MULTIPARTICLE LATTICE GAS AUTOMATA FOR REACTION DIFFUSION SYSTEMS

1994 ◽  
Vol 05 (01) ◽  
pp. 47-63 ◽  
Author(s):  
BASTIEN CHOPARD ◽  
LAURENT FRACHEBOURG ◽  
MICHEL DROZ

Lattice gas automata are a powerful tool to model reaction-diffusion processes. However, the evolution rules limit the number of particles that can be present at each lattice site. This restriction is often a strong limitation to modelling several reaction-diffusion phenomena and, also, lead to very noisy numerical simulations. We propose and study new algorithms which allow for an arbitrary number of particle, while keeping the benefits of the cellular automata approach (close to a microscopic level of description, deal correctly with all degrees of freedom, and is numerically exact).

2019 ◽  
Author(s):  
Satya N. V. Arjunan ◽  
Atsushi Miyauchi ◽  
Kazunari Iwamoto ◽  
Koichi Takahashi

ABSTRACTBackgroundStudies using quantitative experimental methods have shown that intracellular spatial distribution of molecules plays a central role in many cellular systems. Spatially resolved computer simulations can integrate quantitative data from these experiments to construct physically accurate models of the systems. Although computationally expensive, microscopic resolution reaction-diffusion simulators, such as Spatiocyte can directly capture intracellular effects comprising diffusion-limited reactions and volume exclusion from crowded molecules by explicitly representing individual diffusing molecules in space. To alleviate the steep computational cost typically associated with the simulation of large or crowded intracellular compartments, we present a parallelized Spatiocyte method called pSpatiocyte.ResultsThe new high-performance method employs unique parallelization schemes on hexagonal close-packed (HCP) lattice to efficiently exploit the resources of common workstations and large distributed memory parallel computers. We introduce a coordinate system for fast accesses to HCP lattice voxels, a parallelized event scheduler, a parallelized Gillespie’s direct-method for unimolecular reactions, and a parallelized event for diffusion and bimolecular reaction processes. We verified the correctness of pSpatiocyte reaction and diffusion processes by comparison to theory. To evaluate the performance of pSpatiocyte, we performed a series of parallelized diffusion runs on the RIKEN K computer. In the case of fine lattice discretization with low voxel occupancy, pSpatiocyte exhibited 74% parallel efficiency and achieved a speedup of 7686 times with 663552 cores compared to the runtime with 64 cores. In the weak scaling performance, pSpatiocyte obtained efficiencies of at least 60% with up to 663552 cores. When executing the Michaelis-Menten benchmark model on an eight-core workstation, pSpatiocyte required 45- and 55-fold shorter runtimes than Smoldyn and the parallel version of ReaDDy, respectively. As a high-performance application example, we study the dual phosphorylation-dephosphorylation cycle of the MAPK system, a typical reaction network motif in cell signaling pathways.ConclusionspSpatiocyte demonstrates good accuracies, fast runtimes and a significant performance advantage over well-known microscopic particle simulators for large-scale simulations of intracellular reaction-diffusion systems. The source code of pSpatiocyte is available at https://spatiocyte.org.


Author(s):  
István Szalai ◽  
Brigitta Dúzs ◽  
István Molnár ◽  
Krisztina Kurin-Csörgei ◽  
Miklós Orbán

AbstractThe bromate–sulfite reaction-based pH-oscillators represent one of the most useful subgroup among the chemical oscillators. They provide strong H+-pulses which can generate temporal oscillations in other systems coupled to them and they show wide variety of spatiotemporal dynamics when they are carried out in different gel reactors. Some examples are discussed. When pH-dependent chemical and physical processes are linked to a bromate–sulfite-based oscillator, rhythmic changes can appear in the concentration of some cations and anions, in the distribution of the species in a pH-sensitive stepwise complex formation, in the oxidation number of the central cation in a chelate complex, in the volume or the desorption-adsorption ability of a piece of gel. These reactions are quite suitable for generating spatiotemporal patterns in open reactors. Many reaction–diffusion phenomena, moving and stationary patterns, have been recently observed experimentally using different reactor configurations, which allow exploring the effect of different initial and boundary conditions. Here, we summarize the most relevant aspects of these experimental and numerical studies on bromate–sulfite reaction-based reaction–diffusion systems.


2020 ◽  
Vol 82 (10) ◽  
Author(s):  
Andrew L. Krause ◽  
Václav Klika ◽  
Jacob Halatek ◽  
Paul K. Grant ◽  
Thomas E. Woolley ◽  
...  

Abstract Reaction–diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction–diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.


Author(s):  
Brigitta Dúzs ◽  
Istvan Szalai

Operating natural or artificial chemical systems requires nonequilibrium conditions at which temporal and spatial control of the process is realizable. Open reaction-diffusion systems provide a general way to create such...


1999 ◽  
Vol 09 (11) ◽  
pp. 2215-2218 ◽  
Author(s):  
WALTER J. FREEMAN

Brain electrical activity in animals during normal behaviors has aperiodic wave forms suggesting its origin in chaotic dynamics. Attempts at finding experimental proofs using low-dimensional, deterministic chaotic models have not succeeded. The assumptions of autonomy, stationarity,and noise-free operation that are needed to define these at tractors and their embedding dimensions have been shown not to hold for brains, because numerical estimates of correlation dimensions and Lyapunov exponents have failed to converge to normative values. Analysis of EEGs from sensory cortices show that a very different model applies to brains, which is more closely related to lasers than models of twist–flip maps and reaction–diffusion systems. Neurons interact with each other through channels with nonlinear, amplitude-dependent gains, by which they form fields of white noise. When the strengths of interaction are increased by input from receptors, the neurons interact more strongly and lose their high degrees of freedom. The macroscopic constraint on their activity appears as an order parameter in the form of spatially coherent, indeterministic chaos.


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