174696F6E20> Tj 1 0 0 1 479.04 331.20 Tm <726571756972656420> Tj 1 0 0 1 524.16 331.44 Tm <286120> Tj 1 0 0 1 539.04 330.96 Tm <70726F626C656D> Tj 0.72 Tc 1 0 0 1 338.88 319.20 Tm <657370656369616C6C7920> Tj 1 0 0 1 389.76 319.20 Tm <72656C6576616E7420> Tj 1 0 0 1 430.32 318.72 Tm <746F20> Tj 1 0 0 1 442.32 318.72 Tm <7265736F6E616E636520> Tj 1 0 0 1 492.48 318.24 Tm <6D6574686F6473292C20> Tj 1 0 0 1 544.56 317.76 Tm <616E6420> Tj 1 0 0 1 564.48 317.52 Tm <746865> Tj 0.48 Tc 1 0 0 1 338.88 306.48 Tm <70757269747920> Tj 1 0 0 1 371.28 306.24 Tm <6F6620> Tj 1 0 0 1 384.96 306.00 Tm <74686520> Tj 1 0 0 1 403.20 305.76 Tm <73616D706C652E20> Tj 1 0 0 1 443.04 305.76 Tm <54686520> Tj 1 0 0 1 465.60 305.52 Tm <756C74726163656E747269667567652C20> Tj 1 0 0 1 542.88 304.80 Tm <7769746820> Tj 1 0 0 1 567.84 304.56 Tm <697473> Tj 0.72 Tc 1 0 0 1 339.12 293.52 Tm <766572736174696C6974792C20> Tj 1 0 0 1 392.64 293.28 Tm <77696C6C2C20> Tj 1 0 0 1 416.64 292.80 Tm <6265736964657320> Tj 1 0 0 1 454.80 292.56 Tm <72656D61696E696E6720> Tj 1 0 0 1 505.92 292.08 Tm <6120> Tj 1 0 0 1 513.84 292.32 Tm <706F77657266756C20> Tj 1 0 0 1 560.40 291.84 Tm <746F6F6C> Tj 0.72 Tc 1 0 0 1 339.12 280.32 Tm <696E20> Tj 1 0 0 1 351.36 280.32 Tm <69747320> Tj 1 0 0 1 365.04 280.08 Tm <6F776E20> Tj 1 0 0 1 388.80 280.08 Tm <72696768742C20> Tj 1 0 0 1 416.88 279.84 Tm <6265636F6D6520> Tj 1 0 0 1 456.72 279.60 Tm <616E20> Tj 1 0 0 1 470.88 279.60 Tm <696E6372656173696E676C7920> Tj 1 0 0 1 532.56 278.88 Tm <696D706F7274616E74> Tj 0.72 Tc 1 0 0 1 338.64 267.12 Tm <6164646974696F6E616C20> Tj 1 0 0 1 388.56 266.88 Tm <746563686E6971756520> Tj 1 0 0 1 436.56 266.64 Tm <7573656420> Tj 1 0 0 1 460.56 266.40 Tm <696E20> Tj 1 0 0 1 471.12 266.40 Tm <636F6E6A756E6374696F6E20> Tj 1 0 0 1 530.16 266.16 Tm <7769746820> Tj 1 0 0 1 553.68 265.68 Tm <736F6D65> Tj 0.72 Tc 1 0 0 1 338.40 254.40 Tm <6F6620> Tj 1 0 0 1 353.04 254.40 Tm <746865736520> Tj 1 0 0 1 381.84 254.16 Tm <6F7468657220> Tj 1 0 0 1 410.88 253.92 Tm <6D6574686F64732C20> Tj 1 0 0 1 458.64 253.92 Tm <776865746865722C20> Tj 1 0 0 1 504.48 253.20 Tm <666F7220> Tj 1 0 0 1 522.72 253.20 Tm <6120> Tj 1 0 0 1 532.56 253.20 Tm <706172746963756C6172> Tj 0.72 Tc 1 0 0 1 338.40 241.44 Tm <6D6163726F6D6F6C6563756C617220> Tj 1 0 0 1 418.80 240.96 Tm <73797374656D2C20> Tj 1 0 0 1 458.16 240.72 Tm <697420> Tj 1 0 0 1 467.52 240.48 Tm <626520> Tj 1 0 0 1 481.68 240.48 Tm <666F7220> Tj 1 0 0 1 498.48 240.24 Tm <6578616D706C6520> Tj 1 0 0 1 542.40 240.00 Tm <6372797374616C2D> Tj 0.72 Tc 1 0 0 1 338.40 228.48 Tm <6C6F6772617068792C20> Tj 1 0 0 1 387.12 228.24 Tm <4E4D522C20> Tj 1 0 0 1 420.48 227.76 Tm <6C6967687420> Tj 1 0 0 1 445.20 227.76 Tm <73636174746572696E672C20> Tj 1 0 0 1 497.76 227.28 Tm <6D61737320> Tj 1 0 0 1 525.12 227.04 Tm <7370656374726F6D652D> Tj 0.72 Tc 1 0 0 1 337.92 215.52 Tm <7472792C20> Tj 1 0 0 1 356.88 215.52 Tm <6368726F6D61746F67726170687920> Tj 1 0 0 1 438.00 214.80 Tm <6F7220> Tj 1 0 0 1 450.24 214.80 Tm <656C656374726F70686F72657369732E20> Tj 1 0 0 1 528.48 214.08 Tm <54686520> Tj 1 0 0 1 550.80 214.32 Tm <766972747565> Tj 0.72 Tc 1 0 0 1 337.68 202.56 Tm <6F6620> Tj 1 0 0 1 354.96 202.56 Tm <636F6D62696E696E6720> Tj 1 0 0 1 413.52 202.08 Tm <6D6561737572656D656E747320> Tj 1 0 0 1 488.64 201.60 Tm <66726F6D20> Tj 1 0 0 1 519.36 201.36 Tm <696E646570656E64656E74> Tj 0.72 Tc 1 0 0 1 337.68 189.60 Tm <746563686E697175657320> Tj 1 0 0 1 391.92 189.36 Tm <666F7220> Tj 1 0 0 1 408.24 189.12 Tm <636F6E6669726D61746F727920> Tj 1 0 0 1 472.56 189.12 Tm <707572706F73657320> Tj 1 0 0 1 518.16 188.16 Tm <6F7220> Tj 1 0 0 1 531.12 188.16 Tm <6F7468657277697365> Tj 0.72 Tc 1 0 0 1 337.68 176.64 Tm <73686F756C6420> Tj 1 0 0 1 372.96 176.40 Tm <6E6576657220> Tj 1 0 0 1 402.24 176.16 Tm <626520> Tj 1 0 0 1 416.64 176.16 Tm <69676E6F7265642E> Tj 0.48 Tc 1 0 0 1 337.68 131.28 Tm <5265666572656E636573> Tj 0.72 Tc 1 0 0 1 343.68 101.28 Tm <7420> Tj 1 0 0 1 349.20 102.96 Tm <4920> Tj 1 0 0 1 354.48 101.28 Tm <4920> Tj 1 0 0 1 361.20 102.72 Tm <532E452E20> Tj 1 0 0 1 388.08 102.72 Tm <48617264696E672C20> Tj 1 0 0 1 435.12 102.48 Tm <412E4A2E20> Tj 1 0 0 1 461.28 102.24 Tm <526F776520> Tj 1 0 0 1 495.12 102.00 Tm <616E6420> Tj 1 0 0 1 519.60 101.76 Tm <4A2E432E20> Tj 1 0 0 1 546.00 101.76 Tm <486F72746F6E> Tj 0.48 Tc 1 0 0 1 361.92 91.68 Tm <28456469746F7273292C20> Tj 1 0 0 1 415.92 90.72 Tm <416E616C79746963616C20> Tj 1 0 0 1 472.08 90.24 Tm <556C746163656E7472696675676174696F6E20> Tj 1 0 0 1 568.32 90.24 Tm <696E> Tj 0.48 Tc 1 0 0 1 360.72 79.20 Tm <4220> Tj 1 0 0 1 367.68 79.20 Tm <696F6320> Tj 1 0 0 1 380.88 79.20 Tm <686520> Tj 1 0 0 1 390.96 79.20 Tm <6D6920> Tj 1 0 0 1 402.00 78.96 Tm <7374727920> Tj 1 0 0 1 420.00 78.96 Tm <616E6420> Tj 1 0 0 1 438.72 78.96 Tm <5020> Tj 1 0 0 1 444.96 78.72 Tm <6F20> Tj 1 0 0 1 450.72 78.96 Tm <6C7920> Tj 1 0 0 1 458.40 78.72 Tm <6D6520> Tj 1 0 0 1 471.36 78.72 Tm <7220> Tj 1 0 0 1 476.88 78.48 Tm <5320> Tj 1 0 0 1 482.64 78.48 Tm <6320> Tj 1 0 0 1 487.68 78.48 Tm <69656E63652C526F79616C20> Tj 1 0 0 1 543.60 78.24 Tm <536F6369657479> Tj 0.72 Tc 1 0 0 1 360.48 67.20 Tm <6F6620> Tj 1 0 0 1 372.48 67.20 Tm <4368656D69737472792C20> Tj 1 0 0 1 423.36 66.96 Tm <43616D6272696467652C20> Tj 1 0 0 1 479.04 66.72 Tm <313939322C36323920> Tj 1 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The analogous situ-ation in an analyticcl ultracentrifuge permits us toassay for purity. (This was the classical methodused by Meselson, Stahl and Vinograd I 15] toshow that the replication of DNA was semi-con-servative.) The idea is to have as a solvent a densematerial which redistributes so that there is a dis-tribution of density throughout the sedimentationcell. Any dissolved macromolecule will move untilat equilibrium it reaches its isodensity point, i.e.,the position in the cell where its own densitymatches that of the solvent. In aqueous solventscaesium salts are often used to produce the gradient(in the range l.2to 1.7 g/ml). Proteins, polysac-charides and nucleic acids have their isodensitypoints at approximately 1.3, 1.6 and 1.7 glml,respectively. For non-aqueous systems solventslike mixed diiodomethane-tetrahydrofuran sys-tems can be used I I 6 ] . For a monodisperse system(such as a well fractionated polystyrene) densitygradient analysis can also be used to estimate thediffusion coefficient I l5 ] .10. GelsThe technique of sedimentation equilibrium canalso be applied to the study of the structure of gels,especially if the Schlieren optical system is used[ 17], and can provide complementary informationto conventional rheological methods. For example,because the network concentration will vary in thegel as a function of radial position it is possible tomonitor the swelling pressure and other thermo-dynamic properties of the gel as a function of con-centration I l7 ] . Using the absorption opricalsystem and after selection of an appropriate wave-length (i.e., in which the gel matrix is invisible) itis possible in principle to follow the diffusion ofsmall molecules (including small proteins)through