Statistical mechanics models in protein association problems

Abstract

Protein-Protein interactions can lead to disordered states such as precipitates or gels, or to ordered states such as crystals or microtubules. In order to study the different natures of protein-protein interactions we have developed statistical mechanics models in order to interpret the varied behavior of different protein systems. The main point will be to develop theoretical models that infer the time a length scales that characterize the dynamics of the systems analyzed. This approach seek to facilitate a connection to simulations and experiments, where a high resolution analysis in length and time is possible, since the theories can provide insights about the relevant time and length scales, and also about issues that can appear when studying these systems. The first system studied is monoclonal antibodies in solution. Antibody solutions deviate from the dynamical and rheological response expected for globular proteins, especially as volume fraction is increased. Experimental evidence shows that antibodies can reversibly bind to each other via F[subscript]ab and F[subscript]c domains, and form larger structures (clusters) of several antibodies. Here we present a microscopic equilibrium model to account for the distribution of cluster sizes. Antibody clusters are modeled as polymers that can grow via reversible bonds either between two F[subscript]ab domains or between a F[subscript]ab and a F[subscript]c. We propose that the dynamical and rheological behavior is determined by molecular entanglements of the clusters. This entanglement does not occur at low concentrations where antibody-antibody binding contributes to the viscosity by increasing the effective size of the particles. The model explains the observed shear-thinning behavior of antibody solutions. The second system is protein condensates inside living cells. Biomolecule condensates appear throughout the cell serving a wide variety of functions, but it is not clear how functional properties show in the concentrated network inside the condensate droplets. Here we model disordered proteins as linear polymers formed by "stickers" evenly spaced by "spacers". The spacing between stickers gives rise to different network toplogies inside the condensate droplet, determining distinguishing properties such us density and client binding. The third system is protein-protein binding in a salt solutions. Biomolecular simulations are typically performed in an aqueous environment where the number of ions remains fixed for the duration of the simulation, generally with a number of salt pairs intended to match the macroscopic salt concentration. In contrast, real biomolecules experience local ion environments where the salt concentration is dynamic and may differ from bulk. We develop a statistical mechanics model to account for fluctuations of ions concentrations, and study how it affects the free energy of protein-protein binding.