Long range Debye-Hückel correction for computation of grid-based electrostatic forces between biomacromolecules

Calculating Structure Factors of Protein Solutions by Atomistic Modeling of Protein-Protein Interactions

We present a method, FMAPS(q), for calculating the structure factor, S ( q ) , of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function g C ( R ) . At low protein concentrations, g C ( R ) can be approximated as e - β W ( R ) , where W ( R ) is the potential of mean force along the center-center distance R . We calculate W ( R ) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203-8215]. For higher protein concentrations, we obtain S ( q ) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Brownian Dynamics Simulations of Proteins in the Presence of Surfaces: Long-Range Electrostatics and Mean-Field Hydrodynamics

Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with grid-based approaches alone. Here, we develop a treatment of both hydrodynamic and electrostatic interactions to include the presence of surfaces by modeling grid-based and long-range interactions. We describe its application to simulate the self-association and many-molecule adsorption of the well-characterized protein hen egg-white lysozyme to mica-like and silica-like surfaces. We find that the computational model can recover a number of experimental observables of the adsorption process and provide insights into their determinants. The computational model is implemented in the Simulation of Diffusional Association (SDA) software package.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.

ReaDDy 2: Fast and flexible software framework for interacting-particle reaction dynamics

Interacting-particle reaction dynamics (iPRD) combines the simulation of dynamical trajectories of interacting particles as in molecular dynamics (MD) simulations with reaction kinetics, in which particles appear, disappear, or change their type and interactions based on a set of reaction rules. This combination facilitates the simulation of reaction kinetics in crowded environments, involving complex molecular geometries such as polymers, and employing complex reaction mechanisms such as breaking and fusion of polymers. iPRD simulations are ideal to simulate the detailed spatiotemporal reaction mechanism in complex and dense environments, such as in signalling processes at cellular membranes, or in nano- to microscale chemical reactors. Here we introduce the iPRD software ReaDDy 2, which provides a Python interface in which the simulation environment, particle interactions and reaction rules can be conveniently defined and the simulation can be run, stored and analyzed. A C++ interface is available to enable deeper and more flexible interactions with the framework. The main computational work of ReaDDy 2 is done in hardware-specific simulation kernels. While the version introduced here provides single- and multi-threading CPU kernels, the architecture is ready to implement GPU and multi-node kernels. We demonstrate the efficiency and validity of ReaDDy 2 using several benchmark examples. ReaDDy 2 is available at the https://readdy.github.io/ website.

SDA 7: A modular and parallel implementation of the simulation of diffusional association software

The simulation of diffusional association (SDA) Brownian dynamics software package has been widely used in the study of biomacromolecular association. Initially developed to calculate bimolecular protein-protein association rate constants, it has since been extended to study electron transfer rates, to predict the structures of biomacromolecular complexes, to investigate the adsorption of proteins to inorganic surfaces, and to simulate the dynamics of large systems containing many biomacromolecular solutes, allowing the study of concentration-dependent effects. These extensions have led to a number of divergent versions of the software. In this article, we report the development of the latest version of the software (SDA 7). This release was developed to consolidate the existing codes into a single framework, while improving the parallelization of the code to better exploit modern multicore shared memory computer architectures. It is built using a modular object-oriented programming scheme, to allow for easy maintenance and extension of the software, and includes new features, such as adding flexible solute representations. We discuss a number of application examples, which describe some of the methods available in the release, and provide benchmarking data to demonstrate the parallel performance.