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Energy functions are fundamental to biomolecular modeling. Their success depends on robust physical formalisms, efficient optimization, and high-resolution data for training and validation. Over the past 20 years, progress in each area has advanced soluble protein energy functions. Yet, energy functions for membrane proteins lag behind due to sparse and low-quality data, leading to overfit tools. To overcome this challenge, we assembled a suite of 12 tests on independent data sets varying in size, diversity, and resolution. The tests probe an energy function's ability to capture membrane protein orientation, stability, sequence, and structure. Here, we present the tests and use the franklin2019 energy function to demonstrate them. We then identify areas for energy function improvement and discuss potential future integration with machine-learning-based optimization methods. The tests are available through the Rosetta Benchmark Server (https://benchmark.graylab.jhu.edu/) and GitHub (https://github.com/rfalford12/Implicit-Membrane-Energy-Function-Benchmark).

We use direct simulations of particle-polyelectrolyte mixtures using the single chain in mean field framework to extract the phase diagram for such systems. At high charges of the particles and low concentration of polymers, we observe the formation of a coacervate phase involving the particles and polyelectrolytes. At low particle charges and/or high concentration of polymers, the mixture undergoes a segregative phase separation into particle-rich and polymer-rich phases, respectively. We also present results for the influence of particle charge heterogeneity on the phase diagram.

We employed a combination of single chain in mean field methodology and constant pH Monte Carlo framework to compare the influence of charge regulation and charge heterogeneity on the adsorption and bridging characteristics of polyelectrolytes in solution on proteins. By adopting a coarse-grained representation of the proteins as spherical particles and embedding a simple framework for probing charge heterogeneities, we probe the influence of charge patches, net charge of the particle, the ratio of positive to negative charges on the proteins on the net adsorption, and bridging probabilities of polyelectrolytes. Our results demonstrate that charge regulation increases the probability of bridging between two particles when compared to proteins with the same fixed charge. The influence of charge regulation first increases and then decreases with an increase in the number of charge patches of proteins. An increase in the ratio of positive to negative charges and the net charge of the protein are also seen to increase the propensity for polyelectrolyte adsorption and bridging.

We employ a combination of the single chain in mean field simulation approach with the solution of Poisson's equation to study the influence of charge heterogeneities on the structure of protein-polyelectrolyte complexes. By adopting a coarse-grained model of representing proteins as charged nanoparticles, we studied the influence of the pattern of charge heterogeneities, net charge, ratio of positive to negative charges on the patches, and the volume fraction of the particles on the structural and aggregation characteristics of proteins in polyelectrolyte solutions. Our results demonstrate that the pattern of charge heterogeneities can exert a significant influence on the resulting characteristics of the aggregates, in some cases leading to a transformation from polymer-bridged complexes into direct particle aggregates driven by the attraction between oppositely charged patches.

We study the structural characteristics of a system of charged nanoparticles in a neutral polymer solution while accounting for the differences in the dielectric constant between the particles, polymer and the solvent. We use a hybrid computational methodology involving a combination of single chain in mean-field simulations and the solution of the Poisson's equation for the electrostatic field. We quantify the resulting particle structural features in terms of radial distribution function among particles as a function of the dielectric contrast, particle charge, particle volume fraction and polymer concentration. In the absence of polymers, charged macroions experience increased repulsion with a lowering of the ratio of particle to solvent dielectric constant. The influence of the dielectric contrast between the particle and the solvent however diminishes with an increase in the particle volume fraction and/or its charge. In the presence of neutral polymers, similar effects manifest, but with the additional physics arising from the fact that the polymer-induced interactions are influenced by the dielectric contrast of the particle and solvent.

Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks.