1. Quantitative characterization of polymer-polymer, protein-protein and polymer-protein interaction via tracer
sedimentation equilibrium
Adedayo A. Fodeke & Allen P. Minton
Laboratory of Biochemistry and Genetics. NIDDK, NIH
Introduction If these two methods (thermodynamic and scaled particle approximation) are Best fit values of the curve of dependence of M*i,app on polymer or protein
Nonspecific weakly attractive and repulsive interaction have substantial effect on macromolecular equivalent, they should give similar values of wj (∂lnγi/ ∂wj), hence similar concentration: Thermodynamic model; fit with expansion of activity coefficients in powers of solute
stability, structure, state of association and function in highly concentrated or volume –occupied values of M*i,app as a function of wj in both cases should be similar. concentration (black curves). The fitting parameters are M*fic = 23200, M*BSA = 17800, B11 = 27.9 ml/g,
solutions resembling physiological media. B22 = 15.6 ml/g, B12 =21.3 ml/g, B111 = 178 ml2/g2, B222 = 83.1 ml2/g2, B211 = 96.7 ml2/g2, B122 = 84.7
 ∂ ln γ 
Interaction between two species of macromolecules i and j is quantified as dependence of free energy We determined w  using 2 methods:
i
ml2/g2
 ∂w 
j
of solvation of species i, ∆Gsolv,i or the logarithm of the thermodynamic activity coefficient γi, on Structural model, with SPT (magenta curves) using hard spherical model for BSA and spherocylinderical
1. Power series expansion of lnγ in powers of concentration of polymer or protein
j { w}
concentration j hard particle for ficoll 70. The fitting parameters are Mfic = 59100, MBSA = 64,600, vfic = 1.3 ml/g, Lfic =
Thermodynamic interaction between two species may be represented as follows: 2. Scaled particle Theory (SPT) using equivalent hard particle approximations
6.6, vBSA,fic = 1.6 ml/g and vBSA,BSA = 1.9 ml/g
Trace BSA in Ficoll Trace Ficoll in BSA
 ∂ ∆G   ∂ ln γ 
2
  =  i
 ∂c ∂c   ∂c 
i j j { c} 6
< 0: net attractive interaction between i and j 4
∆∆Gsolv/RT
∆∆Gsolv/RT
> 0: net repulsive interaction between i and j 4
Results
2
2
Objective -6 -3 Trace FITC-BSA
0 0
ln(signal)
ln(signal)
in 10 mg/ml Fic
70 M*
app,BSA 0 0.05 0.1 0 0.05 0.1
=12602,
1. To determine the dependence of polymer-polymer interaction and polymer-protein interaction on -7 -3.5 w (g/ml) w (g/ml)
temperature 10 mg/ml ficoll 70,
M* =18775
fic BSA
app,fic
2. To determine how protein interaction compare with polymer interactions and quantify both types of
interactions -8 -4
3. To possibly resolve the uncertainty from conflicting literature reports about the structure of ficoll 70 42 44 46 40 42 44
r (cm2)
2
r2 (cm2)
Methods -4 -3
In this experiment we used the technique of tracer sedimentation equilibrium. Concentration gradient of
ln(signal)
ln(signal)
100 mg/ml ficoll 70,
M* = 2865
Ficoll in the presence of trace BSA was measured refractometrically while the concentration of BSA, app,f ic
trace BSA in Ficoll 70 and trace Ficoll 70 in BSA were measure are measured spectrophotometrically -3.5 Trace FITC-BSA in
80 mg/ml ficoll
M* = 5918
app,BSA
-4.5 -4
40 45 40 45
2 2
r (cm ) r2 (cm2)
4 4
x 10 x 10
2.5 2
~ 48 hours
2 5 oC 5 oC
1.5
20 oC 20 oC
BSA,app
1.5 37 oC
fic,app
37 oC
The concentration gradient of a sedimenting species at sedimentation equilibrium is given by 1
M*
M*
1
Conclusion
0.5
0.5
Where M*I,Tapp denotes the apparent weght-average buoyant mass of tracer [M* = M(dρ/dw)] 1. Tracer sedimentation equilibrium experiment permits quantitative measurement of the dependence
0 0
0 0.05 0.1 0 0.05 0.1 of ficoll-ficoll interaction and BSA-ficoll interaction upon ficoll and BSA concentration
d ln( signal ) d ln w M ω *
i ,Tapp
2
w (g/ml) w (g/ml) 2. The dependence of activity coefficient on concentration of increases in the order BSA vs BSA <
= = i i
fic fic
dr 2
dr 2 RT 2
x 10
4
x 10
4 BSA vs ficoll 70 = ficoll 70 vs BSA < ficoll 70 vs ficoll 70
2 2.5 3. The dependence of M*app,fic on wfic or wBSA is well described by SPT by modeling ficoll as hard
Rivas et al (1999) spherocylinder and BSA as hard sphere
2
1.5
 ∂ ln γ 
BSA,app
1.5
fic,app
M *
i , app = M −∑w
*
i
i
M
*
j , app 1 References
 ∂w 
j j
M*
1
M*
j
1. Hall, D.; Minton, A. P. Biochem. Biophys. Res Commun. 2003, 1649,127
0.5
0.5
2. Rivas, G., Fernandez, J. A.. And Minton, A.P. Biochemistry 1999, 38 9379
0 0 3. Luby-Phelps, K., Castle P. E., Taylor D. L and Lanni F. Cell Biology 1987, 84, 4910
Thermodynamic interaction between ith and jth solute species ---repulsive > 0 ; attractive 0 0.05 0.1 0 0.05 0.1
<0 w (g/ml) w (g/ml)
. BSA BSA 4. Tanford, C. Physical Chemistry of Macromolecules; Wiley & Sons: New York, 1961
5. Boublik, T. Mol. Phy. 1974, 27 1415