[RASMB] upper concentration limit AUC

Mon Sep 8 05:19:33 PDT 2008

Hi-
Food for thought and a serious question.
The "natural" concentration units for k(s) are volume fraction (since it 
is a hydrodynamic term).
The "natural" concentration units for k(D), or k(P) in Arthur's 
discussion, are mole fraction (since it is a thermodynamic term).
Because of the different "natural" concentration units, is there a 
fundamental difficulty in using sedimentation velocity to analyze high 
concentration solutions?
Best wishes,
Tom

Arthur Rowe wrote:
>
>     Hi Christine (and everyone)
>
>     I think this discussion is already in the RASMB Archives.
>
>     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
>
>     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.
>
>     Kind regards - will be seeing you (Christine) and lots of others
>     in Newcastle this week.
>
>     Arthur
>
>     *see "The sedimentation rate of disordered suspensions"  Brady,
>     John F.; Durlofsky, Louis J.
>     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
>     . . . . .
>     *Note: *the value given above for k(s) = 4 ml/g is for *DYNAMIC
>     k(s)*. The usual measured value which gets reported is the
>     *KINEMATIC* 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.
>
>
>     Dear Joris, dear all,
>
>     This reference may be perhaps useful.
>
>
>
>     Solovyova A., Schuck P., Costenaro L., Ebel C,
>
>     Non-ideality by sedimentation velocity of halophilic malate
>     dehydrogenase in complex solvents,
>
>     (2001) /Biophys. J,/ 81 1868-1880.
>
>
>
>     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)
>
>     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.
>
>     All the best
>
>     Christine
>
>
>     Christine EBEL
>
>     Institut de Biologie Structurale CEA-CNRS-UJF
>
>     41 rue Jules Horowitz, F-38027 Grenoble France
>
>     Tel (33) (0) 4 38 78 95 70; Fax (33) (0) 4 38 78 54 94
>
>     christine.ebel at ibs.fr
>
>     http://www.ibs.fr/content/ibs_eng/presentation/lab/lbm/ebel.htm
>     -----Message d'origine-----
>     *De :* rasmb-bounces at rasmb.bbri.org
>     [mailto:rasmb-bounces at rasmb.bbri.org] *De la part de* Beld, Joris
>     *Envoyé :* lundi 1 septembre 2008 15:24
>     *À :* RASMB at rasmb.bbri.org
>     *Objet :* [RASMB] upper concentration limit AUC
>
>
>
>     Dear all,
>
>
>
>     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?!
>
>     Thanks a lot in advance for any feedback.
>
>     Best wishes,
>
>
>
>     Joris Beld
>
>
>
>     Hilvert Group
>
>     ETH Zürich
>
>     Switzerland
>
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Department of Biochemistry and Molecular Biology
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