1. Treatment of Non-ideality in Sedimentation Velocity Experiments Walter Stafford, Boston Biomedical Research Institute, Watertown, MA U.S.A.

2. Hydrodynamic vs Thermodynamic non-ideality

3. Generally empirical
backflow (A.J. Rowe …)
charge effects (Donnan equilibrium)
Except for large asymmetric proteins,
charge effects usually dominate backflow.

4. Both hydrodynamic and thermodynamic contributions
Except for large asymmetric proteins,
charge effects usually dominate excluded volume effects.

5. Frictional coefficient
HYDRODYNAMIC
Frictional coefficient
Affects both s and D

6. Hydrodynamic c-dependence = same for s and D
FD=gradient of chemical potential
FC=gradient of centrifugal potential
frictional resistance is the same for both

7. Thermodynamic concentration dependence
Excluded volume and Donnan equilibrium

8. Colligative virial coefficients
B, C and D are the
2nd, 3rd and fourth virial colligative coefficients, respectively.
(McMillan and Mayer, 1945, statistical thermodynamics)

9. Combined hydrodynamic and thermodynamic concentration dependence of D

11. Expansion truncated after the 2nd virial term …
(Cf. Also Harding and Johnson, 1985;
and Alex Solovyova et al, 2001)

12. Expansion truncated after the 2nd virial term …
And further approximation …
(both Harding and Johnson, 1985;
and Alex Solovyova et al, 2001)

13. Self-associating system
Multiple Species
Self-associating system

14. Cross terms …
Single species (no cross terms)
Multiple species (cross terms)

15. However …
Self-associating system all species must have the same charge to mass ratio and frictional ratio

17. g(s) 6 Non-ideal reversible monomer-dimer system Protein-X Highest c
Lowest c
Intermediate c

19. Sedanal Global fitting with SEDANAL
l = 280 nm and 220 nm; path length = 12mm and 3 mm

21. Global fitting with SEDANAL
l = 280 nm; path length = 12mm and 3 mm

22. Extend to higher concentrations
Future plans
Extend to higher concentrations

23. Add higher order terms …

25. Donnan equilibrium For uni-univalent electrolyte e.g. NaCl
Roark and Yphantis 1971 Biochemistry

27. "Significant" is >= 1% contribution

28. Excluded volume effects

29. Hard sphere approx. or some other model

30. Hard Sphere models
Minton 2007 J. Pharm Sci.

31. Scattering …
Minton 2007, Biophys J.

32. Poly-disperse system

34. Conclusions Non-ideality in interacting systems Simple linear approach
Expand to higher order terms of virial expansion with cross-terms
Or use direct function

35. TURBO-MOLECULAR PUMP
TMP