Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Deterministic Reaction-Diffusion Simulators

  • William W. LyttonEmail author
  • Robert A. McDougal
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_185


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.

Detailed Description

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),...

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This work was partially supported by NIH R01MH086638 and NIH 2T15LM007056.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departments of Physiology & Pharmacology and NeurologySUNY Downstate Medical CenterBrooklynUSA
  2. 2.Department of NeurologyKings County HospitalBrooklynUSA
  3. 3.Department of NeurobiologyYale University School of MedicineNew HavenUSA