5,282 research outputs found
A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems
We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo
(FPKMC) algorithm for continuous time and space systems involving multiple
diffusing and reacting species of spherical particles in two and three
dimensions. The FPKMC algorithm presented here is based on the method
introduced in [Phys. Rev. Lett., 97:230602, 2006] and is implemented in a
robust and flexible framework. Unlike standard KMC algorithms such as the
n-fold algorithm, FPKMC is most efficient at low densities where it replaces
the many small hops needed for reactants to find each other with large
first-passage hops sampled from exact time-dependent Green's functions, without
sacrificing accuracy. We describe in detail the key components of the
algorithm, including the event-loop and the sampling of first-passage
probability distributions, and demonstrate the accuracy of the new method. We
apply the FPKMC algorithm to the challenging problem of simulation of long-term
irradiation of metals, relevant to the performance and aging of nuclear
materials in current and future nuclear power plants. The problem of radiation
damage spans many decades of time-scales, from picosecond spikes caused by
primary cascades, to years of slow damage annealing and microstructure
evolution. Our implementation of the FPKMC algorithm has been able to simulate
the irradiation of a metal sample for durations that are orders of magnitude
longer than any previous simulations using the standard Object KMC or more
recent asynchronous algorithms.Comment: See also arXiv:0905.357
Efficient kinetic Monte Carlo method for reaction-diffusion processes with spatially varying annihilation rates
We present an efficient Monte Carlo method to simulate reaction-diffusion
processes with spatially varying particle annihilation or transformation rates
as it occurs for instance in the context of motor-driven intracellular
transport. Like Green's function reaction dynamics and first-passage time
methods, our algorithm avoids small diffusive hops by propagating sufficiently
distant particles in large hops to the boundaries of protective domains. Since
for spatially varying annihilation or transformation rates the single particle
diffusion propagator is not known analytically, we present an algorithm that
generates efficiently either particle displacements or annihilations with the
correct statistics, as we prove rigorously. The numerical efficiency of the
algorithm is demonstrated with an illustrative example.Comment: 13 pages, 5 figure
Efficient Reactive Brownian Dynamics
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle
simulations of reaction-diffusion systems based on the Doi or volume reactivity
model, in which pairs of particles react with a specified Poisson rate if they
are closer than a chosen reactive distance. In our Doi model, we ensure that
the microscopic reaction rules for various association and disassociation
reactions are consistent with detailed balance (time reversibility) at
thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to
separate reaction and diffusion, and solves both the diffusion-only and
reaction-only subproblems exactly, even at high packing densities. To
efficiently process reactions without uncontrolled approximations, SRBD employs
an event-driven algorithm that processes reactions in a time-ordered sequence
over the duration of the time step. A grid of cells with size larger than all
of the reactive distances is used to schedule and process the reactions, but
unlike traditional grid-based methods such as Reaction-Diffusion Master
Equation (RDME) algorithms, the results of SRBD are statistically independent
of the size of the grid used to accelerate the processing of reactions. We use
the SRBD algorithm to compute the effective macroscopic reaction rate for both
reaction- and diffusion-limited irreversible association in three dimensions.
We also study long-time tails in the time correlation functions for reversible
association at thermodynamic equilibrium. Finally, we compare different
particle and continuum methods on a model exhibiting a Turing-like instability
and pattern formation. We find that for models in which particles diffuse off
lattice, such as the Doi model, reactions lead to a spurious enhancement of the
effective diffusion coefficients.Comment: To appear in J. Chem. Phy
Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
We present computer-assisted methods for analyzing stochastic models of gene
regulatory networks. The main idea that underlies this equation-free analysis
is the design and execution of appropriately-initialized short bursts of
stochastic simulations; the results of these are processed to estimate
coarse-grained quantities of interest, such as mesoscopic transport
coefficients. In particular, using a simple model of a genetic toggle switch,
we illustrate the computation of an effective free energy and of a
state-dependent effective diffusion coefficient that characterize an
unavailable effective Fokker-Planck equation. Additionally we illustrate the
linking of equation-free techniques with continuation methods for performing a
form of stochastic "bifurcation analysis"; estimation of mean switching times
in the case of a bistable switch is also implemented in this equation-free
context. The accuracy of our methods is tested by direct comparison with
long-time stochastic simulations. This type of equation-free analysis appears
to be a promising approach to computing features of the long-time,
coarse-grained behavior of certain classes of complex stochastic models of gene
regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic
Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels
The quantitative description of model protein folding kinetics using a
diffusive collective reaction coordinate is examined. Direct folding kinetics,
diffusional coefficients and free energy profiles are determined from Monte
Carlo simulations of a 27-mer, 3 letter code lattice model, which corresponds
roughly to a small helical protein. Analytic folding calculations, using simple
diffusive rate theory, agree extremely well with the full simulation results.
Folding in this system is best seen as a diffusive, funnel-like process.Comment: LaTeX 12 pages, figures include
MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
Molecular dynamics (MD) simulations can model the interactions between
macromolecules with high spatiotemporal resolution but at a high computational
cost. By combining high-throughput MD with Markov state models (MSMs), it is
now possible to obtain long-timescale behavior of small to intermediate
biomolecules and complexes. To model the interactions of many molecules at
large lengthscales, particle-based reaction-diffusion (RD) simulations are more
suitable but lack molecular detail. Thus, coupling MSMs and RD simulations
(MSM/RD) would be highly desirable, as they could efficiently produce
simulations at large time- and lengthscales, while still conserving the
characteristic features of the interactions observed at atomic detail. While
such a coupling seems straightforward, fundamental questions are still open:
Which definition of MSM states is suitable? Which protocol to merge and split
RD particles in an association/dissociation reaction will conserve the correct
bimolecular kinetics and thermodynamics? In this paper, we make the first step
towards MSM/RD by laying out a general theory of coupling and proposing a first
implementation for association/dissociation of a protein with a small ligand (A
+ B C). Applications on a toy model and CO diffusion into the heme cavity
of myoglobin are reported
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