The Impact of Parallel Fiber Background Activity on the Cable Properties of Cerebellar Purkinje Cells

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Abstract
Neurons in the mammalian CNS receive 104-105 synaptic inputs onto their dendritic tree. Each of these inputs may fire spontaneously at a rate of a few spikes per second. Consequently, the cell is bombarded by several hundred synapses in each and every millisecond. An extreme example is the cerebellar Purkinje cell (PC) receiving approximately 100,000 excitatory synapses from the parallel fibers (p.f.s) onto dendritic spines covering the thin dendritic branchlets. What is the effect of the p.f.s activity on the integrative capabilities of the PC? This question is explored theoretically using analytical cable models as well as compartmental models of a morphologically and physiologically characterized PC from the guinea pig cerebellum. The input of individual p.f.s was modeled as a transient conductance change, peaking at 0.4 nS with a rise time of 0.3 msec and a reversal potential of +60 mV relative to rest. We found that already at a firing frequency of a few spikes per second the membrane conductance is several times larger than the membrane conductance in the absence of synaptic activity. As a result, the cable properties of the PC significantly change; the most sensitive parameters are the system time constant (τ0) and the steady-state attenuation factor from dendritic terminal to soma. The implication is that the cable properties of central neurons in freely behaving animals are different from those measured in slice preparation or in anesthetized animals, where most of the synaptic inputs are inactive. We conclude that, because of the large conductance increase produced by the background activity of the p.f.s, the activity of the PC will be altered from this background level either when the p.f.s change their firing frequency for a period of several tens of milliseconds or when a large population of the p.f.s fires during a narrow time window.