6 - Theoretical studies of equilibrium

Summary

In this chapter we review some of the existing theoretical studies of models for the phase diagram of globular proteins. Almost all studies to date treat the multicomponent solution as a quasi-one-component solution, with a potential energy of interaction (e.g. potential of mean force) between the protein molecules that is usually assumed to be spatially isotropic. Typically, the interactions consist of a repulsive hard core and a short range attractive interaction. The majority of these studies involve simulation techniques, particularly the Gibbs ensemble Monte Carlo method, although studies based on thermodynamic perturbation theory, finite size scaling theory, and various theories for the radial distribution function also exist. These models have in common the feature that, for sufficiently short range attractive interactions, the fluid–fluid coexistence curve is metastable. Their phase diagrams look qualitatively similar to experimental diagrams, such as that shown in Fig. 4.4. In addition to these studies, we discuss a theoretical estimate for the rather narrow window of values for the range R of the attractive interaction within which the boundary between stable and metastable fluid–fluid transitions is located. We also discuss recent theoretical studies of spatially non-isotropic models that are more realistic descriptions of protein–protein interactions.

The idea that the range of the attractive interaction between protein molecules should be small as compared with the molecular size has its roots in the seminal observation by George and Wilson [25] that for several globular proteins the optimal window of crystallization corresponds to small negative values of B₂.