Related papers: A Computational Approach to Extinction Events in C…
We study chemical reaction networks with discrete state spaces, such as the standard continuous time Markov chain model, and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
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…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the structure of the underlying network through Lyapunov functions…
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,…
In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a…
The construction of a reaction network containing all relevant intermediates and elementary reactions is necessary for the accurate description of chemical processes. In the case of a complex chemical reaction (involving, for instance, many…
Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large…
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…
Simulating chemical reactions is a central challenge in computational chemistry, characterized by an uneven difficulty profile: while equilibrium reactant and product geometries are often classically tractable, intermediate transition…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction…