Mathematical models of synaptic plasticity: I. Posttetanic potentiation

A computer model of field potential responses for the study of short-term plasticity in hippocampus

Activity-dependent synaptic plasticity has important implications for network function. The previously developed model of the hippocampal CA1 area, which contained pyramidal cells (PC) and two types of interneurons involved in feed-forward and recurrent inhibition, respectively, and received synaptic inputs from CA3 neurons via the Schaffer collaterals, was enhanced by incorporating dynamic synaptic connections capable of changing their weights depending on presynaptic activation history. The model output was presented as field potentials, which were compared with those derived experimentally. The parameters of Schaffer collateral-PC excitatory model synapse were determined, with which the model successfully reproduced the complicated dynamics of train-stimulation sequential potentiation/depression observed in experimentally recorded field responses. It was found that the model better reproduces the time course of experimental field potentials if the inhibitory synapses on PC are also made dynamic, with expressed properties of frequency-dependent depression. This finding supports experimental evidence that these synapses are subject to activity-dependent depression. The model field potentials in response to various randomly generated and real (derived from recorded CA3 unit activity) long stimulating trains were calculated, illustrating that short-term plasticity with the observed characteristics could play specific roles in frequency processing in hippocampus and thus providing a new tool for the theoretical study of activity-dependent synaptic plasticity.

A model synapse that incorporates the properties of short- and long-term synaptic plasticity

We propose a general computer model of a synapse, which incorporates mechanisms responsible for the realization of both short- and long-term synaptic plasticity-the two forms of experimentally observed plasticity that seem to be very significant for the performance of neuronal networks. The model consists of a presynaptic part based on the earlier 'double barrier synapse' model, and a postsynaptic compartment which is connected to the presynaptic terminal via a feedback, the sign and magnitude of which depend on postsynaptic Ca(2+) concentration. The feedback increases or decreases the amount of neurotransmitter which is in a ready for release state. The model adequately reproduced the phenomena of short- and long-term plasticity observed experimentally in hippocampal slices for CA3-CA1 synapses. The proposed model may be used in the investigation of certain real synapses to estimate their physiological parameters, and in the construction of realistic neuronal networks.

Synaptic competition in developmental binocular plasticity

A mathematical model of the possible physiological and biochemical mechanisms responsible for the changes occurring during binocular development is proposed. The model is based on the mechanisms postulated for the occurrence of well known plastic processes, such as post-tetanic potentiation, sensitization and heterosynaptic inhibition. Because all these processes are of presynaptic nature, we have postulated that the plastic processes occurring during development are of the same nature. The factors we have considered in our model are: the transmitter pool size, the mobilization or synthesis of the transmitter, the transmitter release by the physiological stimulus, the neuroendocrine and genetic activity. With this model we have simulated the following phenomena during ocular development: (1) normal binocular development; (2) monocular deprivation, including the effects of reversing the occluded eye; (3) binocular deprivation and recovery; and (4) effects of alternating deprivation on mature binocularity. The model also allows us to explain in a natural way the possible changes occurring during denervation or disuse.