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Hydrodynamic vs Thermodynamic non-ideality

Treatment of Non-ideality in Sedimentation Velocity Experiments Walter Stafford, Boston Biomedical Research Institute, Watertown, MA 02472 U.S.A. Hydrodynamic vs Thermodynamic non-ideality. Generally empirical backflow (A.J. Rowe …) charge effects (Donnan equilibrium).

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Hydrodynamic vs Thermodynamic non-ideality

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  1. Treatment of Non-ideality in Sedimentation Velocity ExperimentsWalter Stafford,Boston Biomedical Research Institute, Watertown, MA 02472 U.S.A.

  2. HydrodynamicvsThermodynamicnon-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. 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. Thermodynamicconcentration 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

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

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

  12. Multiple Species Self-associating system

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

  14. Self-associating system all species must have the same charge to mass ratioandfrictional ratio However …

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

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

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

  18. Future plans Extend to higher concentrations

  19. Add higher order terms … Higher order terms

  20. Donnan equilibriumFor uni-univalent electrolytee.g. NaCl Roark and Yphantis 1971 Biochemistry

  21. "Significant" is >= 1% contribution

  22. Excluded volume effects

  23. Hard sphere approx.or some other model

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

  25. Scattering … Minton 2007, Biophys J.

  26. Poly-disperse system

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

  28. TURBO-MOLECULAR PUMP TMP

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