?_¹ ÿÿÿÿî©   lpž*g ü‚ ƒ‚ÿ‚ƒ.ƒ1‚ ‡ À&†&ÿƒÀÿ­ÿ‰€&­ “& MathTypeð…ûžý³‚ŠSymbol  ýÒ|íwÛ|íwÐgïw  ý …-‡2 õƒ[y…ûžý³‚ŠSymbol  ]Ò|íwÛ|íwÐgïw  ] …-…ð‡2 ƒ]y…ûþü³‚ŠSymbol  þÒ|íwÛ|íwÐgïw  þ …-…ð‡2 ü6ƒ{y…ûþü³‚ŠSymbol  ^Ò|íwÛ|íwÐgïw  ^ …-…ð‡2 üÈ%ƒ}y„û þ‚ŠSymbol  ÿÒ|íwÛ|íwÐgïw  ÿ …-…ð‡2 !ƒòy‡2 @ ƒòy„û€þ‚ŠSymbol  _Ò|íwÛ|íwÐgïw  _ …-…ð‡2 ƒay‡2 ƒ+y‡2  ƒ-y„û€þƒŸTimes New RomanÛ|íwÐgïw  ƒ …-…ð‡2 #ƒdM‡2 !ƒMM‡2 ̃cM‡2 %ƒMM‡2 áƒcM‡2 RƒdM‡2 DƒtM‡2  ƒrM‡2 ÷ƒMM‡2 D ƒMM‡2  ƒcM‡2 âƒtM‡2 ªƒrM‡2 TƒaM„û€þ‚¥Times New RomanÛ|íwÐgïw  ` …-…ð‡2 "ƒ)M‡2 € ƒ(M‡2 ^ƒln‡2 €ƒ)n‡2 •ƒ(n‡2 ȃ)n‡2 Žƒ,n‡2 pƒ,n‡2 ƒƒL(‡2 à ƒ)(‡2 Ž ƒ((‡2 fƒ)(‡2 Rƒ,(‡2  ƒ(( ‡2 :…Mine„ûÀþ‚¥Times New RomanÛ|íwÐgïw   …-…ð‡2 Hƒ2i ‡2 `@…c(M) †& ÿ…û‚Œ™"SystemwŽf4Š ‰Š …-…ð„.€€ÿÒ_^YÉÂWÈu0ƒù"v+ŽÀ3Ò&>NEu&‹Ž°$øÁè;Ârùë/Ø&‹øë'‹Øž ‰Fö Àt Pèfó[‹Fö邋F Ft5ÿvÿèÂ÷ƒÄ‹FÞÈ ‰Fè‹Fâ+È ‰Fì‹FêF…‡2 Ššƒ)ÿ^èÿÿ²ÿÜÿÿôÿ‰v°ÇF²€NŽÇF¶KÇFžÇFºÁçÄƒÄ ‰Fö Àt Pè‚ô[‹FöéÁ‹F Ft8ó‹ð÷f ‘‹F ÷æÑr ;Vwré;FvN3ÒúuW‹^öÁãğ‹óŒFú&öGu* ÿtÿ‹È÷f ‘÷f Ñr ;Vwr ;Fv+F V _Éʐjjš’€Ožÿÿ^_ÉÊÈBWV!³ITCOMMCHARÎGLOBALGETATOMNAMEžéáÔ Òu)Ç ‰hWjjh†w;2Ÿw ötLÎs 3Àºðÿã0ë?&¡r =tºOWWOWWOWWOWWOWWOWWOWWOW ÿüg&‹Ø‰^üŒFþ&‹#Fð©ÿu鞃~u &öGOWWOWWOWWOWWOWWOWWOWWOWOWWOWWOWWOWWOWWOWWOWWOWÎM 6QÆ\ p2QpŸg§ *2Q*§`6Qš`fþ6Q^ Í72QÎ7V*!ó46Q~4Ví 2QŽ'ý æ=2Qæ=~m]Qn]NN46Q4Æ^j2Qj®kV2Qð ÀtéÏÿvüÿvúÿvÿvšÿÿÄ^&ƒ?ڎÂ3À3ö3ÿ¹ÿÿ Ût&€>étò®F®uú‹ ¬C6Q¬CÆŽ Å#6QÆ#ÆÇ 6Q&Ñ ö_Iã&‹6; uQVW¿ ¹ó§_^Yt&ELEASE@CSTDMALLOC@@VEAKXZt?AL/&;)z4ÿÿ:ÿÿÿÿ|CONTEXTnæ|CTXOMAPɱ|FONT¿|KWBTREE¶|KWDATAŽŽ|KWMAPùµ|SYSTEMùJ|TOPIC?K|TTLBTREE?Î|bm0|bm1è |bm2Ý|bm3å|bm4"|bm5#+|bm6„3|bm7O<|bm8}Dõìlp'g@ž  ‚ ƒ‚ÿ‚ƒ.ƒ1‚ ‡ à#†&ÿƒÀÿœÿ‰ #œ “& MathTypeð…ûžý³‚ŠSymbol‹ äÒ|íwÛ|íwÐgïw‹ ä …-‡2 õƒ[y…ûžý³‚ŠSymbolÀ Ò|íwÛ|íwÐgïwÀ  …-…ð‡2 ƒ]y…ú…-‡€õ‡”õ‡€‡”…ûÜü³‚ŠSymbol‹ åÒ|íwÛ|íwÐgïw‹ å …-…ð‡2 ü6ƒ{y…ûÜü³‚ŠSymbolÀ Ò|íwÛ|íwÐgïwÀ  …-…ð‡2 üä"ƒ}y„û þ‚ŠSymbol‹ æÒ|íwÛ|íwÐgïw‹ æ …-…ð‡2 !ƒòy‡2 @ ƒòy„û€þ‚ŠSymbolÀ Ò|íwÛ|íwÐgïwÀ  …-…ð‡2 4 ƒ¢y‡2 4݃¢y‡2 ƒay‡2 ƒ+y‡2  ƒ-y„û€þƒ¥Times New RomanÛ|íwÐgïw‹ ç …-…ð‡2 5 ƒdM‡2 ÷ƒMM‡2 ƒcM‡2 RƒdM‡2 DƒtM‡2  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RomanÛ|íwÐgïw^ Œ …-…ð‡2 ô ƒs0‡2 +ç ƒM0‡2 íƒa0‡2 +ƒv0‡2 —ƒM0‡2 4ƒv0 †& ÿ…û‚Œ™"Systemw\ fZŠ ‰Š …-…ð‡2 €FƒK‡ûRƒ*y„û€þ‚ Times New RomanÛ|íwÐgïw| 쁅-…ð‡2 €œ*‚y‡2 €e)ƒ*y‡2 €{'‚y‡2 €ã#ƒ*y‡2 €‚y‡2 €mƒ(y‡2 €­‚y‡2 €¢ƒ,y‡2 €g‚y‡2 €§ƒ(y‡2 €A‚y‡2 €Œ ƒ)y‡2 € ‚y‡2 €O ƒ(y„ûÀþ‚¥Times New RomanÛ|íwÐgwJ ' …-…ð‡2 !ƒNy‡2 ÿAƒiy‡2 $*ƒiy‡2 à¢$ƒiy‡2 Úƒiy‡2 ÿMƒry™2 "SystemwfóŠ „Š…-…ðÝD ‹Fì‰Džév=Ru73ɋVø÷¬tQú®rý32Qþ3žC2QD–Ïý2Q[MM‹å]MËXEU‹ìŽØž ŽØÇ  "‹Fö+FòÄ^&9G ~éÄ^‹Fò&G ÿ¡OWWOWWOWWOWWOWWOWWOWWOWÿÿÿÿƒ‡„¶‡˜¶‡!20ÿÿ ÿ EU‹ìŽØžüPèÍžÿPèŃí‹å]MlpüÂ ì ‚ ƒ‚ÿ‚ƒ.ƒ1‚ ‡ €€†&ÿƒÀÿÀÿ‰@@ “& MathTypeP„û€þ‚¥Times New Roman*‚íwÀgïw»  …-‡2 àà ƒ]‡2 à· ƒ23 ‡2 à+…exp[‡2 à/ƒ)y‡2 àïƒ(„ûÀþ‚¥Times New Roman*‚íwÀgïwå Ü …-…ð‡2 4y ƒ23‡2 4Vƒ)x‡2 4¬ƒ2y‡2 41ƒ(3„û€þ‚ŠSymbol» !‚íw*‚íwÀgïw»  …-…ð‡2 à2 ƒtx‡2 àäƒ-y‡2 àƒ=3‡2 àƒtx„û€þƒ¥Times New Roman*‚íwÀgïwå Ý …-…ð‡2 àŠ ƒDq‡2 àIƒg3 †& ÿ…û ‚Œ™"Systemwèf£Š ‰Š …-…ðÄOWWOWWOWWOWWOWWOWWOWWOWOWWOWWOWWOWWOWWOWWOWWOWç ƒM0‡2 íƒa0‡2 +ƒv0‡2 —ƒM0†2  ÿ¿SEEK_LREAD_LWRITEWWINTLSDM '‚M‚i‚n ‚c‚($ ÿTimes New RomanÛ|íwÐgïw| ìž‚(ƒM‚)‚L‚(ƒM‚,ƒþÿ"  lpÞø X‚ …‚ÿ‚….ƒ1‚ ‡  †&ÿƒÀÿŠÿ‰ÀF “& MathType…ûþÝ‚ŽSymbol…-‡2 î߃(…ûþÝ‚ŽSymbol…-…ð‡2 î¶ ƒ) …úƒ"…-‡ ̇  …ûþÝ‚ŽSymbol…-…ð‡2 (…ûþÝ‚ŽSymbol…-…ð‡2 îSƒ)‡ ‡‡ £„ûàþ‚—Times New Roman…-…ð‡2 8у2 ‡2 àç…dim‡2 ÔRƒ)‡2 Ôƒ(‡2 84 ƒ2 ‡2 àJ…dim‡2 Ô—ƒ)‡2 Ô‡ƒ(„û€þ‚—Times New Roman…-…ð‡2 €< ƒ,„ûàþƒ—Times New Roman…-…ð ‡2 Pĉmonomer‡2 àǃer ‡2 Ôˆ‡molar ‡2 P'‰monomer‡2 à* ƒer ‡2 Ôö…abs„û€þƒ—Times New Roman…-…ð‡2 ð ƒc‡2 €4ƒc‡2 €Ø ƒK‡2 ðWƒa‡2 €ƒa‡2 €FƒK„û€þ‚ŽSymbol…-…ð‡2 €Iƒ=‡2 €Žƒ= †& ÿ…û‚Œ"Systemn…-…ð”Times New Ro ÿ„d 0xf…b30cd‹åX­X­…PIC;ƒÿ$L ‡META9‚ ÿ – MÐQè¶LƒÄ3ÿjEÐPèýKƒÄÿþÿ„…ð‡2 "ø ƒn  {ï{ï{ï{ï{ï{ï{ï{÷œ÷œ÷œ÷œ÷œ÷œÿÿÿ ELECTORLIMITœ ALLOCALIAS¬P7Kƒ < ‹\0G.J&ÿ¡3Àë‹FPè=ûŽÀ&‹&‹G_ÉÂU‹ìÿÿl@$l@ã…m@:µn@;ROGRA~1\OLDWORD6\WINWORD.EXEWNl@$l@ã…m@:…n@;™"SystemwŸf’Š ‡2 "ø ƒn ‡2 t+‚ab‹ž Enty¿OWWOWWOWWOWWOWWOWWOWWOW replace the selected table of ÀŽZ$”њþ•$ôw%ö€àŠfŠ>9 ȁƒ ÿàèýžÉÊÈV‹Nƒùÿt3ƒ>Œu,OWWOWWOWWOWWOWWOWWOWWOWôPš×‹ð ötLÿvö†ÈþPVš‹Æ‹N…‚ÿ‚….ß–(–) ˆ1ˆ3O ,6Q,&f ó6Qów ï22Qð2nOWWOWWOWWOWWOWWOWWOWWOWÿŸOWWOWWOWWOWWOWWOWWOWWOWU…ÿQn]6N46Q4.^j2Qj&kV2Q(–FúC2QúCfiž2Qžnw«%2Q¬%OWWOWWOWWOWWOWWOWWOWWOW-!-øšÏ£6 Model 5 Stepping 3, GenuineIn…é‘ ‡2 ×—…ë‘  ÿŸ¿ä ¿¿ ¿¿| ¿¿ž ¿¿è ¿¿4 ¿¿aXlp] Àv ÄS‚ …‚ÿ‚….ƒ1‚ ‡   †&ÿƒÀÿôà ” “& MathTypeð …úƒ"…-‡`̇`× „ûàþƒ—Times New RomanE…- ‡2 L÷‰monomer ‡2 "h‡molar ‡2 ö…abs„û€þƒ—Times New Roman…-…ð‡2 ΞƒK‡2 ÀFƒK„û€þ‚ŽSymbol…-…ð‡2 ì/ƒe‡2 ÀŽƒ=„ûàþ‚—Times New RomanE…-…ð‡2 "2 ƒ)‡2 "ùƒ(‡2 —ƒ)‡2 ‡ƒ(„û€þ‚—Times New Roman…-…ð‡2 Îæƒ2S·&œMathTypeUU ƒK ‚(ƒaƒbƒs‚)Ž †=ˆ2ƒK ‚(ƒmƒoƒlƒaƒr‚)ª „µ ƒmƒoƒnƒoƒmƒeƒr †& ÿ…û‚Œ"Systemn…-…𠂐–Symbolan…-…ð†2 ð ƒc‡2 €4ƒc†2 €Ø ƒK‡2 ðWƒa†2 €ƒa‡2 €FƒK„û€þ‚ŽSymbol…-…ð‡2 €Iƒ=†2 €Žƒ= †& ÿ…û‚Œ"Systemn…-…ð‘Times New Roÿ…d 0xf…b30cd‹åX­X­Ÿƒc ƒmƒoƒnƒo"ƒÿ$L—icrosoft Equation 3.0 …DS Eq"‚ ÿ – MÐQè¶LƒÄ3ÿjEÐPèýKƒÄÿþÿ„…ð‡2 "ø ƒn  {ï{ï{ï{ï{ï{ï{ï{÷œ÷œ÷œ÷œ÷œ÷œÿÿÿ ARDWNDCLASSOleOleOleƒ < ‹\0G.Jÿ¡3Àë‹FPè=ûŽÀ&‹&‹G_ÉÂU‹ìÿÿl@$l@ã…m@:µn@;ROGRA~1\OLDWORD6\WINWORD.EXEWNl@$l@ã…m@:¥n@;OWWOWWOWWOWWOWWOWWOWWOW‡2 "ø ƒn ‡2 t+‚ab‹ž Enty¿OWWOWWOWWOWWOWWOWWOWWOW replace the selected table of ÀŽ‚i‚mƒeƒr ƒcfŠ>9 ȁƒ ÿàèýžÉÊÈV‹Nƒùÿt3ƒ>Œu,OWWOWWOWWOWWOWWOWWOWWOWôPš×‹ð ötLÿvö†ÈþPVš‹Æ‹N…‚ÿ‚….ß–(–) ˆ1ˆ3O ,6Q,&f ó6Qów ï22Qð2nOWWOWWOWWOWWOWWOWWOWWOWÿŸOWWOWWOWWOWWOWWOWWOWWOWAËÂlp—ÀJ J‚ …‚ÿ‚….ƒ1‚ ‡  À†&ÿƒÀÿŠÿ‰€F “& MathType…ûþÝ‚ŽSymbol…-‡2 î߃(…ûþÝ‚ŽSymbol…-…ð‡2 î¶ ƒ) …úƒ"…-‡ ̇ ô …ûþÝ‚ŽSymbol…-…ð‡2 (…ûþÝ‚ŽSymbol…-…ð‡2 îAƒ)‡ u‡ „ûàþ‚—Times New Roman…-…ð‡2 8¶ƒ3‡2 Ô@ƒ)‡2 Ôƒ(‡2 8+ ƒ3‡2 Ô—ƒ)‡2 Ô‡ƒ(„û€þ‚—Times New Roman…-…ð‡2 €* ƒ,„ûàþƒ—Times New Roman…-…ð ‡2 P²‰monomer ‡2 àʇtrimer ‡2 Ôv‡molar ‡2 P'‰monomer ‡2 à?‡trimer ‡2 Ôö…abs„û€þƒ—Times New Roman…-…ð‡2 ðúƒc‡2 €ƒc‡2 €Æ ƒK‡2 ðWƒa‡2 €xƒa‡2 €FƒK„û€þ‚ŽSymbol…-…ð‡2 €7ƒ=‡2 €Žƒ= †& ÿ…û‚Œ"Systemn…-…ð‡stemn‚-!ƒ‚)— „µ ƒmƒoƒn …PIC;ƒÿ$L ‡META9 …úƒ"…-‚š† Îæƒ2S&œMathTypeUUew Roman…-…ðþÿþÿþÿþÿÿ&ƒ < 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This actioK ‚(ƒmƒoƒlƒaƒ ÀuéÃÿvúÄ^ü&ÿw&ÿwšÍ‰Fµ‚i‚mƒeƒr ƒc] Ö| ÄS›  –(–) ˆ2‡PIC ¿G68ŠFˆG ‹8ÁçÄœ&‹E &‹U -‹W‰Fô‰VöÿvòVšD ¿‰Fê‰Vì‹Â Fêuƒ"…-‡`Ì‡× „ûàþƒ§TimeOWWOWWOWWOWWOWWOWWOWWOW‰monomer ‡2 "h…molar‡2 ö…abs„û€þ‚—Times New Roman#|slpU ŒÀ¬  \‚ …‚ÿ‚….ƒ1‚ ‡  ` †&ÿƒÀÿžÿ‰ Ø “& MathTypeà …úƒ"…-‡ž‡ž¶…ûþÝ‚ŽSymbol…-‡2 Š£ƒ(…ûþÝ‚ŽSymbol…-…ð‡2 Ššƒ)‡^‡ „û€þ‚ŽSymbol…-…ð‡2 ŒŒƒr‡2 ŒÛƒ-‡2 ` ƒ=„û€þƒ—Times New Romanl…-…ð‡2 Œõƒv‡2 Œ„ƒD ‡2 nú…sRT‡2 `@ƒM„û€þ‚—Times New Roman8…-…ð‡2 Œñƒ1 †& ÿ…û‚Œ"Systemn…-…ðÀÿƒƒK‡2 ÀFƒK‡û€þƒ= †& ÿ…ð‡2 0Qƒe‡2 Àƒ= †& ÿ     O2„Æ ƒK‡2 ðWƒa‡2 xƒa‡2 €FƒK‚û"…ð‡2 €7ƒ=‡2 Žƒ= †& ÿ…û‚Œ"Systemn…-…ð‡stemn‚-„ûàþƒTimes Ne‚)Ø „µ ƒmƒoƒnƒnƒoƒmƒeƒr –(–ƒr ƒc ƒmƒo"ƒÿ‡ation Equation.3ô9²q‡META9 …úƒ"…-‚š† Îæƒ2S&œMathTypeUUew Roman…-…ðþÿþÿþÿþÿÿ&ƒ < ‹\0G.Jÿÿ¡OWWOWWOWWOWWOWWOWWOWWOWÿÿ¿OWWOWWOWWOWWOWWOWWOWWOWOWWOWWOWWOWWOWWOWWOWWOWl@$l@ã…m@:…n@;5f(žOWWOWWOWWOWWOWWOWWOWWOW„0Œ€’,àŠ\pŒ€æŸt$Wÿ6æ ÿ6ä š¿÷Æt:W÷Æt%¡ÈŸÂ‹Ø&‹&‹W‹ð‰VòWÿvš¢G'ŽÂ‹Ø&‹ F=lÀà: SEDFIT HelpBrowseButtons()€RwRÿÿÿÿ 9ÿÿÿÿE1Fÿÿÿÿ €ÿÿÿÿE^Acontents^ cÀ Nœ€€€‚‚€€‚€ƒãvy€‰€‚ƒãÝ¢Üü€‰€‚ƒãë €‚ƒã£,J€‚ƒãç¢X›€‰€‚ƒã.Á‰F€‰€‚‚ƒã³ŒX€‰€‚ƒãq€‰€‚ƒãÚ)–Ú€‰€‚‚ƒã¢lÛ¶€‰€‚ÿContentsdata handling and loadingload files (sedimentattion velocity or other)add filesload initial dataextrapolation of initial dataset number of data columnsgenerate DLS data fileramp rotor speedscan times from t or w2tignore spikessubtract calculated TI/RI noise from raw data ^Eo® *œ€€ƒã8\>Ȁ‰€‚ƒãÜñðU€‰€‚ƒãpKo퀉€‚‚ƒã%*m €‰€‚ƒã?P˜“€‰€‚ƒãuŒ+€‰€‚ƒã§e8€‰€‚ƒã0_íǀ‰€‚‚‚€€‚€ƒãÿÓü&€‰€‚ÿsort interference fringe offsetseliminate fringe jump within each scaneliminate jitteredit a filetransform intensity to absorbance filestransform intensity to 2 pseudo-absorbance filescorrect equilibrium scan for TI Noisesubtract blank scanLamm equation analysisindependent species model[c‡œ H·€€ƒãjˆ~ò€‰€‚ƒã&ƒDI€‰€‚ƒãœÞ€‰€‚ƒã©Î‹€€‰€‚ƒãtçR­€‰€‚ƒã&ÍíD€‰€‚ƒãš•fD€‰€‚ƒãœ„›B€‰€‚ƒã³ŒX€‰€‚ƒãq·/ñ€‰€‚ƒãa€‰€‚ÿmonomer-dimer modelmonomer-trimer modelmonomer-dimer-tetramer modelmonomer-tetramer-octamer modelnonideal, oncentration dependent sedimentation modelset sedimentation parametersswitch between unknown M or Drun sedimentationramp rotor speedgenerate sedimentation profilesstart fit#ioªº BÓ€€ƒã¯ÎP€‰€‚ƒãõ„"c€‰€‚ƒãB@-€‰€‚ƒãšÉ„&€‰€‚ƒãL »@€‰€‚ƒãšÉ„&€‰€‚ƒãgœKF€‰€‚ƒã׫À‰€‚ƒãw“‘\€‰€‚‚€€‚€ƒã²ÑJ±€‰€‚ÿspeed up fist Simplex fitset t0 time of sedimentationfit t0 time of sedimentationconstrain meniscus and bottomset s for changing Lamm algorithmconstrain meniscus and bottomspecial geometriesElectrophoresis geometryanalyze time-dependent s, MDistribution analysescontinuous c(s) by Lamm analysis{‡ž “ ô€÷€€ƒãz|•ý€‰€‚ƒã¡ë˜€‰€‚ƒã 똀‰€‚ƒã/zeD€‰€‚ƒã¬ÑJ±€‰€‚ƒã~2cE€‰€‚ƒã$©„€‰€‚ƒãCr ΀‰€‚ÿcontinuous Lamm analysis with prior constant diffusion coefficientcontinuous Lamm analysis with prior partial specific volume as function of Mcontinuous Lamm analysis c(s) with conformational changeg*(s) by least-squares direct boundary fittingcontinuous c(M) by Lamm analysistransform distributionsvan Holde-WeischetDLS analyses$_ªÜ Å X¿€€‚€€‚€ƒãžwœª€‰€‚ƒã¹Àk̀‰€‚ƒãÕ}€‰€‚ƒãD_€‚ƒãÑ1s…€‰€‚ƒãŽŠ€‰€‚ƒãþ°A‚€‰€‚ƒã㇏€‰€‚‚€€‚€ƒãt¥€‰€‚ƒãSèœD€‰€‚ÿStatisticsruns testF statisticscalculate variance ratiocalculate confidence intervalmake error contour mapsMonte-Carlo analysisRegularization by Tikhonov-Phillips 2nd derivativeRegularization by maximum entropydisplaying data and fitsset the plot rangetoggle residual plot on/offMž òÉ `›€€ƒãŠ‚œD€‰€‚ƒã?õ€‚ƒãϗ÷选€‚ƒã€L~©€‰€‚ƒã?žš<€‰€‚ƒãývÉۀ‰€‚ƒã¢lÛ¶€‰€‚‚‚€€‚€ƒãH’ùڀ‰€‚ƒãQÿ-s€‰€‚ƒãŽ©€‰€‚ƒã=†|]€‰€‚ÿtoggle data plot on/offdata mark sizedisplay filenamesdetailed simulation outputdisplay residuals as bitmapshow last fit info againsubtract calculated TI/RI noise from raw datadocumenting resultssave fitssave raw data setsave systematic noisesave distribution$[Ü "AÉ `·€€ƒãÔéЀ‰€‚ƒãØï•Ã€‰€‚ƒãÆÔA〉€‚ƒã劈€‰€‚ƒãÕÛ}€‰€‚ƒã©\o}€‰€‚‚‚€€‚€ƒã‘>.„€‰€‚ƒã¿–m®€‰€‚ƒã! qD€‰€‚ƒãœÆj4€‰€‚ƒã­ñA%€‰€‚ÿcopy fit parameterscopy plotscopy residuals bitmapò"A copy data tablesprintmake notesgeneral functions and parameterscalculate frictional coefficientscalculate sedimentation coefficient of spherical particleset partial specific volumechange filename conventions how to get help< ò^A0 0€€€ƒãž ]D€‰€‚ÿExit],"A»A1Wšƒÿÿÿÿ»AµEmodel, concentration dependent sedimentationî¶^A©D8 >€m€€‚€‚€ ‚€‚‚‚‚‚‚‚‚‚ÿConcentration Dependent SedimentationModel | Nonideal SedimentationThis model is only for a single non-ideal component. The nonideality is taken into account by the formulass = s0/(1+ks x c)D = D0 (1+kd x c)where s0 and D0 are the sedimentation and diffusion coefficients at infinite dilution, and ks and kd are non-ideality coefficients. The input of the coefficients ks and kd is in the form of the base 10 logarithm of this parameter (i.e. -2 for 0.01). The units of these coefficients are inverse signal units (e.g. 1/OD280), and for further interpretation should be converted by using appropriate extinction coefficients etc (taking into account the pathlength 1.2cm). æ»AµE& €Í€€‚‚‚ÿThe concentration dependence can be either due to repulsive or attractive interactions. In the repulsive case (default), ks and kd are positive, whereas the attractive case is implemented where both ks and kd are negative. d3©DF1ð €MŠÿÿÿÿF¥Mstatistics, calculate variance ratio (F-statistics)—XµE°H? L€±€€‚€‚€ ‚€‚ã¹Àk̀‰€‚‚‚ÿCalculate F-distributionOptions | Calculator | Calculate Variance Ratio (F-Statistics)For statistically comparing the quality of two fits, this function allows to calculate the variance (or sum of squares) increase that is associated with a given confidence level, for a given number of degrees of freedom. This is done using the F statistics - please see this help-page for more information. It is based on the assumption that we have two fits, both with a certain number of data points considered (n1, and n2), and both with a number of fitted parameters p1 and p2, respectively. žtFNK* "€é€€‚‚‚‚‚‚‚ÿInformation required is the following:1) the desired confidence level (e.g. 68% for one standard deviation, or 95%)2) the first degree of freedom - this is in general the total number of data points considered in the fit minus the number of fitting parameters, i.e. n1 minus p13) the second degree of freedom - n2 minus p2. Information output:1) The minimal increase of the sum of squares that would be required at the given confidence limit for deciding that the two fits are different. Conversely, if the sum of squares is lower than this critical value, the fits cannot be considered statistically distinguishable.¹°HTMM h€s€€‚‚€ € ‚€‚‚ƒã¹Àk̀‰€‚ƒãD_€‚ÿ2) The rmsd that this sum of squares ratio would correspond to, for the given fit. Please Note: The increase in the sum of squares should not be mistaken for the increase in the rmsd of the fit. If the comparison of the fits is made on the basis of the rmsd ratio, then the square root of the critical value given by this routine has to be taken as the cutoff value. See also:F statisticscalculate confidence intervalQ NK¥M1 2€@€€ƒãÑ1s…€‰€‚‚ÿmake error contour mapsb1TMN1MšƒhÿÿÿÿNþ‚calculator, sed-coefficient of spherical particleà¥M/€< F€Á€€‚€‚€ ‚€‚‚‚‚‚‚€ € ‚ÿCalculate s for spherical particleOptions | Calculator | Calculate s(M) for Spherical ParticleCalculates the expected sedimentation coefficient for a spherical particle of the given molar mass. Input required:1) the molar mass of the species in Da2) its partial specific volume in ml/g3) the temperature of the hypothetical experiment - please note: (this is for RT - factor in the Svedberg equation, not for any temperature correN/€¥Mction of v-bar or the viscosity)e2N”‚3 4€e€€‚€ €‚‚‚‚‚‚‚‚‚ÿ4) the buffer density5) the (absolute) viscosity of the buffer - please note: input is required here in Poise (i.e. 0.01002 for water at standard conditions) as is the output from sednterp.Output:1) a summary of the conditions specified2) the calculated s-value for a spherical particle (without hydration!)3) the hydrodynamic radius of the sphere4) the diffusion coefficient.The calculations are based on the formulas from the Laue et al article p. 90-125 in Harding et al (Eds): Analytical Ultracentrifugation in Biochemistry and Polymer Science.j6/€þ‚4 8€l€€‚‚‚ƒã‘>.„€‰€‚‚ÿSee also:calculate frictional coefficientsX'”‚Vƒ1/MŠŒÿÿÿÿVƒ-‰calculator, frictional and axial ratios:ýþ‚…= H€û€€‚€‚€ ‚€‚€ €€ €‚ÿCalculate axial and frictional coefficient ratiosOptions | Calculator | Calculate Axial and Frictional Coefficient RatiosFor calculation of axial ratios of elliptical shape models, once the Lamm equation modeling has revealed s and M. This functionality is similar to that of sednterp, but for convenience included here. The calculations are based on the formulas from the Laue et al article p. 90-125 in Harding et al (Eds): Analytical Ultracentrifugation in Biochemistry and Polymer Science.ÍVƒ—‡: B€›€€‚‚‚‚‚€ € ‚€‚€ €‚ÿInput:1) the molar mass of the species2) its sedimentation coefficient3) the partial-specific volume4) the temperature of the run - please note: (this is for RT - factor in the Svedberg equation, not for any temperature correction of v-bar or the viscosity)5) the buffer density6) the (absolute) viscosity of the buffer - please note: input is required here in Poise (i.e. 0.01002 for water at standard conditions) as is the output from sednterp.–Z…-‰< F€µ€€‚‚‚‚‚‚‚‚‚‚ƒã¿–m®€‰€‚‚ÿOutput:1) a summary of the conditions specified2) the hydrodynamic radius of the species3) the diffusion coefficient 4) the frictional coefficient ratio5) axial ratios for oblate and prolate ellipsoid models that would have the same frictional coefficient ratioSee also:calculate sedimentation coefficient of spherical particleH—‡u‰1hÆ ÿÿÿÿu‰5Ždistribution, transformæ-‰‹4 6€Í€€‚€‚€ ‚€‚‚‚‚‚ÿTransforming s-distributionsOptions | Size-Distribution Options | Transform s-Distribution to r-DistributionThis function allows several transformations of a previously calculated sedimentation cofficient distribution (e.g. obtained from ls-g*(s)). These can only be calcualted in sequence:1) s(app) into s(20) 2) c(s20) into a distribution of hydrodynmic radii c(R). (since s~r^2, a correction factor of 2r will be inserted for transformation of the integral ds into dr)~Pu‰ Ž. *€¡€€‚‚‚‚‚‚‚‚‚‚‚ÿ3) corrections for a radius-dependent signal contribution (such as caused by Mie scattering). For the correction of the signal, a file with the signal as a function of hydrodynamic radius must be provided, expressed in a power-seriessignal(r) = a0 + a1*r + a2*r^2 + a3*r^3 + ... (with r in units of nm)The format of the file should be a simple list of coefficients: a0a1a2with as many lines (and numbers) as coefficients to be taken into account. The distribution c(R) will be divided by this function signal(r), to give relative concentrations as a function of Stokes-radius R.