Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Diffusion Equation

  • Fidel SantamariaEmail author
  • Toma M. Marinov
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_186-3

Synonyms

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

Keywords

Diffusion Equation Mean Square Displacement Anomalous Diffusion Differential Equation Model Parabolic Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgment

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

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of BiologyUniversity of Texas at San AntonioSan AntonioUSA