25 papers · ranked by Valyu relevance
Liu Hong, Hong Qian
The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully appreciated outside the community of physical chemists. In this review, we…
José-Luis Muñoz-Cobo, Cesar Berna
In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network.…
Jaroslav Albert, Ramon Grima
Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may…
Verena Wolf, Rushil Goel, Maria Mateescu, Thomas A Henzinger
Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases…
Eduardo D. Sontag, Abhyudai Singh
We analyze a class of chemical reaction networks for which all moments can be computed by finite-dimensional linear differential equations. This class allows second and higher order reactions, but only under special assumptions on structure and/or conservation laws.
Hong Qian, Lisa M. Bishop
We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with…
JaeJun Lee, Julian Lee
In a stochastic process, noise often modifies the picture offered by the mean field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution, and turns it into a transient peak. We make a quantitative analysis of this…
Yuji Hirono, Ryo Hanai
Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of chemical master equations. In this paper, we describe a novel method for computing…
O Beruski
A new tool for modeling electrochemical kinetics is presented. An extension of the Stochastic Simulation Algorithm framework to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a chemical master equation are provided and discussed. The electrochemical driving forces…
Mauricio J. del Razo, Stefanie Winkelmann, Rupert Klein, Felix Höfling
'Felix Höfling'] The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction–diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction– diffusion processes. The CDME consists of an infinite ordered…
J. Holehouse, R. Grima
Propensity functions of the Hill-type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models…
Steffen Waldherr, Bernard Haasdonk
Background Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally…
John C. Baez
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar purposes in computer science and biology. As noted by Doi and others, techniques…
Shakti Nath Singh, Athokpam Langlen Chanu, Md. Zubbair Malik, R.K. Brojen Singh
Delay is everywhere, no matter how small or big it is. Experimental evidences show the existence and importance of time delayed reactions specially in biological systems. The role of delay is found to be multifunctional and is seemed to be system dependent. The analytically solved P(X, t) of gene regulatory process…
Manuel Eduardo Hernández-García, Eduardo Moreno-Barbosa, Jorge Velázquez-Castro
'Jorge Velázquez-Castro'] 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 models such as the chemical master equation are…
Mauricio J. del Razo, Daniela Frömberg, Arthur V. Straube, Christof Schütte + 2 more
'Christof Schütte' 'Felix Höfling' 'Stefanie Winkelmann'] The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. At the level of particle-resolved descriptions, where chemical reactions are coupled to the spatial diffusion of…
Tânia Tomé, Mário J. de Oliveira
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 chemical reaction systems based on a master equation defined on the space of…
Michael Margaliot, Lars Grüne, Thomas Kriecherbauer
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or…
Jegathambal Palanichamy, Sundarambal Palani
Background The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of…
Authors not listed
Deriving versatile and robust mechanistic models from experimental data is a key challenge in engineering and natural sciences. This is especially true in chemical reaction engineering, where reactor manufacturers and operators increasingly pursue the development and maintenance of digital twins that rely on frequent…
Authors not listed
Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been…
Authors not listed
The modeling of chemical reactions using artificial intelligence is rapidly advancing but still heavily relies on abundant and costly experimental data. In the context of computational chemistry, we present SymChemAI, a chemically informed neural network capable of simulating the dynamic evolution of reactions from…
Frank Tipler
Quantum chemists have recorded a huge number of data points which standard quantum mechanics cannot interpret. Many-Worlds quantum mechanics can. Many-Worlds quantum mechanics differs from standard quantum mechanics because in Many-Worlds, the wave function is a relative density of universes in the multiverse amplitude…
Authors not listed
How to accelerate a reaction has been a critical question in physical organic chemistry, eliciting multiple models describing the interplay between kinetics and thermodynamic driving forces. However, existing models often come with inevitable limitations: valid only within finite thermodynamic ranges, rely on heavy…
Stephen Goldup, Ivan Aprahamian
All chemists are familiar with the idea that, at equilibrium steady state, the relative concentrations of species present in a system are predicted by the corresponding equilibrium constants, which are in turn related to the relative free energy difference of the system components. There is also no net flux between…