Stochastic dynamics of bionanosystems: Multiscale analysis and specialized ensembles

Abstract

An approach for simulating bionanosystems such as viruses and ribosomes is presented. This calibration-free approach is based on an all-atom description for bionanosystems, a universal interatomic force field, and a multiscale perspective. The supramillion-atom nature of these bionanosystems prohibits the use of a direct molecular dynamics approach for phenomena such as viral structural transitions or self-assembly that develop over milliseconds or longer. A key element of these multiscale systems is the cross-talk between, and consequent strong coupling of processes over many scales in space and time. Thus, overall nanoscale features of these systems control the relative probability of atomistic fluctuations, while the latter mediate the average forces and diffusion coefficients that induce the dynamics of these nanoscale features. This feedback loop is overlooked in typical coarse-grained methods. We elucidate the role of interscale cross-talk and overcome bionanosystem simulation difficulties with (1) automated construction of order parameters (OPs) describing suprananometer scale structural features, (2) construction of OP-dependent ensembles describing the statistical properties of atomistic variables that ultimately contribute to the entropies driving the dynamics of the OPs, and (3) the derivation of a rigorous equation for the stochastic dynamics of the OPs. As the OPs capture hydrodynamic modes in the host medium, "long-time tails" in the correlation functions yielding the generalized diffusion coefficients do not emerge. Since the atomic-scale features of the system are treated statistically, several ensembles are constructed that reflect various experimental conditions. Attention is paid to the proper use of the Gibbs hypothesized equivalence of long-time and ensemble averages to accommodate the varying experimental conditions. The theory provides a basis for a practical, quantitative bionanosystem modeling approach that preserves the cross-talk between the atomic and nanoscale features. A method for integrating information from nanotechnical experimental data in the derivation of equations of stochastic OP dynamics is also introduced.

Thermal nanostructure: An order parameter multiscale ensemble approach

“…To define the ⌽ ៝ k គ more concretely, we construct them to have the maximum information by minimizing the mass-weighted total square residual. [1][2][3][4]6 One finds…”

“…[1][2][3][4] The OPs describe nanoscale features and evolve via stochastic equations. In the present context, OPs describe overall features of a nanosystem such as shape, global orientation, or large scale structure.…”

“…Hence, a novel multiscale analysis was used to derive rigorous equations for the stochastic dynamics of OPs. [2][3][4]6 These equations are driven by thermal-average forces that are the gradient of the free energy constructed from an ensemble constrained to fixed OP values. Here, we present an algorithm for constructing these thermal-average forces and demonstrate it for determining the thermal structure of a virus.…”

“…This theme has been explored in detail in the context of nanosystems. 3 In the next order in the multiscale theory, an equation of stochastic OP evolution is obtained wherein the coherent dynamics is driven by a diffusivity matrix and thermal-average forces, and by a random force whose correlation properties are determined by the same diffusivities. To apply this multiscale methodology, the thermal-average forces and diffusion factors for a set of OPs must be calculated.…”

“…It was shown that they provide a natural starting point for a multiscale analysis. 1,3 The end point of this analysis is a Smoluchowski equation for stochastic OP dynamics driven by thermal-average forces ͑Sec. III͒.…”