(‹5Ž$ €€€‚‚ÿV% Ž‹Ž1 Œx†ÿÿÿÿ‹ŽQÉstatistics, maximum entropy principleNæ5ŽåÁh ž€Ï€€‚€‚€ ‚€‚‚‚€†"€‚€‚€ €€€ã¹Àk̀‰€ã¬ÑJ±€‰€‚ÿRegularization by maximum entropy principleOptions | Size-Distribution Options | Regularization by Maximum EntropyThe maximum entropy principle can be used for regularization of a distribution analysis by executing a constrained fit:The first term repres‹ŽåÁ5Žents the unconstrained linear Lamm equation fit with a distribution, e.g. c(M), and the second term is the maximum entropy constraint. The constraint is controlled by the parameter a, which can be adjusted with the use of F statistics. This is similar to the technique described by Steven Provencher and implemented in the program CONTIN. For a more detailed description of the regularization strategy, see the help page continuous c(M) by Lamm analysis. k(‹ŽPÄC T€Q€€‚€ €€ €€ €€ €€ €‚ÿThe specific form of the maximum entropy functional is derived from the statistical (Bayesian) consideration that in the absence of any prior knowledge on the distribution c(M), all the M values are a priori equally probable. The form clog(c) can be shown by combinatorial methods to be proportional to the number of microstates that can form the macroscopic distribution c(M). This can also be related to the informational entropy introduced by Shannon. For a more complete description, see e.g. Press et al. Numerical Recipes in C. áåÁbÆ1 0€Ã€€‚€ €€ €‚ÿThe use of the maximum entropy functional as a constraint allows one to calculate the distribution c(M) that fits the data well (statistically indistinguishable from the unconstrained case), but provides only the minimal information required to fit the data. In other words, this allows us to deviate only as little as possible from the underlying principle of not giving any preference to any particular value of M, and in this way extract only the essence of the data. ÜPÄkÈ- (€¹€€‚‚‚€ € ‚ÿIn practice such regularization is often used for suppressing noise amplification in the inversion of Fredholm integral equations.Please Note: Maximum entropy helps suppress artificial oscillation in the derived size-distributions. In my hands, it worked better than the Tikhonov-Phillips second derivative regularization when using the continuous Lamm equation model. However, for regularizing the least-squares g*(s), the Tikhonov-Phillips seems to work better. æ“bÆQÉS t€'€€ ‚€‚ƒãþ°A‚€‰€‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚‚ÿSee also:Regularization by Tikhonov-Phillips 2nd derivativecontinuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysis],kÈ®É17 Æ 9ÿÿÿÿ®É²statistics, Tikhonov-Phillips regularizationõuQɣ̀ ΀퀀‚€‚€ ‚€‚ã㇏€‰€‚‚€†"€‚€‚€ €€€ã¹Àk̀‰€ã/zeD€‰€ã¬ÑJ±€‰€‚ÿTikhonov-Phillips regularization using 2nd derivativeOptions | Size-Distribution Options | Regularization by Tikhonov-Phillips 2nd derivativeIn contrast to the Regularization by maximum entropy, the Tikhonov-Phillips method implemented here uses a second-derivative operator for regularization.This represents a constrained fit, where the first term represents the unconstrained fit with a distribution, e.g. c(M), and the second term is the second derivative constraint. The constraint is controlled by the parameter a, which can be adjusted with the use of F statistics. This is similar to the technique described by Steven Provencher and implemented in the program CONTIN. For a more detailed description of the regularization strategy, see the help pages g*(s) by least-squares direct boundary fitting and continuous c(M) by Lamm analysis. oB®É- (€…€€‚€ €‚‚‚ÿThe use of this constraint allows one to select the smoothest distribution that leads to a fit that is statistically indistinguishable from the unconstrained case. This strategy is frequently used to suppress noise in the inversion of Fredholm integral equations, using a priori information that the sought distribution is smooth. This prior knowledge of smoothness of the distribution can be well justified for g*(s) distributions because of the broadening of the true sedimentation coefficient distribution g(s) via diffusion. This diffusional broade£ÍQÉning can be imagined as a convolution of the true distribution by a Gaussian. Therefore, we know that this apparent sedimentation coefficient distribution must be smooth, because Gaussian-shaped for a single species, or a superposition of Gaussians for several species. ”9£Í²[ „€s€€‚€ € ‚€‚‚ƒã㇏€‰€‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚‚ÿPlease Note: This regularization seems to work better with ls-g*(s) than the maximum entropy regularization. Therefore, this option is switched on when using the ls-g*(s) model.See also:Regularization by maximum entropycontinuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysisE÷1 x†ÿÿÿÿ÷Œdata, subtract blankP²G1 0€?€€‚€‚€ ‚€‚‚ÿSubtract blank scan from data setOptions | Loading Options | Subtract Blank ScanWhen working with interference data and external loading cells, it can be advantageous to subtract a single scan from a set of scans. For example, a before-blank or after-blank taken before or after the experiment, respectively, can be subtracted from equilibrium profiles (or approach-to-equilibrium) profiles to reduce the influence of time-invariant noise components. (For a discussion, see for example, Ansevin et al., Anal Biochem 1970, 237-261) uE÷Œ0 0€Š€€‚ãQÿ-s€‰€‚ÿThe new data can be saved, as described in save raw data set.Z)G1û9¶ ÿÿÿÿ· data, eliminate fringe jumps within scans8ùŒN? L€ó€€‚€‚€ ‚€‚‚‚ãQÿ-s€‰€‚ÿElimination of fringe jumps within each scanOptions | Loading Options | Remove Integral Fringe Jumps (within one scan)Sometimes, interference data exhibit integral fringe jumps within a single scan. This function iterates through each scan and looks for sudden jumps in the fringe values of more than 0.8 at neighboring radial values. If such a jump is found, an integral offset is added to this and all following data points.The new data can be saved, as described in save raw data set.i · I `€A€€‚€ € ‚€‚€€€‚‚‚ƒã¢lÛ¶€‰€‚ÿPlease Note: several rounds of executing this functions may be needed to remove multiple jumps within one scan.Important: Meniscus, bottom, and left and right fitting limit must be set before using this function.See also:subtract calculated TI/RI noise from raw dataS"N 1,¿ˆ ÿÿÿÿ “Kstatistics, Monte Carlo simulationrA· | 1 0€ƒ€€‚€‚€ ‚€‚‚ÿMonte-Carlo simulationsStatistics | Monte-Carlo for distributionsFor studying the statistical confidence limits in distribution analyses. The idea of the Monte-Carlo analysis is the generation of a large number (e.g. 100 - 1000) synthetic data sets that are similar to the experimental data set, but each with a (different) random normally distributed noise. Each of these new data sets is analyzed, and the distributions are stored. The resulting set of distributions can then be studied, point by point, and the mean and probability contours can be calculated. n1 ê= H€c€€‚ã¬ÑJ±€‰€ã/zeD€‰€‚ÿIn essence, the Monte-Carlo statistics allows to build up a probability distribution function, and allows to study how much the noise of the data is translated into the distribution. Because distribution analyses tend to produce artificial oscillations (see e.g. the help-pages continuous c(M) by Lamm analysis and g*(s) by least-squares direct boundary fitting ), the Monte-Carlo procedure can be useful for investigating what features of the distribution are a result of these oscillations and what features are essential for describing the data.¢^| ˜AD V€œ€€‚‚‚€€ãžwœª€‰€€‚‚€ €‚ÿThe procedure is implemented here as follows:1) with a distribution model, the best fitted values for all data points are stored. Important: The best-fit distribution has to be found before executing theê˜A·  Monte-Carlo analysis, and the residuals should be random and show no systematics (for example, this may be assessed by the runs test)2) the number of iterations N must be specified. It is suggested to perform a test Monte-Carlo with a small (e.g. 10-100) number of iterations, first, to check the performance of the procedure, and then make a large statistics (100-1000) overnight. Ùê¢C1 0€³€€‚€ €€ €‚ÿ3) The confidence level: After calculating the N new distributions based on the N generated data sets, the distribution plot will show 3 curves, the mean curve in black, and a blue and a red curve, which enclose a specified percentile of the data. For example, if the confidence level is 0.7, then the middle 70% is enclosed by the 0.15 (in blue) and the 0.85 (in red) quantile. Setting this confidence level changes these percentiles of the display and storage. ܘA«F- (€¹€€‚€ €‚‚‚ÿ4) A directory for the storage of the calculated distributions has to be specified. This will contain N distributions, named 1.dat,2.dat,...,N.dat, as well as a distribution called mean.dat, and different percentiles called lim***.dat, e.g. lim160.dat for the 16% percentile. 5) The calculation of the Monte-Carlo iterations follows. Synthetic data sets are generated based on the previously found best-fit data (see point 1 above), with normally distributed noise added in the same magnitude as was obtained in the previous best-fit. Each of these new data sets is analyzed in the same way as the original distribution analysis. Each new calculated distribution is stored in memory, and in a file (see point 3 above). k¢C;I% €×€€‚‚ÿ6) The statistics of the curves is analyzed: As described in point 3, the mean and specified quantiles of the distributions are shown. For example, if the confidence level was 0.68, the curves shown in the display are the mean and 1 standard deviation contour for each point in the distribution. A continuous loop allows to probe new confidence levels, each of which will subsequently be displayed and stored in the specified directory. This way, a complete statistical analysis can be performed, without any need to re-calculate the Monte-Carlo iterations. This loop is stopped by pressing the cancel button.Š«FMKˆ ހ€€‚‚‚ƒã$©„€‰€‚ƒã/zeD€‰€‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚ƒãz|•ý€‰€‚ƒã¡ë˜€‰€‚ƒã 똀‰€‚ÿSee also:van Holde-Weischetg*(s) by least-squares direct boundary fittingcontinuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysiscontinuous Lamm analysis with prior constant diffusion coefficientcontinuous Lamm analysis with prior partial specific volume as function of Mcontinuous Lamm analysis with prior sed-coefficient as function of MF;I“K1 2€*€€ƒã¹Àk̀‰€‚‚ÿF statisticsNMKáK1 ¶. ÿÿÿÿáK ˆmodel, time-dependent s and M/þ“KN1 0€ý€€‚€‚€ ‚€‚‚ÿtime-dependent s and MModel | Special | Fit time-dependent s, M (e.g. in Archibald Analysis)Sometimes it can be useful to allow for (apparent) changes in M and s with time. In Archibald-type analyses, for example, where the initial depletion at the meniscus is analyzed in the context of a Lamm equation model, heterogeneity can be detected by a drop of M and s with time, because the larger species are depleted more rapidly, therefore lowering the average observed in the vicinity of the meniscus.ÑxáKí€Y €€ñ€€‚ãÿÓü&€‰€‚‚‚‚ã&ÍíD€‰€ãë €ã£,J€‚ÿWhile a normal Archibald-type analysis can be performed by a straight-forward application of the independent species model, studying the time-dependence can be done by this function. In a sequence of analyses, a different subset of the available scans is considered, either in a moving time-window approach, or by continually increasing the time-window. This procedure consists of the following steN퀓Kps:1) The analysis mode needs to be switched to experimental initial conditions (see set sedimentation parameters), and an initial scan must be loaded (see load initial data and extrapolation of initial data).-ÜN„Q p€¹€€‚€ €‚‚€ €€ €€ €€ €€ €€ €‚ÿ2) The number of scans n that are pooled in the time-dependence analysis must be specified. The best value here will depend on the number of scans available, the desired resolution in time, and the level of noise in the scans. Usually, the best number can be empirically determined. It should not be too small, though, because this increases the noise and decreases the stability of the procedure.3) The choice of a moving average 1 to n, 2 to (n+1), 3 to (n+2),... or an increasing window 1 to n, 1 to (n+1), 1 to (n+2), etc. appears. Because of the increasing number of scans in the second option, this is numerically more stable and leads to slightly higher precision, although smaller changes with time. Нí€ê†3 4€;€€‚€ €‚‚€€ ‚ÿ4) A series of fits is made, each to a subset of the scans. Please Note: Sometimes during the course of this series of fits, bad parameters are encountered in the Simplex routines. If the gridsize is slightly reduced (e.g. to 250), and if the number of scans per set is increased, this can improve the stability of the method. 5) The results are stored in two files: mwdcdt.dat and sdcdt.dat (or Mw(t).dat and s(t).dat if the increasing time-window option is selected), each containing two-column ASCII text with the average times of the scan subsets considered, and the best-fit M and s, respectively. The files are located in the directory with the data."µ„ ˆm š€k€€‚‚€ € ãÿÓü&€‰€‚€ ‚€‚‚ƒãë €‚ƒã£,J€‚ƒãÿÓü&€‰€‚‚‚ÿPlease Note: This works only with the independent species model.See also:load initial dataextrapolation of initial dataindependent species modelNê†Zˆ1Æ¿ˆìƒ ÿÿÿÿZˆkÈmodel, g*(s) by least squares–e ˆðŠ1 0€Ë€€‚€‚€ ‚€‚‚ÿls-g*(s) distribution by least-squares boundary modelingModel | ls-g*(s)This allows to calculate a g*(s) distribution, based on direct boundary fitting and algebraic systematic noise decomposition. The result of this analysis is an apparent sedimentation coefficient equivalent to the g(s*) analysis of dc/dt. However, there is no need for differencing data and calculating with dc/dt here, which eliminates a source of broadening from finite time-differences between the scans. Therefore, this method is far more tolerant of large time-steps, such as commonly occurring in absorbance optical data. UZˆE> J€/€PÈ:€‚‚‚‚‚ƒ€€ãþ°A‚€‰€‚ÿA detailed description of the procedure is given in the reference indicated below. The model requires the following user input in the modified parameter box:1.Resolution: This specifies the increments of s-values for the calculation. Default and recommended value is 100, higher or lower values can be chosen. Generally, with higher values, more noise is introduced into the distribution, but this can be efficiently reduced by Tikhonov-Phillips regularization (Regularization by Tikhonov-Phillips 2nd derivative). g4ðŠ¬3 4€i€€ƒ€€‚ƒ€€‚ÿ2.s-min and s-max: These values should bracket the range of s-values expected for the sample.3.confidence level (F-ratio): This input is required for the statistical adjustment of the regularization constraint. Recommended is a value of 0.95 or 0.68 (one standard deviation). If the value entered here is < 0.5, then regularization is switched off. If the value is > 1, then the entered value is taken as the requested fractional variance increase accompanied by regularization. (I would assume that a value larger than 1.5 would not make sense.). ÷ŠE¯Ãm š€€€‚‚‚€㜄›B€‰€‚‚‚€‚ã=†|]€‰€ãØï•Ã€‰€㬏¯Ã ˆåŠˆ€‰€㎝Š€‰€‚ÿThe other parameters are as usual; a floating baseline should be allowed, and when working with interference data, the time-invariant and radial-invariant noise (jitter) should also be allowed for (i.e. checked).The g*(s) analysis is executed by selecting the menu command run sedimentation command (or by using the ctrl-R keyboard shortcut).After calculating the distribution, a new plot appears in the lower part of the sedfit window, showing the distribution. It can be saved to a file (save distribution), copied as graphics metafile (copy plots) or data table (copy data tables) into the clipboard. Also available for inspection are the step-functions involved in the g*(s) model, shown in the data plot, and residuals of the fit. For statistical analysis (provided the fit was good, with evenly distributed residuals), the Monte-Carlo analysis can be performed. 塬”ÆD V€C€€‚‚€ € ‚€‚€€€‚€‚€‚ƒ‚ÿPlease Note: The regularization method is automatically switched to Tikhonov-Phillips. However, it can be manually set back to the maximum entropy method, if desired. Please note: The distribution will automatically clipped to the maximal s-value that can be observed for the given rotor speed and time of the first scan.Tips: 1) For best results, it is advisable to start with a relative small range of s-values. It is recommended to increase s-max if there is an upward curvature of the distribution at the highest s-values, and conversely, to decrease the s-min value if there is a significant contribution in the distribution at this lower s-value.¯H¯ÃCÈg œ€‘€€‚‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚ƒãþ°A‚€‰€‚‚‚‚€€€€€€‚‚‚ÿSee also:continuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysisRegularization by Tikhonov-Phillips 2nd derivativeReference: P. Schuck and P. Rossmanith. (2000) Determination of the sedimentation coefficient distribution g*(s) by least-squares boundary modeling. Biopolymers 54:328-341(”ÆkÈ% €€@‘€€‚ÿi8CÈÔÈ1æ.ÿˆ ÿÿÿÿÔÈQÎmodel, continuos distribution with conformational changeЏkÈ€ÌA P€€€‚€‚‚€ ‚‚€‚ã²ÑJ±€‰€‚‚‚ÿcontinuous distribution c(s) Lamm equation modelModel | Continuous c(s) Conformational Change ModelModel | Continuous c(s) with constant DThese models are very similar to the standard c(s) distribution (continuous c(s) by Lamm analysis). However, the conformational change model additionally allows to incorporate prior knowledge on on species that may undergo a conformational change, and therefore sediment with different s-values because of differences in shape rather than in mass. Essentially, this model assumes a constant molar mass for all species sedimenting in a specified range of s-values. Outside this range, a constant frictional ratio is assumed. The advantage is an enhanced precision in the distribution analysis by making use of the known molar mass value (and to calculate D within the preassigned s-range via Svedberg equation, instead of Stokes-Einstein relationship). ­„ÔÈQÎ) € €€‚‚‚‚‚‚ÿThe constant D model, on the othe hand, allows to enter prior knowledge on the diffusion coefficient, assuming that it is constant throughout the distribution. This could be the approximately the case for narrow distributions, or for molecules like ferritin. An average D could also be known from dynamic light scattering. The weight-average D can also be fitted to the data. _.€Ì°Î1샢ÿÿÿÿ°Îñmodel, continuos distribution with prior v-bar­QΟU x€]€€‚€‚€ ‚€‚ã¬ÑJ±€‰€‚‚€†"€‚€€ €‚ÿcontinuous distribution c(M) Lamm equation model using prior knowledge on partial-specific volumeModel | continuous c(M) with prior knowledge | c(M) with prior knowledge v-bar(M)This continuous distribution model is very similar to the conti°ÎŸQÎnuous c(M) by Lamm analysis(see this help-page for more information), but it makes use of a known dependency of the partial-specific volume on the molar mass of particles. Input is required for a zero-order v-bar, an amplitude a, and the M-scale s on which this power-law applies. It is assumed that experimental knowledge on v-bar as a function of M could be approximated sufficiently close by this empirical formula. Ÿ°ÎËn ª€?