Influence of various temporal recoding on pavlovian eyeblink conditioning in the cerebellum

We consider the Pavlovian eyeblink conditioning (EBC) via repeated presentation of paired conditioned stimulus (tone) and unconditioned stimulus (US; airpuff). In an effective cerebellar ring network, we change the connection probability $$ from Golgi to granule (GR) cells, and make a dynamical classification of various firing patterns of the GR cells. Individual GR cells are thus found to show various well- and ill-matched firing patterns relative to the US timing signal. Then, these variously-recoded signals are fed into the Purkinje cells (PCs) through the parallel-fibers (PFs). Based on such unique dynamical classification of various firing patterns, we make intensive investigations on the influence of various temporal recoding (i.e., firing patterns) of the GR cells on the synaptic plasticity of the PF-PC synapses and the subsequent learning process for the EBC. We first note that the variously-recoded PF signals are effectively depressed by the (error-teaching) instructor climbing-fiber (CF) signals from the inferior olive neuron. In the case of well-matched PF signals, they are strongly depressed through strong long-term depression (LTD) by the instructor CF signals due to good association between the in-phase PF and the instructor CF signals. On the other hand, practically no LTD occurs for the ill-matched PF signals because most of them have no association with the instructor CF signals. This kind of "effective" depression at the PF-PC synapses coordinates firings of PCs effectively, which then makes effective inhibitory coordination on the cerebellar nucleus neuron [which elicits conditioned response (CR; eyeblink)]. When the learning trial passes a threshold, acquisition of CR begins. In this case, the timing degree $$ of CR becomes good due to presence of the ill-matched firing group which plays a role of protection barrier for the timing. With further increase in the number of trials, strength $$ of CR (corresponding to the amplitude of eyelid closure) increases due to strong LTD in the well-matched firing group, while its timing degree $$ decreases. In this way, the well- and the ill-matched firing groups play their own roles for the strength and the timing of CR, respectively. Thus, with increasing the number of learning trials, the (overall) learning efficiency degree $$ (taking into consideration both timing and strength of CR) for the CR is increased, and eventually it becomes saturated. Finally, we also discuss dependence of the variety degree for firing patterns of the GR cells and the saturated learning efficiency degree $$ of the CR on $$ and their relations.