Related papers: Diffusion Controlled Reactions, Fluctuation Domina…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
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…
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…
Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
Many cellular components are present in such low numbers that individual stochastic production and degradation events lead to significant fluctuations in molecular abundances. Although feedback control can, in principle, suppress such…
Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
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…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
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…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
We explore a new framework for describing the kinetics of a heterogeneous chemical reaction where two particles of the same chemical species form a reaction product of another chemical species on the surface of a seed particle. Traditional…
Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that,…
Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent…
Local interactions among biomolecules, and the role played by their environment, have gained increasing attention in modelling biochemical reactions. By defining the automaton of molecular perceptions, we explore an agent-based…