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Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
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…
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities…
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…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…
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 models of reaction networks are becoming increasingly important in Systems Biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this…
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…
Compartmentalised biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyse…
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural…
We consider the problem of estimating parameter sensitivities for stochastic models of multiscale reaction networks. These sensitivity values are important for model analysis, and, the methods that currently exist for sensitivity estimation…
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…