Hierarchical multiscale modeling of macromolecules and their assemblies

Abstract

Soft materials (e.g., enveloped viruses, liposomes, membranes and supercooled liquids) simultaneously deform or display collective behaviors, while undergoing atomic scale vibrations and collisions. While the multiple space-time character of such systems often makes traditional molecular dynamics simulation impractical, a multiscale approach has been presented that allows for long-time simulation with atomic detail based on the co-evolution of slowly-varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations. However, this approach breaks down when the structural change is extreme, or when nearest-neighbor connectivity of atoms is not maintained. In the current study, a self-consistent approach is presented wherein OPs and a reference structure co-evolve slowly to yield long-time simulation for dynamical soft-matter phenomena such as structural transitions and self-assembly. The development begins with the Liouville equation for N classical atoms and an ansatz on the form of the associated N-atom probability density. Multiscale techniques are used to derive Langevin equations for the coupled OP-configurational dynamics. The net result is a set of equations for the coupled stochastic dynamics of the OPs and centers of mass of the subsystems that constitute a soft material body. The theory is based on an all-atom methodology and an interatomic force field, and therefore enables calibration-free simulations of soft matter, such as macromolecular assemblies.

A Review of Two Multiscale Methods for the Simulation of Macromolecular Assemblies: Multiscale Perturbation and Multiscale Factorization

“…However, one finds [19,23] that this formulation enables a novel procedure for constructing a closed equation for W when is small. Note that the expressions for Π k and π k can be determined explicitly by Equations (8) and (9).…”

“…As in [19,44], OPs labeled by indices k = {000, 100, 010, 001} are denoted as lower-order, while k > {000, 100, 010, 001} are higher-order. Notice that basis functions do not depend on each atomic position r i , but rather on the intermediate scale variables, R, thereby ensuring a hierarchical foundation.…”

“…However, as many systems are easily deformed by thermal stress and fluctuation, large deformations cannot be considered as coherent changes determined by merely a few OPs. To deal with this, a slowly evolving hierarchical structure was introduced [19] about which the construction of OPs is formulated. Instead of OPs depending explicitly on the N -atom configuration, intermediary variables, representing the centers of mass (CMs) of subsystems within the structure, are utilized, and OPs which depend only on these CMs are constructed.…”

“…While this aspect often makes traditional MD simulation impractical, multiscale approaches have recently been presented that allow for long-time simulation with atomic detail based on the co-evolution of slowly-varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations [19][20][21][22][23][24][25]. In subsequent sections, two recently-discovered multiscale techniques are discussed that enable one to efficiently model and dynamically simulate evolving macromolecular systems.…”

“…Similarly, a coarse-grained strategy has been introduced which uses dissipative particle dynamics (DPD) simulations with an effective potential obtained by applying the inverse Monte Carlo method to an initial MD simulation [15,16]. The advantages and shortcomings of these approaches in the context of macromolecular simulations are reviewed in [17][18][19] and the references therein.…”