The Concept of Transmission Coefficient Among Different Cerebellar Layers: A Computational Tool for Analyzing Motor Learning

Abstract

High-fidelity regulation of information transmission among cerebellar layers is mainly provided by synaptic plasticity. Therefore, determining the regulatory foundations of synaptic plasticity in the cerebellum and translating them to behavioral output are of great importance. To date, many experimental studies have been carried out in order to clarify the effect of synaptic defects, while targeting a specific signaling pathway in the cerebellar function. However, the contradictory results of these studies at the behavioral level further add to the ambiguity of the problem. Information transmission through firing rate changes in populations of interconnected neurons is one of the most widely accepted principles of neural coding. In this study, while considering the efficacy of synaptic interactions among the cerebellar layers, we propose a firing rate model to realize the concept of transmission coefficient. Thereafter, using a computational approach, we test the effect of different values of transmission coefficient on the gain adaptation of a cerebellar-dependent motor learning task. In conformity with the behavioral data, the proposed model can accurately predict that disruption in different forms of synaptic plasticity does not have the same effect on motor learning. Specifically, impairment in training mechanisms, like in the train-induced LTD in parallel fiber-Purkinje cell synapses, has a significant negative impact on all aspects of learning, including memory formation, transfer, and consolidation, although it does not disrupt basic motor performance. In this regard, the overinduction of parallel fiber-molecular layer interneuron LTP could not prevent motor learning impairment, despite its vital role in preserving the robustness of basic motor performance. In contrast, impairment in plasticity induced by interneurons and background activity of climbing fibers is partly compensable through overinduction of train-induced parallel fiber-Purkinje cell LTD. Additionally, blockade of climbing fiber signaling to the cerebellar cortex, referred to as olivary system lesion, shows the most destructive effect on both motor learning and basic motor performance. Overall, the obtained results from the proposed computational framework are used to provide a map from procedural motor memory formation in the cerebellum. Certainly, the generalization of this concept to other multi-layered networks of the brain requires more physiological and computational researches.

Keywords: cerebellar motor learning; multi-layer neural network; optokinetic reflex; synaptic plasticity; transmission coefficient.

Figure 1

Cytoarchitecture of the cerebellum. (A) Cross-sectional views of the cerebellum showing the folding pattern and layered character of the cortex. (B) Schematic representation of cerebellar microcircuit. There are two principal afferents to the cerebellar cortex: (1) MFs, which provide sensory information of screen oscillation to GCs, GOs, and DN, and (2) CFs, which convey the retinal image slip information to PCs and drive cortical learning by changing the synaptic efficacy at PF-PC synapses. The ascending axons of the GCs branch in a T-shaped manner to form PFs, which, in turn, make excitatory synaptic contacts with MLIs and PCs. PF-PC and MF-DN synapses are respectively considered as the main sites of learning and consolidation. Synaptic weights are indicated by $\stackrel{⃡}{W}$.

Figure 2

Simulation of OKR adaptation in normal condition. OKR gain changes (top) and evolution of synaptic weights at PF-PC, PF-MLI, and MF-DN (bottom) during eight sessions of training. The dashed black line indicates the initial level of OKR gain before any training has taken place. The amounts of short- and long-term learning for the 4th and 8th days are indicated by STM and LTM labels. The shaded region specifies the 1-h training period on the first day. The learning curve of the model for the last 3 days, in the absence of experimental data, is plotted by a dashed line.

Figure 3

Lesion in the transmission of the granular layer. (A) Schematic representation of lesion location in the granular layer. (B) Simulated OKR adaptation (top) and evolution of synaptic weights (bottom) during five sessions of training, while the transmission coefficient of MF-GC synapses (α) is attenuated from 1 to 0.3.

Figure 4

Lesion in the transmission of the molecular and the Purkinje layers. (A) Schematic representation of lesion sites and the corresponding transmission coefficients. (B–D) Dynamics of the model in gain-up training for 5 days. Each panel consists of the learning curve(s) of OKR gain at the top and its corresponding time-dependent changes in synaptic weights at the bottom. Experimental data in (C) are plotted in red dots.

Figure 5

Lesion in the transsynaptic shift of memory trace from cerebellar cortex to DN. (A) Schematic representation of lesion location. (B) Dynamics of the model in gain-up training for 4 days. Lesion is made by interruption of PC-DN transmission immediately after 1-h training on the 4th day. Experimental data are plotted in red dots.

Figure 6

Quantitative data of the model's behavior in confronting different lesion scenarios. (Top) Bar graph displaying the long-term or slow adaptation of OKR gain measured by gain differences after training on the 5th day and before training on the first day. Positive and negative long-term gain increments are respectively, considered as the occurrence of motor learning and disruption of basic motor performance. Blockade of CF signaling to cerebellar cortex had the most destructive effect on both motor learning and basic motor performance. Conversely, blockade of PF-MLI plasticity had the least negative impact on the increment of OKR gain. Additionally, blockade of spontaneous PF-PC LTD was completely compensated by overinduction of train-induced LTD. Notably, the more increment in this case does not mean the greater final OKR gain than normal, since the initial state of OKR gain started from 0 rather than 0.3. (Middle) Bar graph showing the short-term or fast adaptation of OKR gain measured by gain differences before and after 1 h of training on the 5th day. Dashed lines indicate normal values. (Bottom) Bar graph showing the percentage of synaptic weight changes at the fifth session of learning.

Figure 7

Conceptual map of procedural motor memory formation in the cerebellum. Sensory input is transmitted to the cortical and nuclear modules by MFs. The granular layer, benefiting from abundant clusters of granule and Golgi cells, conveys the encoded sensory information to both molecular and Purkinje layers by PFs. Conjunctive activation of PFs and CF forms short-term memory at the main and peripheral learning sites. Then, the formed memory is transferred to the nuclear module through inhibition exerted by PCs on DN mostly at the late phase of LTD. Finally, the postsynaptic activity of DN drives the formation of long-term memory at the consolidation site.