the gel, as a probe into gel structure.11. Diffusion analysisHistorically the ultracentrifuge was used as atool for measuring the diffusion coefficients ofmacromolecules in solution using a procedureknown as 'boundary spreading'. How fast a sedi-menting boundary broadened out was a function ofthe diffusion coefficient (then by combining thediffusion coefficient with the sedimentation coef-ficient the molecular weight could be obtained via 445a relation known as the 'svedberg equation,).Nowadays the more rapid technique of dynu*i.light scattering is the method of choice for diffusionmeasurements, but for certain systems the analvti_cal ultracentrifuge has clear advantages. One ofthese is for the analysis of the diffusion of mole_cules or macromolecules through concentratedmedia, including gels and two-phase systems. Withthe latter it is possible to model membrane phenom_ena. Applied in this way, the ultracentrifuge is notbeing used as a sedimentation tool as such, butratherthe optical system alone is being used. A lowrotor speed is chosen simply to minimise convec_tion effects I l8 ] .12. The futureAs long as there is a need to measure the size,shape and interaction properties of macromole-cules in solution there will always be a need for theanalytical ultracentrifuge. True, for certain systemsthere are more powerful methods for weight, con-formation or interaction analysis but each methodhas its own limitations, usually relating to maxi-mum or minimum size of the macromolecule thatcan be studied, whether or not it can be crystallized,the minimum concentration required (a problemespecially relevant to resonance methods), and thepurity of the sample. The ultracentrifuge, with itsversatility, will, besides remaining a powerful toolin its own right, become an increasingly importantadditional technique used in conjunction with someof these other methods, whether, for a particularmacromolecular system, it be for example crystal-lography, NMR, light scattering, mass spectrome-try, chromatography or electrophoresis. The virtueof combining measurements from independenttechniques for confirmatory purposes or otherwiseshould never be ignored.Referencest I I S.E. Harding, A.J. Rowe and J.C. Horton(Editors), Analytical Ultacentrifugation inB ioc he mi stry and P o ly me r S c ience,Royal Societyof Chemistry, Cambridge, 1992,629 pp.[2] I. Fiebrig, S.E. Harding and S.S. Davis, Progr.Colloid Polym. Sci.,94 (1994) 66-73.t3l W.F. Stafford, III, in S.E. Harding, A.J. Rowe andJ.C. 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246.72 374.88 Tm <526F776520> Tj 1 0 0 1 275.52 375.12 Tm <616E6420> Tj 1 0 0 1 294.24 375.12 Tm <4A2E432E> Tj 0.24 Tc 1 0 0 1 96.72 362.40 Tm <486F72746F6E20> Tj 1 0 0 1 131.28 363.12 Tm <2820> Tj 1 0 0 1 135.84 362.40 Tm <456469746F727320> Tj 1 0 0 1 168.72 360.96 Tm <292C20> Tj 1 0 0 1 178.08 362.64 Tm <416E616C79746963616C20> Tj 1 0 0 1 227.04 362.64 Tm <5520> Tj 1 0 0 1 234.24 362.88 Tm <6C74726163656E747269667520> Tj 1 0 0 1 283.68 363.36 Tm <676174696F6E> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 405.36 722.16 Tm <7472656E647320> Tj 1 0 0 1 428.88 722.16 Tm <696E20> Tj 1 0 0 1 436.80 722.16 Tm <616E616C79746963616C20> Tj 1 0 0 1 471.60 722.16 Tm <6368656D69737472792C20> Tj 1 0 0 1 510.00 721.92 Tm <766F6C2E20> Tj 1 0 0 1 525.36 721.92 Tm <31332C20> Tj 1 0 0 1 536.88 721.68 Tm <6E6F2E20> Tj 1 0 0 1 551.04 721.68 Tm <66712C20> Tj 1 0 0 1 564.00 721.68 Tm <3139393420> Tj 1 0 0 1 582.96 719.52 Tm <2D> Tj 0.24 Tc /F3 10.0 Tf 1 0 0 1 365.52 