€€‚‚‚‚‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚ƒãz|•ý€‰€‚ƒã¡ë˜€‰€‚ƒã 똀‰€‚ÿAfter this information has been entered, the v-bar entry in the parameter box can be ignored. See also:continuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysiscontinuous Lamm analysis with prior constant diffusion coefficientcontinuous Lamm analysis with prior partial specific volume as function of Mcontinuous Lamm analysis with prior sed-coefficient as function of M&Ÿñ# €€€‚ÿ[*ËL1%ÿˆ‰ÿÿÿÿL model, continuos distribution with prior Dx;ñÄ= H€w€€‚€‚€ ‚€‚ã¬ÑJ±€‰€‚ÿcontinuous distribution c(M) Lamm equation model using prior knowledge on DModel | continuous c(M) with prior knowledge | c(M) with invariant DThis continuous distribution model is very similar to the continuous c(M) by Lamm analysis (see this help-page for more information), but it makes use of knowledge of a constant diffusion coefficient for all species. One example where this case applies is ferritin, or other structures that may have different mass, but are identical in size and shape (and therefore also identical in hydrodynamic radius and D). ¥LÏf š€K€€‚€ €‚‚‚‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚ƒãz|•ý€‰€‚ƒã¡ë˜€‰€‚ÿA slightly modified input is required in the parameter box. No v-bar or buffer density is needed, because the mass distributions will be buoyant molar mass distributions. See also:continuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysiscontinuous Lamm analysis with prior constant diffusion coefficientcontinuous Lamm analysis with prior partial specific volume as function of MGÄ @ N€€€ƒã 똀‰€‚‚€€€€‚‚ÿcontinuous Lamm analysis with prior sed-coefficient as function of MReference: P. Schuck. (2000) Size distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and Lamm equation modeling. Biophysical Journal 78:1606-1619[*Ïq 1ð¢{ÿÿÿÿq ]…model, continuos c(s) distribution by LammüË m 1 0€—€€‚€‚€ ‚€‚‚ÿcontinuous distribution c(s) Lamm equation modelModel | continuous c(s) distributionIf certain knowledge on the size and shape of the molecules under study is available, this can be used for an enhanced sedimentation coefficient distribution analysis. While the resolution that can be achieved is similar or slightly higher than in the van Holde-Weischet analysis, for the continuous Lamm equation modeling ANY data from the complete sedimentation experiment can be included in the analysis. In fact, the largest possible range of data from the very beginning (meniscus does not need to be cleared) to the end of the sedimentation experiment (no plateaus necessary) should be included for best results. ¯~q (A1 0€ý€€‚ã/zeD€‰€‚ÿA detailed technical description is given in the reference below. In short, this function increments the s-values in a way similar to the g*(s) by least-squares direct boundary fitting, but instead of using step-functions, it fits a series of Lamm equation simulations to the data, each using a different s-value. The distribution is then the combination of loading concentration for each of the Lamm equation solutions which describes the data best. For each of these Lamm equation simulations at any particular s-value, a diffusion coefficient is calculated based on the estimates for the frictionalm (A  ratio, and the partial-specific volume of the particle. This allows to substantially sharpen up the sedimentation coefficient distribution as comparted to g*(s) distributions, and to deconvolute diffusion effects, while it is not very sensitive to the estimated frictional ratio. Ü©m B3 4€S€PÈ:€‚‚‚ƒ€€ €‚ÿThe parameters required in the parameter input box are:1.resolution: This is the number of s-increments on which the analysis will be based (default is 100). ŒH(ADD V€‘€€ƒ€€ €‚ƒ€€‚ƒ€€€ €‚ÿ2.s-min and s-max: These values should bracket the sedimentation coefficients expected for the sample3.frictional ratio: This would be 1 for globular proteins (the default), and slightly higher than 1 for assymmetric (or elongated) shapes. This parameter can be fitted for in the analysis (although this is somewhat time-consuming). 4.partial-specific volume: Knowledge on v-bar is required to calculate the hydrodynamic shape of the species, although the results of this c(s) analysis are not very sensitive to this parameter. The default is 0.73 for proteins.ªYB:GQ p€³€€ƒ€€€€‚ƒ€€ã㇏€‰€ãþ°A‚€‰€‚ÿ5.buffer density and viscosity: These values can be obtained, for example, using sednterp. They will not be temperature corrected in sedfit!6.a confidence level: This is required for adjusting the regularization constraint (see below). A value of 0.68 - 0.95 is recommended. Entering a value < 0.5 switches off the regularization, and values > 1 are interpreted directly as desired variance ratios. The preferred regularization method is Regularization by maximum entropy (the default), but it can be switched manually to Regularization by Tikhonov-Phillips 2nd derivative. TýDŽJW |€û€€‚‚‚ã=†|]€‰€ãØï•Ã€‰€ã劈€‰€㎝Š€‰€‚ÿThe other parameters are as usual; a floating baseline should be allowed, and when working with interference data, the time-invariant and radial-invariant noise (jitter) should also be allowed for (i.e. checked).After calculating the distribution, a new plot appears in the lower part of the sedfit window, showing the distribution. It can be saved to a file (save distribution), copied as graphics metafile (copy plots) or data table (copy data tables) into the clipboard. Also available for inspection are the step-functions involved in the g*(s) model, shown in the data plot, and residuals of the fit. For statistical analysis (provided the fit was good, with evenly distributed residuals), the Monte-Carlo analysis can be performed. S:GáME X€€€‚€ €€ €€ €‚‚€€€ €‚ÿWhen the distribution analysis c(s) has finished, it can be switched to c(M) (based on the Svedberg equation). If this is done while the s-distribution is still displayed, then it does not need to be recalculated and directly the M-distribution is shown. (This may be slightly different in the details, however, from the results of executing the c(M) analysis, because of the different way of spacing the s-intervals and M-intervals). Please note: Because the inversion of integral equations tends to produce artificial oscillations, great care should be taken in the interpretation of the fine structure of the obtained distributions. Too little regularization can produce such artificial fine-structure. However, this can be assessed by Monte-Carlo analysis. ÒŽJ €9 @€¥€€‚€€€€‚‚€€‚ÿPlease note: The calculation will be aborted if the distribution contains s-values exceeding the maximum s-value that can be observed for the given rotor speed and time of the first scan. To fix this problem, either load earlier data, or reduce the entry in the s-max field appropriately (see message box). It is recommended to stay well below this maximal s-value to avoid artifactual increases of the size-distribution near the maximal value. Tips: áM € -úáM9‚3 4€õ€€ƒ‚ƒãL »@€‰€‚ÿ1) For best results, it is advisable to start with a relative small range of s-values. It is recommended to increase s-max if there is an upward curvature of the distribution at the highest s-values, and conversely, to decrease the s-min value if there is a significant contribution in the distribution at this lower s-value.2) If the Lamm equation simulations during this method are very slow, the value for changing methods (set s for changing Lamm algorithm) should be increased (e.g. to 10).3à €l„p ®€‡€€ƒ‚€‚‚ƒã¬ÑJ±€‰€‚ƒã/zeD€‰€‚ƒãŽŠ€‰€‚ƒãþ°A‚€‰€‚ƒã㇏€‰€‚ÿ3) In order to achieve smoother distributions, for example when studying synthetic polymers that are known to have a broad distribution, the value of P should be increased, to values close to 1 (e.g. 0.99), or even to 1.1. See also:continuous c(M) by Lamm analysisg*(s) by least-squares direct boundary fittingMonte-Carlo analysisRegularization by Tikhonov-Phillips 2nd derivativeRegularization by maximum entropyñŸ9‚]…3 4€}€€‚‚€€€€‚‚ÿReference: P. Schuck. (2000) Size distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and Lamm equation modeling. Biophysical Journal 78:1606-1619[*l„ž…1$‰žÿÿÿÿž… model, continuos c(M) distribution by LammþÍ]…¶ˆ1 0€›€€‚€‚€ ‚€‚‚ÿcontinuous distribution c(M) Lamm equation modelModel | continuous c(M) distributionIf certain knowledge on the size and shape of the molecules under study is available, this can be used for a mass-distribution analysis. While the resolution that can be achieved is similar or slightly higher than in the van Holde-Weischet analysis, for the continuous Lamm equation modeling ANY data from the complete sedimentation experiment can be included in the analysis (including interference data sets). In fact, the largest possible range of data from the very beginning (meniscus does not need to be cleared) to the end of the sedimentation experiment (no plateaus necessary) should be included for best results."ñž…؋1 0€ã€€‚ã²ÑJ±€‰€‚ÿIn short, in this method, the M-values are incremented and a series of Lamm equation simulations are performed, and fitted to the data. The distribution is then the combination of loading concentration for each of the Lamm equation solutions which describes the data best. In each Lamm simulation, a s-value is calculated based on the molar mass of the species and the prior estimates of the hydrodynamic shape of the species (f/f0). The methods c(s) and c(M) are very closely related (continuous c(s) by Lamm analysis). They are essentially only different representation of the same size-distribution method. However, this c(M) analysis is more sensitive in the results than the c(s) analysis on the estimates of the frictional coefficient. Ü©¶ˆŽŒ3 4€S€PÈ:€‚‚‚ƒ€€ €‚ÿThe parameters required in the parameter input box are:1.resolution: This is the number of s-increments on which the analysis will be based (default is 100). ŒH؋@D V€‘€€ƒ€€ €‚ƒ€€‚ƒ€€€ €‚ÿ2.M-min and M-max: These values should bracket the sedimentation coefficients expected for the sample3.frictional ratio: This would be 1 for globular proteins (the default), and slightly higher than 1 for assymmetric (or elongated) shapes. This parameter can be fitted for in the analysis (although this is somewhat time-consuming). 4.partial-specific volume: Knowledge on v-bar is required to calculate the hydrodynamic shape of the species, although the results of this c(s) analysis are not very sensitive to this parameter. The default is 0.73 for proteins.ªYŽŒöÁQ p€³€€ƒ€€€€‚ƒ€€ã㇏€‰€ãþ°A‚€‰€‚ÿ5.buffer density and viscosity: These values can be obtained, for example, using sednterp. They will not@öÁ]… be temperature corrected in sedfit!6.a confidence level: This is required for adjusting the regularization constraint (see below). A value of 0.68 - 0.95 is recommended. Entering a value < 0.5 switches off the regularization, and values > 1 are interpreted directly as desired variance ratios. The preferred regularization method is Regularization by maximum entropy (the default), but it can be switched manually to Regularization by Tikhonov-Phillips 2nd derivative. Rü@HÅV z€ù€€‚‚ã=†|]€‰€ãØï•Ã€‰€ã劈€‰€㎝Š€‰€‚ÿThe other parameters are as usual; a floating baseline should be allowed, and when working with interference data, the time-invariant and radial-invariant noise (jitter) should also be allowed for (i.e. checked).After calculating the distribution, a new plot appears in the lower part of the sedfit window, showing the distribution. It can be saved to a file (save distribution), copied as graphics metafile (copy plots) or data table (copy data tables) into the clipboard. Also available for inspection are the step-functions involved in the g*(s) model, shown in the data plot, and residuals of the fit. For statistical analysis (provided the fit was good, with evenly distributed residuals), the Monte-Carlo analysis can be performed. N öÁ–ÈB R€€€‚€ €€ €€ €‚‚€€€‚ÿWhen the distribution analysis c(M) has finished, it can be switched to c(s) (based on the Svedberg equation). If this is done while the s-distribution is still displayed, then it does not need to be recalculated and directly the s-distribution is shown. (This may be slightly different in the details, however, from the results of executing the c(s) analysis, because of the different way of spacing the s-intervals and M-intervals). Please note: Because the inversion of integral equations tends to produce artificial oscillations, great care should be taken in the interpretation of the fine structure of the obtained distributions. Too little regularization can produce such artificial fine-structure. However, this can be assessed by Monte-Carlo analysis.@HÅÖË; D€ €€‚€€€‚€‚€€‚ƒ‚ÿPlease note: The calculation will be aborted if the distribution contains s-values exceeding the maximum s-value that can be observed for the given rotor speed and time of the first scan. To fix this problem, either load earlier data, or reduce the entry in the M-max field appropriately. It is recommended to stay well below this maximal value to avoid artifactual increases of the size-distribution near the maximal value.Tips: 1) For best results, it is advisable to start with a relative small range of M-values. It is recommended to increase M-max if there is an upward curvature of the distribution at the highest M-values, and conversely, to decrease the M-min value if there is a significant contribution in the distribution at this lower M value.•P–ÈkÎE X€¡€€ƒãL »@€‰€‚ƒ‚€‚‚€€€€‚ÿ2) If the Lamm equation simulations during this method are very slow, the value for changing methods (set s for changing Lamm algorithm) should be increased (e.g. to 10).3) In order to achieve smoother distributions, for example when studying synthetic polymers that are known to have a broad distribution, the value of P should be increased, to values close to 1 (e.g. 0.99), or even to 1.1. Reference: P. Schuck. (2000) Size distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and Lamm equation modeling. Biophysical Journal 78:1606-1619|ÖË a €7€€‚‚‚ƒã²ÑJ±€‰€‚ƒãz|•ý€‰€‚ƒã¡ë˜€‰€‚ƒã 똀‰€‚‚‚‚ÿSee also:continuous c(s) by Lamm analysiscontinuous Lamm analysis with prior constant diffusion coefficientcontinuous Lamm analysis with prior partial specific volume as function of Mcontinuous Lamm analysis with prior sed-coefficient as function of MkÎ ]…5kÎA1ÿÿÿÿÿÿÿÿÿÿÿÿAsexit'ç h@ N€Ï€€€‚‚€ €‚€‚ãH’ùڀ‰€‚ÿExitData | ExitThis closes the program. Results of the data analysis should be stored manually. (Saving Fits). However, some information on the analysis remains stored on the hard disk, in a file xxxxxxxx.~p located in the data directory. This includes some of the fitting parameters and meniscus and bottom location. Also, this file contains information if the program crashed or was properly closed, giving opportunity to restore the analysis after loading of files. ÑAs: B€£€€‚€€ã©\o}€‰€€‚ÿPlease Note Bug: Sometimes some information is not completely restored after reloading. Therefore, independent documentation of best-fit parameters, or use of the notepad (make notes) is advised. Ghº1Šÿÿÿÿÿÿÿÿÿÿÿÿºýdisplay, last fit infoC sý6 :€€€€‚‚€ €‚€‚‚‚‚ÿShow Last Fit Info AgainDisplay | Display last fit info againThis simply reproduces the screen output from the fit operation. This can be helpful when an operation caused the sedfit window to redraw and erase, for example, the rmsd values of the best-fit.JºG1ïÿÿÿÿÿÿÿÿÿÿÿÿGì sedimentation, start time0ÜýwT v€¹€€€‚‚€ €‚€‚€ €‚‚ãq€‰€ã³ŒX€‰€‚ÿSedimentation Time OffsetModel | Special | Sedimentation Time OffsetIn some cases, it can be useful to introduce an offset time of simulated sedimentation. This will set the start of the sedimentation to a specified time t (in sec). One possible use of this function is an alternative way (alternative to scan times from t or w2t or ramp rotor speed) of treating the time necessary for the acceleration of the rotor. Most likely, however, this function will be useful for cases where temperature-driven convection causes mixing in the initial part of the experiment, and an empirical modeling of the profiles is still desired (e.g. for getting the time-invariant noise from an approach to equilibrium run).u6Gì ? L€m€€‚ãB@-€‰€‚‚‚‚€ € ‚€‚ÿThis function can be useful in conjunction with fit t0 time of sedimentation. If a nonzero offset time is being used, a checkmark appears at this menu item. Please Note: This feature only works with the non-interacting Lamm equation modeling and should be switched off when using other models.[*wG 1}ÿÿÿÿÿÿÿÿÿÿÿÿG a@sedimentation, simulate acceleration phase)éì p @ N€Ó€€€‚‚€ €‚€‚€€€€‚ÿSimulate Rotor Acceleration PhaseOptions | Loading Options | Ramp Rotor SpeedThe entries in the file headers saved by the XLA/XLI contains both a w2t entry and an elapsed seconds entry. From the combination of known rotor speed, the elapsed seconds, and the elapsed w2t can be calculated how long it took to bring the rotor to speed (assuming a linear acceleration). This is being calculated when loading files. If the option ramp rotor speed is toggled on (it will then have a checkmark), the acceleration phase is incorporated into the finite element solutions of the Lamm equation. Technically, this is done by discretizing the time, and recalculating after small intervals the matrix intervals related to the rotor speed. œ‚G 9@; D€€€‚ãq€‰€‚‚‚‚€ € ‚ÿIf this option is used, the alternative way to deal with the rotor accelleartion - the use of an effective sedimentation time (scan times from t or w2t) - is toggled off. In theory, ramping the rotor speed for the Lamm equation solution is the most precise way to deal with the rotor acceleration, since it can correctly account for both diffusion and sedimentation in this phase.Please Note: Information about the state of this switch is not being stored in the information on the previous best-fit. Therefore, when reloading analyses from the harddrive, this feature will not automap 9@ì tically be switched to its original state .