Abstract
Simple-spike synchrony between Purkinje cells projecting to a common neuron in the deep cerebellar nucleus is emerging as an important factor in the encoding of output information from cerebellar cortex. A phenomenon known as stochastic synchronization happens when uncoupled oscillators synchronize due to correlated inputs. Stochastic synchronization is a viable mechanism through which simple-spike synchrony could be generated, but it has received scarce attention, perhaps because the presence of feedforward inhibition in the input to Purkinje cells makes insights difficult. This paper presents a method to account for feedforward inhibition so the usual mathematical approaches to stochastic synchronization can be applied. The method consists in finding a single Phase Response Curve, called the equivalent PRC, that accounts for the effects of both excitatory inputs and delayed feedforward inhibition from molecular layer interneurons. The results suggest that a theory of stochastic synchronization for the case of feedforward inhibition may not be necessary, since this case can be approximately reduced to the case of inputs characterized by a single PRC. Moreover, feedforward inhibition could in many situations increase the level of synchrony experienced by Purkinje cells.
Highlights
The cerebellum has a striking and relatively clear anatomical organization, which has brought hope that it could be the first brain system whose function could be Neuroscience, University of Colorado Boulder, Boulder, CO, USAS
Synapses from a source neuron/axon type toward a target neuron type will be denoted by the abbreviation of the source and target connected by a dash; e.g. PF-PC denotes the synapse between parallel fibers and Purkinje cells
The results show that the oscillators with feedforward inhibition and those with equivalent PRCs produce output spike trains with a significant level of coherence, so if stochastic synchronization happens among oscillators with feedforward inhibition, it will most likely happen in oscillators with the corresponding equivalent PRCs
Summary
The cerebellum has a striking and relatively clear anatomical organization, which has brought hope that it could be the first brain system whose function could be. When explaining how the timing of PC simple spikes affect their DCN targets, and how different types of CF-mediated plasticity affect cerebellar output, it may be important to pay attention to synchrony among Purkinje cells innervating the same DCN cell. This synchrony can modulate the response of the target DCN cell [24,25,26,27]. The equivalent PRC lumps the effect of both excitatory and delayed inhibitory PRCs so we only have one type of inputs, and yet the response of the oscillator to a spike train is similar to that when using both excitation and delayed feedforward inhibition. In most scenarios the effect of delayed feedforward inhibition would be a synchronizing one
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