Coarse-grained brownian dynamics simulation of rule-based models

International audienceStudying spatial effects in signal transduction, such as co-localization along scaffold molecules, comes at a cost of complexity. In this paper, we propose a coarse-grained, particle-based spatial simulator, suited for large signal transduction models. Our approach is to combine the particle-based reaction and diffusion method, and (non-spatial) rule-based modeling: the location of each molecular complex is abstracted by a spheric particle, while its internal structure in terms of a site-graph is maintained explicit. The particles diffuse inside the cellular compartment and the colliding complexes stochastically interact according to a rule-based scheme. Since rules operate over molecular motifs (instead of full complexes), the rule set compactly describes a combinatorial or even infinite number of reactions. The method is tested on a model of Mitogen Activated Protein Kinase (MAPK) cascade of yeast pheromone response signaling. Results demonstrate that the molecules of the MAPK cascade co-localize along scaffold molecules, while the scaffold binds to a plasma membrane bound upstream component, localizing the whole signaling complex to the plasma membrane. Especially we show, how rings stabilize the resulting molecular complexes and derive the effective dissociation rate constant for it

A new framework for extracting coarse-grained models from time series with multiscale structure

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion

Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism

The Mori–Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark example is studied both numerically and via a formal asymptotic expansion. The example considered demonstrates the importance of memory effects in determining the correct temporal behaviour of such systems

Equation of State Based Slip Spring Model for Entangled Polymer Dynamics

A mesoscopic, mixed particle- and field-based Brownian dynamics methodology for the simulation of entangled polymer melts has been developed. Polymeric beads consist of several Kuhn segments, and their motion is dictated by the Helmholtz energy of the sample, which is a sum of the entropic elasticity of chain strands between beads, slip springs, and nonbonded interactions. The entanglement effect is introduced by the slip springs, which are springs connecting either nonsuccessive beads on the same chain or beads on different polymer chains. The terminal positions of slip springs are altered during the simulation through a kinetic Monte Carlo hopping scheme, with rate-controlled creation/destruction processes for the slip springs at chain ends. The rate constants are consistent with the free energy function employed and satisfy microscopic reversibility at equilibrium. The free energy of nonbonded interactions is derived from an appropriate equation of state, and it is computed as a functional of the local density by passing an orthogonal grid through the simulation box; accounting for it is necessary for reproducing the correct compressibility of the polymeric material. Parameters invoked by the mesoscopic model are derived from experimental volumetric and viscosity data or from atomistic molecular dynamics simulations, establishing a "bottom-up" predictive framework for conducting slip spring simulations of polymeric systems of specific chemistry. The mesoscopic simulation methodology is implemented for the case of cis-1,4-polyisoprene, whose structure, dynamics, thermodynamics, and linear rheology in the melt state are quantitatively predicted and validated without a posteriori fitting the results to experimental measurements.Comment: 80 pages, 17 figure

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles

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 like 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. We elucidate the role of interscale cross-talk and overcome bionanosystem simulation difficulties with automated construction of order parameters (OPs) describing supra-nanometer scale structural features, 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 the derivation of a rigorous equation for the stochastic dynamics of the OPs. Since the atomic scale features of the system are treated statistically, several ensembles are constructed that reflect various 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.Comment: 24 page