Related papers: On hybrid simulation schemes for stochastic reacti…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange)…
We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end we study a dimerization kinetics of protein as a model system. We follow the dimerization…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
The quantum jump approach, where pairs of state vectors follow Stochastic Schroedinger Equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is first described. In this work the non-uniqueness of such…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
The molecular energies of chemical systems have been successfully calculated on quantum computers, however, more attention has been paid to the dynamic process of chemical reactions in practical application, especially in catalyst design,…
We construct path integrals for stochastic hybrid reaction-diffusion (RD) processes, in which the reaction terms depend on the discrete state of a randomly switching environment. We proceed by spatially discretizing a given RD system and…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred…
Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of…
We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…
The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…
The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model stochastic processes in physics, chemistry and biology. To characterize the evolving joint probability distribution in the…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…