(p a@$ €€€‚‚ÿG9@š@1ÿÿÿÿÿÿÿÿÿÿÿÿš@àDplot, residuals bitmapܘa@„DD V€1€€€‚‚€ ‚€‚€ €‚€‚‚‚€ €‚ÿDisplay Residuals as BitmapDisplay | Show Resdiduals BitmapOptions | Bitmaps | black and whiteOptions | Bitmaps | continuous shadingIn order to gain a more detailed representation of the residuals, the residuals can be displayed as a picture. This function toggles the display of the current residuals as a bitmap. Each horizontal line of screen pixels corresponds to one scan (ordered according to time), and each pixel within that line corresponds to a radial position. The values of the residuals between data and fit are normalized to the larges residual, and then transformed into a color. The outcome of this will depend on the color settings of your display, therefore there are two switches: black/white vs color, and continuous shading (brightness of pixel corresponds to magnitude of residual) vs discrete shading (only sign of the residual is regarded and translated into a brightness).\)š@àD3 6€R€€‚‚ƒãÆÔA〉€‚‚ÿSee also:copy residuals bitmap[*„D;E1Uÿÿÿÿÿÿÿÿÿÿÿÿ;E5Jplot, subtract calculated systematic noiseFàDG3 4€'€€€‚‚€ ‚‚‚€‚‚ÿSubtract Calculated Systematic Noise From Raw DataDisplay | subtract calculated TI noise from raw dataDisplay | subtract calculated RI noise from raw dataDisplay | subtract all systematic noise from raw dataFor presentation purpuse, the calculated systematic noise can be subtracted from the raw data. This allows sometimes a better visual inspection of the data and the fit. The subtraction can be done because if the systematic noise is calculated, then the analysis is invariant against these systematic changes. Œ];E J/ ,€»€€‚‚‚‚‚€€‚ÿThis subtraction can be done separately for the time-invariant noise (TI) and the radial-invariant noise (jitter, RI), or both combined.For convenience, the combined subtraction of all calculated systematic noise can be invoked by using a keyboard shortcut Ctrl-N.Please Note: All the following data analyses must also allow for the calculation of these systematic noise parameters (although it might be tempting to consider the noise problem solved and to continue without systematic noise). Otherwise, a bias will be introduced into the further analysis, which will lead to incorrect results!(G5J$ €€€‚‚ÿG J|J1Ôÿÿÿÿÿÿÿÿÿÿÿÿ|J Lcopy, residuals bitmap:5J LS t€u€€€‚‚€ €‚€‚‚ã?žš<€‰€‚‚‚‚ƒã?žš<€‰€‚‚ÿCopy Residuals BitmapCopy | Copy Residuals BitmapThis function puts the bitmap formed by the residuals (display residuals as bitmap) into the clipboard. This way, the picture can be pasted into any other windows program, such as Origin, or Powerpoint.See also:display residuals as bitmap@|JIL19ÿÿÿÿÿÿÿÿÿÿÿÿILAƒfit, start time · LTNT v€o€€€‚‚€ €‚€‚€ €‚‚ãq€‰€ã³ŒX€‰€‚ÿFit t0 of SedimentationModel | Special | fit t0 of sedimentationIn some cases, it can be useful to introduce an offset time of simulated sedimentation. This will set the start of the sedimentation to a specified time t (in sec). One possible use of this function is an alternative way (alternative to scan times from t or w2t or ramp rotor speed) of treating the time necessary for the acceleration of the rotor. ËILb7 <€—€€‚ã§e8€‰€€€‚ÿAnother situation where this option can be useful is the calculation of TI noise through approach to equilibrium scans, with the intent to subtract the TI noise from the equilibrium data (see correct equilibrium scan for TI Noise). Floating the offset time may not make direct sense for the interpretation of the approach to equilibrium in terms of s-values of the cTNb Lomponents, but it can be helpful to find Lamm equation solutions that fit and smooth the data appropriately with any Lamm equation solution to extract the TI noise. (The offset time, for example, may be able to adapt to the effects of convection caused by temperature gradients, which would effectively delay the sedimentation process.) ßžTNAƒA P€=€€‚ãõ„"c€‰€‚‚‚‚€ € ‚€‚‚‚ÿWhile the function set t0 time of sedimentation sets a specific time as starting time, this function determines this time as a floating parameter to be optimized. If a nonzero offset time is a floating fitting parameter, a checkmark appears at this menu item. Please Note: This feature only works with the non-interacting Lamm equation modeling and should be switched off when using other models.> bƒ1ú#{'ÿÿÿÿƒAdata, loading ÂAƒˆ…G \€…€€‚€‚€ €‚€ ‚€‚€ €‚€ €‚‚‚ÿFile LoadData | Load New FilesData | Other Data Types | Load DLS DataData | Other Data Types | Load Electrophoresis DataData | Other Data Types | Load Equilibrium DataOpens the dialog box for selecting a number of Optima XL-A or XL-I data files for analysis. At least two files from a series of sedimentation velocity scans have to be selected, unless a list of previously selected files is selected (e.g. list.ip1, see below). š]ƒ"‰= H€»€€‚ãž ]D€‰€ãt¥€‰€‚ÿOnce a set of files has been selected, automatically a ASCII file containing the directory and the names of the files will be stored under the filename list.*. (This text-file facilitates later the loading of the same subset, and it can be edited for example with the notepad: Insertion of a '%' character at the beginning of a line immediately preceding a filename will omit loading of this file)). If a data analysis has been performed previously on the same experiment (same directory and same file extension), a prompt will ask if you want to restore the results of the last analysis (see Exit). Then, the data are plotted in the upper graphics (residuals are in the lower portion of the screen, but without a fit, initially the residuals may be identical to the data). The appearance of these graphics can be changed (set the plot range). 7Áˆ…YŒv º€ƒ€€‚€€€ãœÆj4€‰€ãÚ)–Ú€‰€€ €€ €ãq€‰€ã³ŒX€‰€ã8\>Ȁ‰€‚ÿOptions: Two different data filename conventions can be selected (change filename conventions). Absorbance, intensity, and interference data can be loaded and will be automatically distinguished. Spikes can be automatically ignored (ignore spikes). To reduce errors from the acceleration phase of the centrifuge, the scan times can optionally be calculated from the w2t entry of the files instead of the t entry (scan times from t or w2t), or alternatively, the acceleration phase can be included into the Lamm simulations (ramp rotor speed) In case interference data have some fringe offsets, these can be eliminated later using the menu eliminate interference offset. VÜ"‰»Ãz €¹ €€‚‚€€€€€€€€€€€€€€€€€€€ €€€€€€€€€‚ÿIMPORTANT: After the loading of the files, before any analysis can take place, the position of the meniscus, bottom, as well as inner and outer analysis range has to be located. (By default, the meniscus and bottom are simply placed at the first and last data point, respectively, of one of the scans.) First, the bottom position should be specified by double clicking the left mouse button while holding the control key down, and while pointing the mouse to the radial position of the bottom. A black line appears indicating the tentative bottom position, and the exact radius value is shown in the upper left part of the window. It can be relocated by double clicking once more in the same way (again with the left mouse button while holding the control key down), or by using the arrow keys. The YŒ»ÃAƒbottom input can be aborted by pressing the escape key. Once the black line has been located satisfactorily, the bottom position must be fixed by pressing either the enter key, or the tab key. When the bottom has been properly specified, its location is shown as a blue vertical line. The entry of the meniscus location follows the same procedure (control key + double click left mouse button => confirmation by tab or enter). The meniscus entry is shown in red. Next, the outer (right) data analysis limit has be to specified. It follows the same procedure, except that no control key must be pressed while double clicking the mouse to the location. But it also needs a confirmation by tab or enter. The data analysis range is shown by green vertical lines. After specification of the right limit, the left limit is automatically set to a place near the meniscus. It has be to clicked to its proper position.0ýYŒëÅ3 4€û€€‚ã^‹ ۀ‰€‚‚‚ÿSometimes, after multiple mouse input to define locations of these boundaries, multiple of these colored lines can show; they are not always erased. In this case, one can use the command Update Display to clarify the current valid positions. In the end, there should be 4 vertical lines, indicating from left to right meniscus (red), left analysis limit (green), right analysis limit (green), and bottom (blue). The residuals plot should show only data in the radial range between the green lines.»ÃòÈz €€€‚ãÝ¢Üü€‰€‚‚€ € €ã&ÍíD€‰€‚‚€€€ãÚ)–Ú€‰€ãq€‰€ã³ŒX€‰€€‚ÿMore data files of the same experiment can be loaded by using the function adding files.Please Note: If a different data set has been loaded previously, the previous bottom and meniscus location may not be easy to set if the old ones are out of range of the display. In this case, enter the meniscus and bottom first manually in the parameter dialog box (set sedimentation parameters), then refine it graphically. Please Note: The selected loading options (ignore spikes , scan times from t or w2t, and d ramp rotor speed) will have side-effects on the numerical values of the data loaded, and on the data range. r-ëÅdÌE X€[€€‚‚€€‚€€ã.Á‰F€‰€€ €‚ÿVariants: Sedfit can also work with data from dynamic light scattering, Tom Laues electrophoresis apparatus, or XLA/XLI sedimentation equilibrium data files. 1) Loading DLS data: For DLS data, first several raw autocorrelation data sets from Protein Solutions 99 (version 5.20.05) or Brookhaven Instruments are transformed into a new data format. This is described in generate DLS data file. The generated data format can then be loaded with Data | Other Data Types | Load DLS Data. The data will be converted into field autocorrelation functions by using the relationship g(1) = sqrt(abs(g(2)-1)). DLS data can be analyzed in terms of size-distribution, diffusion coefficient distribution, or single species, all using the same framework and in analogy to the sedimentation velocity analyses. º‡òÈÏ3 4€€€€€ €€€‚ÿ2) Electrophoresis data: Electrophoresis data in the new format (with E as a type character in the file header can be loaded in the same way as sedimentation velocity data. However, data from previous formats must be loaded with Data | Other Data Types | Load Electrophoresis Data. The data can be analyzed in analogy to the sedimentation velocity analyses, substituting the s-value by velocities v (in mm/sec), and making use of the fact that the electrophoresis is a process that ressembles sedimentation with a constant force and linear geometry. From the velocities and the known field, electrophoretic mobilities can be calculated.Ÿ‘dÌè- (€#€€€€ €‚ÿ3) Sedimenation Equilibrium Data: Equilibrium data can be loaded (Data | Other Data Types | Load Sedimentation Equilibrium Data), in order to allow the use of the size-distributÏèAƒion formalism for equilibrium analysis. In contrast to the loading of sedimentation velocity data, here only a single file should be loaded. It should be noted that the analysis of molar mass distributions can be very ill-conditioned. The concentrations here are referring to concentrations in the loaded sample (e.g. when the species were uniformly distributed initially), making use of the specified meniscus and bottom position to integrate through the solution column.Y'ÏA2 4€N€€‚‚‚ãë €‚ÿSee also loading initial data= è~1ž°ÿÿÿÿ~Xdata, addingÚ‰AXQ p€€€‚€‚€ €‚€‚ãvy€‰€‚ƒ‚ƒãvy€‰€‚‚ÿAdding FilesData | Add More Files to Set 1This function allows to increase the number of scans that are included into the analysis, by loading additional data files. (These additional data files will not be added to the files documented in the file list.*). If no data previously have been loaded, this will invoke the same function as load files. See also:File LoadJ~¢1±'tÿÿÿÿ¢ data, generating DLS dataGXéE X€€€‚€‚€ €‚€ €‚€ €‚€‚‚‚‚‚ÿGenerating DLS Data Files from Protein Solutions ExportsOptions | Loading Options | Make DLS Data (Protein Solutions 99)Options | Loading Options | Make DLS Data (Brookhaven)Options | Loading Options | Save Mean DLS Data in sedfit formatThis assumes intensity autocorrelation data from homodyne configuration.When working with Protein Solutions (requires Dynamics version 5.20.05), first, several raw autocorrelation data sets from Protein Solutions 99 should be exported in the DynaPro software with the options: analysis results, autocorrelation coefficients, all measurements, ASCII text, include headers. Then, with the Make DLS Data function, they can be loaded into sedfit. This allows selection of good measurements, and to avoid bad ones. *¢ ' €€€‚‚‚‚ÿThe data can then be averaged and saved in sedfit DLS format with the function save mean DLS data.... They can then be analyzed in terms of single species analysis with M and s (instead of D), or in terms of size-distribution analysis (Rh-distribution or D-distribution). For the Brookhaven data, the *.dat file is read and directly saved as *.dlsdat file. In the process, the counts per channel are divided by the measured baseline entry of the BIC data to generate the normalized autocorrelation function.ö¿é 7 <€€€‚‚‚ƒ‚ƒãCr ΀‰€‚‚ÿWhen the *.dlsdat files are later loaded into sedfit for analysis, the data are transformed to the field autocorrelation function by taking the squre root. See also:DLS analysesC L 1­ °ôƒÿÿÿÿL 0Edata, load initial Ù V1 0€³€€‚€‚€ ‚€‚‚ÿLoading Initial DataData | Set Initial Data for Set 1Single species and species that self-association can be analyzed by using an experimental scan as initial condition for the calculated evolution in the centrifugal field. This has the advantage that imperfections in the sedimentation before the initial scan was taken become irrelevant. These can be, for example, artifacts from imperfect synthetic boundary experiments, from acceleration of the rotor, or from an initial temperature-driven convection. While this does not propagate experimental noise into the analysis, it necessitates extrapolation from the analysis limits to the meniscus and bottom, respectively, which may introduce some errors (see below). l)L Î@C T€S€€‚€ €€€ã&ÍíD€‰€€ €‚ÿBy default when loading files, constant initial distribution at time t = 0 is assumed, and this setting has to be switched to experimental initial condition in the parameter dialog box before loading the initial data (see set sedimentation parameters; check this option and press enter). Then, chose the set initial data function in the menu and VÎ@ select the experimental scan that should initialize the calculated evolution (e.g., the first of the series of sedimentation velocity scans). The initial data will be shown by a green line. <ñV EK d€ã€€‚ã£,J€‚‚€ €€ €€ €€ €‚ÿThe experimental data between meniscus and left analysis limit, and between the right analysis limit and the bottom, which may contain optical artifacts, will be replaced by a polynominal extrapolation. The parameters of this polynominal can be changed in (extrapolation of initial data). The results of the extrapolations should be inspected and the parameters optimized. Please Note: If the experimental scan at t = t1 is used as initial condition for a independent species model with more than one component, one makes the assumption that the fractional absorbance of all components is the same across the cell at t = t1. This may not be true. In theory, in this model for each component a separate initial condition would be necessary. Therefore, for more than one independent species, falling back to constant distributions at t = 0 may be necessary. Essentially, use of an initial scan is recommended only for single species model and for species in selfassociation equilibrium.&Î@0E# €€€‚ÿA EqE1CtĄÿÿÿÿqEsFdata, edit filesÐ0EsF2 2€¡€€‚€‚€ ‚€‚‚‚ÿEdit Data FilesData | Edit Data FilesThis function will start the notepad and load the selected file for inspection of original data. This allows changes, such as the manual elimination of spikes.: qE­F13 ôƒÁŒÿÿÿÿ­FŠOsave, fitÒsFÄHE X€¥€€‚€‚€ ‚€‚‚‚€ €ãœÆj4€‰€‚ÿSave FitsData | Save Fit DataFitted distributions, residuals and fitting parameters can be stored on the hard disk. First, the calculated best-fit radial distributions can be saved in files with filenames that can be specified in the save fitted data as dialog box. The filenames of the fitted curves proposed depend on the filename convention that was specified (newer 8-hole XLA software assumed as default, see change filename conventions ). ൭F€K+ $€k€€‚€ €‚ÿFor the newer convention (8-hole XLA software), it is suggested to replace for each distribution the first character of the original data filename with a f - for fitted and to keep the rest of the name the same. This way, for each data file (e.g., 00006.ra2) a new file (f0006.ra2, eventually for the second data set f2006.ra2) is created containing the calculated distributions in XLA format. Similarly, in the save residuals as dialog box, it is suggested to use a r for residuals to denote the XLA formatted files containing the residuals. For the parameters, a file fitparams.ra2 will be generated, with the proper extension. Information saved in this file will be, for example, yÄHNZ ‚€?€€‚€!‚ƒƒƒ‚ƒƒƒƒƒ‚‚‚ƒƒƒ‚ƒƒƒ‚‚ƒƒƒ‚‚‚‚€‚€ €‚‚€€€‚ÿcomponent 1 included:M=54874.457031 g/Mol(floated)s=3.824 S(floated)meniscus at 6.8660 cm(fixed)bottom at 7.2310 cm(fixed)baseline at 0.00000 OD(fitxed)fitted from 6.8839 to 7.2019 cmwith constant initial distributionIf cancel is pressed in one of the dialog boxes, the respective operation is skipped. Please Note Bug: Filename entries deviating from this convention currently do not work, yet, and will be ignored. Also, in this version no warning is given to protect from overwriting older data. ‰W€KŠO2 2€¯€€‚‚€‚€€ €ÿFor the older convention (old 4-hold software) with extension specifying the scan sequence, this extension is kept for the saved distributions, but filename can be changed (e.g., fitcell1.r01). Please Note Bug: Although filename entries in the dialog boxes here do work, no warning is given to protect from overwriting older data. S"N €1ÛĄ· ÿÿÿÿ €(ƒsave, intensity data as absorbanceŠO €ŠO£rŠO¯‚1 0€å€€‚€‚€ ‚€‚‚ÿSave Intensity Data as Absorbance DataOptions | Loading Options | Save Intensity Data as Absorbance DataSince it may be advantageous for the determination of the bottom position or the buffer background absorbance, data that have been collected as intensity files with the XLA can be loaded and analyzed. However, for compatibility of these data files with other software, or for improved visual representation, they can be saved with this function as absorbance files. The file extensions will be automatically changed from *.ri* to *.ra*. . These files will have the reference intensities in the third column. yE €(ƒ4 8€Š€€‚ƒ‚ƒãuŒ+€‰€‚‚ÿSee also:transform intensity to 2 pseudo-absorbance files\+¯‚„ƒ1cÁŒ !