Order parameters for macromolecules: application to multiscale simulation

Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10(-14) s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.     

Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.     

Design of anti-icing coatings using supercooled droplets as nano-to-microscale probes

A multiscale simulation-based approach is presented for predicting anti-icing properties of nanocomposite coatings. Development of robust anti-icing coatings is a challenging task. An anti-icing coating that can prevent in-flight icing is of particular interest to the aircraft industry. A multiscale simulations based approach is developed to provide insights into the complex effect of coating material and surface topology on the prevention of in-flight icing. Chemical properties of different coatings and kinetics of icing or inhibition of ice nucleation are calculated from nanoscale atomistic simulations. In addition, in-flight icing environments including impingement and rolling of supercooled microdroplet and nucleation of ice under wind shear have been implemented using fluid dynamics methodologies. A model for icing in nano-to-microscale for surfaces with known chemical composition and surface topology is used for developing predictive capabilities regarding anti-icing performance of potential coatings. In this work, fluorinated polyhedral oligomericsilsesquioxanes molecules have been used to increase nanoscale roughness when embedded in a polycarbonate polymeric matrix. The findings suggest that a successful anti-icing coating will require precise control over nanoscale and microscale roughness. The multiscale methodology presented therefore can potentially help in identifying coupled effects of material, surface topology, and icing environment for promising coatings before performing icing tunnel experiments.     

聚氨酯制备的多尺度模拟方案

针对聚氨酯材料特性设计了多尺度计算机模拟方案,并研究了不同原料及相同原料但不同官能度对所制备的聚氨酯材料力学性能和玻璃化转变温度的影响.基于原子级别的结构,建立了耦合聚合反应的粗粒化耗散粒子动力学模型来描述组分扩散及交联网络结构的形成过程.并反映射这个粗粒化结构到全原子级别来分析材料的力学性能和热力学性能.这个多尺度研究方案也可推广到研究多个竞争性因素同时主导的复杂体系中.     

聚氨酯制备的多尺度模拟方案

针对聚氨酯材料特性设计了多尺度计算机模拟方案, 并研究了不同原料及相同原料但不同官能度对所制备的聚氨酯材料力学性能和玻璃化转变温度的影响. 基于原子级别的结构, 建立了耦合聚合反应的粗粒化耗散粒子动力学模型来描述组分扩散及交联网络结构的形成过程. 并反映射这个粗粒化结构到全原子级别来分析材料的力学性能和热力学性能. 这个多尺度研究方案也可推广到研究多个竞争性因素同时主导的复杂体系中.     

Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: mapping all-atom molecular dynamics to capillary waves

We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.     

From atomistic simulation to the dynamics, structure and helical network formation of dendronized polymers: the Janus chain model

It is the purpose of this paper to establish a bottom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers, we introduce a "Janus chain" (JC) model which adds a vectorial degree of freedom (Janus vector)--related to the sectorial amphiphilicity--to each segment of the linear backbone of a (classical) uncharged, semiflexible, and multibead chain representation of a polymer. The JC features induced polymeric curvature and ultimately triggers complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation and can be seen as a member of a universality class which is one (two) level(s) above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers but also structures belonging to the same class-exhibiting induced (or spontaneous) curvature--such as single stranded DNA and actin filaments.     

Modelling of solid polymers in chemical detail - gases in amorphous polymers

The diffusion of gases in dense polymers, above and below the glass-transition temperature, is described with a new Transition State Theory model that is based on the concept that the dynamics of small molecules dissolved in dense polymers is separated from the structural relaxation of the dense polymers. The model is used to study the dynamics of rare gases dissolved in atomistic micro-structures of four polymers at 300 K: poly(dimethylsiloxane), poly(isobutylene), atactic poly(vinylchloride) and the polycarbonate of 4,4′-isopropylidenediphenol (bisphenol-A). Short-time-scale MD runs (5 ps) are used to characterize the elastic thermal motion of the host matrix; this information on mobility is then used for a stochastic simulation of solute dynamics up to ca. 1ms. All dissolved molecules show similar behavior by displaying three time regimes: a short-time, high-mobility domain, an intermediate time domain of anomalous diffusion, and a diffusive regime at long times. From the long-time data diffusion coefficients are estimated; comparison with experimental data results in good agreement.     

Coarse-grained computations for a micellar system

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms), and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the Monte Carlo simulation, and on (computational) time scale separation between these and the remaining "slaved," fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g., equations of state), may provide a computational bridge between direct atomistic/stochastic simulation and the analysis of its macroscopic, system-level consequences.     

A multiscale coarse-graining method for biomolecular systems

A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.     

