Open Boundary Simulations of Proteins and Their Hydration Shells by Hamiltonian Adaptive Resolution Scheme

The recently proposed Hamiltonian Adaptive Resolution Scheme (H-AdResS) allows to perform molecular simulations in an open boundary framework. It allows to change on the fly the resolution of specific subset of molecules (usually the solvent), which are free to diffuse between the atomistic region and the coarse-grained reservoir. So far, the method has been successfully applied to pure liquids. Coupling the H-AdResS methodology to hybrid models of proteins, such as the Molecular Mechanics/Coarse-Grained (MM/CG) scheme, is a promising approach for rigorous calculations of ligand binding free energies in low-resolution protein models. Towards this goal, here we apply for the first time H-AdResS to two atomistic proteins in dual-resolution solvent, proving its ability to reproduce structural and dynamic properties of both the proteins and the solvent, as obtained from atomistic simulations.Comment: This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Chemical Theory and Computation, copyright \c{opyright} American Chemical Society after peer review and technical editing by the publishe

Subdiffusive-Brownian crossover in membrane proteins: a Generalized Langevin Equation-based approach

In this paper, we propose a Generalized Langevin Equation (GLE)-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (non instantaneous) component modeled respectively through a Dirac delta function and a three-parameter Mittag-Leffler type function. By imposing a specific relationship between the parameters of the three-parameters Mittag-Leffler function, the different dynamical regimes, namely ballistic, subdiffusive and Brownian, as well as the crossover from one regime to another, are retrieved. Within this approach, the transition time from the ballistic to the subdiffusive regime and the distribution of relaxation times underlying the transition from the subdiffusive to the Brownian regime are given. The reliability of the model is tested by comparing the Mean Squared Displacement (MSD) derived in the framework of this model and the MSD of a protein diffusing in a membrane calculated through molecular dynamics (MD) simulations

Estimating the influence of finite instrumental resolution on elastic neutron scattering intensities from proteins

Recent experimental and simulation studies show that the fractional Ornstein-Uhlenbeck process describes well the single particle motions in internal protein dynamics. Here the authors use this model to estimate the influence of finite instrumental resolution on elastic neutron scattering intensities from hydrated protein powders. They give, in particular, an estimation of the attenuation factor for the observed atomic position fluctuations, assuming a Gaussian and a triangular resolution function

Influence of pressure on the low and fast fractional relaxation dynamics in lysozyme: a simulation study

The article reports on a molecular dynamics simulation study of the influence of moderate, nondenaturing pressure on the slow and fast internal relaxation dynamics of lysozyme. The model parameters of the fractional Ornstein–Uhlenbeck process are used to quantify the changes. We find that the nonexponential character for diffusive motions on time scales above 10 ps is enhanced and that the diffusion processes are slowed down. The diffusive motions on the subpicosecond time scale appear, in contrast, accelerated, whereas the nonexponential character is not altered by pressure. We attribute these findings to the different natures of slow and fast relaxation processes, which are characterized by structural rearrangements and collisions, respectively. The analyses are facilitated by the use of spatially resolved relaxation rate spectra

Fractional protein dynamics seen by nuclear magnetic resonance spectroscopy: Relating molecular dynamics simulation and experiment

We propose a fractional Brownian dynamics model for time correlation functions characterizing the internal dynamics of proteins probed by NMR relaxation spectroscopy. The time correlation functions are represented by a broad distribution of exponential functions which are characterized by two parameters. We show that the model describes well the restricted rotational motion of N–H vectors in the amide groups of lysozyme obtained from molecular dynamics simulation and that reliable predictions of experimental relaxation rates can be obtained on that basis

Protein dynamics from a NMR perspective: networks of coupled rotators and fractional brownian dynamics

Nuclear magnetic resonance (NMR) has proven to be the most valuable tool for investigating internal dynamics of proteins. In this perspective, the interpretation of NMR relaxation data eventually relies on a model of the motions. In this article, we propose to compare two radically different approaches that aim at describing internal dynamics in proteins. It is shown that the correlation functions predicted by a network of coupled rotators can be interpreted in terms of a heuristic approach based on fractional Brownian dynamics for each of the vectors in the network. Our results are interpreted in terms of the probability distributions of relaxation modes in both processes, the median of which turns out to be the relevant quantity for the comparison of both models

Open-Boundary Molecular Mechanics/Coarse-Grained Framework for Simulations of Low-Resolution G-Protein-Coupled Receptor–Ligand Complexes

