Protein Interactions in Solution Characterized by Light and Neutron Scattering: Comparison of Lysozyme and Chymotrypsinogen


Molecular basis of the second virial coefficient


B22 characterizes two-body interactions between protein molecules in dilute solution

Virial coefficient formula

The interactions are manipulated mainly through electrostatics by varying pH and ionic strength. Unlike usual colloidal particles, electrostatic interactions between protein molecules can have both repulsive and attractive contributions (the latter arising from the anisotropic distribution of charges). Calculated titration curves show lysozyme to have higher net charge, but chymotrypsinogen to have less uniform charge distribution, as measured by dipole moment, and whence higher attractive electrostatics. A simplified description may be obtained by the DLVO theory approximating the protein shape as a sphere and calculating the van der Waals, charge-charge, charge-dipole and dipole-dipole interactions


Sum of interaction energies


The following values of the fitted parameters were obtained:


Hamaker constant

Protein diameter


13.8 kT

3.68 nm


10.2 kT

4.36 nm


This simplified approach gives a qualitatively correct picture, but it does not capture the details of the complex protein biophysics, so the fitted values of the Hamaker constant appear unrealistically high. A detailed calculation should preserve the angular dependence in the inner integral Iin. An example of why such a calculation is important is presented below (B.L. Neal, et al., J. Cryst. Growth, 196, 377, 1999)

Sum of interaction energies

The detailed data obtained in this study is in good correlation with the predictions of an approximate DLVO theory and provides the basis for further and more explicit theoretical interpretations of protein-protein interactions in solution


    © Copyright O. D. Velev et al. 1999


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