686.16 Tm <696E20> Tj 1 0 0 1 380.88 686.16 Tm <42696F6368656D697374727920> Tj 1 0 0 1 445.44 686.40 Tm <616E6420> Tj 1 0 0 1 469.44 686.40 Tm <506F6C796D657220> Tj 1 0 0 1 513.36 685.92 Tm <536369656E636520> Tj 1 0 0 1 554.16 685.92 Tm <526F79616C> Tj 0.48 Tc 1 0 0 1 365.52 674.16 Tm <536F636965747920> Tj 1 0 0 1 401.52 674.16 Tm <6F6620> Tj 1 0 0 1 413.52 674.16 Tm <4368656D69737472792C20> Tj 1 0 0 1 464.40 674.16 Tm <43616D6272696467652C20> Tj 1 0 0 1 520.32 674.16 Tm <313939322C20> Tj 1 0 0 1 546.96 674.40 Tm <70702E20> Tj 1 0 0 1 563.76 673.92 Tm <36332D> Tj 0.96 Tc 1 0 0 1 365.52 661.92 Tm <38392E> Tj 0.48 Tc 1 0 0 1 342.48 648.24 Tm <6C6C336C20> Tj 1 0 0 1 365.52 649.68 Tm <532E452E20> Tj 1 0 0 1 386.16 649.68 Tm <48617264696E672C20> Tj 1 0 0 1 426.96 649.68 Tm <502E4A2E20> Tj 1 0 0 1 444.96 649.92 Tm <4D6F7267616E20> Tj 1 0 0 1 481.92 649.68 Tm <616E6420> Tj 1 0 0 1 500.64 649.68 Tm <4B2E20> Tj 1 0 0 1 513.36 649.68 Tm <50657472616B2C20> Tj 1 0 0 1 546.24 649.44 Tm <4A2E20> Tj 1 0 0 1 556.56 649.68 Tm <506879732E> Tj 0.72 Tc 1 0 0 1 365.76 637.44 Tm <4368656D2E2C393420> Tj 1 0 0 1 413.52 638.64 Tm <28313939302920> Tj 1 0 0 1 448.32 637.68 Tm <3937382E> Tj 0.48 Tc 1 0 0 1 342.24 623.76 Tm <4920> Tj 1 0 0 1 347.76 625.44 Tm <31345D20> Tj 1 0 0 1 365.52 625.20 Tm <502E4A2E20> Tj 1 0 0 1 389.76 625.20 Tm <4D6F7267616E2C20> Tj 1 0 0 1 435.36 625.20 Tm <532E452E20> Tj 1 0 0 1 462.00 625.44 Tm <48617264696E6720> Tj 1 0 0 1 506.16 625.20 Tm <616E6420> Tj 1 0 0 1 530.88 625.20 Tm <4B2E20> Tj 1 0 0 1 549.84 625.20 Tm <50657472616B2C> Tj 0.48 Tc 1 0 0 1 365.28 612.96 Tm <4D20> Tj 1 0 0 1 374.16 612.96 Tm <616320> Tj 1 0 0 1 384.96 613.20 Tm <726F6D6F6C6563756C65732C20> Tj 1 0 0 1 443.28 613.20 Tm <323320> Tj 1 0 0 1 457.68 614.16 Tm <28313939305C20> Tj 1 0 0 1 492.24 613.20 Tm <4D366C2E> Tj 0.48 Tc 1 0 0 1 342.24 599.28 Tm <7420> Tj 1 0 0 1 348.00 600.96 Tm <6C356C20> Tj 1 0 0 1 365.52 600.72 Tm <4D2E20> Tj 1 0 0 1 381.12 600.72 Tm <4D6573656C736F6E2C20> Tj 1 0 0 1 428.88 600.72 Tm <462E572E20> Tj 1 0 0 1 454.08 600.72 Tm <537461686C20> Tj 1 0 0 1 479.52 600.72 Tm <616E6420> Tj 1 0 0 1 498.48 600.72 Tm <4A2E20> Tj 1 0 0 1 509.28 600.96 Tm <56696E6F677261642C20> Tj 1 0 0 1 556.80 600.48 Tm <50726F632E> Tj 0.72 Tc 1 0 0 1 365.04 588.48 Tm <4E616C20> Tj 1 0 0 1 385.92 588.72 Tm <416361642E20> Tj 1 0 0 1 414.24 588.48 Tm <5363692E20> Tj 1 0 0 1 433.92 588.48 Tm <552E532E412E2C343320> Tj 1 0 0 1 481.20 589.44 Tm <28313935372920> Tj 1 0 0 1 516.24 588.48 Tm <3538312E> Tj 0.72 Tc 1 0 0 1 342.24 574.80 Tm <4920> Tj 1 0 0 1 347.76 576.48 Tm <6C366C20> Tj 1 0 0 1 365.28 576.48 Tm <572E20> Tj 1 0 0 1 380.88 576.48 Tm <4D3F696368746C652C20> Tj 1 0 0 1 421.92 576.48 Tm <696E20> Tj 1 0 0 1 432.72 576.24 Tm <532E452E20> Tj 1 0 0 1 453.36 576.48 Tm <48617264696E672C20> Tj 1 0 0 1 494.16 576.48 Tm <412E4A2E20> Tj 1 0 0 1 514.32 576.24 Tm <526F77652C20> Tj 1 0 0 1 545.28 576.24 Tm <616E6420> Tj 1 0 0 1 563.28 576.24 Tm <4A2E432E> Tj 0.24 Tc 1 0 0 1 365.52 564.00 Tm <486F72746F6E20> Tj 1 0 0 1 399.84 564.72 Tm <28456469746F7273292C20> Tj 1 0 0 1 446.16 564.24 Tm <416E616C79746963616C20> Tj 1 0 0 1 495.12 564.00 Tm <556C74726163656E7472696675676174696F6E> Tj 0.24 Tc 1 0 0 1 365.28 552.00 Tm <696E20> Tj 1 0 0 1 380.16 552.00 Tm <42696F6368656D697374727920> Tj 1 0 0 1 444.00 552.00 Tm <616E6420> Tj 1 0 0 1 467.52 552.24 Tm <506F6C796D657220> Tj 1 0 0 1 511.20 552.00 Tm <536369656E63652C20> Tj 1 0 0 1 554.40 552.00 Tm <526F79616C> Tj 0.48 Tc 1 0 0 1 365.28 539.76 Tm <536F636965747920> Tj 