G-protein-coupled receptors (GPCRs) constitute as much as 30% of the overall proteins targeted by FDA-approved drugs. However, paucity of structural experimental information and low sequence identity between members of the family impair the reliability of traditional docking approaches and atomistic molecular dynamics simulations for in silico pharmacological applications. We present here a dual-resolution approach tailored for such low-resolution models. It couples a hybrid molecular mechanics/coarse-grained (MM/CG) scheme, previously developed by us for GPCR–ligand complexes, with a Hamiltonian-based adaptive resolution scheme (H-AdResS) for the solvent. This dual-resolution approach removes potentially inaccurate atomistic details from the model while building a rigorous statistical ensemble—the grand canonical one—in the high-resolution region. We validate the method on a well-studied GPCR–ligand complex, for which the 3D structure is known, against atomistic simulations. This implementation paves the way for future accurate in silico studies of low-resolution ligand/GPCRs models

Quasi-two-dimensional diffusion of interacting protein monomers and dimers: a MPC simulation study

Understanding lateral diffusion of proteins along a membrane is of importance in biological soft matter science. An example in case is postsynaptic neuronal signal transduction where specific proteins diffuse alongside a postsynaptic membrane, triggering a cascade of biochemical processes. There are challenging questions to answer such as how the collective and self-diffusion of the proteins are affected by their direct and hydrodynamic interactions for larger areal protein concentrations.Using the multi-particle collision dynamics (MPC) simulation methods [1], we explore protein diffusion under quasi-two-dimensional (Q2D) confinement, for two different model systems of proteins. In the first system, the proteins are modeled as Brownian spheres interacting, respectively, by a hard-sphere potential serving as a reference potential, and by a soft potential with competing short-range attractive and long-range repulsive parts. For a minimalistic description of proteins diffusing along a cytosol-membrane interface, the Brownian spheres are confined to lateral motion in a planar monolayer embedded in an unbound three-dimensional Newtonian fluid. The time scales in the dynamic simulations extend from very short times where inertial effects are resolved, up to long times where the solvent-mediated hydrodynamic interactions between the proteins are fully developed and non-retarded [2]. By computing velocity autocorrelation functions, mean-square displacements and Fourier-space current auto-correlation functions, we quantify how concentration-induced correlations affect, e.g., the anomalous enhancement of large-scale collective diffusion under Q2D confinement [3], and the development of inter-protein hydrodynamic interactions by multiple scattering of sound and by vorticity diffusion [2]. The second model system relates to the diffusion of a human dumbbell-shaped M2 muscarinic acetylcholine receptor protein where one segment is embedded in the neuronal cell membrane, and the other one in the cytosol. The protein is simply modeled by a two-beads dimer with the upper bead immersed in a high-viscosity fluid sheet (fluid A) mimicking the membrane, and the lower one in a lower-viscosity fluid B mimicking the intra- and also extracellular environment. We use a recently developed MPC scheme for generating a fluid sheet A inside another fluid B [4]. Using this mesoscale method, diffusion can be probed over time spans not accessible in atomistic MD simulations of proteins. We study the mean squared displacement and velocity autocorrelation function of the individual bead centers, as well as of the hydrodynamic center of mobility of the dumbbell, in dependence of the viscosity ratio, sheet thickness, and interfacial bead distances.References:[1] G. Gompper, T. Ihle, D. M. Kroll, R. G. Winkler, Adv. Polym. Sci, 221, 1-87 (2008). [2] Z. Tan, J. K. G. Dhont, V. Calandrini, and G. Nägele, paper in preparation.[3] S. Panzuela and R. Delgado-Buscalioni, Phys. Rev. Lett., 121, 048101 (2018).[4] Z. Tan, J. K. G. Dhont, R. G. Winkler, and G. Nägele, paper in preparation

Quasi-two-dimensional diffusion of interacting globular proteins

Diffusion of proteins along lipid membranes plays a vital role in cell signaling processes. How the collective and self-diffusion of proteins are affected by direct and hydrodynamic interactions is relevant, e.g., for protein clustering and oligomerization of receptor protein subunits. Using mesoscale hydrodynamic simulations, the dynamic predictions by a minimalistic protein-membrane-cytosol model are explored. The model describes globular proteins as Brownian spheres, confined to lateral motion in a planar monolayer embedded in a three-dimensional viscous fluid. The proteins are assumed to interact pairwisely either via a hard-core potential or a soft potential consisting of competing short-range attractive and long-range repulsive parts. We analyze spatio-temporal correlations from short times where inertial motion is resolved up to long times where the solvent-mediated hydrodynamic interactions between proteins are fully developed. In this context, we investigate the short-time buildup of inter-protein hydrodynamic interactions by multiple scattering of sound and vorticity diffusion, and long-time anomalous enhancement of collective diffusion, in their dependence on protein concentration