ÿÿÿÿ„ƒ‹‰save, intensity as 2 pseudo-absorbance sets^-(ƒâ…1 0€[€€‚€‚€ ‚€‚‚ÿSave Intensity Data as Two Pseudo-Absorbance Data SetsOptions | Loading Options | Save Intensity as 2 Pseudo-Absorbance Data setsFor sedimentation velocity studies, it is possible to generate fill both reference and sample sector with sample. When scanned as intensity data, this function allows to generate two separate absorbance data sets, one for each channel. Of course, since there is no reference transmission recorded (this is simply set to the default of 1000), the data are not true absorbance data, hence the name pseudo-absorbance. 9„ƒˆ% €)€€‚‚ÿSuch data have systematic noise components that are similar in structure to the systematic noise components of the interference optics. Therefore, they can be analyzed using algebraic RI and TI noise decomposition. There will be small correlation of the additional noise and baseline parameters with species of small sedimentation coefficient. For larger particles, however, this is not the case. Therefore, this method can effectively double the capacity of a AUC run for velocity experiments. This method is described in:pâ…‹‰Q p€?€€‚€€€€‚‚ƒ‚ƒã?P˜“€‰€‚ƒã¢lÛ¶€‰€‚‚ÿS.R. Kar, J.S. Kinsbury, M.S. Lewis, T.M. Laue, and P. Schuck. (2000) Analysis of transport experiments using pseudo-absorbance data. Analytical Biochemistry 285:135-142See also:transform intensity to absorbance filessubtract calculated TI/RI noise from raw dataHˆӉ1r· | "ÿÿÿÿӉýŒsave, distribution dataKÆ‹‰Œ… ؀€€‚€‚€ ‚€‚€ €€ €‚‚‚ƒã$©„€‰€‚ƒã/zeD€‰€‚ƒã¬ÑJ±€‰€‚ƒã²ÑJ±€‰€‚ƒãz|•ý€‰€‚ÿSave Calculated DistributionData | Save Continuous Distribution.This feature allows to save the calculated distribution (e.g. van Holde-Weischet, g*(s), or c(M)) to a file, as a two-column tab-delimited ASCII text.van Holde-Weischetg*(s) by least-squares direct boundary fittingcontinuous c(M) by Lamm analysiscontinuous c(s) by Lamm analysiscontinuous Lamm analysis with prior constant diffusion coefficientߟӉýŒ@ N€?€€ƒã¡ë˜€‰€‚ƒã 똀‰€‚‚ÿcontinuous Lamm analysis with prior partial specific volume as function of Mcontinuous Lamm analysis with prior sed-coefficient as function of MGŒD1P € #ÿÿÿÿDÎÀsave, systematic noise€OýŒď1 0€Ÿ€€‚€‚€ ‚€‚‚ÿSave Systematic NoiseData | Save Systematic Noise | Save Noise in FileIf the data analysis has been performed with the time-independent noise and/or the radial-independent noise option, these files can be stored to the hard disk using this menu item. Suggested filenames for the time-independent noise (i.e. the systematic offset in radial direction superimposed to all scans) are *.TIN, filenames for the radial-independent noise (i.e. a systematic noise component that causes an offset to each scan which is constant in radial direction, but different for each scan) are *.RIN. þÎDÎÀ0 .€€€‚€€ €‚‚‚ÿPlease NoďÎÀýŒte Bug: Filename entries deviating from this convention currently do not work, yet, and will be ignored. Also, in this version no warning is given to protect from overwriting older data. PďÁ1G | J‹ $ÿÿÿÿÁÍTI noise correction for eq dataê·ÎÀÆ3 4€o €€‚€‚€ ‚€‚‚‚‚ÿCorrect Equilibrium Scan for TI NoiseData | Save Systematic Noise | Subtract Noise from Eq. DataIf the data analysis has been performed with the time-independent noise option, the calculated systematic TI noise can be subtracted from an equilibrium scan. The strategy would be the following: First, load as set of approach to equilibrium scans (should cover a substantial part of the visible sedimentation process), and analyze them allowing for TI noise. Second, use this menu to load any radial scan in sedimentation equilibrium (absorbance, interference, or intensity data), and subtract the previously calculated TI noise. Save the new file with a new name (suggested extension: is *.RTI). This new file contains data corrected for the systematic noise contribution, as identified by the sequence of approach to equilibrium scans. This should improve the quality of the equilibrium profile and of their analysis. In particular, this can eliminate or reduce the errors in the equilibrium scans resulting from imperfections in the window. The radial grid points of the equilibrium data are not changed for the subtraction. The method seems to work best for low loading concentrations.áÁ%Ì< F€Ã €€‚‚‚€€€ãB@-€‰€‚ÿThe experimental procedure for eliminating the time-invariant noise contribution from equilibrium scans is the use of external loading cells and the acquisition of before and after-blanks. This is described in detail in Ansevin et al., Anal Biochem 1970, 237-261.Please Note (important for work with absorbance data): If working with absorbance data, great care should be taken that the TI noise component does not contain systematic patterns, resulting from a the use of an insufficient model in the approach to equilibrium analysis. This is not as critical in interference data analysis, since there the statistical accuracy is much better. The quality of fit of the approach to equilibrium data should be optimal, and the use of a very large model is recommended, which not necessarily has to reflect properties of the true solutes. After all, the modeling of the approach to equilibrium could be considered here an informed smoothing operation employing all possible solutions of the Lamm equation, without any further interpretation beyond the extraction of TI noise. For example, with absorbance data, fitting with floating t0 has been found very useful. If the TI noise contains any systematic drift, this can introduce systematic errors into the equilibrium data. If the TI noise does not contain a systematic pattern or drift, but looks randomly distributed, it should provide a good correction, and not be a source of systematic error later in the equilibrium data analysis. ð²ÆÍ> J€e€€‚€€€"€€€€‚‚‚‚‚ÿReference: P. Schuck. (1999) Sedimentation equilibrium analysis of interference optical data by systematic noise decomposition. Analytical Biochemistry 272:199-2089%ÌNÍ1)€  %ÿÿÿÿNÍ4printingÿ³ÍYL f€g€€‚€‚€ ‚‚€‚ãH’ùڀ‰€‚‚ãØï•Ã€‰€‚ÿPrintingData | PrintData | Page SetupOnly limited options for printing are currently available. It is suggested that for publication quality graphics, the saved fitted distributions and residuals (save fits) be used in a commercial graphics program. Basically, sedfit can only print the contents of the current sedfit Window (similar to a print screen operation). The position and size of the graphics on the paper will somewhat dependent on the position and size of the sedfit Window in the desktop. This restricts the use of printouts of the sedfit graphics to simple documentation. For directNÍYÍ transfer of the graphics to a word processing program see copy plots. ۝NÍ4> J€;€€‚ãSèœD€‰€㊂œD€‰€‚‚ÿFor better results, the residuals or the data plot, respectivelyy may be toggled off (toggle residual plot on/off and toggle data plot on/off). EYy1&J‹ ( &ÿÿÿÿyZcopy, fit parametersá‹4ZV z€€€‚€‚€ ‚€‚€ €‚‚‚ƒãH’ùڀ‰€‚ƒãØï•Ã€‰€‚‚ÿCopy Fit ParametersCopy | Copy Fit ParametersFor rapid documentation when working with the discrete ideal species model, the fit parameters can be copied into the Windows clipboard using this function. After copying the parameters, switch to any word processing program under Windows, and paste (control - V) this as text into a document. See also:save fitscopy plots?y™1ì R 'ÿÿÿÿ™Fcopy, graphicsFZßE X€€€‚€‚€ ‚‚‚€‚ãÔéЀ‰€€ €‚ÿCopy Graphics of Data and ResidualsCopy | Copy Data PlotCopy | Copy Residuals PlotCopy | Copy Distribution PlotSimilar to copying text to the Windows clipboard for pasting into a word processor or a slide (copy fit parameters), the data graphics and the residual graphics can be pasted as windows graphics metafiles (a vector graphics) into word processors or slide shows. After copying in sedfit, switch to the recipient program and paste the graphics into a document or slide (control - V). g)™F> J€S€€‚ãSèœD€‰€㊂œD€‰€‚‚ÿThe presentation can be changed somewhat by connecting the data points with lines, and by using black and white graphics instead of colors. For better results, the residuals or the data plot, respectively may be toggled off (toggle residual plot on/off and toggle data plot on/off). Oß•1( [ (ÿÿÿÿ•Jcopy, data tables to clipboardzDF 6 :€‰€€‚€‚€ ‚‚‚‚‚‚€‚‚ÿCopy Data TablesCopy | Copy Data TableCopy | Copy Fit Data TableCopy | Copy Residuals TableCopy | Copy Distribution TableCopy | Copy TI Noise TableCopy | Copy RI Noise TableIn order to circumvent the limited plotting and printing capabilities of the current version of sedfit, these menu functions each copy a matrix of numbers in ASCII text format to the clipboard. The data can then be pasted in principle into any spreadsheet program. In particular, it is compatible with pasting into worksheets of the Origin graphics program that comes with the centrifuge. —r•Š % €å€€‚‚ÿThe format of the data, fit data, and residuals are slightly different for interference and absorbance. In interference data, all scans have the same radial grid. Therefore, the radial grid points will be the first column in the table, and all subsequent columns are only the fringe values at these radial positions. For absorbance data, the grid points are slightly different for each scan, and therefore the columns will be a sequence of pairwise (r,A) data. The order of the scans is in general the reverse of the loading order (i.e. of the marking the files when loading data, except for the first and last scan). ~P $. *€¡€€‚€€ €‚ÿPlease Note if Using Origin: For pasting absorbance data into Origin, a worksheet template that has multiple x columns (alternating x and y columns) can be generated (or if using Origin 4.*, the one in the sedfit directory called XLAData.otw can be copied into the Origin root directory), and loaded before pasting the data. For interference data, the default worksheet works fine. After pasting, the data can be easily plotted by marking the whole worksheet and using the menu function in Origin plot and selecting the desired plot type. This avoids handling each scan separately. &Š J# €€€‚ÿ< $†1‰R ž )ÿÿÿÿ†ƒCplot, range ÏJŸA> J€Ÿ€€‚€‚€ ‚‚‚€‚‚‚€€€‚ÿSetting the Display RangeDisplay | Set RangeDisplay | †ŸAJFull RangeDisplay | Data RangeThe plot range of the data graphics can be changed either by manual input of the minimum and maximum radius and absorbance, respectively, or by using the mouse. For mouse input, position the mouse to the upper left corner to be displayed, and drag the cross to the lower right corner of the desired display range, while holding the right mouse button pressed. 䞆ƒCF Z€=€€‚‚‚‚‚‚ƒã?õ€‚ƒãϗ÷选€‚‚ÿDouble click with the right mouse button changes back to the last display range. Full data range can be achieved using the menu function. For convenience, the displayed range can also be adjusted to include only the data within the fitting limits. This is done with the function data range, which can also be invoked by the keyboard shortcut Ctrl.-DSee also: data mark sizedisplay filenamesIŸAÌC1“[ &ˆ *ÿÿÿÿÌCKdata, align interferenceµƒƒCF2 2€€€‚€‚€ ‚‚€‚‚ÿAlign Interference DataOptions | Loading Options | Eliminate Interference OffsetInterference data sometimes have integral fringe offsets, which are artifacts from the data acquisition software. This menu function allows to align all the data at one specific radial point. The alignment algorithm will add new integral offsets to all scans such that at the specifically selected radial point, they all have a fringe value that is as close as possible to the fringe value of scan #1. Therefore, a good selection of the radial point is a region in the plateau, where little change occurs during the observed sedimentation process. &ÉÌC§J] ˆ€“€€‚ãQÿ-s€‰€‚‚€€€ã&ÍíD€‰€€€€ã¢lÛ¶€‰€‚ÿA potential problem might occur if no point can be found within the solution column that does not change less than 0.5 fringes during the time observed. After alignment of the data, the new data can be saved (save raw data set) for documentation or analysis with other methods. However, the alignment is not necessary, if the option fit RI noise is switched on in the parameter box (set sedimentation parameters). Calculating RI noise is the recommended treatment. The reason is, that the algebraical elimination of jitter in the scans can without any further problems be applied to the integral shifts as well. The only difference is that elimination of the fringe shift looks nicer. Mathematically, there is no difference. Furthermore, calculated radial invariant noise offsets including integral fringe shifts can be subtracted from the raw data after, or at any stage of the analysis (subtract calculated TI/RI noise from raw data). o<FK3 6€x€€‚‚ƒã¢lÛ¶€‰€‚‚ÿsee subtract calculated TI/RI noise from raw dataG§J]K1µž U +ÿÿÿÿ]Kvƒdata, eliminate jitterBKŸM? L€€€‚€‚€ ‚‚€‚‚ã&ÍíD€‰€‚ÿEliminate JitterOptions | Loading Options | Eliminate JitterProbably due to vibrations and thermal fluctuations in the ultracentrifuge, interference scans can exhibit radially independent, but time-dependent offsets (jitter). This radial-invariant noise should be eliminated or taken into account for an optimal data analysis. The function eliminate jitter can be used to align the data in the air-to-air region, in order to avoid calculating RI noise algebraically (set sedimentation parameters).ò­]K€E X€[€€‚€€ãt¥€‰€‚‚ã劈€‰€‚ÿThe function assumes that the viewing window of the data plot defines the air-to-air in which the alignment should take place. Therefore, usually one would have to change the displayed section of the data. This can be done by using the function set the plot range in conjunction with the right mouse button. If this has been done, press YES in the menu box, if not, press NO, make the required radial selection, and invoke this menu again. The magnitude of the jitter will be stored in the RI Noise data array, and can be retriŸM€Keved using the copy RI noise table (copy data tables) function, which allows to paste the data into a spreadsheet program, such as Origin. jŸMƒQ p€3€€‚ã8\>Ȁ‰€ãQÿ-s€‰€‚‚€€ã¢lÛ¶€‰€‚ÿAfter elimination of the jitter, data can be aligned for possible integral fringe offsets (sort interference fringe offsets). The new data can be saved (save raw data set) for documentation or analysis with other methods. Please note: The calculation of RI noise generally seems to give better results than this air-to-air alignment. Furthermore, calculated radial invariant noise offsets can be subtracted from the raw data after, or at any stage of the analysis (subtract calculated TI/RI noise from raw data). o<€vƒ3 6€x€€‚‚ƒã¢lÛ¶€‰€‚‚ÿsee subtract calculated TI/RI noise from raw data@ƒ¶ƒ1æ&ˆ ž ,ÿÿÿÿ¶ƒ\…plot, residualsŠcvƒ\…C T€Ç€€‚€‚€ ‚€‚‚‚ƒ‚ƒãŠ‚œD€‰€‚‚ÿView the ResidualsDisplay | Show ResidualsIn the default operation, the residuals are displayed in the lower half of the sedfit window. However, the residuals plot can be toggled off and on. This may be useful for generating graphics to be pasted into word processor, slide software, or for printing. See also:toggle data plot on/off= ¶ƒ™…1`U © -ÿÿÿÿ™…Œ†plot, update#ñ\…Œ†2 2€ã€€‚€‚€ ‚€‚‚‚ÿUpdate all GraphicsDisplay | UpdateThis refreshes the plot of data and residuals, avoiding the results of the simulations. This can be used, for example, to clarify the position of the meniscus, bottom, and fitting limit markers.; ™…÷†1Þž  .ÿÿÿÿ÷†šˆplot, data£`Œ†šˆC T€Á€€‚€‚€ ‚€‚‚‚ƒ‚ƒãSèœD€‰€‚‚ÿToggling the Data GraphicsDisplay | Show DataIn the default operation, the data are displayed in the upper half of the sedfit window. However, the data plot can be toggled off and on. This may be useful for generating graphics to be pasted into word processor, slide software, or for printing. See also:toggle residual plot on/offE÷†߈1G© Ž /ÿÿÿÿ߈á‹plot, data mark sizeS"šˆ2‹1 0€E€€‚€‚€ ‚€‚‚ÿChanging the Data Mark SizeDisplay | Data Mark SizeSince the display of a large number of data points contained in the sequence of sedimentation velocity scans can be problematic, this function allows to optimize the data mark size for the screen that is being used. This may help inspection of the quality of the fit. The default size, circles with 2 pixel radius, can be changed to single screen pixels (values 0 or 1), or to larger circles. The entry -1 changes the presentation of the data from points to lines for each data set.