Coarse-grained protein-protein stiffnesses and dynamics from all-atom simulations

Abstract

Large protein assemblies, such as virus capsids, may be coarse-grained as a set of rigid domains linked by generalized (rotational and stretching) harmonic springs. We present a method to obtain the elastic parameters and overdamped dynamics for these springs from all-atom molecular dynamics simulations of one pair of domains at a time. The computed relaxation times of this pair give a consistency check for the simulation, and (using a fluctuation-dissipation relationship) we find the corrective force needed to null systematic drifts. As a first application we predict the stiffness of an HIV capsid layer and the relaxation time for its breathing mode. PACS numbers: 87.10.Pq,87.15.ap,87.15.hg,87.15.Ya Large protein assemblies-our particular interest is the capsids (shells) of viruses-are pertinent to most of the softmatter physics in cells; how can one calculate their elastic properties and corresponding dynamics? Such assemblies are too large to handle by all-atom simulations, but numerical coarse graining techniques are opening the door to direct simulations [1]. Nevertheless, we still prefer simplified parametrizations for the purposes of human understanding, analytic treatment, transmission to other researchers, and building up coarse-grained models [2]. In this paper we propose an approach to extract these simplified parameters from all-atom molecular dynamics (MD) of small subsystems.Assume we already know how to extract an appropriate subsystem and an intelligent way to project the 3N coordinates of its configurations onto s small number x. (Below, we do this explicitly for the case of the HIV capsid protein.) Our aim is, from the observed trajectories x(t), to extract the parameters for an effective Hamiltonian and equation of motion. We will model x(t) as an overdamped random walk in a biased harmonic potential. This walk is parametrized primarily by two important tensors: one to describe the shape of the harmonic well, and the other to describe the (mainly hydrodynamic) damping and the associated stochastic noise. Combining these tensors gives a matrix whose eigenvalues are the relaxation rates. With detailed measurement of the dynamics, we can identify whether the simulation is equilibrated during the simulation time, and can compute the external forces we must add so as to measure the behavior near the biologically proper configuration. This is similar in spirit to computing a potential of mean force or free energy landscape with Jarzynski's equality [3], except that our coarse-grained x has more than one component, and (at minimum) represents angular degrees of freedom in addition to stretching. As an application, we simulate the important inter-domain interactions in the HIV capsid and estimate the Young's modulus and Poisson ratio of the capsid lattice, as well as the relaxation rate of the breathing mode.Coarse graining as stochastic dynamics. We represent our system as a vector of generalized coordinates x i , i = 1 . . . N , where N is far smaller than the number of atoms and is obtained by s...

Quantification and modification of the equilibrium dynamics and mechanics of a viral capsid lattice self-assembled as a protein nanocoating

“…63 This agreement supports the validity of this simplified theoretical approach to predict the mechanical elasticity of protein lattices. 63 This agreement supports the validity of this simplified theoretical approach to predict the mechanical elasticity of protein lattices.…”

Modeling Viral Capsid Assembly

“…The degree of specificity used within coarse-grained models can be roughly estimated based on the physical interaction length scales (e.g. [188]) or it can be calculated systematically via coarse graining [15, 113]. …”

Biomolecular engineering of virus-like particles aided by computational chemistry methods

“…22 A limiting factor for computational modeling of VLPs is their large size, as it requires extensive computational resources and long time periods for simulation. Multi-scale models [51][52][53] have thus been used to reduce the required computing resources for various VLPs, 22 as illustrated in Fig. 1.…”