Hydrodynamic vs Thermodynamic non-ideality
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Treatment of Non- ideality in Sedimentation Velocity Experiments Walter Stafford, Boston Biomedical Research Institute, Watertown, MA 02472 U.S.A.
description
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). - PowerPoint PPT Presentation
Transcript of 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.
Hydrodynamicvs
Thermodynamicnon-ideality
s f (c)Dg(c)
s f (c)Generally empirical
backflow (A.J. Rowe …)charge effects (Donnan equilibrium)
Except for large asymmetric proteins,charge effects usually dominate backflow.
Dg(c)Both hydrodynamic and thermodynamic contributions
Except for large asymmetric proteins,charge effects usually dominate excluded volume effects.
f (c) f (0) 1K sc
Frictional coefficient
HYDRODYNAMIC
Affects both s and D
Hydrodynamic c-dependence= same for s and D
sso
1 ksc and D
Do1 ksc
FC=gradient of centrifugal potential FD=gradient of chemical potential
frictional resistance is the same for both
Thermodynamicconcentration dependence
1 ln(y)
ln(c)
Excluded volume and Donnan equilibrium
Colligative virial coefficients
ln(y) BcCc2 Dc3 ...
B, C and D are the 2nd, 3rd and fourth virial colligative coefficients, respectively.(McMillan and Mayer, 1945, statistical thermodynamics)
Combined hydrodynamic and thermodynamic concentration
dependence of D
D D o
1 ln(y)
ln(c)
1 ksc
ln(yi ) Bici Cici2 Dic i
3 ...
ci ln(yi )
ci
ln(yi )
ln(ci )2Bci 3Cci
2 4Dci3 ...
DDo12BM1c
1 ksc
Expansion truncated after the 2nd virial term …
(Cf. Also Harding and Johnson, 1985; and Alex Solovyova et al, 2001)
DDo 12BM1c ksc
Expansion truncated after the 2nd virial term …And further approximation …
(both Harding and Johnson, 1985; and Alex Solovyova et al, 2001)
1
1ax1 ax ... for small a
Multiple Species
Self-associating system
ln(yi ) Bici Cici2 Dic i
3 ...
ln(yi ) Biici Bijc jji
n
Ciici2 Cijkc jck
ji
n
ki
n
Diic i3 Dijklc jckcl
li
n
ki
n
ji
n
...
Cross terms …
Single species (no cross terms)
Multiple species (cross terms)
Self-associating system all species must have the same charge to mass ratio
andfrictional ratio
However …
Di Dio 12BM1cT
1 ksjc jj1
n
g(s) 6
Non-ideal reversible monomer-dimer system
Protein-X
Lowest cIntermediate c
Highest c
Sedanal
Global fitting with SEDANAL
= 280 nm and 220 nm; path length = 12mm and 3 mm
Global fitting with SEDANAL
= 280 nm; path length = 12mm and 3 mm
Future plans
Extend to higher concentrations
Higher order terms
Add higher order terms …
ln(yi )
ln(ci )2Bci 3Cci
2 4Dci3 ...
Donnan equilibriumFor uni-univalent electrolyte
e.g. NaCl
BZ 2
4M22m3
C 0
D Z 4
64M24m3
3
Roark and Yphantis 1971 Biochemistry
BZ 2
4M22m3
DB2
4m3
"Significant" is >= 1% contribution
Excluded volume effects
BM1 4vL
d
Hard sphere approx.or some other model
ln(i) f (c,{a})
Hard Sphere models
Minton 2007 J. Pharm Sci.
Minton 2007, Biophys J.
Scattering …
M1 M1,app 1 ln(y1)
ln(c1)
ln(y1)
ln(c j )M j ,app
ji
n
M1 ln(y1)
ln(c j )M j ,app
ji
n
M1,app 1 ln(y1)
ln(c1)
M1,app
M1 1 ln(y1) ln(c j )
M j ,app
M1ji
n
1 ln(y1) ln(c1)
M1,app
M1 1 ln(y1) ln(c j )
M j ,app
M1ji
n
1 ln(y1) ln(c1)
sRTc
1 ln(y1) ln(c j )
M j ,app
M1ji
n
D 1 ln(y1) ln(c1)
D1,app D1 1 ln(y1)
ln(c1)
1 ln(y1) ln(c j )
M j ,app
M1ji
n
Poly-disperse system
D1,app D 1 ln(y1)
ln(c1)
1 ln(y1) ln(c j )
M j ,app
M1ji
n
Conclusions
Non-ideality in interacting systemsSimple linear approachExpand to higher order terms of virial
expansion with cross-termsOr use direct function
TMP
TURBO-MOLECULAR PUMP
