Related papers: Reaction rates for mesoscopic reaction-diffusion k…
Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting…
In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this…
Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such…
A novel approach to simulate simple protein-ligand systems at large time- and length-scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD…
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 diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction-radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the…
We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
Computing reaction rates in biomolecular systems is a common goal of molecular dynamics simulations. The reactions considered often involve conformational changes in the molecule, either changes in the structure of a protein or the relative…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Mean-Field Ring Polymer Molecular Dynamics (MF-RPMD) is a powerful, efficient, and accurate method for approximate quantum dynamic simulations of multi-level system dynamics. Initial efforts to compute nonadiabatic reaction rates using…
The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…