¯‰ßˆá‹& €€€‚‚‚ÿIf working with interference data, changing the data representation to lines may accellerate the drawing of the data to the screen. J2‹+Œ1ú  + 0ÿÿÿÿ+Œۍplot, with data filenames°wá‹ۍ9 @€ï€€‚€‚€ ‚€‚‚‚€€‚ÿDisplay Data FilenamesDisplay | Show FilenamesTo get information on the scans that are currently loaded for analysis, the data filenames can be displayed (toggled on/off) across the sedfit window. The color of the filenames corresponds to the color of the respective data symbols. Please Note Bug: This color code mapping dose not seem to be always correct. K+Œ&Ž1ÚŽ Q 1ÿÿÿÿ&Ž{Âmodel, independent speciesPۍ‚À< F€)€€‚€‚€ ‚€‚‚‚€ €€ ‚ÿIndependent Species ModelModel | Non-InteractingThis model describes the ideal sedimentation of one or more (up to four) independent, non-interacting species. In case of more than one species, the distributions are separately calculated and added. Please Note: In this model, the parameter input dialog box has the total loading concentration (i.e. total initial absorbance, or total fringe shift, re&Ž‚Àۍspectively) in the entry for component one, and all other concentrations are expressed as fractions of the total. ùQ&Ž{š £€€‚‚‚ƒã³ŒX€‰€‚ƒãõ„"c€‰€‚ƒãgœKF€‰€‚ƒãw“‘\€‰€‚‚‚‚ƒã&ÍíD€‰€‚ƒãgœKF€‰€‚ƒãjˆ~ò€‰€‚ƒã&ƒDI€‰€‚ƒã$©„€‰€‚‚ÿA number of variants of the non-interacting models are available, such asramp rotor speedset t0 time of sedimentationspecial geometriesanalyze time-dependent s, MSee also:set sedimentation parametersspecial geometriesmonomer-dimer modelmonomer-trimer modelvan Holde-Weischet\+‚À×Â1Ù+ :ˆ 2ÿÿÿÿ×ÂTÊmodel, special geometry independent speciesùÇ{ÂÐÆ2 2€€€‚€‚€ ‚‚€‚‚ÿSpecial GeometryModel | Electrophoresis and Other Geometries | linear Lamm equationModel | Electrophoresis and Other Geometries | external loading cellWhen working with six-channel centerpieces or external loading cells, the wall of the solution column are not sector-shaped. While this usually does not allow sedimentation velocity experiments, low-speed runs are little affected by the walls (as long as the lateral diffusion is smaller than the sedimentation). Accordingly, for example, the systematic noise elimination procedure is still possible. However, it has to be taken into account that the different geometry of the cell leads to different redistribution of the material, e.g. the absence of radial dilution. This can be achieved by using the linear Lamm equation model. Technically, these functions switch the simulations to use different finite element matrix elements, which have been calculated for the specified geometries accordingly.œ˜×É% €1€€‚‚ÿWhen using external loading cells without oil, the rounded corners of the centerpiece can have a very small effect on the redistribution of the material. In this case, the external loading cell model can be used. Dependent on the volume of oil used in the experiment (entry required in ml), based on the geometry of external loading cells the bottom location of the solution column is calculated. This allows to take the effect of the rounded corners quantitatively into account. Because of the greater complexity of this Lamm equation model, this function is much slower. In practice, probably the linear Lamm equation model is in most cases sufficient. NJÐÆTÊ= H€€€‚‚€ ‚€‚‚ƒãÿÓü&€‰€‚‚ÿPlease Note: These models only work in conjunction with the independent species model. See also:independent species modelU$É©Ê1 Q & 3ÿÿÿÿ©Ê”model, autocorrelation data from DLS”JTÊ=ÍJ b€•€€‚€‚€ ‚‚€‚ã²ÑJ±€‰€ã¬ÑJ±€‰€‚ÿDLS analyses: Fitting Autocorrelation Data by Diffusion Coefficient and Hydrodynamic Radius DistributionsModel | Dynamic Light Scattering | DLS: Continuous I(Rh)-DistributionModel | Dynamic Light Scattering | DLS: Continuous I(D)-DistributionThese models are variants of the continuous Lamm equation distribution analyses (continuous c(s) by Lamm analysis and continuous c(M) by Lamm analysis), adapted for DLS data analysis. This is done by simply replacing the Lamm equation solutions by the exponential expression for a single species autocorrelation function. Òš©Ê8 >€7 €€‚€†"€‚€‚‚‚‚ÿIn case of the diffusion coefficient distribution, D is directly used in the model for the autocorrelation function, in case of Rh-distribution, D is calculated via Stokes-Einstein equation. All other parameters and distribution methods are similar to those for the continuous Lamm equation modeling, which makes this analysis very similar to the one performed in CONTIN described by Stephen Provencher. One difference to the c(s) and other distribution models is that here the Rh or D grid are spaced (and displayed) logarithmically. This relates better to the resolution of the method. However, one difficulty arises from this is that the=ÍTÊ differential distribution functions can be either defined on a logarithmic scale, which displays the area under the curves in log units proportional to the scattering intensity of the subpopulations, or it can be defined in linear units, in which case the area under the curve does NOT correspond to the scattering intensity of the subpopulations. However, in this case, if the data are (exported and) displayed on a linear scale, this relationship is restored. [In short, this problem comes from the nonlinearity of the integration variable in log units]. Therefore, which units are better depends on the framework of the desired interpretation. For this reason, there is a switch in the parameter box allowing to change the integration variable between linear and log units.y&=Í”S t€M€€‚‚‚‚‚ƒã²ÑJ±€‰€‚ƒã㇏€‰€‚ƒã.Á‰F€‰€‚‚ÿAutocorrelation data can also be analyzed with the single species model (this is the standard ), also simply replacing the Lamm equations by the exponential decay described above. continuous c(s) by Lamm analysisRegularization by maximum entropygenerate DLS data fileFÚ1±:ˆ = 4ÿÿÿÿÚEstatistics, runs test,”, &€€€‚€‚€‚ÿRuns TestThe display after simulation and during the fitting procedure contains the runs-test. It gives a measure, Z, for how random the residuals are. The Z-value gives the number of standard deviations by which the given number of runs is statistically different from the expectation value for normally distributed noise. For Z-values smaller than 2-4, the residuals are pretty random, for very large Z-values the residuals are non-random, and have systematics (runs or positive or negative residuals).?ÚE( €/€€‚‚‚‚‚ÿThis feature is useful to assess the statistical quality of the fit, in particular, when the large number of scans does obscure their inspection for randomness. This test is implemented as described in ML Johnson, Methods Enzymol 1992, (Numerical Methods volume 210) p 96.> ƒ1& O 5ÿÿÿÿƒGstatistics, FIEÌ , &€;€€‚€‚€‚ÿF StatisticsFor analyzing the quality of fits obtained with different parameter values, the variance of the fit (chi-square) is a very useful statistical quantity. The ratio of the chi-square of two fits is distributed like a Fisher distribution. Therefore, this distribution can be used to judge if a given variance increase (e.g. after change of a parameter value) has a magnitude in a range that could occur just by statistical error in the data (assuming normally distributed noise), or if the variance increase is significant. ž‡ƒ„1 0€€€‚€ €€ €‚ÿThe principle of using the F-statistics for parameter error analysis is constraining one parameter (the one for which the error estimates are being calculated) while optimizing (floating) all others to achieve the best-fit given this one constraint. F-statistics can predict the increase of the sum of squares that is associated e.g. with one standard deviation contour (depending on the number of data points and the overall best-fit sum of squares). This procedure, as described in Bevington: Data Reduction in the Physical Sciences and in Press et al.: Numerical Recipes in C, incorporates correlation of the fit parameters into the error estimates, and does not make assumptions about the shape of error contour map. The F-statistics is implemented as described in Johnson & Straume (1994) Comments on the analysis of sedimentation equilibrium experiments. Schuster & Laue Book, p. 37-56ÃnÌ GU z€Ü€€‚‚€€‚ƒãÕ}€‰€‚ƒãD_€‚ƒãÑ1s…€‰€‚ÿSee also:calculate variance ratiocalculate confidence intervalmake error contour mapsP„—1×= Մ 6ÿÿÿÿ—xJstatistics, confidence intervalK GîD@ N€ €€‚€‚€ ‚‚€‚‚‚ã¹Àk̀‰€‚ÿCalculate Confidence IntervalStatist—îDGics | Confidence Interval for sStatistics | Confidence Interval for MBoth functions work similar for calculating the confidence intervals of s or M of the first component. (If the other components are of interest, they should be exchanged and brought into the position of the first species.) The calculation performed by sedfit works as follows: Starting from the best fit value, the parameter which error limit is sought is moved to a non-optimal value and kept fix. Then, all other parameters are floated and allowed to compensate this constraint. The resulting variance of the fit is observed, and the parameter in question is moved a little bit further, again followed by constrained fit, etc. Goal is to bring the variance of the constrained fit close to the value that is predicted by F-statistics (F statistics) for the given confidence limit. The parameter value that corresponds to this variance increase constitutes one error limit. This is followed by a constrained fit moving the parameter in question into the opposite direction, again looking for the right variance increase. This will give the other error limit. These errors are not necessarily symmetric (!) and take correlation of the parameters into account. ã—G3 4€Ç€€‚‚ƒ‚ƒ€€‚ƒ‚ƒ‚ÿFor starting this function:1) a confidence level has to be specified (typically 0.68 or 0.95)2) a test-interval needs to be specified, which should ideally be 1/4 of expected standard deviation of the parameter, or smaller3) a message box reminds to make sure to start from best-fit situation, and that all unknown parameter should be floated4) multiple fitting operations will start, one can follow the test parameters in the display (first moving up, then going down) ÐîDI; D€¡€€ƒ‚‚€ ‚€ƒãa€‰€ ‚ÿ5) a message box appears with the result: best-fit value (lower limit, upper limit). Also displayed is the rmsd of the fit that was calculated to be the statistical cutoff value.Please Note: 1) It is absolutely necessary for realistic results that before calculating the confidence interval the best-fit has been found. This should be verified by a couple times invoking the start fitfunction and ensuring that the parameter dont change anymore. i"GxJG \€E€€ ‚‚€‚‚ƒã¹Àk̀‰€‚ƒãÑ1s…€‰€‚‚ÿ2) The fits should not be interrupted, otherwise the variance increase will be artificially high, and the error limits underestimated3) if the procedure doesnt converge, try a different test interval for s (this usually helps)See also:F statisticsmake error contour mapsJIÂJ1(O  7ÿÿÿÿÂJ,Ãmodel, van Holde-Weischet1êxJóNG \€Õ€€‚€‚€ ‚‚€‚‚€ ‚€‚ã²ÑJ±€‰€‚ÿvan Holde-Weischet analysisModel | van Holde-WeischetModel | extrapolate ls-g*(s) vs 1/sqrt(time)A) Model | van Holde-WeischetThe basic model follows the procedure outline by van Holde and Weischet, 1978, and Demeler et al 1997. For an introduction, best see Borries Demelers tutorial on van Holde-Weischet analysis on his website, but note that the implementation in sedfit is slightly different. In addition to the plots showing the linear extrapolation of s, which allows to do the diagnostics according to where the lines meet, sedfit shows the best-fit position of each of the boundary fractions directly in the raw data space, i.e. it calculates the model-function, and residuals. This has the advantage that it allows to judge how well the data are described by the van Holde-Weischet analysis. [The implementation in sedfit is mainly for allowing to compare different analyses, for the actual interpretation of the data, I recommend the continuous c(s) by Lamm analysis.];ÂJ:‚+ $€!€€‚€€‚ÿBriefly, in our implementation, for each scan the sedimentation boundaries are divided in N fractions of the plateau signal, and the best-fit least-squares radial positions of the boundary fractions are calculated by averagióN:‚xJng the radii of all data points that have absorbancies within a fraction. The first and last fraction is omitted because of the large noise in those fractions. The resolution N is chosen by the user, but reduced if necessary in case empty fractions were encountered (i.e. the division of the boundary was too fine). Apparent s-values are calculated for each boundary fraction, and s-values at infinite time are determined by extrapolation in a inverse of the square-root of time scale, defining an integral sedimentation coefficient distribution G(s).pHóNª„( €‘€€‚€‚ÿImportant: It is essential for the van Holde-Weischet method to have a clearly defined solution plateau near the bottom. For defining this plateau region, sedfit will use the 0.05 cm of data just inside the set right fitting limit (green line). Only data can be analyzed that have virtually horizontal sections of the scans next to this limit, and this condition should be met BY ALL SCANS. Similarly, solven plateaus need to be defined, but for these, it is sufficient that ALL SCANS CLEAR THE MENUSCUS AND the 0.05 cm of data in the LAST SCAN exibit a clear solvent PLATEAU.Œƒ:‚f‡9 @€€€‚‚€‚€ €#€$€#€ ‚ÿFor interference data, one needs to use the extrapolation of ls-g*(s) to infinite time (see below), because of time-invariant noise problems Input is required from the user specifying the number of fractions. (This number will be reduced to the highest feasible value, if this user-defined value is too high. A reasonable number is usually 20 - 30). Values can be changed by clicking once more on the menue function for this analysis (Model | van Holde-Weischet). After specifying the number, it is necessary to start executing the analysis by using the Simulate->for loaded data (ctrl-R) command, or the Fit command (ctrl-F). Ùª„„ŠE X€³€€‚‚‚ãØï•Ã€‰€ã劈€‰€€€‚ÿA second question will appear for determining if the procedure is to be applied for sedimentation (default, press yess button) or flotation (press no). In case of flotation, all the information about required plateaus is understood in reverse, i.e. Solution plateau near the meniscus for all scans and solvent plateau near the bottom required for the last scan. If selected by the user, after the calculation, the plot of s(app) vs 1/sqrt(time) is displayed in the area where usually the data are shown. This plot and its data can be copied using the copy plots and copy data tables functions, by using the copy data plot and copy fit data table menu points. This plot is switched off by using the ESCAPE key. Ýf‡—6 :€»€€‚€ €‚‚‚€ ‚€‚‚ÿPressing the ESCAPE key will return to the usual display of the data and residuals, where the calculated boundary fractions shown together with the raw data, and residuals are displayed. In the bottom part of the window, the integral distribution G(s) is shown as a curve boundary fraction w-versus-s.B) Model | extrapolate ls-g*(s) vs 1/sqrt(time)In this variant, the position of the boundary frations are not obtained directly from the data. Instead, apparent s-values for boundary fractions are obtained via equivalent area fractions of a series of ls-g*(s) curves, which then are subjected to the same 1/sqrt(time) extrapolation. This allows working in the presence of time-invariant and radial invariant noise. 'ö„ŠÊÁ1 0€í€€‚ã/zeD€‰€‚ÿSome additional input is required for the calculate of ls-g*(s): These are the resolution, smin and smax, and confidence level of the ls-g*(s) (see g*(s) by least-squares direct boundary fitting), as usual. Because we need ls-g*(s) curves at different times, the total number of scans is subdivided in subsets, which are input in the field #scans for g*(s). Some care has to be taken that this number is not too small, resulting in instable ls-g*(s) curves, and not too large, resulting in poor time resolution. Since I have not optimized this to the stage o—ÊÁxJf developing a general rule for good default values, some testing with different numbers may have to be done. Connected to this is the way in which the bunches of scans are made, either in sequence like [1,2,3] [4,5,6], etc. or like a moving box [1,2,3], [2,3,4], [3,4,5], etc. Check slide frame box for this second method. Obviously, the sliding frame has the advantage of providing more ls-g*(s) curves, but it also will take much more time.b—,Ãa €€€‚‚‚‚‚ƒã²ÑJ±€‰€‚ƒã 똀‰€‚ƒã¬ÑJ±€‰€‚ƒã=†|]€‰€‚‚ÿThe rest of the input and output is similar to the van Holde-Weischet method. See also:continuous c(s) by Lamm analysiscontinuous Lamm analysis c(s) with conformational changecontinuous c(M) by Lamm analysissave distributionEÊÁqÃ1Մ b… 8ÿÿÿÿqùÈmodel, monomer-dimerí,ÏÅ1 0€Û€€‚€‚€ ‚€‚‚ÿMonomer-Dimer Self-Association ModelModel | Monomer-Dimer instant.This model describes the ideal sedimentation of one species that is in rapid (instantaneous on the time scale of the centrifugation) monomer-dimer self-association equilibrium. It is assumed that the buoyant molar masses are additive, which allows to calculate the dimer diffusion coefficient using the Svedberg equation from monomer sedimentation and diffusion coefficient and the dimer sedimentation coefficient. ÃqÞÇL f€‹€€‚€ €‚‚ƒ†"€‚‚‚‚€ƒ†"€€‚‚ÿPlease Note: Here, the parameter input dialog box has a field for the dimerization (association) constant. It is used here as the base 10 logarithm of the binding constant in the same units as the data. Assuming, for example absorbance data, the binding constants would be and consequently, the binding constants would transform according to(please note that the extinction coefficients should correct for the pathlength 1.2 cm).¯Å¹Èl Š€_€€‚‚ƒãÿÓü&€‰€‚ƒã&ƒDI€‰€‚ƒãœÞ€‰€‚ƒã©Î‹€€‰€‚ƒã&ÍíD€‰€‚‚ÿSee also:independent species modelmonomer-trimer modelmonomer-dimer-tetramer modelmonomer-tetramer-octamer modelset sedimentation parametersFžÇÿÈ1— ʉ 9ÿÿÿÿÿÈPÎmodel, monomer-trimer#ò¹È"Ë1 0€å€€‚€‚€ ‚€‚‚ÿMonomer-Trimer Self-Association ModelModel | Monomer-Trimer instant.This model describes the ideal sedimentation of one species that is in rapid (instantaneous on the time scale of the centrifugation) monomer-trimer self-association equilibrium. It is assumed that the buoyant molar masses are additive, which allows to calculate the trimer diffusion coefficient using the Svedberg equation from monomer sedimentation and diffusion coefficient and the trimer sedimentation coefficient. ÅÿÈ4ÍM h€€€‚€ €‚‚ƒ†"€‚‚‚‚€ƒ†"€€‚‚‚ÿPlease Note: Here, the parameter input dialog box has a field for the trimerization (association) constant. It is used here as the base 10 logarithm of the binding constant in the same units as the data. Assuming, for example absorbance data, the binding constants would be and consequently, the binding constants would transform according to(please note that the extinction coefficients should correct for the pathlength 1.2 cm).