Models that contain the Modeling Application : CalC Calcium Calculator (web link to model) (Home Page)

(CalC ("Calcium Calculator") is a modeling tool for integrating the 3D reaction-diffusion problem (or the corresponding reduced 1D and 2D problems) arising in biophysical modeling of intracellular calcium dynamics. CalC simulates the entry of calcium into a volume through point-like channels, and its diffusion, buffering and binding to calcium receptors.)
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    Models   Description
1.  Ca2+ current versus Ca2+ channel cooperativity of exocytosis (Matveev et al. 2009)
"... While varying extracellular or intracellular Ca2+ concentration assesses the intrinsic biochemical Ca2+ cooperativity of neurotransmitter release, varying the number of open Ca2+ channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca2+ channels in triggering exocytosis. ... Here we provide a detailed analysis of the Ca2+ sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca2+ current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca2+ current magnitude, and the underlying Ca2+ channel cooperativity, defined as the average number of channels involved in the release of a single vesicle. ... Further, we use three-dimensional computational modeling of buffered Ca2+ diffusion to analyze these distinct Ca2+ cooperativity measures, and demonstrate the role of endogenous Ca2+ buffers on such measures. We show that buffers can either increase or decrease the Ca2+ current cooperativity of exocytosis, depending on their concentration and the single-channel Ca2+ current."
2.  Facilitation model based on bound Ca2+ (Matveev et al. 2006)
"Facilitation is a transient stimulation-induced increase in synaptic response, a ubiquitous form of short-term synaptic plasticity that can regulate synaptic transmission on fast time scales. In their pioneering work, Katz and Miledi and Rahamimoff demonstrated the dependence of facilitation on presynaptic Ca2+ influx and proposed that facilitation results from the accumulation of residual Ca2+ bound to vesicle release triggers. However, this bound Ca2+ hypothesis appears to contradict the evidence that facilitation is reduced by exogenous Ca2+ buffers. This conclusion led to a widely held view that facilitation must depend solely on the accumulation of Ca2+ in free form. Here we consider a more realistic implementation of the bound Ca2+ mechanism, taking into account spatial diffusion of Ca2+, and show that a model with slow Ca2+ unbinding steps can retain sensitivity to free residual Ca2+. ..."
3.  Facilitation through buffer saturation (Matveev et al. 2004)
"... Using computer simulations, we study the magnitude of synaptic facilitation (SF) that can be achieved by a buffer saturation mechanism (BSM), and explore its dependence on the endogenous buffering properties. ..."
4.  New and corrected simulations of synaptic facilitation (Matveev et al. 2002)
"A three-dimensional presynaptic calcium diffusion model developed to account for characteristics of transmitter release was modified to provide for binding of calcium to a receptor and subsequent triggering of exocytosis. When low affinity (20 FLM) and rapid kinetics were assumed for the calcium receptor triggering exocytosis, and stimulus parameters were selected to match those of experiments, the simulations predicted a virtual invariance of the time course of transmitter release to paired stimulation, stimulation with pulses of different amplitude, and stimulation in different calcium solutions. ..."
5.  Permeation and inactivation of CaV1.2 Ca2+ channels (Babich et al. 2007)
The authors present data and a kinetics model of the CaV1.2 channel supporting the idea that Ca2+ block of the pore generates the U-shaped inactivation curve.
6.  Stochastic automata network Markov model descriptors of coupled Ca2+ channels (Nguyen et al. 2005)
"... 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. ..."
7.  Transmitter release and Ca diffusion models (Yamada and Zucker 1992)
"A three-dimensional presynaptic calcium diffusion model developed to account for characteristics of transmitter release was modified to provide for binding of calcium to a receptor and subsequent triggering of exocytosis. ..."

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