Deterministic Reaction-Diffusion Simulators
A deterministic reaction–diffusion simulator is software designed to approximate the dynamics of a system governed by the diffusion and interaction of species within a domain in a deterministic fashion.
In neuroscience, these species can be one of many classes of molecules: ions, enzymes, polypeptides, globular proteins, microRNAs, etc. The interactions are chemical reactions, such as phosphorylation or binding, the synthesis of a new molecule out of substrates, or the breakdown of a molecule. Unlike stochastic simulators, which approximate these dynamics using pseudorandom processes, deterministic simulators solve a system of partial differential equations (PDEs). Thus, while stochastic simulators need to be run many times to identify the range of likely outcomes, deterministic simulators need only be run once, as the result is unique.
Deterministic simulators are most appropriate when they can rely on the law of large numbers (Kotelenez 1986),...
KeywordsDiffusion Equation Finite Volume Method Kinetic Scheme Computational Neuroscience Cartesian Mesh
This work was partially supported by NIH R01MH086638 and NIH 2T15LM007056.
- Blackwell KT, Kotaleski JH (2003) Modeling the dynamics of second messenger pathways. In: neuroscience databases: a practical guide. Springer Science + Business Media, New York, pp 63–79Google Scholar
- Kutta MW (1901) Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeitschrift Math Phys 46:435–453Google Scholar
- Ray S, Bhalla US (2008) PYMOOSE: interoperable scripting in Python for MOOSE. Front Neuroinform 2(6):1–16Google Scholar