<HTML dir=ltr><HEAD><TITLE>Re: RE : [RASMB] upper concentration limit AUC</TITLE>
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<DIV dir=ltr><FONT face=Arial color=#000000 size=2></FONT>There is a missing vbar term, k(P) should be = 2BM - vbar, an error in Tanford's otherwise powerful book. Paley Johnson and myself looked at this in 1984 in a paper published in Biochemical Journal:</DIV>
<DIV dir=ltr><A href="http://www.nottingham.ac.uk/ncmh/harding_pdfs/Paper28.PDF">http://www.nottingham.ac.uk/ncmh/harding_pdfs/Paper28.PDF</A></DIV>
<DIV dir=ltr>It is not significant for highly concentration dependent systems such as polysaccharides, but for globular proteins it can be,</DIV>
<DIV dir=ltr>Steve</DIV>
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<FONT face=Tahoma size=2><B>From:</B> rasmb-bounces@rasmb.bbri.org on behalf of Arthur Rowe<BR><B>Sent:</B> Mon 08/09/2008 12:28<BR><B>To:</B> Christine Ebel; 'Beld, Joris'; RASMB@rasmb.bbri.org<BR><B>Subject:</B> Re: RE : [RASMB] upper concentration limit AUC<BR></FONT><BR></DIV>
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<BLOCKQUOTE>Hi Christine (and everyone)<BR><BR>I think this discussion is already in the RASMB Archives.<BR><BR>To summarise very briefly, k(D) is indeed lower than k(s), but not hugely so. For simple, spherical particles, defining all coefficients in volume fraction terms and at limiting infinite dilution, we can write<BR><BR>k(D) = k(P) - k(s) where k(P), the concentration dependence of the chemical potential which is the force driving the flux in translational diffusion, and is given for s single component by (2BM + higher terms) where B is the 2nd virial coefficient. For spheres, 2BM = 8 ml/g; k(s) = 4* ml/g: so k(D) = 4 ml/g. I am afraid that neglecting k(D) is not a good approximation. <BR><BR>Kind regards - will be seeing you (Christine) and lots of others in Newcastle this week. <BR><BR>Arthur<BR><BR>*see "The sedimentation rate of disordered suspensions" Brady, John F.; Durlofsky, Louis J.<BR>Physics of Fluids 1988 31 717-727 for the last word from the fluid mechanics people. You can also look up my Chapter in the 1992 Book (the 'black book') ed s Harding, Rowe & Horton) for details of my own derivation. Which happens to be in total numerical agreement with the Brady/Durlovsky treatment, right p to 64% volume fraction . . . . . <BR><B>Note: </B>the value given above for k(s) = 4 ml/g is for <B>DYNAMIC k(s)</B>. The usual measured value which gets reported is the <B>KINEMATIC</B> k(s), which for spheres has the value 5.0 ml/g. You can get either value out of theory, depending how you play it. Brady & Durlovsky report the kinematic value. All of which was first noted by Burgers in 1939/40, and has been much ignored ever since! As no density 'correction' is called for in the estimation of k(D) or of k(P), it seems reasonable to use the dynamic k(s) in the equation above.<BR><BR></BLOCKQUOTE><BR>
<BLOCKQUOTE><FONT size=2><FONT face=Arial>Dear Joris, dear all, <BR></FONT></FONT><BR><FONT size=2><FONT face=Arial>This reference may be perhaps useful.</FONT></FONT> <BR><BR><FONT size=2><FONT face=Arial><BR></FONT></FONT><BR><FONT size=2><FONT face=Arial>Solovyova A., Schuck P., Costenaro L., Ebel C,</FONT></FONT> <BR><BR><FONT size=2><FONT face=Arial>Non-ideality by sedimentation velocity of halophilic malate dehydrogenase in complex solvents, <BR></FONT></FONT><BR><FONT size=2><FONT face=Arial>(2001) <I>Biophys. J,</I> 81 1868-1880.</FONT></FONT> <BR><BR><FONT size=2><FONT face=Arial><BR></FONT></FONT><BR><FONT size=2><FONT face=Arial>In this work, we analyzed sedimentation velocity profiles considering hydrodynamic and thermodynamic non ideality. (i.e. concentration dependency of s and D) in the case of an homogeneous solution of our protein of interest. The modified Lamm equation was implemented in a model of analysis in Sedfit (note that, unless the programme was recently modified, the kS and kD are expressed in signal unit in sedfit)</FONT></FONT> <BR><BR><FONT size=2><FONT face=Arial>From my experience, the sedimentation velocity profiles are essentially modified by the concentration dependency of the sedimentation coefficient. Thus the concentration dependency of D can be neglected in a first approximation. Also from a theoretical point of view, kD is much lower that ks. <BR></FONT></FONT><BR><FONT size=2><FONT face=Arial>All the best</FONT></FONT> <BR><BR><FONT size=2><FONT face=Arial>Christine <BR></FONT></FONT><BR><FONT size=2><FONT face=Arial><BR></FONT><FONT face="Courier New">Christine EBEL</FONT></FONT> <BR><BR><FONT size=2><FONT face="Courier New">Institut de Biologie Structurale CEA-CNRS-UJF</FONT></FONT> <BR><BR><FONT size=2><FONT face="Courier New">41 rue Jules Horowitz, F-38027 Grenoble France</FONT></FONT> <BR><BR><FONT size=2><FONT face="Courier New">Tel (33) (0) 4 38 78 95 70; Fax (33) (0) 4 38 78 54 94 <BR></FONT></FONT><BR><FONT size=2><FONT face="Courier New">christine.ebel@ibs.fr</FONT></FONT> <BR><BR><FONT size=2><FONT face="Courier New">http://www.ibs.fr/content/ibs_eng/presentation/lab/lbm/ebel.htm</FONT></FONT> <BR><FONT size=2>-----Message d'origine-----<BR><B>De :</B> rasmb-bounces@rasmb.bbri.org [mailto:rasmb-bounces@rasmb.bbri.org] <B>De la part de</B> Beld, Joris<BR><B>Envoyé :</B> lundi 1 septembre 2008 15:24<BR><B>À :</B> RASMB@rasmb.bbri.org<BR><B>Objet :</B> [RASMB] upper concentration limit AUC</FONT> <BR><BR><FONT size=2><BR></FONT><BR><FONT size=2>Dear all,</FONT> <BR><BR><FONT size=2><BR></FONT><BR><FONT size=2>A colleague asked me whether analytical ultracentrifugation has an upper limit with regard to the concentration of the protein. They want to measure the protein at the same concentration as the NMR experiments (> 1 mM). I am not entirely sure but I thought this should be no problem. One could easily measure off-peak at another wavelength than 230nm, e.g. 235nm or 280nm, right?! Or does one run into non-ideality phenomena when doing sedimentation equilibrium at these high protein concentrations?!</FONT> <BR><BR><FONT size=2>Thanks a lot in advance for any feedback.</FONT> <BR><BR><FONT size=2>Best wishes,</FONT> <BR><BR><FONT size=2><BR></FONT><BR><FONT size=2>Joris Beld</FONT> <BR><BR><FONT size=2><BR></FONT><BR><FONT size=2>Hilvert Group</FONT> <BR><BR><FONT size=2>ETH Zürich</FONT> <BR><BR><FONT size=2>Switzerland</FONT> <BR><BR><TT>_______________________________________________<BR>RASMB mailing list<BR>RASMB@rasmb.bbri.org<BR>http://rasmb.bbri.org/mailman/listinfo/rasmb<BR><BR></TT></BLOCKQUOTE><TT><BR></TT><BR>
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