Computational studies on acquisition and adaptation of ocular following responses based on cerebellar synaptic plasticity

To investigate how cerebellar synaptic plasticity guides the acquisition and adaptation of ocular following response (OFR), a large-scale network model was developed. The model includes the cerebral medial superior temporal area (MST), Purkinje cells (P cells) of the ventral paraflocculus, the accessory optic and climbing fiber systems, the brain stem oculomotor network, and the oculomotor plant. The model reconstructed temporal profiles of both firing patterns of MST neurons and P cells and eye movements. Model MST neurons (n = 1,080) were set to be driven by retinal error and exhibited 12 preferred directions, 30 preferred velocities, and 3 firing waveforms. Correspondingly, each model P cell contained 1,080 excitatory synapses from granule cell axons (GCA) and 1,080 inhibitory synapses. P cells (n = 40) were classified into four groups by their laterality (hemisphere) and by preferred directions of their climbing fiber inputs (CF) (contralateral or upward). The brain stem neural circuit and the oculomotor plant were modeled on the work of Yamamoto et al. The initial synaptic weights on the P cells were set randomly. At the beginning, P cell simple spikes were not well modulated by visual motion, and the eye was moved only slightly by the accessory optic system. The synaptic weights were updated according to integral-differential equation models of physiologically demonstrated synaptic plasticity: long-term depression and long-term potentiation for GCA synapses and rebound potentiation for inhibitory synapses. We assumed that maximum plasticity was induced when GCA inputs preceded CF inputs by 200 ms. After more than 10,000 presentations of ramp-step visual motion, the strengths of both the excitatory and inhibitory synapses were modified. Subsequently, the simple spike responses became well developed, and ordinary OFRs were acquired. The preferred directions of simple spikes became the opposite of those of CFs. Although the model MST neurons were set to possess a wide variety of firing characteristics, the model P cells acquired only downward or ipsilateral preferred directions, high preferred velocities and stereotypical firing waveforms. Therefore the drastic transition of the neural representation from the population codes in the MST to the firing-rate codes of simple spikes were learned at the GCA-P cell synapses and inhibitory cells-P cell synapses. Furthermore, the model successfully reproduced the gain- and directional-adaptation of OFR, which was demonstrated by manipulating the velocity and direction of visual motion, respectively. When we assumed that synaptic plasticity could only occur if CF inputs preceded GCA inputs, the ordinary OFR were acquired but neither the gain-adaptation nor the directional adaptation could be reproduced.