Exocytosis & Neurotransmitter Release Mathematical Models

Secretion mathematical models from our lab—including exocytosis and neurotransmitter release—are listed below. These models address issues of whether secretion is controlled by calcium in the immediate vicinity of open calcium channels or bulk cytosolic calcium or vesicle trafficking; whether each vesicle sees calcium from one channel or many; and determinants of the kinetics of secretion, such as synaptic facilitation, a building block of short-term memory, and early and late phases of insulin secretion.

View other models from our lab by subject on our Mathematical Models page. Visit GitHub.com to view a list of models by publication citation.

Buffer Saturation Model for Synaptic Facilitation

This study examines the conditions under which buffer saturation can result in synaptic facilitation, as proposed by Erwin Neher and colleagues.

Facilitation through buffer saturation: Constraints on endogenous buffering properties.
Matveev V, Sherman A, Zucker RS.
Biophys. J. (2004) 86:2691-2709. Abstract/Full Text
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Calcium Cooperativity

We distinguish two concepts of calcium cooperativity of exocytosis that are often lumped together. Calcium current cooperativity is the relationship between whole-cell calcium current and exocytosis rate, whereas calcium channel cooperativity is the number of calcium channels involved in the release of a single vesicle.

Ca2+ current vs. Ca2+ channel cooperativity of exocytosis.
Bertram R, Matveev V, Sherman A.
J. Neurosci. (2009) 29(39):12196-12209. Abstract/Full Text
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Domain Overlap

We discuss the extent to which calcium cooperativity of exocytosis can be used to determine the degree of overlap between calcium nanodomains controlling release of vesicles.

Calcium cooperativity of exocytosis as a measure of Ca2+ channel domain overlap.
Bertram R, Matveev V, Sherman A.
Brain Research Reviews. (2011) 1398:126-128. Abstract/Full Text
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Highly Calcium Sensitive Pool (HCSP)

This is an extended model for insulin vesicle release that accounts for optical observations suggesting that the second phase of insulin secretion is due to newcomer vesicles arriving at the plasma membrane. The model further identifies the newcomer vesicles with a previously proposed highly calcium sensitive pool of vesicles.

Newcomer insulin secretory granules as a highly calcium-sensitive pool.
Pedersen MG, Sherman A.
PNAS. (2009) 106(18):7432-6. Abstract/Full Text
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Insulin Vesicle Kinetics (Chen08)

This is a model for the dynamics insulin vesicle exocytosis that accounts for the kinetics of first- and second-phase insulin secretion. The fast (10 min) first phase is due to a readily releasable pool of vesicles that only require calcium from a nearby calcium channel to release, while the slow (60 min) second phase depends on delivery of new vesicles to the plasma membrane.

Identifying the targets of the amplifying pathway for insulin secretion in pancreatic beta-cells by kinetic modeling of granule exocytosis.
Chen YD, Sherman A, Wang S.
Biophys. J. (2008) 95(5):2226-41. Abstract/Full Text
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Nanodomain Model

This model was designed to show that synaptic facilitation could be explained by an increase in calcium bound to vesicles associated with single calcium channels.

The single domain/bound calcium hypothesis of transmitter release and facilitation.
Bertram R, Sherman A, Stanley E.
J. Neurophysiol. (1996) 75:1919-1931. Abstract/Full Text
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Residual Bound Calcium

This study demonstrates that a model in which synaptic facilitation is governed by the dynamics of calcium bound to release sites is consistent with experiments showing that calcium buffers reduce facilitation provided diffusion of free calcium is included.

Residual bound Ca2+ can account for the effects of Ca2+ buffers on synaptic facilitation.
Bertram R, Matveev V, Sherman A.
J. Neurophysiol. (2006) 96(6):3389-97. Abstract/Full Text
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Residual Free Calcium Model for Synaptic Facilitation

This model illustrates synaptic facilitation governed by residual free calcium in concert with the dynamics of calcium binding sites. It corrects errors in a model previously published by others.

New and Corrected Simulations of Synaptic Facilitation.
Matveev V, Sherman A, Zucker RS.
Biophys. J. (2002) 83:1368-73. Abstract/Full Text
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Synapse Population Model

This paper describes how to model a population of synaptic release sites, each stochastically driven by a colocalized calcium channel, using a mean field approximation.

Population dynamics of synaptic release sites.
Bertram R, Sherman A.
SIAM J. Applied Math. (1998) 58:142-169. Abstract/Full Text
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Last Reviewed February 2023