Pattern separation based on rate coding in a biologically detailed cerebellar network model

The cerebellum is involved in motor learning, temporal information processing and cognition. Inspired by the well-characterised anatomy of the cerebellum, several network models and theories of cerebellar function have been developed, such as the Marr-Albus-Ito theory of cerebellar learning. However, although morphologically realistic cerebellar neuronal models with realistic ion channel dynamics exist in isolation, a complete cerebellar cortical model comprising such biologically detailed neurons is still missing. Sudhakar et al. have implemented a cerebellar granular layer (GL) model composed of biologically detailed granule and Golgi cells (GrCs and GoCs). Here, we modified this model and integrated it with a multi-compartmental PC model, which included detailed Hodgkin-Huxley type representations of ion channels. The original GL model had a length of 1.5 mm along the transversal axis. As parallel fibres (PFs), the axons of GrCs, extend for 2.0 mm along this axis, we rescaled the GL network model to 4.0 mm in transversal direction and placed the dendritic tree of the PC model at the centre of the network. Additionally, to reduce the computational requirements, we employed a sparser density of 1.92 million GrCs per mm3 in our GL model. Each spine of the PC model was connected to the nearest PF within the sagittal-vertical plane, which resulted in 143,725 PF inputs to the PC model. Inhibitory input from molecular layer interneurons (MLIs) to the PC was modelled implicitly by providing inhibitory Poisson input from 1,695 spike generators. Most of our simulations were run with 5 Hz MF background excitation and 8 Hz background MLI inhibition, which resulted in PC baseline spike rates between 50 and 60 Hz.

In a first set of simulations, our network was tested in a simple pattern separation task: a patch of excitatory mossy fibre (MF) input to the GL was stimulated; the network learnt the input pattern based on long-term depression (LTD) at PF-PC synapses; and the PC behaviour in response to learnt and novel patterns was compared. The stimulated MF patch had a radius of 100 um. The stimulation resulted in the activation of a cylindrical region of the GL above the patch. Activated GoCs spread out of the patch along the transversal axis. The initial GrC excitation lasted for about 5 ms, after which feedback inhibition from GoCs reduced the GrC spike rate to about 50% of the peak value. The resulting burst of GrC activity activated the PC model with a delay up to 5 ms. In the presence of a sufficient amount of MLI inhibition, the PC firing rate initially increased sharply in response to stimulation of the MF patch. After the MF input had been learnt based on LTD at the PF-PC synapses, the PC spike rate increases in response to learnt MF input disappeared, while equivalent novel MF stimuli still resulted in spike rate increases. These simulation results predict that a biophysically detailed PC model embedded in a realistic cerebellar network model can, under certain circumstances, employ a rate code to distinguish between learnt and novel MF input patterns.