Thermal nanostructure: An order parameter multiscale ensemble approach

Abstract

Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD ™ , achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.

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

“…Here, the stochastic process ξ k (t) is stationary, and all average random forces vanish. More specifically, the solution of Equation (19) must be the probability density for the collection of stochastic processes Ψ(t) that satisfies the Langevin Equation (20). As the latter equation completely describes the evolution of coarse variables, it can be used to simulate the dynamics of the pertinent modes within the N -atom system.…”

“…The starting point for the multiscale computational algorithm is the deformation of the initial reference configuration and the Langevin Equations (20). Given the all-atom structure of a macromolecular assembly at time t = 0, the number of subsystems N sys is identified, and their CMs R S are calculated.…”

“…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.…”

Reverse Coarse-Graining for Equation-Free Modeling: Application to Multiscale Molecular Dynamics

“…A necessary condition for an efficient multiscale simulation is the separation of timescales between the atomistic fluctuations and coherent, slow changes captured by the CG variables. [2][3][4]18,19 Furthermore, the MD phase of the multiscale computation should be sufficiently long to generate a representative ensemble of fluctuations in the CG momenta (i.e. longer than the 'stationarity time' 16 ).…”

“…Therefore, a theory of the dynamics of these systems must somehow account for the coevolution of coarse-grained (CG) and microscropic (atomistic) variables. Multiscale coevolution, [1][2][3][4][5] an equation-free method, [6][7][8][9] has been proposed as an alternative to purely coarse-grained methods; [10][11][12][13][14][15] coevolution methods operate via a cycle consisting of microscopic and coarse-grained phases. These methods do not involve deriving CG dynamical equations in closed form.…”