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Encyclopedia of Computational Neuroscience pp 1–5Cite as

Diffusion Equation

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Synonyms

Fick’s second law; Heat equation

Definition

The diffusion equation (DE) is a second-order parabolic partial differential equation describing mass transport phenomena due to thermal motion of particles (Crank 1975).

Detailed Description

Diffusion is an important transport mechanism in neurons (Bloodgood 2005; Ehlers et al 2007; Korkotian and Segal 2006; Makin and Malinow 2009; Qian and Sejnowki 1988; Renner et al. 2009; Sabatini et al. 2002; Santamaria 2006; Schmidt 2007a. Smith et al. 1993; Soler and Sabatini 2006). It takes place in the cytosol, the cell membrane and the endoplasmic reticulum. Subject to diffusion are both ions (Ca+, Na+, K+, Cl-, etc) and large complex molecules (lipids, proteins, DNA, RNA, etc.). The physical process of diffusion in absence of any chemical reactions is described by the diffusion equation:

$$ \frac{\partial C\left(\mathbf{x},t\right)}{\partial t}=\nabla \cdotp \left(D\left(\mathbf{x},t\right)\nabla C\left(\mathbf{x},t\right)\right) $$

where D...

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References

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Acknowledgment

This work was partially supported by NSF IOS-1209029 and NSF EF-1137897

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Authors and Affiliations

  1. Department of Biology, University of Texas at San Antonio, San Antonio, TX, USA

    Fidel Santamaria & Toma M. Marinov

Authors
  1. Fidel Santamaria
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  2. Toma M. Marinov
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Corresponding author

Correspondence to Fidel Santamaria .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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Santamaria, F., Marinov, T.M. (2013). Diffusion Equation. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_186-3

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_186-3

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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