Transferability of coarse-grained force fields: the polymer case

A key question for all coarse-graining methodologies is the degree of transferability of the resulting force field between various systems and thermodynamic conditions. Here we present a detailed study of the transferability over different thermodynamic states of a coarse-grained (CG) force field developed using the iterative Boltzmann inversion method. The force field is optimized against distribution functions obtained from atomistic simulations. We analyze the polymer case by investigating the bulk of polystyrene and polyamide-6,6 whose coarse-grained models differ in the chain length and in the number of atoms lumped in one bead. The effect of temperature and pressure on static, dynamic, and thermodynamic properties is tested by comparing systematically the coarse-grain results with the atomistic ones. We find that the CG model describing the polystyrene is transferable only in a narrow range of temperature and it fails in describing the change of the bulk density when temperature is 80 K lower than the optimization one. Moreover the calculation of the self-diffusion coefficient shows that the CG model is characterized by a faster dynamics than the atomistic one and that it overestimates the isothermal compressibility. On the contrary, the polyamide-6,6 CG model turns out to be fully transferable between different thermodynamic conditions. The transferability is checked by changing either the temperature or the pressure of the simulation. We find that, in this case, the CG model is able to follow all the intra- and interstructural rearrangements caused by the temperature changes. In addition, while at low temperature the difference between the CG and atomistic dynamics is remarkable due to the presence of hydrogen bonds in the atomistic systems, for high temperatures, the speedup of the CG dynamics is strongly reduced, leading to a CG diffusion coefficient only six times bigger than the atomistic one. Moreover, the isothermal compressibility calculated at different temperatures agrees very well with the experimental one. We find that the polymer chain length does not affect the transferability of the force field and we attribute such transferability mainly to the finer model used in describing the polyamide-6,6 than the polystyrene.     

Multiscale coupling of mesoscopic- and atomistic-level lipid bilayer simulations

A multiscale method is presented to bridge between the atomistic and mesoscopic membrane systems. The atomistic model in this case is the united atom dimyristoylphosphatidylcholine membrane system, although the method is completely general. Atomistic molecular dynamics provides the expansion modulus which is used to parametrize a mesoscopic elastic membrane model. The resulting elastic membrane model, including explicit mesoscopic solvent, shows appropriate static and dynamic undulation behaviors. Large membranes of approximately 100 nm in length can then be easily simulated using the mesoscopic membrane system. The critical feedback from the mesoscopic system back down to the atomistic-scale system is accomplished by bridging the stress (or surface tension) of a small region in the mesoscopic membrane to the corresponding atomistic membrane system. Because of long length-scale modes of membranes such as undulation and buckling, the local tension responds differently from the frame tension, when subjected to external perturbations. The effect of these membrane modes is shown for the stress response of a local membrane region and therefore the atomistic membrane system. In addition, certain equilibrium static and dynamic properties of stand-alone and multiscale coupled systems are presented for several different membrane sizes. Although static properties such as two-dimensional pair-correlation function and order parameters show no noticeable discrepancy for the different systems, lipid self-diffusion and the rotational relaxation of lipid dipoles have a strong dependence on the membrane size (or long-wavelength membrane motions), which is properly modeled by the present multiscale method.     

Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.     

Multiscale Lagrangian fluid dynamics simulation for polymeric fluid

We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the multiscale simulation approach incorporating Lagrangian particle fluid dynamics technique (the modified smoothed particle hydrodynamics) with stochastic coarse‐grained polymer simulators (the dumbbell model). We have confirmed that our approach is well in agreement with the macroscopic results obtained by a constitutive equation corresponding to the dumbbell model, and observed that microscopic thermal fluctuation appears in macroscopic fluid dynamics as dispersion phenomena. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 886–893, 2010     

A hybrid fluctuating hydrodynamics and kinetic Monte Carlo method for modeling chemically-powered nanoscale motion

We present a stochastic multiscale method for modeling heterogeneous catalysis at the nanoscale. The system is decomposed into the fluid domain and the catalyst-fluid interface. We implemented the fluctuating hydrodynamics framework to model the diffusion of the chemical species in the fluid domain, and the chemical master equation to describe the catalytic activity at the interface. The coupling between the domains occurs simultaneously. Using a simple one-dimensional (1D) linear model, we showed that the predictions of our scheme are in excellent agreement with deterministic simulations. The method was specifically developed to model the spatially asymmetric catalysis on the surface of self-propelled nanoswimmers. Numerical simulations showed that our approach can estimate the uncertainty in the swimming velocity resulting from inherent stochastic nature of the chemical reactions at the catalytic interface. Although the method has been applied to simple 1D and 2D models, it can be generalized to handle different geometries and more sophisticated chemical reactions. Therefore, it can serve as a practical mathematical tool to study how the efficiency of chemically powered nanomachines is affected by the interplay between structural complexity, nonlinear reactivity, and nonequilibrium fluctuations.