¯"ËPÎm š€_€€‚‚‚ƒãÿÓü&€‰€‚ƒãjˆ~ò€‰€‚ƒãœÞ€‰€‚ƒã©Î‹€€‰€‚ƒã&ÍíD€‰€‚‚ÿSee also:independent species modelmonomer-dimer modelmonomer-dimer-tetramer modelmonomer-tetramer-octamer modelset sedimentation parametersN4ÍžÎ1Šb… Š:ÿÿÿÿžÎšmodel, monomer-dimer-tetramerì§PΖE X€O€€‚€‚€ ‚€‚‚‚€ €ãjˆ~ò€‰€‚ÿMonomer-Dimer-Tetramer Self-Association ModelModel | Monomer-Dimer-Tetramer instant.This model describes the ideal sedimentation of one species that is in rapid (instantaneous on the time scale of the centrifugation) monomer-dimer-tetramer self-association equilibrium. It is žÎ–PÎassumed that the buoyant molar masses are additive, which allows to calculate the dimer and tetramer diffusion coefficients via the Svedberg equation.Please Note: Here, the parameter input dialog box has fields for the monomer-dimer (K12) and the monomer-tetramer (K14) association constants. It is used here as the base 10 logarithm of the binding constant in the same units as the data. Transformations of the binding constants from signal units into other (e.g. molar) units works similar as in the other self-association models (see monomer-dimer model), and the optical pathlength (usually 1.2 cm) should also be taken into account.ŠžÎšl Š€M€€‚‚ƒãÿÓü&€‰€‚ƒãjˆ~ò€‰€‚ƒã&ƒDI€‰€‚ƒã©Î‹€€‰€‚ƒã&ÍíD€‰€‚‚ÿSee also:independent species modelmonomer-dimer modelmonomer-trimer modelmonomer-tetramer-octamer modelset sedimentation parametersP–ø1Rʉ ÷;ÿÿÿÿøúmodel, monomer-tetramer-octamerò­šêE X€[€€‚€‚€ ‚€‚‚‚€ €ãjˆ~ò€‰€‚ÿMonomer-Tetramer-Octamer Self-Association ModelModel | Monomer-Tetramer-Octamer instant.This model describes the ideal sedimentation of one species that is in rapid (instantaneous on the time scale of the centrifugation) monomer-tetramer-octamer self-association equilibrium. It is assumed that the buoyant molar masses are additive, which allows to calculate the dimer and tetramer diffusion coefficients via the Svedberg equation.Please Note: Here, the parameter input dialog box has fields for the monomer-dimer (K12) and the monomer-tetramer (K14) association constants. It is used here as the base 10 logarithm of the binding constant in the same units as the data. Transformations of the binding constants from signal units into other (e.g. molar) units works similar as in the other self-association models (see monomer-dimer model), and the optical pathlength (usually 1.2 cm) should also be taken into account.€øúl Š€I€€‚‚ƒãÿÓü&€‰€‚ƒãjˆ~ò€‰€‚ƒã&ƒDI€‰€‚ƒãœÞ€‰€‚ƒã&ÍíD€‰€‚‚ÿSee also:independent species modelmonomer-dimer modelmonomer-trimer modelmonomer-dimer-tetramer modelset sedimentation parametersGêA 12Š_ <ÿÿÿÿA ,model, electrophoresis:ãú{ W |€Ç€€‚€‚€ ‚‚‚€‚ãÿÓü&€‰€ãz|•ý€‰€ã/zeD€‰€‚ÿElectrophoresis Geometry: Linear Lamm Equation With Linear ForceModel | Electrophoresis and Other Geometries | Electrophoresis: Lamm equation for discrete speciesModel | Electrophoresis and Other Geometries | Electrophoresis: ls-g*(v)Model | Electrophoresis and Other Geometries | Electrophoresis: c(v) distribution with constant DThese models are variants of the corresponding Lamm equation models (independent species model, continuous Lamm analysis with prior constant diffusion coefficient) and ls-g*(s) models (g*(s) by least-squares direct boundary fitting), adapted for the linear geometry of the electrophoresis apparatus (no radial dilution), and the linear force (no radial dependency of the force). ±…A ,, &€ €€‚€ €‚‚ÿPlease Note: Due to the different geometry, the sedimentation velocity are actually true linear velocities. The are assumed to be in units of micrometers per second. Also, because the length of the electrophoresis cell is usually known, the bottom position is not speciefied in the parameter input box by its absolute location, but only relative to the location of the meniscus. R!{ ~1Þ÷«‚=ÿÿÿÿ~JDsedimentation, execute simulation~,Ac ”€7€€‚€‚€ ‚€‚ã&ÍíD€‰€‚‚ã²ÑJ±€‰€ã$©„€‰€ã/zeD€‰€‚ÿSimulate SedimentationRunSolves the Lamm equation for the given model, sedimentation parameters (set sedimentation parameters), and initial condition. The distributions at the times of the loaded scans are displayed as lines in the data graphics, and the new residuals are d~A,isplayed in the residuals plot. In case of distribution models, such as continuous c(s) by Lamm analysis, van Holde-Weischet or g*(s) by least-squares direct boundary fitting, this function executes the calculation of the distribution.G~—CH ^€€€‚ãývÉۀ‰€‚‚€ € €ãq·/ñ€‰€‚ÿAfter the sedimentation, additional information will be given in the left hand side of the sedfit window, including the rms error (rmsd), the number of data points (n) and the sum of squared residuals (SSR). This information can be restored with the menu function show last fit info again.Please Note: This function requires data to be loaded. For models involving non-linear regression, executing a run before starting the fit allows to inspect if the starting values of the floating parameters are OK. If no data are loaded, use generate sedimentation profiles³dAJDO n€È€€‚‚ƒã&ÍíD€‰€‚ƒãq·/ñ€‰€‚ƒãa€‰€‚‚ÿSee also:set sedimentation parametersgenerate sedimentation profilesstart fit\+—CŠD1à_ >ÿÿÿÿŠD9‚sedimentation, generate synthetic data setsq*JDGG \€U€€‚€‚€ ‚€‚‚‚‚‚€ €ã! qD€‰€‚ÿGenerate Sedimentation ProfilesSimulate | Generate DataThis tool allows to calculate and store simulated sedimentation distributions. Before invoking this function, the appropriate model has to be selected. Then, after using this Generate Data function, the user is prompted to give the following information:1) Fit with M and s or D and s. This allows to use either diffusion coefficients or - via the Svedberg equation - molar masses (assuming the partial specific volume specified, see set partial specific volume ) as input. TŠDŠI; D€©€€‚€ €‚‚€ €‚‚€ €‚ÿ2) density of points (cm). This will be the radial increment for the data to be saved (not for the discretization of the Lamm equation). Typical, 0.003 cm seems realistic, corresponding to the entry in the .scn file of the XLA software. 3) rotor speed. This requests the rotor speed in rpm for simulated sedimentation. 4) simulate with rotor acceleration phase? This means that the Lamm equation can be solved with or without simulating an initial linear increase in rotor speed (typical experimental values on the XLA with maximal acceleration settings are about 200rpm/sec).û¬G¡LO l€Y€€‚€ €‚‚€ €‚‚€ €‚‚€ €ã&ÍíD€‰€‚ÿ5) time interval of scans. Time interval in seconds of the distributions to be stored in files (similar as the entry in the method dialog of the XLA software). 6) number of scans. Similar to the entries in the XLA software.7) std of noise. To make the simulation realistic, Gaussian distributed noise can be added to the simulated distributions. Typical values would be in the range of 0.01. 8) Fit and Simulation Parameters. This is the same dialog box as described in set sedimentation parameters. Please note here that the meniscus is automatically suggested to be at 6.5 cm, and the bottom at 7.2 cm. Change these entries as needed in the simulation. œNŠI=ON j€€€‚€ €‚‚€ € €㜄›B€‰€ãH’ùڀ‰€‚ÿ9) Save generated data as. Requests filenames for the distributions to be saved. The calculations have to be saved, otherwise the simulation will be aborted. Files will be saved in the XLA format. Please Note: In the current version, data can only be generated for constant initial distribution. (No experimental file can be taken to initialize the propagation). This limitation could be circumvented, however, loading data files with the right time intervals, and using the run sedimentation function (run sedimentation), followed by saving the fits (save fits). ðµ¡L9‚; D€k€€‚€€€‚€‚€%€€ÿIf the data are reloaded, note that the selected loading options will affect the data. In particular, the treatment of the rotor acc=O9‚JDeleration phase will lead to errors in the Elapsed Seconds, which translate to very small errors if re-analyzing the saved data. Extension in the new version: For generating sedimentation data for given model distributions, essentially the same procedure as described above can be used. The model distribution should be placed in a ASCII file called distrib.dat and should be copied to the folder c:\temp. The format of the file is simple two-column matrix, and should be copied best from the saved results of a previous distribution analysis. ; =Ot‚1x«‚}?ÿÿÿÿt‚±ˆfit, startp'9‚ä„I `€O€€‚€‚€ ‚€‚ã&ÍíD€‰€ã&ÍíD€‰€‚ÿStart FitFitThis menu function starts the optimization of all parameters that are chosen to be treated as floating parameters (see set sedimentation parameters). The optimization routine currently implemented is a Simplex routine. Since the Simplex routine starts the optimization from parameter values randomly chosen around the starting guesses entered in the parameter entry box (set sedimentation parameters), it will be automatically restarted, until the final parameter values do not change more than a specified percentage. Bt‚e‡? L€…€€‚‚‚€&€€ €ãžwœª€‰€‚ÿIn some cases, the linear parameters (concentration, baseline, RI- and TI noise) are calculated algebraically, i.e. they are not included in the Simplex, but their least-squares values are calculated analytically for each of the simulations done while optimizing.Please Note New Feature: During the fit, a runs test is performed (ML Johnson, Methods Enzymol 1992, p 96), counting the number of runs and displaying the number of standard deviations by which this number is larger than the normally distributed expectation value for the given number of data points.L䄱ˆ8 >€)€€‚€㞠]D€‰€€‚‚ÿPlease Note: The fitting procedure will store temporary best-fit parameters to allow restoring the analysis in case of a crash of the program (see Exit). Unfortunately, however, sometimes some information about which parameter was floated is lost in this process. 6e‡çˆ1}c@ÿÿÿÿçˆ.‹notesⱈ‹= H€Å€€‚€‚€ ‚€‚ãœÆj4€‰€‚ÿNotesNotesThis tool starts the Windows notepad, with a default filename that is notes.xxx, where xxx is the extension of the currently loaded files. (If the old filename convention (change filename conventions) is chosen, the default filename will be xxxx.not.) This offers a method to keep a record of sample investigated, the results or remarks of the analysis stored on the harddisk and can be easily altered or extended, simply by clicking on this menu function.(çˆ.‹$ €€€‚‚ÿH‹v‹1z}> Aÿÿÿÿv‹špartial specific volume ×.‹€3 4€¯€€‚€‚€ ‚€‚‚‚ÿPartial Specific VolumeOptions | Set v*rhoThis function allows to enter the partial specific volume (in ml/g) of the solutes, and the density of the buffer (in g/ml). This is used to calculate the buoyancy factor in the Svedberg equation. Alternatively, this partial specific volume can be set to zero, which converts the molar masses to buoyant molar masses. Default values are 0.73 ml/g for the partial specific volume, and 1 g/ml for the buffer density.(v‹š$ €€€‚‚ÿ< €ä1Tc€Bÿÿÿÿ䍵Àfit, M or DŸXšÀG \€³€€€'€‚€‚€ ‚€‚‚‚ƒƒƒ†"€‚‚‚ÿFitting M and s vs D and sOptions | Fitting Options | Fit M and sThis toggles the use of M and s (default) or of D and s as independent parameters to be fitted for each of the solutes. Both treatments are equivalent and related through the Svedberg equation:Dependent on what is chosen, the parameter dialog box will show either M or D, and values are being transformed accordingly. If the checkmark is visible, M and s are in use. If no data are l䍏Àšoaded when switching, the transformation will assume 20C as sample temperature, until this value is overwritten by loading data. &䍵À# €€€‚ÿLÀÁ1Ò> (ƒCÿÿÿÿÁ‡Äfit, speed up first Simplex¢qµÀ£Ã1 0€ã€€‚€‚€ ‚€‚‚ÿSpeed Up First Simplex FitOptions | Fitting Options | Speed Up First Simplex FitThis toggles the use of a smaller grid size (half of what has been entered in the Parameter Input Box) for the first round of Simplex Optimizations. In most cases it will be sufficient to employ a coarser grid for achieving a fast initial convergence. At least one additional Simplex procedure will follow, and all of these simulations will be performed at the specified grid size. The criterion for repeating additional rounds of Simplex optimizations are parameter within the specified tolerance after convergence of the Simplex. äŽÁ‡Ä0 .€i€€‚‚€€‚€‚ÿPlease note: If this feature is used and the rmsd increases during the first round of Simplex, then the step-size is too coarse, and this feature should be switched off = £ÃÄÄ1Á€z„DÿÿÿÿÄÄHÆdata, spikes„R‡ÄHÆ2 2€¥€€‚€‚€ ‚€‚‚‚ÿElimination of SpikesOptions | Loading Options | Dont Load SpikesIf this switch is turned on, spikes (defined as an isolated jump in the absorbance signal by more than 0.4) will be eliminated from the data set. The checkmark indicates the status of this switch. By default, this switch (elimination of spikes) is turned on. LÄÄ”Æ1N(ƒ‡Eÿÿÿÿ”Æ–Édata, set number of columnsHHÆÜÈ1 0€/€€‚€‚€ ‚€‚‚ÿSet Number of Data ColumnsOptions | Loading Options | Set n ColumnsIf this switch is turned on, the user defines the number of columns in a data set. This allows to use data that deviate from the default format from the XLA/XLI in that they have additional data columns. If this function is turned on, a input box appears that allows to set the number of columns. The first column should always be the radial data, the second column the concentration distribution to be analyzed (e.g. in units of absorbance or fringes). º‹”Æ–É/ ,€€€‚€ € €‚‚ÿPlease Note: If a this option is used and the number of columns doesnt match that of the data, the program most likely will crash.EÜÈÛÉ1sz„ƒ‹FÿÿÿÿÛÉ Ïdata, times of scansÉ–ÉáË= H€“€€€(€‚€‚€ ‚€‚€€‚ÿTimes from w2tOptions | Loading Options | Times from w^2tThis switch allows to calculate the time of scan after start of the centrifuge from the w2t entry of the file (on, is default), instead of taking it from the t entry. The advantage of this is that the time needed for acceleration of the rotor, while the centrifugal field is not fully established yet, is not weighted as much. The status of this switch is indicated by the checkmark. ú˜ÛÉÛÎb ’€1€€‚㳌X€‰€‚‚㳌X€‰€ãq€‰€‚‚€ €)€ ãq·/ñ€‰€ ‚ÿAn alternative method, ramp rotor speed,the incorporation of the rotor acceleration phase into the Lamm equation solution is a little more precise, and recommended for larger particles, or if less than the maximum acceleration at the XLA is used. Switching ramp rotor speed on will toggle scan times from t or w2t off, and vice versa.Please Note: The w2t entry of the centrifuge file format has a limited precision. The errors introduced by this in the calculated elapsed seconds can be observed if data are simulated (generate sedimentation profiles), saved, and re-analyzed. For real data, however, this error will be insignificant. .áË Ï( € €€‚€‚‚ÿJÛÎSÏ1 ‡DGÿÿÿÿSÏødata, extrapolate initialŒ ÏdI `€y€€‚€‚€ ‚€‚ãë €ãvy€‰€‚ÿExtrapolation of Initial DataOptions | Loading Options | Set Polynomial Order for Initial ExtraSÏd ÏpolationAn experimental scan can be used as an initial condition for the simulated sedimentation (e.g. if using synthetic boundary techniques) (see load initial data). Unfortunately, however, the experimental scan will not yield reliable data in the regions of the optical artifacts near the meniscus and bottom of the cell. In order to prevent these optical artifacts from sedimenting into the analysis range, an extrapolation procedure is used replacing the original data in the unreliable region, and estimating absorbance values in the region between the meniscus and the left fitting limit (which has been set as the left limit of reliable data, as explained in load files ), and between the right fitting limit and the bottom of the cell. The initial distribution used over the entire range from meniscus to bottom is drawn in green. íÃSÏQ* "€‡€€‚‚‚‚‚‚‚ÿThe extrapolation procedure used is a polynomial extrapolation, based on a data interval within the reliable region next to the fitting limit. The user has two parameters for possible adjustment in case the default extrapolation does not generate satisfying results: 1) the polynomial order, where the default value of 1, and 2) the extrapolation distance factor, with a default value of 1.The distance factor determines the size of the data basis that is used for the extrapolation, in multiples of the distance meniscus - left fit limit (or right fit limit - bottom, respectively). A value of 1 means that the data basis for extrapolation has the same size as the region excluded from the fit.