A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

TL;DR

This study evaluates the validity of a perturbative approximation for protein-protein interactions modeled by a Yukawa potential, confirming its accuracy under certain conditions through simulations and integral equations, aiding interpretation of scattering experiments.

Contribution

It demonstrates that a first-order perturbative RDF approximation remains valid for charged globular proteins in dilute solutions with moderate screening, validated by Monte Carlo and integral equation comparisons.

Findings

Perturbative RDF approximation is valid at strong Coulomb coupling with sufficient screening.

HNC closure outperforms PY in integral equation predictions.

Results support the use of simplified models for interpreting scattering data.

Abstract

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), for a simple perturbative approximation to the radial distribution functions (RDF), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein ($\beta $-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick (PY) closures have a satisfactory behavior under these regimes, with the HNC being superior throughout. The relevance of our findings for interpreting SAS results is also discussed.