23 papers · ranked by Valyu relevance
R Dobrescu, VL Purcarea
The paper discusses the connection between emergence, pattern formation and nonlinear dynamics, focusing on the similarity between discrete patterns and fractal structures, and then describes different solutions to model reaction-diffusion systems as representative processes in morphogenesis. A specific example is the…
Changhao Li, Jianfeng Li, Yuliang Yang, Jens-Uwe Sommer
This work is devoted to deriving a more accurate reaction-diffusion equation for an A/B binary system by summing over microscopic trajectories. By noting that an originally simple physical trajectory might be much more complicated when the reactions are incorporated, we introduce diffusion-reaction-diffusion (DRD)…
Alberto Montefusco, Christof Schütte, Stefanie Winkelmann
The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of…
Miloslav Pekař, José S. Urieta, Ana M. Mainar
Self-balancing diffusion is a theoretical concept that restricts the introduction of extents of reactions. This concept is analyzed in detail for general mass- and molar-based balances of reaction-diffusion mixtures, in relation to non-self-balancing cases, and with respect to its practical consequences. Self-balancing…
Charles G. Cameron, Cameron A. Smith, Christian A. Yates
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 regime conversion method (RCM) to spatial settings, the SRCM employs a discrete…
Mauricio J. del Razo
scales Authors: ['Mauricio J. del Razo'] Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic…
Stephen Smith, Ramon Grima
Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically…
Denis S. Grebenkov, Anan Yaghmur
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the…
Kai Trepka
Building models of organismal growth enables predictions of natural variability and responses to perturbations. Complex systems such as animal pattern development and bacterial colonies can be modeled numerically using a reaction-diffusion system with relatively few factors and yield qualitatively accurate results…
Authors not listed
Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a…
Andrew J. Loza, Marc S. Sherman
Biological systems frequently contain biochemical species present as small numbers of slowly diffusing molecules, leading to fluctuations that invalidate deterministic analyses of system dynamics. The development of mathematical tools that account for the spatial distribution and discrete number of reacting molecules…
Yin Hoon Chew, Fabian Spill
Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are…
Michael Klann, Heinz Koeppl
Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of…
Denis S. Grebenkov
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin boundary condition accounting for eventual failed reaction events, and the…
Steven S. Andrews
Biological cells are complex environments that are densely packed with macromolecules and subdivided by membranes, both of which affect the rates of chemical reactions. It is well known that crowding reduces the volume available to reactants, which increases reaction rates, and also inhibits reactant diffusion, which…
Yin Hoon Chew, Fabian Spill
Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are…
Joseph W. Baron, Tobias Galla
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same patterns. If particles are short-lived, the transient dynamics are captured as well.…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Denis S. Grebenkov
Autocatalytic processes underlie diverse systems in which replication is triggered at interfaces, including heterogeneous catalysis on solid substrates, enzyme activity at membranes, viral infections, biofilm growth, and spatially structured ecosystems. In a typical scenario, particles move in a bulk medium and…
Srijana Pandey, Dinesh Gautam, Jixin Chen
Many interactions between small molecules and particles occur in solutions. They are surrounded by other molecules that do not react, for example, biological processes in water, chemical reactions in gas or liquid solutions, and environmental reactions in air and water. Predicting the rate of such interactions involves…
Anıl Cengiz, Sean D. Lawley
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 describing the evolution of both molecular diffusion and molecule-receptor…