§dø& €€€‚‚‚ÿThe polynomial order determines the highest power of the polynomial used for the extrapolation. For example, the value of 1 will calculate the best-fit straight line through the data used as basis for extrapolation, and then just extrapolates linearly into the regions of artifacts. A value of 2 would take a parabolic fit through the data basis and extrapolate with that, etc. KQC1À ƒ‹€HÿÿÿÿCCstatistics, error contours`ø£ K d€+€€‚€‚€ ‚‚‚€‚ã¹Àk̀‰€€ €€ €‚ÿCalculate Error Contour MapsOptions | Statistical Analysis | s,M rmsd ContourOptions | Statistical Analysis | s1,s2 rmsd ContourOptions | Statistical Analysis | K ContourThese functions automate the repeated fitting required in the evaluation of the statistical accuracy of the best-fit parameters via F statistics.. The principle behind the F-statistics error analysis is constraining one parameter (the one for which the error estimates are being calculated) while optimizing (floating) all others to achieve the best-fit given this one constraint. F-statistics can predict the increase of the sum of squares that is associated e.g. with one standard deviation contour (depending on the number of data points and the overall best-fit sum of squares). This procedure, as described in Bevington: Data Reduction in the Physical Sciences and in Press et al.: Numerical Recipes in C, incorporates correlation of the fit parameters into the error estimates, and does not make assumptions about the shape of error contour map. R!Cõ1 0€C€€‚€ €€ €‚ÿIt can be helpful to calculate 2-dimensional confidence intervals. The functions s,M rmsd contour, and s1,s2 rmsd contour can trace a given confidence limit (to be specified by the user as a given rmsd level) in a 2-parameter space, floating all parameters other than s and M (or s1, and s2, respectively). Also, limits for the parameter range and the resolution for which the map is examined have to be provided. If the rmsd for tracing is specified as 0, all best-fits rmsd in the entire grid of the specified grid are calculated. ÿž£ CG \€q€€‚€ €‚‚‚‚€ã¹Àk̀‰€€€€‚ÿThe K contour function is analogous to the other contours, but calculates the rmsd only for a given grid of K-values (association constants), while floating all other parameters.The results õCøare stored as a ASCII table in the specified file for further analysis. Please Note: These functions are very time-consuming and the independent calculation for the determination of the confidence level is required (F statistics.). Also, while the algorithm that traces a given confidence level in the error surface can be extremely useful in reducing the computation time, it sometimes can loose the trace, or leave the trace incomplete. This can result in reduced apparent confidence intervals. For these reasons, these functions should only be considered as aides, automating part of the computationally intensive and repetitive fitting procedures. Control calculations should be performed, and critical evaluation is absolutely crucial.k:õkC1‰Dm†IÿÿÿÿkC‰Jsedimentation, transition between Lamm equation algorithmsyBCäE7 <€…€€‚€‚€ ‚€‚€€‚ÿSet s for changing Lamm equation algorithmOptions | Fitting Options | set s for changing methodsThe moving hat method for solving the Lamm equation is highly recommended for simulations at high ratio w^2s/D, i.e. for the fitting of data sets that exhibit a relative clear and steep sedimentation boundary. On the other hand, for small sedimentation coefficients or simulations of the approach to equilibrium the Claverie method is advantageous because it allows the use of an adaptive time increment, which can be made very large for slow sedimentation processes. â‘kCÆHQ p€#€€‚€€ã&ÍíD€‰€€ €‚‚€ €€ €)€ €‚ÿIn order to simplify the use of the program, if the checkbox auto method is checked, the algorithms can be automatically switched, according to s-value of the simulation (see set sedimentation parameters ). This option is on by default. The function in the menu Option ->Fitting Options -> set s for changing methods allows the user to specify the sedimentation coefficient, at which the algorithms are changed (Claverie below the specified value, moving hat above the specified value). The default value is 5. The actual s-value that is used for changing the method is corrected for different rotor speeds by the factor (w/30000)^2.ÚäE‰J) €5€€‚‚‚‚‚‚ÿIt may be useful to change this value if, for example, during the fitting procedure error messages show up prompting the user to increase the discretization grid size (an error message from the Claverie procedure, if negative concentrations occur due to too coarse grids or time-steps). Also, this setting might be changed to a higher value if the Lamm equation distributions are initially very slow. JÆHÓJ1£%€JÿÿÿÿÓJ5 sedimentation, parameters)ö‰JüL3 4€í€€‚€‚€ ‚€‚‚‚‚ÿFitting Parameters and ControlsParametersThis menu item invokes a parameter input dialog box, which will be slightly different dependent on the model used. The following is valid for the independent species model, changes in the monomer-dimer and monomer-trimer system are indicated. For other models, more information is given in the help pages corresponding to those models. The upper part contains four similar sections for entering the following parameters for up to four components: «ÓJ€h ž€W€€ƒ€€€€‚ƒ€€€€‚€ƒ€€€€ãš•fD€‰€ã! qD€‰€‚ÿ1) Component switches a component on/off Note: if the component is not switched on, it will be ignored2) concentration in absorbance units or fringes, respectively, dependent on the data type - Note: if multiple components are used, the entry for the first component is the total concentration, the entry of all following components are fractions of the first3) Molar mass in Da, or Diffusion coefficient in 10-7cm2/sec, respectively, switch between unknown M or D - transformation uses the Svedberg equation. The partial specific volume used by default is 0.73, at a buffer density of 1. These settings can be changed using set partial specüL€‰Jific volumeWüLrƒ? L€1€€ƒ€€‚‚€€ €*€ €*€ ‚ÿ4) sedimentation coefficient in Svedberg units. All of these parameters have fields for entry of numerical values, and check boxes that will indicate if this particular will be floated in the fitting process, or kept constant. Note: floating the linear parameters concentration and baseline will cause algebraic optimization not only in the fitting routine (start fitHELP_FITSTART), but also following a single simulation (run sedimentationHELP_SIMULATE). Since algebraic optimization is much better (it avoids non-linear regressions, replacing them by unambiguous direct calculateions with precise optimal values), this is implemented where possible. Therefore, if no optimization and parameter change at all should be performed, make sure that all parameters are unchecked. ÷€‘…( €ï€€‚‚‚‚‚ÿFor the self-associating models, this upper section is simplified, using analogous input for total concentration, monomer molar mass, and s-values of monomer and dimer. The input of the binding constant is referring to the base 10 logarithm of the binding (association) constant in units of absorbance (for absorbance data) or in units of fringes (for interference data) . The middle section contains some controls for the baselines, meniscus and bottom, and initial condition. In more detail:f'rƒ÷‡? L€O€€ƒ€€‚ƒ€€ã¢lÛ¶€‰€‚ÿ1) The checkbox FIT TI Noise fits (algebraically) a background profile that is constant in time (i.e. global to all scans), but is different at each radial grid point. If this is checked, it will be optimized with each simulation.2) The check box FIT RI Noise fits (algebraically) an offset that is constant in radial direction, but different for each scan. If this is checked, it will be optimized with each simulation. (These two noise components can be subtracted from the raw data by subtract calculated TI/RI noise from raw data.)9ú‘…0‹? L€õ€€ƒ€€‚ƒ€€ãšÉ„&€‰€‚ÿ3) The field Baseline allows to enter and float a constant baseline that is common to all scans and that is constant in radial direction. If this is checked, it will be optimized with each simulation. If FIT TI Noise is checked, this field will be ignored. 4) Meniscus position could be entered or changed here (this field will show what has been graphically entered before). The value of the meniscus position can be treated as a fitting parameter. In this case, constraints for a the lowest and highest possible values are necessary, and a prompt will automatically ask for these values. They should be carefully entered, since the default interval could be off. The range constraints can also be set through constrain meniscus and bottom. å®÷‡Ž7 <€]€€ƒ€€ãšÉ„&€‰€‚ÿ4) Bottom position of the cell could be entered or changed here (this field will show what has been graphically entered before). The value of the meniscus position can be treated as a fitting parameter. In this case, constraints for a the lowest and highest possible values are necessary, and a prompt will automatically ask for these values. They should be carefully entered, since the default interval could be off. The range constraints can also be set through constrain meniscus and bottom. This parameter is particularly important when fitting data with high diffusion or low rotor speed, or when fitting the steep part of the profiles in the vicinity of the bottom. ×0‹/À7 <€¯€€‚‚€€€€ ‚‚€‚ÿThe lower section determines the values of parameters that control the solution of the Lamm equation and fitting. Please note: The following control parameters do not have to be changed for the majority of all problems. Therefore, detailed knowledge of the mathematical details of Lamm equation algorithms should not be necessary for running sedfit, in particular if the default values are accepted. In the lower left cornerŽ/À‰J is a series of parameter fields:À~ŽïÄB R€ý€€ƒ€€‚ƒ€€㯏ÎP€‰€€‚ÿ1) Tolerance determines during the fitting (Simplex) routine the tolerance of the final parameter values (in %) that are considered equal. The simplex routine is repeatedly restarted, until all final parameter values are within this tolerance in two sequential simplex runs. Default value is 1.2) Grid Size determines the number of radial increments (dividing the solution column from meniscus to bottom) on which the Lamm equation is discretized. Usually, ~ 100 per mm solution column is a reasonable value. Higher accuracy of the Lamm equation solution can be achieved with higher values, but generally the experimental noise is higher than the error at a discretization of 100/mm. Coarser grids are faster for simulation, but less precise. For complicated situations with time-consuming Lamm simulations, it can be a good strategy to use a coarse grid to get the floating parameter values in a good range, and to use a very high number of grid points only in the end as a final refinement step. If speed up fist Simplex fit is checked, half of the specified grid size is used for the first round of Simplex optimization only.#ñ/ÀÈ2 2€ã€€‚ƒ€€€€‚ÿ3) max dc/c (or dt) has two different functions, dependent on which Lamm simulation algorithm is chosen, and dependent on if fixed dt (see below) is checked. Claverie simulations are based on a stationary grid, and in are implemented in sedfit using an adaptive time-step. max dc/c controls this size of the time-step by limiting the maximal relative change of concentration in the grid to a certain fractional concentration. 1 is a good default value. For moving hat simulations, input in this field has no function. However, if fixed dt is chosen, the time-steps in both the Claverie and moving hat algorithm are constrained to the value given in this field. Note: Usually this default value works fine, and does not need to be changed.4üïÄFË8 >€ù€€‚‚ƒ€€‚ƒ€€€‚ÿThe last section in the lower mid controls the choice of the Lamm solution algorithm.1) Claverie simulation toggles on the use of the finite element method with stationary equidistant grid as described by Claverie. This works best for small s or low rotor speed (i.e. in cases where diffusion influences are high relative to sedimentation). 2) move hat toggles on the use of a finite element algorithm with a moving frame of reference. This method is preferred for cases of high influence of sedimentation versus diffusion, i.e. for high rotor speed and larger molecules. The input field next to the radiobutton allows to change the sedimentation coefficient of the frame of reference. However, this input will be effective only if the check box …IÈËÍ< F€“€€ƒ€€€€€‚ƒ€€‚ÿ3) auto s hat The default configuration is auto s hat on, which adjusts automatically the movement of the frame of reference to the sedimentation coefficient of the simulated solute. This algorithm also works automatically with a fixed time-step, which is determined by the movement of the frame of reference. This size of the time-step, however, can be constrained to smaller values (not to larger ones). 4) fixed dt is a checkbox that can be used to constrain the time-step size. The effective value (in sec) will be the one entered in the field max dc/c (or dt). 2éFË I `€Ó€€ƒ€€€€ãL »@€‰€€€€€‚ÿ5) auto method is by default on. This automatically switches during an optimization from the Claverie method at low s to the moving hat method at higher s. The transition point is by default 2 S, but it can be changed using the function set s for changing Lamm algorithm. Note: If auto method is on, the user does not have to specify which Lamm equation solution technique is used. Instead, automatically the one considered the best for the particular s-value is chosen.ËÍ ‰J)ËÍ5 $ € €€‚‚ÿ ? t 1óm†7Kÿÿÿÿt ( save, raw data Ó5  8 >€§€€‚€‚€ €‚€ €‚‚‚ÿSave Raw Data SetOptions | Loading Options | Save Raw Data SetOptions | Loading Options | Save Raw Data In 3 SubsetsThis menu function allows to save the data set that is being fitted. This can be useful, for example, after elimination of spikes, or after alignment of integral interference offset, in order to facilitate data analysis using other software. Also, equilibrium data can be loaded, and saved using this option to eliminate their spikes. ƒ\t  ' €¹€€‚‚‚‚ÿThe filename specified in the file input dialog box is appended by the original filename and extension.When the raw data are saved in three subsets, the current directory is used, and the first character of the filename will be changed to i for inner sector, m for middle sector, or o for outer sector, respectively. The radii where to cut the data are asked from the user, suggesting 6.2 and 6.7, which are just in the middle between the sectors for the six-channel centerpieces. Further, a integer will be added or subtracted to the scans such that the signal in between the cut radii (i.e. 6.0, 6.45 and 6.95) will be as close to zero as possible. This function therefore should be convenient to simplify subsequent data processing in equilibrium analyses, but separating the different subsets, and eliminating some estimated integral fringe shift.& ( # €€€‚ÿ@ h 1&žLÿÿÿÿh N how to get helpU( œ < F€3€€‚€‚€‚€‚‚‚€ € € ‚ÿHow to get HELPHelp on the menu functions can be obtained by highlighting the menu point (without activating - this can be achieved, for example by using the arrow keys), and pressing F1. The corresponding help page will be displayed. Alternatively, the HELP INDEX can be used. Please note: Sometimes the link between the context highlighted in sedfit and the help-file does not work. A message appears that this help-topic does not exist. However, the help topics can be accessed through the index of the help file. ‘hh N ) "€Ð€€‚‚‚‚‚‚‚ÿIf there are remaining questions, please contactPeter Schuck(301) 435-1950pschuck@helix.nih.govS"œ ¡ 1 7ë Mÿÿÿÿ¡ n fit, constrain meniscus and bottomh+N = H€W€€‚€‚€ €‚‚ã&ÍíD€‰€‚ÿConstraints for Fitting of Meniscus and BottomOptions | Fitting Options | set s for changing methodsIf the meniscus or bottom position is treated as a floating parameter to be optimized (set sedimentation parameters), it can be very useful to introduce constraints (i.e. limits) for these parameter values. For example, while the precise position of the ends of the solution columns may not be visible due to optical artifacts, the boundaries of these optical artifacts in general represent limits for the possible positions of the bottom. ?¡ H : B€ €€‚‚‚‚€ ã?P˜“€‰€ €‚ÿAlways when checking the meniscus or bottom the first time, this menu function is automatically invoked to remind the user of the importance of entering reasonable limits for these parameters. With this menu function, these limits can be changed. TIP: If intensity data are collected instead of absorbance data, the bottom position is easier to specify. Once the intensity data have been inspected, they can be transformed to conventional absorbance data using transform intensity to absorbance files. & n # €€€‚ÿKH ¹ 1¡žÿÿÿÿNÿÿÿÿ¹ FB data, filename conventionsOn A 7 <€1€€‚€‚€ €‚‚‚‚‚€ ‚ÿFilename ConventionsOptions | Loading Options | Old Filename ConventionIf the old 4-hole rotor software is used, the naming conventions for the data files are different from the newer conventions. For example, in the old software the sequence of data files is re¹ A n presented in incrementing the number of the extension and the cell number is encoded in the filename, while in the newer software does it the other way around. This menu function is intended to help adapting the sedfit program to these different data names. 2÷¹ FB ; D€ï€€ ‚€€ €‚€ ‚€€‚‚‚ÿThis option is by default off (i.e. newer filename conventions are the default). The status of this switch is indicated by a check mark in the menu.Please Note: Unfortunately, this option is not yet fully supported in all functions.1A ÿÿÿÿ1ÿÿÿÿÿÿÿÿOÿÿÿÿÿÿÿÿÿÿÿÿ è+(HelvTms RmnSymbolCourierTimes New RomanArialMS SerifMS Sans SerifTimesHelveticaSystemCourier NewAvantGardeITC BookmanHelvetica-NarrowNewCenturySchlbkPalatinoZapfChanceryZapfDingbatsMarlettLucida ConsoleLucida Sans UnicodeMonotype SortsBookshelf Symbol 1Bookshelf Symbol 2Bookshelf Symbol 3Abadi MT CondensedAlmanac MTBaskerville Old FacBauhaus 93Beesknees ITCBell MTBernard MT CondenseBon Apetit MTBradley Hand ITCCalisto MTCentury GothicCooper BlackCopperplate GothicCurlz MTDirections MTEngravers MTEras Bold ITCEras Demi ITCEras Light ITCEras Medium ITCEras Ultra ITCEurostileFelix TitlingForteFranklin Gothic BooFranklin Gothic DemFranklin Gothic HeaFranklin Gothic MedFrench Script MTGill Sans MT Ext CoGloucester MT ExtraGoudy Old StyleGoudy StoutGradlHarringtonHolidays MTImprint MT ShadowJuice ITCKeystrokes 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distribution by Lamm€model, continuos c(s) distribution by Lamm„model, continuos distribution with conformational changeˆmodel, continuos distribution with prior DŒmodel, continuos distribution with prior v-barmodel, electrophoresis”model, g*(s) by least squares˜model, independent speciesœmodel, monomer-dimer model, monomer-dimer-tetramer€model, monomer-tetramer-octameršmodel, monomer-trimer¬model, special geometry independent species°model, time-dependent s and MŽmodel, van Holde-WeischetžnotesŒpartial specific volumeÀplot, dataÄplot, data mark sizeÈplot, rangeÌplot, residualsÐplot, residuals bitmapÔplot, subtract calculated systematic noiseØplot, updateÜplot, with data filenamesàprintingäsave, distribution dataèsave, fitìsave, intensity as 2 pseudo-absorbance setsðsave, intensity data as absorbanceôsave, raw dataøsave, systematic noiseü\SFHELP7.rtf 50 K464B9C67Ösedimentation, execute simulation׏еÐ\Ð6ÖÖ3Í^ÖCÏ€Ì2Ïp×ÝÕõՐÕ@ÐTׯӹËûÎÄΠ΍ÎRÎÕãÍPÓnÔ±ÔÛԏÔwÓ¹ÍHÔ§Õ¹ÕòÒ 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