1 0 0 1 400.32 539.76 Tm <6F6620> Tj 1 0 0 1 411.36 539.76 Tm <4368656D69737472792C20> Tj 1 0 0 1 461.76 540.00 Tm <43616D6272696467652C20> Tj 1 0 0 1 516.72 540.00 Tm <313939322C20> Tj 1 0 0 1 543.36 540.24 Tm <70702E20> Tj 1 0 0 1 559.68 539.76 Tm <31343720> Tj 1 0 0 1 574.56 542.16 Tm <2D> Tj 0.96 Tc /F3 12.0 Tf 1 0 0 1 366.48 527.76 Tm <7237352E> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 342.00 513.60 Tm <4920> Tj 1 0 0 1 347.76 515.28 Tm <31375D20> Tj 1 0 0 1 365.52 515.04 Tm <482E20> Tj 1 0 0 1 377.76 515.04 Tm <43646C66656E20> Tj 1 0 0 1 409.68 515.28 Tm <616E64572E20> Tj 1 0 0 1 442.56 515.28 Tm <426F7263686172642C20> Tj 1 0 0 1 487.92 515.28 Tm <50726F672E20> Tj 1 0 0 1 515.28 515.04 Tm <436F6C6C6F696420> Tj 1 0 0 1 550.08 515.28 Tm <506F6C796D2E> Tj 0.72 Tc 1 0 0 1 365.04 502.80 Tm <2E5363692E2C20> Tj 1 0 0 1 387.12 502.56 Tm <383620> Tj 1 0 0 1 401.28 503.52 Tm <28313938392920> Tj 1 0 0 1 437.04 503.04 Tm <3130322E> Tj 0.72 Tc 1 0 0 1 342.00 488.64 Tm <4920> Tj 1 0 0 1 347.76 490.32 Tm <6C385D20> Tj 1 0 0 1 365.28 490.08 Tm <532E452E20> Tj 1 0 0 1 385.92 490.32 Tm <48617264696E6720> Tj 1 0 0 1 423.84 490.56 Tm <616E6420> Tj 1 0 0 1 441.84 490.56 Tm <4D2E502E20> Tj 1 0 0 1 465.12 490.56 Tm <546F6D62732C20> Tj 1 0 0 1 501.12 490.56 Tm <696E20> Tj 1 0 0 1 512.16 490.56 Tm <4B2E442E20> Tj 1 0 0 1 535.68 490.32 Tm <53636877656E6B65> Tj 0.24 Tc 1 0 0 1 365.04 477.84 Tm <616E6420> Tj 1 0 0 1 385.68 478.08 Tm <422E20> Tj 1 0 0 1 400.08 478.08 Tm <5261616220> Tj 1 0 0 1 427.92 479.04 Tm <28456469746F7273292C20> Tj 1 0 0 1 476.40 478.32 Tm <496E746572616374696F6E7320> Tj 1 0 0 1 534.72 478.08 Tm <696E20> Tj 1 0 0 1 547.92 478.08 Tm <50726F7465696E> Tj 0.48 Tc 1 0 0 1 365.04 465.60 Tm <53797374656D732C20> Tj 1 0 0 1 412.56 465.84 Tm <416268616E646C756E67656E20> Tj 1 0 0 1 486.48 466.08 Tm <64657220> Tj 1 0 0 1 510.96 465.84 Tm <416B6164656D696520> Tj 1 0 0 1 566.16 466.08 Tm <646572> Tj 0.48 Tc 1 0 0 1 365.28 453.60 Tm <57697373656E736368616674656E20> Tj 1 0 0 1 442.08 453.60 Tm <64657220> Tj 1 0 0 1 464.64 453.60 Tm <4444522C20> Tj 1 0 0 1 499.20 453.60 Tm <416B6164656D69652D5665726C61672C> Tj 0.72 Tc 1 0 0 1 365.28 441.12 Tm <4265726C696E2C20> Tj 1 0 0 1 399.12 441.12 Tm <313938392C20> Tj 1 0 0 1 425.28 441.60 Tm <70702E20> Tj 1 0 0 1 442.08 441.12 Tm <36352D37322C> Tj 0.24 Tc 1 0 0 1 342.96 400.32 Tm <5374657068656E20> Tj 1 0 0 1 386.64 400.56 Tm <452E20> Tj 1 0 0 1 400.80 400.56 Tm <48617264696E6720> Tj 1 0 0 1 442.80 400.80 Tm <697320> Tj 1 0 0 1 454.32 400.80 Tm <617420> Tj 1 0 0 1 468.00 400.80 Tm <74686520> Tj 1 0 0 1 486.96 400.80 Tm <4E6174696F6E616C20> Tj 1 0 0 1 531.60 400.56 Tm <43656E74726520> Tj 1 0 0 1 568.32 400.80 Tm <666F72> Tj 0.00 Tc 1 0 0 1 341.28 388.32 Tm <4D6163726F6D6F6C6563756C617220> Tj 1 0 0 1 427.92 388.32 Tm <487964726F64796E616D6963732C20> Tj 1 0 0 1 515.52 388.32 Tm <556E697665727369747920> Tj 1 0 0 1 571.92 388.56 Tm <6F66> Tj 0.24 Tc 1 0 0 1 341.52 376.08 Tm <4E6F7474696E6768616D20> Tj 1 0 0 1 411.36 376.08 Tm <5363686F6F6C20> Tj 1 0 0 1 457.92 376.32 Tm <6F6620> Tj 1 0 0 1 480.00 376.32 Tm <4167726963756C747572652C20> Tj 1 0 0 1 549.60 376.32 Tm <537566746F6E> Tj 0.24 Tc 1 0 0 1 341.52 363.60 Tm <426F6E696E67746F6E2C20> Tj 1 0 0 1 396.96 363.84 Tm <4C456C3220> Tj 1 0 0 1 424.80 363.84 Tm <7352442C20> Tj 1 0 0 1 452.88 363.84 Tm <554B2E> Tj 1.68 Tc /F3 26.0 Tf 1 0 0 1 73.68 290.64 Tm <6C6E746572707265746174696F6E20> Tj 1 0 0 1 232.80 290.88 Tm <616E6420> Tj 1 0 0 1 281.28 291.12 Tm <616E616C7973697320> Tj 1 0 0 1 