1. A simulation of fast excitatory synaptic transmission at a hippocampal synapse is presented. Individual neurotransmitter molecules are followed as they diffuse through the synaptic cleft and interact with the postsynaptic receptors. The ability of the model to reproduce published results of patch-clamp experiments on CA3 pyramidal cells is illustrated; parameters of the model that affect the time course and variability of the excitatory postsynaptic current (EPSC) are then investigated. 2. To simulate an EPSC, we release 4,000 neurotransmitter molecules simultaneously from a point source centered 15 nm above a rectangular grid of 14 x 14 postsynaptic receptors. The simulated EPSC at room temperature has a 10-90% rise time of 0.28 ms and a peak open probability of 0.27, and decays with a time constant of 2.33 ms, comparing well with values in the literature. 3. To simulate changes in temperature, we use a 10 degrees temperature coefficient (Q10) for diffusion of 1.3 and apply a Q10 of 3.0 to all the rate constants of the kinetic scheme. At 37 degrees C, the 10-90 rise time is 0.07 ms, the peak open probability is 0.56, and the decay time constant is 0.70 ms. The coefficient of variation (CV) at the peak of the EPSC is 9.4% at room temperature; at 37 degrees C, the CV at the peak drops to 6.6%. 4. We use the diffusion coefficient of glutamine, 7.6 x 10(-6) cm2/s, to model the random movement of glutamate molecules in the synaptic cleft. Slower rates of diffusion increase the peak response and slow the time course of decay of the EPSC. 5. Random variations in release site position have little effect on the time course of the average EPSC or on the CV of the peak response. We simulate a dose-response curve for the effects of releasing between 100 and 7,500 neurotransmitter molecules per vesicle. The half-maximal response occurs for 1,740 molecules. For a simulation with 100 postsynaptic receptors and a diffusion coefficient of 2.0 x 10(-6) cm2/s, 4,000 molecules approaches a saturating dose. 6. Changes to the width of the synaptic cleft, or to the number and spacing of the postsynaptic receptors, have marked effects on the peak height of the simulated EPSC. 7. We extend the model to include a spherical vesicle (50 nm diam) connected to the synaptic cleft by a cylindrical pore 15 nm long. Neurotransmitter molecules are randomly distributed within the vesicle and allowed to diffuse into the synaptic cleft through the pore, which opens to its full diameter in one time step. We find that the pore must open to a diameter of > or = 7 nm within 1 microsecond in order to match the time courses of EPSCs in the literature.