Calculations of the second virial coefficients of protein solutions with an extended fast multipole method

Abstract

The osmotic second virial coefficients B2 are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B2 of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B2 are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions. Disciplines Chemistry CommentsThis article is from Physical Review E 83 (2011) The osmotic second virial coefficients B 2 are directly related to the solubility of protein molecules in electrolyte solutions and can be useful to narrow down the search parameter space of protein crystallization conditions. Using a residue level model of protein-protein interaction in electrolyte solutions B 2 of bovine pancreatic trypsin inhibitor and lysozyme in various solution conditions such as salt concentration, pH and temperature are calculated using an extended fast multipole method in combination with the boundary element formulation. Overall, the calculated B 2 are well correlated with the experimental observations for various solution conditions. In combination with our previous work on the binding affinity calculations it is reasonable to expect that our residue level model can be used as a reliable model to describe protein-protein interaction in solutions.

A molecular Debye-Hückel theory and its applications to electrolyte solutions

“…Dynamical extension of the above result can be formulated in a similar fashion, namely, a rigorous statistical mechanics derivation of the macroscopic Maxwell Eqs. (14) and (15) from the microscopic ones is needed just as how Eq. (16) is derived.…”

“…A comprehensive review of the DH theory and its extensions can be found in Ref. 14. Essentially, all of these works are for the static case and there is no clear route to extend to dynamical cases, where the frequency-dependent screening may play important roles such as protein-protein interaction models in electrolyte solutions 15 and solvation dynamics in ionic fluids. 16 With these motivations in mind, we began to develop not only static extension of the traditional DH theory, but also systematic extension to the dynamical case.…”

Model for screened, charge-regulated electrostatics of an eye lens protein: Bovine gammaB-crystallin

“…Because many known cataractogenic mutations of γ -crystallins involve changes of residue charge, it is natural to study the protonation configuration probability distributions in detail. While many models of orientation-dependent protein-protein interactions have been developed at various levels of coarse graining [3–6,11,132–134], some of which incorporate charge regulation, including models for lysozyme interactions [4–6,132,135,136] and for gamma crystallin interactions [52,88,137], achieving the degree of fine graining for the more predictive modeling needed in many contexts remains an outstanding challenge [19]. …”

“…Because its acidic and basic residues continually exchange protons with the surrounding solution, an individual protein molecule presents many different spatial patterns of positive and negative charges to its neighbors, and the corresponding voltage patterns around each molecule keep changing. Each possible pair of such charging patterns can in principle give rise to a distinct spatial and orientational dependence of the screened electrostatic interaction between two nearby protein molecules [4–6], and the basins of attraction and repulsive parts of the corresponding potential energy landscape may change in depth or height, angular and spatial extent, and number.…”

Quantifying Protein-Protein Interactions in Molecular Simulations

“…18 As we will discuss here, this approximation is only accurate for strong binders. B ij can be estimated by integration over configuration space, [19][20][21] Mayer-sampling, 22,23 and from molecular simulations using radial distributions or potentials of mean force. [24][25][26][27] Here we show that K d is fully determined by B ij and the fraction p b (V ) of bound proteins estimated from molecular simulations of two pro-teins in a box with volume V , i.e,…”