381.12 291.36 Tm <6F6620> Tj 1 0 0 1 409.44 291.60 Tm <636F6D706C6578> Tj 1.92 Tc /F3 27.0 Tf 1 0 0 1 72.72 262.56 Tm <656E7669726F6E6D656E74616C20> Tj 1 0 0 1 242.40 263.04 Tm <6461746120> Tj 1 0 0 1 297.84 263.52 Tm <7573696E6720> Tj 1 0 0 1 366.48 263.76 Tm <6368656D6F6D6574726963> Tj 1.68 Tc /F3 26.0 Tf 1 0 0 1 73.68 234.96 Tm <6D6574686F6473> Tj 0.96 Tc /F3 12.0 Tf 1 0 0 1 72.96 196.08 Tm <5269636861726420> Tj 1 0 0 1 123.60 196.08 Tm <4A2E20> Tj 1 0 0 1 138.24 196.32 Tm <57656E6E696E67> Tj 0.00 Tc 1 0 0 1 73.20 183.12 Tm <506F72746C616E642C20> Tj 1 0 0 1 123.84 183.36 Tm <4D452C20> Tj 1 0 0 1 148.56 183.12 Tm <555341> Tj 0.96 Tc 1 0 0 1 72.72 166.08 Tm <476572616C6420> Tj 1 0 0 1 116.64 166.32 Tm <412E20> Tj 1 0 0 1 133.92 166.32 Tm <457269636B736F6E20> Tj 1 0 0 1 192.24 171.36 Tm <78> Tj 0.48 Tc 1 0 0 1 74.64 153.12 Tm <53656174746C652C20> Tj 1 0 0 1 117.60 153.60 Tm <57412C20> Tj 1 0 0 1 142.56 153.36 Tm <555341> Tj 0.48 Tc 1 0 0 1 72.48 128.16 Tm <416E20> Tj 1 0 0 1 90.96 128.16 Tm <6F7665727669657720> Tj 1 0 0 1 143.28 128.40 Tm <6F6620> Tj 1 0 0 1 156.96 128.40 Tm <74686520> Tj 1 0 0 1 177.60 128.64 Tm <6170706C69636174696F6E20> Tj 1 0 0 1 240.96 128.88 Tm <6F6620> Tj 1 0 0 1 254.88 128.88 Tm <6368656D6F6D652D> Tj 0.72 Tc 1 0 0 1 72.24 115.44 Tm <7472696320> Tj 1 0 0 1 92.88 115.44 Tm <6461746120> Tj 1 0 0 1 118.80 115.44 Tm <616E616C7973697320> Tj 1 0 0 1 166.80 115.92 Tm <6D6574686F647320> Tj 1 0 0 1 216.24 115.92 Tm <746F20> Tj 1 0 0 1 229.92 115.92 Tm <636F6D706C657820> Tj 1 0 0 1 278.40 116.40 Tm <6368656D2D> Tj 0.72 Tc 1 0 0 1 72.72 102.48 Tm <6963616C20> Tj 1 0 0 1 94.08 102.48 Tm <6D6978747572657320> Tj 1 0 0 1 144.24 102.72 Tm <696E20> Tj 1 0 0 1 156.24 102.96 Tm <766172696F757320> Tj 1 0 0 1 198.96 102.96 Tm <656E7669726F6E6D656E74616C20> Tj 1 0 0 1 279.12 103.44 Tm <6D65646961> Tj 0.48 Tc 1 0 0 1 72.96 89.52 Tm <697320> Tj 1 0 0 1 86.88 90.24 Tm <70726573656E7465642E20> Tj 1 0 0 1 149.28 90.00 Tm <5265766965777320> Tj 1 0 0 1 199.20 90.24 Tm <6F6620> Tj 1 0 0 1 214.56 90.24 Tm <73656C656374656420> Tj 1 0 0 1 264.72 90.48 Tm <7265736561726368> Tj 0.72 Tc 1 0 0 1 72.48 76.56 Tm <61726520> Tj 1 0 0 1 93.84 77.28 Tm <676976656E20> Tj 1 0 0 1 127.68 76.80 Tm <617320> Tj 1 0 0 1 144.48 77.04 Tm <6578616D706C657320> Tj 1 0 0 1 200.88 77.28 Tm <6F6620> Tj 1 0 0 1 215.52 77.28 Tm <74686520> Tj 1 0 0 1 236.88 77.52 Tm <6170706C69636174696F6E20> Tj 1 0 0 1 301.20 77.76 Tm <6F66> Tj 0.72 Tc 1 0 0 1 72.72 64.32 Tm <7072696E636970616C636F6D706F6E656E747320> Tj 1 0 0 1 192.24 64.32 Tm <616E616C7973697320> Tj 1 0 0 1 239.04 64.56 Tm <616E6420> Tj 1 0 0 1 261.12 64.56 Tm <6F7468657220> Tj 1 0 0 1 291.60 64.80 Tm <7374612D> Tj 0.72 Tc 1 0 0 1 72.24 50.64 Tm <746973746963616C20> Tj 1 0 0 1 116.88 51.12 Tm <6D6574686F647320> Tj 1 0 0 1 172.08 51.36 Tm <746F20> Tj 1 0 0 1 191.28 51.60 Tm <6964656E7469667920> Tj 1 0 0 1 239.28 51.60 Tm <636F6E747269627574696F6E73> Tj 0.72 Tc 1 0 0 1 72.24 38.16 Tm <66726F6D20> Tj 1 0 0 1 100.08 38.40 Tm <6D756C7469706C6520> Tj 1 0 0 1 145.44 38.40 Tm <736F757263657320> Tj 1 0 0 1 191.28 38.64 Tm <6F6620> Tj 1 0 0 1 203.76 38.64 Tm <636F6E74616D696E6174696F6E20> Tj 1 0 0 1 283.44 39.12 Tm <696E20> Tj 1 0 0 1 294.72 39.12 Tm <6169722C> Tj 0.72 Tc 1 0 0 1 72.24 25.44 Tm <77617465722C20> Tj 1 0 0 1 108.48 25.68 Tm <736564696D656E74732C20> Tj 1 0 0 1 170.88 25.68 Tm <616E6420> Tj 1 0 0 1 194.40 25.92 Tm <62696F74612E20> Tj 1 0 0 1 227.28 26.16 Tm <4F7468657220> Tj 1 0 0 1 260.16 26.16 Tm <6578616D706C6573> Tj 0.72 Tc 1 0 0 1 72.48 12.48 