Related papers: Efficient Stochastic Simulations of Complex Reacti…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
Biological cells can exchange messages through soluble molecules or membrane-bound receptors. In particular in the latter case, the interaction is usually located in specific regions of the interacting cells and may depend on or induce…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…
The kinetic processes in nanoparticle-based catalysis are dominated by large fluctuations and spatiotemporal heterogeneities, in particular for diffusion-influenced reactions which are far from equilibrium. Here, we report results from…
In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…
A growing amount of evidence points to the fact that many enzymes exhibit fluctuations in their catalytic activity, which are associated with conformational changes on a broad range of timescales. The experimental study of this phenomenon,…
In this study we demonstrate for the first time that the unified Monte Carlo approach can be applied to model gas-grain chemistry in large reaction networks. Specifically, we build a time-dependent gas-grain chemical model of the…
In this paper, we investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schl\"ogl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…