Contemporary Mathematics
Diffusion in cellular microdomains: application to synapses
D. Holcman
Abstract. Modern technologies driven by biological questions such as single
particle tracking or electron microscopy have revealed how molecular activity
underlies cell physiology. Because direct measurements or live monitoring are
not always possible, understanding cellular activity at the molecular level has
greatly benefit from cell reconstruction which requires multiple data sources
coming in particular from electrophysiological recordings. This reconstruc-
tion was made possible by the use of theoretical approach using biophysical
modeling, statistical physics and applied mathematics. Merging multiple data
sources was applied successfully to better understand neuronal synapses, which
are micro-contact between neurons underlying neuronal communication in the
brain. Because direct measurements at a single synapse are still possible, by
integrating physiological information from various scales and using physical
modeling and mathematical analysis of reaction diffusion in micro-domains
involving few molecules, several quantitative aspects of the synaptic function
have recently emerged. We review here some recent progress of diffusion in
cellular microdomains, which is a fundamental phenomena underlying cellular
biochemical activity and we focus specifically in the second part of this review
on synaptic transmission and regulation.
1. Introduction
Over the past 40 years, various technological revolutions such as patch clamp
recordings [41], confocal imaging, dye fluorescent molecules [68], single particle
tracking have revealed the complexity of biological cellular processes: cells are
complex and dynamically regulated factories where molecules are synthesized and
used for a specific function. A single cell can be spatially and functionally separated
in several microdomains (Figure 1) and this architecture serves multiple functions.
An eukaryotic cell contains a nucleus where the genetic material is protected and
regulated through gene activation. Defects in the nucleus architectural organiza-
tion are responsible for several human diseases [40]. However nuclear organization,
gene expression and maintenance of genome integrity remain poorly understood
[66]. Many organelles play a fundamental role in protein cycle: before being trans-
ported by a yet unknown coding signaling to the correct location, proteins (see fig.
1) mature in Golgi apparatus while being synthesized in endoplasmic reticulum.
1991 Mathematics Subject Classification. Primary 92B05,35B40; Secondary 35J05, 35Q80.
Key words and phrases. Diffusion in microdomains, small hole, Synapses, Laplace equation.
This research was supported by an ERC-Starting Grant and a HFSP Research Grant.
c XXXX American Mathematical Society
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Contemporary Mathematics
Volume 494, 2009
c 2009 American Mathematical Society
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