Related papers: Rule-Based Gillespie Simulation of Chemical System…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some…
Markov State Models (MSMs) are a powerful framework to reproduce the long-time conformational dynamics of biomolecules using a set of short Molecular Dynamics (MD) simulations. However, precise kinetics predictions of MSMs heavily rely on…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles,…
We develop new unbiased estimators of a number of quantities defined for functions of conditional moments, like conditional expectations and variances, of functions of two independent random variables given the first variable, including…
Cells exhibit a wide variety of different shapes. This diversity poses a challenge for computational approaches that attempt to shed light on the role cell geometry plays in regulating cell physiology and behavior. The simulation platform…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
The syntactic nature and compositionality characteristic of stochastic process algebras make models to be easily understood by human beings, but not convenient for machines as well as people to directly carry out mathematical analysis and…
Molecular dynamics simulations are an invaluable tool in numerous scientific fields. However, the ubiquitous classical force fields cannot describe reactive systems, and quantum molecular dynamics are too computationally demanding to treat…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…
We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and…
Researchers have employed stochastic simulations to determine the validity of their theoretical findings and to study analytically intractable spreading dynamics. In both cases, the correctness and efficiency of the simulation algorithm are…
We have developed and implemented a numerical evolution scheme for a class of stochastic problems in which the temporal evolution occurs on widely-separated time scales, and for which the slow evolution can be described in terms of a small…