Information coding capacity of cerebellar parallel fibers

Understanding synaptic connectivity is a prerequisite to gaining insight on how the central nervous system processes information. Cerebellar parallel fibers make an impressive number of synapses with the Purkinje cells. These synapses are the major structural elements of a large information processing system. The objective of the present report is to describe a method to estimate the coding capacity of this information processing system. We propose to derive the coding capacity from the linear distribution pattern of synaptic varicosities along parallel fibers in a manner consistent with Shannon's information theory formalism. The coding capacity of an average parallel fiber synapse is S = −κΣPl(i) ln Pl(i), where κ = 1/ln 2, Pl(i) is the probability of observing a particular inter-varicosital distance l(i), and ln is the natural logarithm to the base e. In the cerebellar parallel fibers of the mouse, and in a number of other unmyelinated axonal systems, the distribution pattern of Pl(i) as a function of l(i) is exponential-like. According to information theory, the exponential-like distribution pattern suggests that information transmission in these axonal synaptic systems is operating at near-optimal coding capacity. This optimization in information coding may be the result of a stochastic-like process regulating the formation or elimination of parallel fiber synapses during development and maturation. In the adult nervous system, neuroplasticity-mediated synaptic remodeling may also regulate the coding capacity of axonal synapses via a similar stochastic-like process. The conceptual framework herein may be applicable to other axonal systems in the nervous system.