An MCell model of calcium dynamics and frequency-dependence of calmodulin activation in dendritic spines
Introduction
Hebbian synaptic plasticity in pyramidal neurons depends on the relative timing of presynaptic and postsynaptic activity [18]. Moreover, when action potentials are paired in synaptically coupled cortical neurons, long-term potentiation (LTP) is induced in a frequency-dependent manner [16]. Specifically, when 5 pairings of pre- and postsynaptic action potentials are presented at, or slower than, , no change in synaptic efficacy resulted, however 5 pairings at induces a persistent synaptic potentiation that increases with pairing frequency and saturated at . Calcium-calmodulin-dependent kinase II (CaMK II) in the postsynaptic density (PSD) is, at least initially, dependent on activated calmodulin (CaM) for its own activation, and implicated in the induction of LTP [12]. CaM activation requires the binding of four Ca2+ ions, and because CaM's affinity for Ca2+ is low relative to resting free intracellular Ca2+ concentration, typically around , few of the sites are bound at rest [3]. When the cell is active, Ca2+ enters through either voltage- or ligand-gated channels [10]. CaM must compete with other intracellular Ca2+-binding proteins (CBPs) for available Ca2+, and only activates when all four sites are bound. Consequently, there is a highly non-linear relationship between Ca2+ influx and the activation of its downstream effectors.
If, for a given epoch of neural activity the total influx of Ca2+ is constant, then within a range, the total influx of Ca2+ depends linearly on the number of such epochs, but not on the frequency of their presentation; intracellular free Ca2+ concentration, however, is strongly dependent on pairing frequency [13]. First, the major source of Ca2+ in postsynaptic spines are NMDA channels [10], [11], localized on the synaptic face [9], and Ca2+ diffuses through the cytoplasm from its site of entry. At high pairing frequencies, Ca2+ will accumulate near the NMDA channels before it has a chance to diffuse away. Second, pumps slowly return cytosolic Ca2+ concentration to resting levels by either pumping it out of the cell or sequestering it in intracellular stores [11]. The shorter the interval between successive pairings, less Ca2+ will have been pumped out of the cell since the previous pairing. Endogenous CBPs buffer free Ca2+, but only indirectly affect the dependence of free Ca2+ concentration on pairing frequency. When Ca2+ first enters the spine it readily binds these proteins, however, their capacity saturates with sufficient Ca2+, and the rate at which they recover is a function of both their Koff and the clearance rate via the pumps [13].
In this paper, we explore the relationship between Ca2+ dynamics (the activity-dependent influx of Ca2+ versus the cellular homeostatic mechanisms to maintain low levels of free intracellular Ca2+ and the activation of calmodulin, an intracellular Ca2+-dependent effector protein. We first show how, for a given set of parameters, CaM activation is dependent on input-frequency. Then, by varying either the total amount of available CaM, or by changing the amount of CBPs, show how this frequency-dependence can be modulated. Previous models of Ca2+-activation of calmodulin [6], [7] are improved upon here by including individual channels rather than a non-specific Ca2+ flux into the cell and including the 3D-spatial organization of the spine. Furthermore, we include competition with other endogenous CBPs, where a previous model did not [6].
Section snippets
Methods
To examine the relationship between neural activity and CaM activation, we use MCell (www.mcell.cnl.salk.edu), a Monte Carlo simulator of microphysiology [2]. Briefly, this program allows for the 3D-simulation of Ca2+ diffusion by Brownian dynamics random walk and kinetic state transitions of channels and reactive molecules as diffusion-driven bimolecular associations and probabilistic, unimolecular Markov processes. Here, we model Ca2+ influx into a postsynaptic spine, modeled as a cube,
Results
To characterize the input frequency-dependence of calmodulin activation, we begin by simulating a single pairing of pre- and postsynaptic action potentials. The presynaptic action potential, represented as an excitatory postsynaptic potential (EPSP) in the postsynaptic cell, occurred before the postsynaptic action potential (Fig. 1A). This generates an influx of Ca2+, the details of which are described elsewhere (Franks et al., in preparation) Following a single pairing, most of the Ca2+
Discussion
The buffering actions of other CBPs and the necessity of quadruple Ca2+ binding entail a low probability of activating CaM after a single pairing. Similarly, if repeated pairings are presented sufficiently far apart, both Ca2+ concentration and CBP occupancy will have returned to resting levels before each next pairing, and the pairings are read as independent events. As the interval between pairings gets smaller, residual Ca2+ from previous pairings decrease competition for CaM and the
Acknowledgements
This work was supported by the NIH, NSF, Howard Hughes Medical Institute and the Human Frontier Science Program.
Kevin Franks received his B.Sc. Biomedical Science and B.A. in Philosophy from the University of Guelph in Canada. He is presently a doctoral candidate at University of California, San Diego, working in the Computational Neurobiology Lab at the Salk Institute. He is interested in the mechanisms by which synapses change their weights. On weekends, he tames lions and massages porcupines.
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Kevin Franks received his B.Sc. Biomedical Science and B.A. in Philosophy from the University of Guelph in Canada. He is presently a doctoral candidate at University of California, San Diego, working in the Computational Neurobiology Lab at the Salk Institute. He is interested in the mechanisms by which synapses change their weights. On weekends, he tames lions and massages porcupines.
Tom Bartol is a research associate in the Computational Neurobiology Laboratory at the Salk Institute. He earned his Ph.D. in Neurobiology & Behavior in the laboratory of Miriam Salpeter at Cornell University. He is a co-author of the MCell Monte Carlo simulator of cellular microphysiology.
Terrence Sejnowski is an Investigator with the Howard Hughes Medical Institute and a Professor at The Salk Institute for Biological Studies where he directs the Computational Neurobiology Laboratory. He is also Professor of Biology at the University of California, San Diego, where he is Director of the Institute for Neural Computation. Dr. Sejnowski received his B.S. in Physics from the Case-Western Reserve University, M.A. in Physics from Princeton University, and a Ph.D. in Physics from Princeton University in 1978. In 1988, Dr. Sejnowski founded Neural Computation, published by the MIT Press. He is also the President of the Neural Information Processing Systems Foundation. The long-range goal of Dr. Sejnowski's research is to build linking principles from brain to behavior using computational models. This goal is being pursued with a combination of theoretical and experimental approaches at several levels of investigation ranging from the biophysical level to the systems level.