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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…
In this paper, we provide a graphic formulation of non-isothermal reaction systems and show that a non-isothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold…
Many biological processes exhibit oscillatory behavior. Among these, glycolytic oscillations have been extensively studied due to their well-characterized biochemical reaction networks. However, the complexity of these networks necessitates…
By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which…
We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common…
The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar…
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…
We present the spatial regime conversion method (SRCM), a novel hybrid modelling framework for simulating reaction-diffusion systems that adaptively combines stochastic discrete and deterministic continuum representations. Extending the…
We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…
Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical…
Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we…
To claim similarity of multiple dose-response curves in interlaboratory studies in regulatory toxicology is a relevant issue during the assay validation process. Here we demonstrated the use of dose-by-laboratory interaction contrasts,…
The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying theories of chemical kinetics, which are transition state theory, collision…
This paper studies a system of Ordinary Differential Equations modeling a chemical reaction network and derives from it a simulation tool mimicking Loss of Function and Gain of Function mutations found in cancer cells. More specifically,…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
In this paper, we discuss and compare two probabilistic approaches for associating a stochastic differential equation with a McKean-type partial differential equation featuring a reaction term and path-dependent coefficients. The…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
While Large Language Models (LLMs) have revolutionized scientific text processing, they exhibit a significant capability gap when interpreting chemical reaction diagrams. We identify two fundamental bottlenecks restricting current systems:…