Thermodynamic modeling of protein interactions and phase behavior
Date
2012
Authors
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Journal ISSN
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Publisher
University of Delaware
Abstract
Protein phase behavior encompasses the formation of dense phases, which include amorphous aggregates, gels, dense liquids, and crystals. The major solution variables that dictate the type of dense phase that is formed are pH, temperature, type of precipitant, precipitant concentration, and protein concentration. Because of the large parameter space and rich variety of phase transitions possible, protein phase behavior is a complex phenomenon. Fundamentally, macroscopic phase transitions are governed by the molecular interactions between proteins in solution. One promising way of quantifying protein-protein interactions and relating them to phase behavior is through the osmotic second virial coefficient B22, a dilute-solution property that characterizes two-particle interactions. The relationship of B22 to overall phase behavior of proteins is explored in this work. The goal of this thesis is to quantitatively relate protein-protein interactions to protein phase diagrams in order to develop predictive models of phase behavior under different solution conditions. A continuum-level approach is used initially to relate experimental B22 data and phase diagrams of proteins by appealing to existing thermodynamic models, with the expectation that a simple continuum model could provide a useful mechanistic framework for predicting protein phase behavior. The first approach attempted was to relate protein interactions and phase behavior within the Flory-Huggins theory of polymer solutions. The second approach utilized the model of Haas and Drenth, which is based on the free energy of mixing for hard spheres. Finally, phase equilibrium was predicted from virial coefficients using the osmotic virial equation. A qualitative relationship was found between B22 and phase behavior from these continuum models; however, quantitative agreement could not be obtained. The isotropic assumption shared among these models in addition to the orientationally-averaged nature of B22 suggests that the anisotropic character of protein interactions cannot be neglected, demonstrating the need for more detailed molecular-level models. The role of anisotropy in protein interactions was explored through analysis of “patch-antipatch” pairs in the computation of B22 in atomistic detail. Patch-antipatch pairs represent highly attractive orientations resulting from geometric complementarity between protein surfaces. Previous work used simple Monte Carlo integration for the calculation of B22 from atomistic models of proteins. However, the presence of patch-antipatch pairs led to significant numerical concerns. These concerns warranted a reexamination of the numerical methods for computing B22. A hybrid Monte Carlo/patch integration approach is utilized to calculate B22 for lysozyme and chymosin B. This method involves a combination of numerical integration techniques in an attempt to obtain better convergence in predicting B22. The overall B22 for the proteins studied was separated into three components: contributions from the excluded volume, from the patch-antipatch pairs, and from background configurations. The excluded volume component was found to be adequately determined using simple Monte Carlo integration. The contributions from individual patch-antipatch pairs were accounted for by carefully integrating the subregions of the configuration space occupied by these pairs using a globally adaptive integration routine. The background component to B22 was also calculated by simple Monte Carlo integration in which the regions of the configuration space occupied by the patch-antipatch pairs were excluded. The calculations performed that account for the full protein structure emphasize the importance of several features of protein interactions. First, the difference in the interaction behavior of the two proteins studied was found to be largely attributed to the charge anisotropy of patch-antipatch pairs. However, the relation of the results to experimental data is limited by the omission of accounting for the specific hydration of proteins. Hydration effects are known to affect, and usually attenuate, patch-antipatch configurations, and therefore would be expected to significantly impact the accurate prediction of B22. Classical colloidal as well as atomistic models that omit these important features are inadequate in providing a quantitative representation of protein interactions for a wide range of solution conditions.