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We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations,…
To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves…
In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…
In this survey paper, we will present a number of core algorithmic questions concerning several transitive reduction problems on network that have applications in network synthesis and analysis involving cellular processes. Our starting…
In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…
An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
We show that if a chemical reaction network (CRN) admits nondegenerate (resp., linearly stable) oscillation, and we add new reversible reactions involving new species to this CRN, then the new CRN so created also admits nondegenerate…
Complex balanced mass-action systems (CBMASs) are of great importance in the filed of biochemical reaction networks. However analyzing the persistence of these networks with high dimensions and time delays poses significant challenges. To…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
Chemical reaction network is an important method for modeling and exploring complex biological processes, bio-chemical interactions and the behavior of different dynamics in system biology. But, formulating such reaction kinetics takes…
Despite their widespread utility across domains, basic network models face fundamental limitations when applied to complex biological systems, particularly in neuroscience. This paper critically examines these limitations and explores…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction…
Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a well-mixed "soup" of molecules is stochastic, asynchronous, concurrent, and often involves…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a…
One of the main tasks of post-genomic informatics is to systematically investigate all molecules and their interactions within a living cell so as to understand how these molecules and the interactions between them relate to the function of…
This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of…
Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted…