Abstract:As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (fil… Show more
“…Stochastic particle-based reaction diffusion simulations have become increasingly popular in the past decade [36][37][38][39][40][41][42][43][44][45][46] . Such simulation methods and frameworks evolve the reaction-diffusion processes microscopically and have experienced advancements both in accuracy and computational a) Equal contributions b) Electronic mail: frank.noe@fu-berlin.de c) Electronic mail: f.hoefling@fu-berlin.de performance [47][48][49][50][51] .…”
The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions. arXiv:1908.07764v1 [cond-mat.soft]
“…Stochastic particle-based reaction diffusion simulations have become increasingly popular in the past decade [36][37][38][39][40][41][42][43][44][45][46] . Such simulation methods and frameworks evolve the reaction-diffusion processes microscopically and have experienced advancements both in accuracy and computational a) Equal contributions b) Electronic mail: frank.noe@fu-berlin.de c) Electronic mail: f.hoefling@fu-berlin.de performance [47][48][49][50][51] .…”
The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions. arXiv:1908.07764v1 [cond-mat.soft]
“…This approach does allow for volume exclusion but due to the nature of Brownian motion is numerically intensive. Both Spatiocyte and our approach address this problem by restricting particles to diffuse across a lattice [ 13 , 15 , 36 ]. The software package Spatiocyte is generally similar to what we present here; particles diffuse and react across a lattice obeying volume exclusion.…”
Section: Availability and Future Directionsmentioning
confidence: 99%
“…Numerical approaches are computationally prohibitive, leaving direct simulation as the first and frequently only line of attack. The recent IPS simulation package Spatiocyte [ 13 ] and its numerous extensions address simulation biases generated under a lattice-based spatial structure [ 14 ] and parallelize the original simulation code [ 15 ]. We provide a more detailed description of the differences between our approach and Spatiocyte in the section “Availability and Future Directions.”…”
Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.
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