A multi-layer mean-field model for the cerebellar cortex: design, validation, and prediction

Mean-field (MF) models can be used to summarize in a few statistical parameters the salient properties of an inter-wired neuronal network incorporating different types of neurons and synapses along with their topological organization. MF are crucial to efficiently implement the modules of large-scale brain models maintaining the specificity of local microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar network (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF satisfactorily reproduced the average dynamics of the different neuronal populations in response to various input patterns and predicted the modulation of Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool that will allow to investigate the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions. ### Competing Interest Statement The authors have declared no competing interest.