Tm <61726520> Tj 1 0 0 1 93.84 12.48 Tm <636974656420> Tj 1 0 0 1 124.80 12.72 Tm <7468617420> Tj 1 0 0 1 150.72 12.96 Tm <696C6C7573747261746520> Tj 1 0 0 1 202.56 13.20 Tm <686F7720> Tj 1 0 0 1 229.68 13.20 Tm <736369656E746973747320> Tj 1 0 0 1 286.32 13.44 Tm <68617665> Tj 0.72 Tc 1 0 0 1 341.28 197.04 Tm <7573656420> Tj 1 0 0 1 371.52 197.28 Tm <636C617373696669636174696F6E20> Tj 1 0 0 1 446.88 197.52 Tm <616E6420> Tj 1 0 0 1 470.88 197.52 Tm <72656772657373696F6E20> Tj 1 0 0 1 533.28 197.76 Tm <6D6574686F6473> Tj 0.72 Tc 1 0 0 1 340.80 184.08 Tm <746F20> Tj 1 0 0 1 357.12 184.32 Tm <6D6F64656C20> Tj 1 0 0 1 395.52 184.32 Tm <74686520> Tj 1 0 0 1 417.60 184.56 Tm <646973747269627574696F6E20> Tj 1 0 0 1 485.04 184.56 Tm <6F6620> Tj 1 0 0 1 500.88 184.56 Tm <616E7468726F706F67656E6963> Tj 0.72 Tc 1 0 0 1 341.04 171.12 Tm <636F6E74616D696E616E747320> Tj 1 0 0 1 418.56 171.60 Tm <616E6420> Tj 1 0 0 1 442.56 172.56 Tm <7072656469637420> Tj 1 0 0 1 483.36 171.60 Tm <746865697220> Tj 1 0 0 1 511.68 171.84 Tm <656E7669726F6E6D656E2D> Tj 0.48 Tc 1 0 0 1 340.80 158.40 Tm <74616C20> Tj 1 0 0 1 357.12 158.40 Tm <6566666563747320> Tj 1 0 0 1 396.96 158.64 Tm <6F7220> Tj 1 0 0 1 410.88 158.64 Tm <666174652E> Tj 0.96 Tc 1 0 0 1 341.52 117.84 Tm <312E20> Tj 1 0 0 1 358.08 117.84 Tm <6C6E74726F64756374696F6E> Tj 0.48 Tc 1 0 0 1 353.28 90.72 Tm <456E7669726F6E6D656E74616C20> Tj 1 0 0 1 426.24 91.20 Tm <736369656E746973747320> Tj 1 0 0 1 471.84 91.44 Tm <61726520> Tj 1 0 0 1 488.40 91.44 Tm <636F6E66726F6E74656420> Tj 1 0 0 1 543.12 91.68 Tm <7769746820> Tj 1 0 0 1 566.40 91.68 Tm <746865> Tj 0.48 Tc 1 0 0 1 341.04 78.00 Tm <6461756E74696E6720> Tj 1 0 0 1 387.36 78.24 Tm <7461736B20> Tj 1 0 0 1 410.40 78.24 Tm <6F6620> Tj 1 0 0 1 424.56 78.48 Tm <617373657373696E6720> Tj 1 0 0 1 472.56 78.72 Tm <65636F73797374656D20> Tj 1 0 0 1 526.80 78.72 Tm <616E6420> Tj 1 0 0 1 548.40 78.72 Tm <68756D616E> Tj 0.48 Tc 1 0 0 1 341.28 65.04 Tm <6865616C746820> Tj 1 0 0 1 373.68 65.04 Tm <696D706163747320> Tj 1 0 0 1 413.52 65.52 Tm <61726973696E6720> Tj 1 0 0 1 448.56 65.76 Tm <66726F6D20> Tj 1 0 0 1 474.48 65.76 Tm <6120> Tj 1 0 0 1 482.64 65.76 Tm <6D756C74697475646520> Tj 1 0 0 1 531.36 65.76 Tm <6F6620> Tj 1 0 0 1 544.80 65.76 Tm <6D6F6465726E> Tj 0.48 Tc 1 0 0 1 341.04 52.08 Tm <64617920> Tj 1 0 0 1 361.44 52.32 Tm <706F6C6C7574616E74732E20> Tj 1 0 0 1 414.00 52.56 Tm <46726F6D20> Tj 1 0 0 1 442.32 52.80 Tm <74686520> Tj 1 0 0 1 459.60 52.80 Tm <626173696320> Tj 1 0 0 1 486.48 52.80 Tm <737465707320> Tj 1 0 0 1 513.36 52.80 Tm <6F6620> Tj 1 0 0 1 525.84 52.80 Tm <6461746120> Tj 1 0 0 1 548.40 52.80 Tm <636F6C6C65632D> Tj 0.48 Tc 1 0 0 1 341.28 39.36 Tm <74696F6E2C20> Tj 1 0 0 1 369.84 39.36 Tm <6461746120> Tj 1 0 0 1 396.96 39.60 Tm <616E616C797369732F73747275637475726520> Tj 1 0 0 1 489.60 40.08 Tm <696E746572707265746174696F6E2C20> Tj 1 0 0 1 563.76 40.32 Tm <616E64> Tj 0.48 Tc /F3 10.0 Tf 1 0 0 1 348.00 17.52 Tm <2A20> Tj 1 0 0 1 355.92 13.68 Tm <436F72726573706F6E64696E6720> Tj 1 0 0 1 420.72 14.16 Tm <617574686F722E> Tj ET endstream endobj 71 0 obj 22134 endobj 72 0 obj << /Length 73 0 R >> stream 446centrifugation in Biochemistry and PolymerScience, Royal Society of Chemistry, Cambridge,1992, pp.359-393.[4] S.E. Harding, in S.E. Harding and A.J. Rowe(Editors), Dynamic Properties of BiomolecularAssemblies, Royal Society of Chemistry,Cambridge, 1989, pp. 32-56.[ 5l J. Garcia de la Torre, ( 1989) in S.E. Harding andA.J. Rowe (Editors), Dynamic Propenies ofBiomolecular Assemblies, Royal Society ofChemistry, Cambridge, 1989, pp. 3-31.