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Stochastic automata network Markov model descriptors of coupled Ca2+ channels (Nguyen et al. 2005)
Accession: 118894
"... Here we present a formalism by which mathematical models for Ca2+-regulated Ca2+ release sites are derived from stochastic models of single-channel gating that include Ca2+ activation, Ca2+ inactivation, or both. Such models are stochastic automata networks (SANs) that involve a large number of functional transitions, that is, the transition probabilities of the infinitesimal generator matrix of one of the automata (i.e., an individual channel) may depend on the local [Ca2+] and thus the state of the other channels. Simulation and analysis of the SAN descriptors representing homogeneous clusters of intracellular Ca2+ channels show that (1) release site density can modify both the steady-state open probability and stochastic excitability of Ca2+ release sites, (2) Ca2+ inactivation is not a requirement for Ca2+ puffs or sparks, and (3) a single-channel model with a bell-shaped open probability curve does not lead to release site activity that is a biphasic function of release site density. ..."
Reference: Nguyen V, Mathias R, Smith GD (2005) A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bull Math Biol 67:393-432 [PubMed]
Citations  Citation Browser
Model Information (Click on a link to find other models with that property)
Model Type:  Channel;
Brain Region(s)/Organism:  
Cell Type(s):   
Channel(s):  I Calcium;  
Gap Junctions:  
Receptor(s):  
Gene(s):  
Transmitter(s):  
Simulation Environment:  CalC Calcium Calculator (web link to model);
Model Concept(s):  Ion Channel Kinetics; Calcium dynamics;
Implementer(s):  Matveev, Victor V. [m a t v e e v at n j i t . e d u ];
Search NeuronDB for information about:  I Calcium;
Model files (located externally to ModelDB) Help downloading and running models
Calcium Calculator Simulation Scripts

Note from the ModelDB Adminsitrator: the below is a snapshot of Matveev's Calcium Calculator Simulation Scripts web page taken on April 13th, 2009. The 4th listed item contains the link for the code associated with Nguyen et al. 2005.
Calcium Calculator Simulation Script Files
CalC Download CalC Manual CalC Scripts CalC Publications Victor's Homepage

DEMO SCRIPTS Example script files with comments, in lieau of a tutorial. Hopefully, enough to get you started.

Publication Scripts:

1.    L.N. Cornelisse, R.A.J. van Elburg, R.M. Meredith, R. Yuste, and H.D. Mansvelder (2007)
High Speed Two-Photon Imaging of Calcium Dynamics in Dendritic Spines: Consequences for Spine Calcium Kinetics and Buffer Capacity. PLoS ONE 2(10): e1073.
Full Text SCRIPTS
2.   O. Babich, V. Matveev, A. L. Harris, R. Shirokov (2007)
Ca2+-dependent inactivation of CaV1.2 channels prevents Gd2+ block: does Ca2+ block the pore of inactivated channels? Journal of General Physiology, 129: 477-483.
Abstract Full Text PDF SCRIPTS
3.   V. Matveev, R. Bertram, A. Sherman (2006)
Residual Bound Ca2+ Can Account for the Effects of Ca2+ Buffers on Synaptic Facilitation
Journal of Neurophysiology, 96: 3389-3397.
Abstract Full Text PDF SCRIPTS
4.   Nguyen V, Mathias R, Smith GD (2005)
A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bull Math Biol, 67(3):393-432.
Abstract PDF script
The script markov.par (linked above) demonstrates the use of Markov variables to simulate stochastic Ca2+ channel gating, examining the coupling of two stochastic Ca2+ channels with 4-state gating kinetics by Nguyen et al. (2005).
5.   V. Matveev, R.S. Zucker, A. Sherman (2004)
Facilitation through Buffer Saturation: Constraints on Endogenous Buffering Properties
Biophysical Journal, 86:2691-2709
Abstract Full Text PDF SCRIPTS
6.   V. Matveev, A. Sherman, R.S. Zucker, (2002)
New and Corrected Simulations of Synaptic Facilitation
Biophysical Journal, 83:1368-1373.
Abstract Full Text PDF SCRIPTS
7.   Yamada, W.M., and R.S. Zucker (1992)
Time course of transmitter release calculated from simulations of a calcium diffusion model.
Biophysical Journal, 61:671-682.
Abstract Full Text PDF script
The script YamadaZucker.par (linked above) reproduces Fig. 3B of Yamada and Zucker (1992)

This material is based upon work supported by the National Science Foundation grant 0417416 and 0817703.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation
Victor Matveev
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Last modified: Feb 15, 2009


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