Silent Synapses, LTP, and the Indirect Parallel-Fibre Pathway: Computational Consequences of Optimal Cerebellar Noise-Processing

Abstract

Computational analysis of neural systems is at its most useful when it uncovers principles that provide a unified account of phenomena across multiple scales and levels of description. Here we analyse a widely used model of the cerebellar contribution to sensori-motor learning to demonstrate both that its response to intrinsic and sensor noise is optimal, and that the unexpected synaptic and behavioural consequences of this optimality can explain a wide range of experimental data. The response of the Marr-Albus adaptive-filter model of the cerebellar microcircuit to noise was examined in the context of vestibulo-ocular reflex calibration. We found that, when appropriately connected, an adaptive-filter model using the covariance learning rule to adjust the weights of synapses between parallel fibres and Purkinje cells learns weight values that are optimal given the relative amount of signal and noise carried by each parallel fibre. This optimality principle is consistent with data on the cerebellar role in smooth pursuit eye movements, and predicts that many synaptic weights must be very small, providing an explanation for the experimentally observed preponderance of silent synapses. Such a preponderance has in its turn two further consequences. First, an additional inhibitory pathway from parallel fibre to Purkinje cell is required if Purkinje cell activity is to be altered in either direction from a starting point of silent synapses. Second, cerebellar learning tasks must often proceed via LTP, rather than LTD as is widely assumed. Taken together, these considerations have profound behavioural consequences, including the optimal combination of sensori-motor information, and asymmetry and hysteresis of sensori-motor learning rates. The cerebellum or “little brain” is a fist-sized structure located towards the rear of the brain, containing as many neurons as the rest of the brain combined, whose functions include learning to perform skilled motor tasks accurately and automatically. It is wired up into repeating microcircuits, sometimes referred to as cerebellar chips, in which learning alters the strength of the synapses between the parallel fibres, which carry input information, and the large Purkinje cell neurons, which produce outputs contributing to skilled movements. The cerebellar chip has a striking resemblance to a mathematical structure called an adaptive filter used by control engineers, and we have used this analogy to analyse its information-processing properties. We show that it learns synaptic strengths that minimise the errors in performance caused by unavoidable noise in sensors and cerebellar circuitry. Optimality principles of this kind have proved to be powerful tools for understanding complex systems. Here we show that optimality explains neuronal-level features of cerebellar learning such as the mysterious preponderance of “silent” synapses between parallel fibres and Purkinje cells and behavioural-level features such as the dependence of rate of learning of a motor skill on learning history.