Coding Capacity of Purkinje Cells With Different Schemes of Morphological Reduction

Abstract

The brain as a neuronal system has very complex structures with a large diversity of neuronal types. The most basic complexity is seen from the structure of neuronal morphology, which usually has a complex tree-like structure with dendritic spines distributed in branches. To simulate a large-scale network with spiking neurons, the simple point neuron, such as the integrate-and-fire neuron, is often used. However, recent experimental evidence suggests that the computational ability of a single neuron is largely enhanced by its morphological structure, in particular, by various types of dendritic dynamics. As the morphology reduction of detailed biophysical models is a classic question in systems neuroscience, much effort has been taken to simulate a neuron with a few compartments to include the interaction between the soma and dendritic spines. Yet, novel reduction methods are still needed to deal with the complex dendritic tree. Here, using 10 individual Purkinje cells of the cerebellum from three species of guinea-pig, mouse and rat, we consider four types of reduction methods and study their effects on the coding capacity of Purkinje cells in terms of firing rate, timing coding, spiking pattern, and modulated firing under different stimulation protocols. We found that there is a variation of reduction performance depending on individual cells and species, however, all reduction methods can preserve, to some degree, firing activity of the full model of Purkinje cell. Therefore, when stimulating large-scale network of neurons, one has to choose a proper type of reduced neuronal model depending on the questions addressed. Among these reduction schemes, Branch method, that preserves the geometrical volume of neurons, can achieve the best balance among different performance measures of accuracy, simplification, and computational efficiency, and reproduce various phenomena shown in the full morphology model of Purkinje cells. Altogether, these results suggest that the Branch reduction scheme seems to provide a general guideline for reducing complex morphology into a few compartments without the loss of basic characteristics of the firing properties of neurons.

Transcranial direct current stimulation of cerebellum alters spiking precision in cerebellar cortex: A modeling study of cellular responses

“…Studies in vitro and in vivo , e.g., [ 53 , 77 , 78 ], have shown that the spiking pattern of Purkinje cells also depends on the morphology of the dendrites, which would suggest that the effects of the electric fields may be cell-specific. However, the morphology of the dendritic arborization varies modestly across Purkinje cells [ 78 ] and mainly affects the average firing rate [ 79 ]. Hence, even though morphology-related changes to the Purkinje cell’s firing activity are expected, it is plausible that the application of electric fields will result in discharge patterns that fall within the classification and class-transition map reported in our study.…”

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

“…The number of spikes was counted during 1 second and averaged over all cells for each trial. These four measures were used as metrics of neural firing [44] for each type of GoC inhibition in the network. The same analysis was The frequency spectrum of firing rate over 10 seconds was obtained by Fast Fourier Transform using fft function in MATLAB.…”

“…The number of spikes was counted during 1 second and averaged over all cells for each trial. These four measures were used as metrics of neural firing [ 44 ] for each type of GoC inhibition in the network. The same analysis was performed in S7 Fig in order to determine the effect of gap junctions on top of different inhibition of network structures.…”

Dissecting cascade computational components in spiking neural networks

“…The complexity of dendritic organization in neurons depends on the type of neurons. For some neurons, such as Purkinje cells in the cerebellum, there is a large dendritic tree receiving tens of thousands of presynaptic inputs [ 51 ]. However, some neurons, such as unipolar cells of the cerebellum, have only one dendrite receiving one presynaptic input [ 52 ].…”