Modeling inhibitory plasticity in the electrosensory system of mormyrid electric fish

Mathematical analyses and computer simulations are used to study the adaptation induced by plasticity at inhibitory synapses in a cerebellum-like structure, the electrosensory lateral line lobe (ELL) of mormyrid electric fish. Single-cell model results are compared with results obtained at the system level in vivo. The model of system level adaptation uses detailed temporal learning rules of plasticity at excitatory and inhibitory synapses onto Purkinje-like neurons. Synaptic plasticity in this system depends on the time difference between pre- and postsynaptic spikes. Adaptation is measured by the ability of the system to cancel a reafferent electrosensory signal by generating a negative image of the predicted signal. The effects of plasticity are tested for the relative temporal correlation between the inhibitory input and the sensory input, the gain of the sensory signal, and the presence of shunting inhibition. The model suggests that the presence of plasticity at inhibitory synapses improves the function of the system if the inhibitory inputs are temporally correlated with a predictable electrosensory signal. The functional improvements include an increased range of adaptability and a higher rate of system level adaptation. However, the presence of shunting inhibition has little effect on the dynamics of the model. The model quantifies the rate of system level adaptation and the accuracy of the negative image. We find that adaptation proceeds at a rate comparable to results obtained from experiments in vivo if the inhibitory input is correlated with electrosensory input. The mathematical analysis and computer simulations support the hypothesis that inhibitory synapses in the molecular layer of the ELL change their efficacy in response to the timing of pre- and postsynaptic spikes. Predictions include the rate of adaptation to sensory stimuli, the range of stimulus amplitudes for which adaptation is possible, the stability of stored negative images, and the timing relations of a temporal learning rule governing the inhibitory synapses. These results may be generalized to other adaptive systems in which plasticity at inhibitory synapses obeys similar learning rules.