[6]J. Garcia de la Torre and V.A. Bloomfield,Biopolymers, 16 (1977 ) 177 9.t7l S.J. Perkins, in S.E. Harding and A.J. Rowe(Editors), Dynamic Properties of BiomolecularAssemblies, Royal Society of Chemistry,Cambridge, 1989, pp. 226-245.[8]J. Garcia de la Torre and V.A. Bloomfield,Biochemistry, l9 (1980) 5118.t9l S.E. Harding, G. Berth, A. Ball, J.R. Mitchell andJ. Garcia de la Torre, Carbohydr. Polym., 16(1991) l.t l0l O. Smidsrod and I.-L. Andresen, Bio'polymerkjemi, Tapir, Trondheim, 1979,383 pp.I I I ] E.N. Marsh and S.E. Harding, Biochem. J., 290(1993) 551.I l2] T.M. Laue, in S.E. Harding, A.J. Rowe and J.C.Horton ( Editors ), Analytical U ltracentrifu gation trends in analytical chemistry, vol. 13, no. fq, 1994 -in Biochemistry and Polymer Science RoyalSociety of Chemistry, Cambridge, 1992, pp. 63-89.ll3l S.E. Harding, P.J. Morgan and K. Petrak, J. Phys.Chem.,94 (1990) 978.I 14] P.J. Morgan, S.E. Harding and K. Petrak,M ac romolecules, 23 (1990\ M6l.t l5l M. Meselson, F.W. Stahl and J. Vinograd, Proc.Nal Acad. Sci. U.S.A.,43 (1957) 581.I l6l W. M?ichtle, in S.E. Harding, A.J. Rowe, and J.C.Horton (Editors), Analytical Ultracentrifugationin Biochemistry and Polymer Science, RoyalSociety of Chemistry, Cambridge, 1992, pp. 147 -r75.I 17] H. Cdlfen andW. Borchard, Prog. Colloid Polym..Sci., 86 (1989) 102.I l8] S.E. Harding and M.P. Tombs, in K.D. Schwenkeand B. Raab (Editors), Interactions in ProteinSystems, Abhandlungen der Akademie derWissenschaften der DDR, Akademie-Verlag,Berlin, 1989, pp. 65-72,Stephen E. Harding is at the National Centre forMacromolecular Hydrodynamics, University ofNottingham School of Agriculture, SuftonBonington, LEl2 sRD, UK. lnterpretation and analysis of complex environmental data using chemometric methods Richard J. WenningPortland, ME, USAGerald A. Erickson xSeattle, WA, USAAn overview of the application of chemome-tric data analysis methods to complex chem-ical mixtures in various environmental mediais presented. Reviews of selected researchare given as examples of the application ofprincipalcomponents analysis and other sta-tistical methods to identify contributionsfrom multiple sources of contamination in air,water, sediments, and biota. Other examplesare cited that illustrate how scientists have used classification and regression methodsto model the distribution of anthropogeniccontaminants and predict their environmen-tal effects or fate.1. lntroductionEnvironmental scientists are confronted with thedaunting task of assessing ecosystem and humanhealth impacts arising from a multitude of modernday pollutants. From the basic steps of data collec-tion, data analysis/structure interpretation, and * Corresponding author. endstream endobj 73 0 obj 3141 endobj 74 0 obj << /Length 75 0 R >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj69 Do Q endstream endobj 75 0 obj 45 endobj 76 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 6 0 R >> /XObject << /Obj69 69 0 R >> /Subtype 72 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 68 0 R 74 0 R 70 0 R ] >> endobj 11 0 obj << /Kids [ 12 0 R 22 0 R 31 0 R 40 0 R 49 0 R 58 0 R 67 0 R 76 0 R ] /Count 8 /Type /Pages >> endobj xref 0 1 0000000000 65535 f 11 1 0000924783 00000 n 68 9 0000829323 00000 n 0000829402 00000 n 0000898978 00000 n 0000921167 00000 n 0000921190 00000 n 0000924386 00000 n 0000924408 00000 n 0000924508 00000 n 0000924528 00000 n trailer << /Size 77 /Info 1 0 R /Root 13 0 R /Prev 828994 >> startxref 924898 %%EOF