We present a biophysical model of electrical and Ca2' dynamics following activation of N-methyl-Daspartate (NMDA) receptors located on a dendritic spine. The model accounts for much of the phenomenology of the induction of long-term potentiation at a Hebbian synapse in hippocampal region CAI. (12,13). This increase is thought to be mediated by Ca>2 influx through the N-methyl-D-aspartate (NMDA) receptor-gated channel (13,14). Because the channel requires both ligand binding and postsynaptic depolarization for activation, it is ideally suited to contribute to the interactive requirement (4) for a Hebbian synapse.We have been interested in the role of the dendritic spine in LTP induction (9,11,15) and have constructed a biophysical model of electrical and Ca>2 dynamics in a spine after activation of NMDA receptors. Computer simulations indicate that the model can account for much of the known phenomenology of LTP induction at a Hebbian synapse in the CA1 region of the hippocampus. The results suggest that the microphysiology of the spine plays a critical role in the induction of this form of LTP.
MODELThe biophysical mechanism of LTP induction has been best studied at the Schaffer collateral/commissural inputs to pyramidal cells of the CA1 region of the rodent hippocampus in the in vitro brain slice preparation. At least two pharmacologically distinguishable receptors mediate the excitatory postsynaptic response in this system. NMDA receptors mediate a slow current (16) with a substantial Ca2" component.
The associated channel is voltage-dependent due to block byMg2`that is relieved by membrane depolarization (17-19).Non-NMDA receptors mediate a more rapid current with a negligible Ca`component.We simulated Ca`influx, transport, and buffering following activation of NMDA receptor-gated channels located on a spine head. The model (Fig. 1) consisted of separate electrical and Ca2+ components (15). The equations describing electrical and chemical dynamics were advanced independently and at the end of each time step electrical current was converted to ionic flux through Faraday's constant. These equations were discretized and then solved using alternating implicit-explicit steps (20, 21). Spine and Synapse. Total synaptic current (Fig. 1) was the sum of separate NMDA and non-NMDA components. An alpha function (22), I(t) = (Esyn -Vm) Kgpt exp(-t/tp), [1] was used for the non-NMDA current, with K = e/tp, e the base of the natural logarithm, tp = 1.5 msec, Esyn = 0 mV, and the peak conductance gp = 0.5 nS (9,23 tTo whom reprint requests should be addressed.
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