Quantifying the role of inhibition in associative long-term potentiation in dentate granule cells with computational models.

In the dentate gyrus, coactivation of a mildly strong ipsilateral perforant path (pp) input with a weak contralateral pp input will not induce associative long-term potentiation in the weak input path unless both inputs project to the same part of the molecular layer. This "spatial convergence requirement" is thought to arise from either voltage attenuation between input locations or inhibition. Simulations with a detailed model of a dentate granule cell were performed to rule out voltage attenuation and to quantify the inhibition necessary to obtain the spatial convergence requirement. Strong lateral and weak medial or strong medial and weak lateral pp input were activated eight times at 400 Hz. Calcium current through N-methyl-D-aspartate receptor channels and subsequent changes in calcium concentration and the concentration of calmodulin bound with four calcium ions ([Cal-Ca4]) in the spine head were computed for a medial and a lateral pp synapse. To satisfy the spatial convergence requirement, peak [Cal-Ca4] had to be much larger in the strongly activated path synapse than in the weakly activated path synapse. With no inhibition in the model, differences in peak [Cal-Cal4] at the two synapses were small, ruling out voltage attenuation as the explanation of the spatial convergence requirement. However, with shunting inhibition, modeled by reducing membrane resistivity to 1,600 omega cm2 in the distal two-thirds of the dendritic tree, peak [Cal-Ca4] was 3-5 times larger in the strongly activated path synapse than in the weakly activated path synapse. The magnitude of shunting inhibition was varied to determine the level that maximized this difference in peak [Cal-Ca4]. For strong lateral and weak medial pp input, the optimal level was one that prevented the cell from firing an action potential. For strong medial and weak lateral pp input, the optimal level was one at which the cell fired two action potentials. The distribution of shunting inhibition that best satisfied the spatial convergence requirement was inhibition on the distal two-thirds of the dendritic tree with or without inhibition at the soma, with inhibition stronger in the distal third than in the middle third. It was estimated that the number of inhibitory synapses involved in the shunting inhibition should be 25-50% of the number of excitatory synapses activated by the eight-pulse, 400-Hz tetanus. This number could be 20-50% of the total number of inhibitory synapses in the distal two-thirds of the dendritic tree. The addition of a single inhibitory synapse on a dendrite had a significant effect on peak spine head [Cal-Ca4] in nearby spines. Inhibitory synapses had to be activated four or more times at 100 Hz for effective shunting to take place, and the inhibition had to begin no later than 2-5 ms after the first excitatory input. The results suggest that inhibition can isolate potentiated synapses to particular dendritic domains and that the location of activated inhibitory synapses may affect potentiation of individual synapses on individual dendrites.