Related papers: Large Differences Between Stochastic and Determini…

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…

A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…

Mechanistic understanding of organic reactions can facilitate reaction development, impurity prediction, and in principle, reaction discovery. While several machine learning models have sought to address the task of predicting reaction…

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…

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…

Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of…

Intra-cellular biochemical reactions exhibit a rich dynamical phenomenology which cannot be explained within the framework of mean-field rate equations and additive noise. Here, we show that the presence of metastable states and radically…

We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of…

Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of…

Motivated by the theory of reaction kinetics based on nonequilibrium thermodynamics and the linear stability of driven reaction-diffusion, we apply the Fokker-Planck equation to describe the population dynamics of an ensemble of reactive…

We investigate the sharp asymptotic behavior at criticality of the large fluctuations of extensive observables in renewal models of statistical mechanics, such as the Poland-Scheraga model of DNA denaturation, the Fisher-Felderhof model of…

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes Generalized Mass…

Stochastic modeling of reaction networks is a framework used to describe the time evolution of many natural and artificial systems, including, biochemical reactive systems at the molecular level, viral kinetics, the spread of epidemic…

The equilibration of enzyme and complex concentrations in deterministic Michaelis-Menten reaction networks underlies the hyperbolic dependence between the input (substrates) and output (products). This relationship was first obtained by…

The industrialization of catalytic processes requires reliable kinetic models for their design, optimization and control. Mechanistic models require significant domain knowledge, while data-driven and hybrid models lack interpretability.…