Diffusion of nitric oxide can facilitate cerebellar learning: A simulation study

Abstract

The gaseous second messenger nitric oxide (NO), which readily diffuses in brain tissue, has been implicated in cerebellar long-term depression (LTD), a form of synaptic plasticity thought to be involved in cerebellar learning. Can NO diffusion facilitate cerebellar learning? The inferior olive (IO) cells, which provide the error signals necessary for modifying the granule cell-Purkinje cell (PC) synapses by LTD, fire at ultra-low firing rates in vivo, rarely more than 2-4 spikes within a second. In this paper, we show that NO diffusion can improve the transmission of sporadic IO error signals to PCs within cerebellar cortical functional units, or microzones. To relate NO diffusion to adaptive behavior, we add NO diffusion and a "volumic" LTD learning rule, i.e., a learning rule that depends both on the synaptic activity and on the NO concentration at the synapse, to a cerebellar model for arm movement control. Our results show that biologically plausible diffusion leads to an increase in information transfer of the error signals to the PCs when the IO firing rate is ultra-low. This, in turn, enhances cerebellar learning as shown by improved performance in an arm-reaching task.

Figure 1

Structure of the model of the cerebellar cortex and example of NO diffusion. We modeled four microzones: a flexor and an extensor microzone for the shoulder and the elbow joints. Each microzone contained nine columns and three rows of PCs as drawn on the left (shoulder extensor microzone). The color picture shows an example of the spatial aspect of NO diffusion in the model (k = 0.3 s⁻¹, D = 3,300 μm²/s); light colors show high NO concentrations. The large NO concentration in the most rightward microzone (elbow flexor microzone) was caused by a large error in the elbow flexor during this movement; conversely, low concentration in the most leftward microzone (shoulder extensor microzone) was caused by a small error in the shoulder extensor.

Figure 2

Mutual information between sinusoidal excitation and NO concentration with and without diffusion. (A) As a function of IO mean firing rate. When the mean firing rate is low, diffusion provides better information to the learning synapses. (B) As a function of the sinusoidal input frequency. NO diffusion process is a low-frequency pass filter and it cannot carry high-frequency signals, so the efficiency of the error information transmission by NO decreased when the signal frequency increased.

Figure 3

MSE for an arm reaching learning task after 200 movements. (A) As a function of the diffusion constant D for k = 0.3 s^-1 for the normal cerebellar cortex (plain line) and an idealized cerebellar cortex in which the microzones were artificially separated for NO diffusion (dashed line). (B) As a function of the inferior olive mean firing rate.