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Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the…
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…
In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
The predictive ability of stochastic chemical reactions is currently limited by the lack of closed form solutions to the governing chemical master equation. To overcome this limitation, this paper proposes a computational method capable of…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming…
We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship…