INSIGHTS INTO ASSOCIATIVE LONG-TERM POTENTIATION FROM COMPUTATIONAL MODELS OF NMDA RECEPTOR-MEDIATED CALCIUM INFLUX AND INTRACELLULAR CALCIUM-CONCENTRATION CHANGES

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 <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. Such increases are too small to explain the selective induction of associative LTP in light of the sine qua non control experiment. 5. The three- to fourfold increases in Ca2+ influx obtained by increasing input frequency were amplified into 20- to 30-fold increases in free Ca2+ concentration in the spine head. This amplification of small changes in influx to large changes in concentration occurred because of transient saturation of the fast Ca2+ buffering systems. Varying the concentration and location of Ca2+ binding sites in the spine head provided insight into the range of Ca2+ binding site concentration values for which this amplification occurs. 6. The experimentally described temporal requirements of dentate gyrus associative potentiation studied with two stimulating electrodes, one activating a weakly excitatory input and the other activating a strongly excitatory input, were examined in the context of the present model. The temporal input patterns that produced the best potentiation of the weak input response in previous experiments were the same ones that produced the largest Ca2+ influx and the largest peak spine head values of [Ca2+] in the model. Parameter values estimated independently in the development of the quantitative synaptic conductance descriptions were critically reponsible for this correspondence; the timing results in the model depended on two slow rate constants in the activation of the NMDA receptor-mediated conductance. 7. In conclusion, the nonlinearity in Ca2+ influx through NMDA-receptor channels because of increases in input frequency and intensity, although very important, was not sufficient to explain associative LTP. However, the transient saturation of the fast Ca2+ buffering systems significantly amplified the nonlinearity in Ca2+ influx to provide a large, steep nonlinearity in the alteration of spine head Ca2+ concentration as a function of convergent coactivity. Successive calcium-triggered reactions could further amplify this nonlinearity.