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This Feature Article presents an overview of the current status of Ring Polymer Molecular Dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical…
The metabolic state of a cell, comprising fluxes, metabolite concentrations and enzyme levels, is shaped by a compromise between metabolic benefit and enzyme cost. This hypothesis and its consequences can be studied by computational models…
Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability…
We describe modeling approaches to a "network" of connected enzyme-catalyzed reactions, with added (bio)chemical processes that introduce biochemical filtering steps into the functioning of such a biocatalytic cascade. Theoretical…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize…
The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of high-yield robust metabolic pathways producing, for instance, drug precursors and…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of…
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…
Genetically identical cells under the same environmental conditions can show strong variations in protein copy numbers due to inherently stochastic events in individual cells. We here develop a theoretical framework to address how…
Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees…
Quantitative studies of cell metabolism are often based on large chemical reaction network models. A steady state approach is suited to analyze phenomena on the timescale of cell growth and circumvents the problem of incomplete experimental…
The article presents new model of equilibrium in open chemical systems suggesting a linear dependence of the reaction shift from equilibrium in presence of the external thermodynamic force. Basic equation of this model contains traditional…
A mathematical model for chemical reactions in electrolytes is developed using an Energy variational method consistent with classical thermodynamics. Electrostatics and chemical reactions are included in properly defined energetic and…
We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks…
Modeling of process for reaction kinetics is a fashionable subject of publications. The meaning of both the mortality and fertility terms are mathematically analyzed in details involving variation of their power exponents. We developed an…
We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is…