1. Because induction of associative long-term potentiation (LTP) in the dentate gyrus is thought to depend on Ca2+ influx through channels controlled by N-methyl-D-aspartate (NMDA) receptors, quantitative modeling was performed of synaptically mediated Ca2+ influx as a function of synaptic coactivation. The goal was to determine whether Ca2+ influx through NMDA-receptor channels was, by itself, sufficient to explain associative LTP, including control experiments and the temporal requirements of LTP. 2. Ca2+ influx through NMDA-receptor channels was modeled at a synapse on a dendritic spine of a reconstructed hippocampal dentate granule cell when 1-115 synapses on spines at different dendritic locations were activated eight times at frequencies of 10-800 Hz. The resulting change in [Ca2+] in the spine head was estimated from the Ca2+ influx with the use of a model of a dendritic spine that included Ca2+ buffers, pumps, and diffusion. 3. To use a compelling model of synaptic activation, we developed quantitative descriptions of the NMDA and non-NMDA receptor-mediated conductances consistent with available experimental data. The experimental data reported for NMDA and non-NMDA receptor-channel properties and data from other non-LTP experiments that separated the NMDA and non-NMDA receptor-mediated components of synaptic events proved to be limiting for particular synaptic variables. Relative to the non-NMDA glutamate-type receptors, 1) the unbinding of transmitter from NMDA receptors had to be slow, 2) the transition from the bound NMDA receptor-transmitter complex to the open channel state had to be even slower, and 3) the average number of NMDA-receptor channels at a single activated synapse on a single spine head that were open and conducting at a given moment in time had to be very small (usually less than 1). 4. With the use of these quantitative synaptic conductance descriptions. Ca2+ influx through NMDA-receptor channels at a synapse was computed for a variety of conditions. For a constant number of pulses, Ca2+ influx was calculated as a function of input frequency and the number of coactivated synapses. When few synapses were coactivated, Ca2+ influx was small, even for high-frequency activation. However, with larger numbers of coactivated synapses, there was a steep increase in Ca2+ influx with increasing input frequency because of the voltage-dependent nature of the NMDA receptor-mediated conductance. Nevertheless, total Ca2+ influx was never increased more than fourfold by increasing input frequency or the number of coactivated synapses.(ABSTRACT TRUNCATED AT 400 WORDS)

Holmes, W. R., & Levy, W. B. (1990). Insights into associative long-term potentiation from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. Journal of Neurophysiology, 63(5), 1148–1168.