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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…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
All biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
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…
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…
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical…
This short paper presents a simple approximate analytical estimate of the characteristic time of crossing a high, long and arbitrary bumpy free energy barrier in a course of chemical, biochemical or physical reaction.
A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton,…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
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…
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,…
A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…
Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one…
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…