Computational Neuroscience of Neuronal Networks

Abstract

A fundamental challenge in modeling the brain is how to deal with the enormous complexity that exists at multiple spatial and temporal scales. This complexity is already encountered at the level of the single neuron, but it becomes still more apparent, and daunting, when creating models at the level of neuronal networks, a term that generally describes models on the scale of tens to millions of connected neurons. Complexity occurs across scales. Rapid interneuronal communication manifests on scales of microns and milliseconds, while learning across cortex may take place on scales of centimeters and on temporal scales of hours, days, and years. It is impossible for a single model to include all complexity at all levels, so decisions must be made as to what is to be left out of a given model. Part of the simplification process involves model embedding while crossing multiple scales (multiscale modeling). This chapter describes that the basic model of the neuron that is used in networks is greatly simplified from the complex models that we developed in the prior chapter. Multiple other simplifications are also made: using only a restricted number of cell types (excitatory and inhibitory; fast and slow) instead of the many types that exist; leaving out large parts of the neuron function – for example, the axon; and assuming that the network is being driven rather than creating activity through its own mechanisms.

Once a sufficiently simplified network model is obtained, a variety of mathematical, data-mining, and visualization tools can be used to investigate its properties. Oscillations in a network can be investigated by frequency spectra. Activity synchrony can be measured by looking at various correlation tools. The structure of a network can be analyzed through graph theory, by considering properties as path length, centrality, and clustering. Communication in a network can be analyzed through information theory, which quantifies the extent to which neurons influence and transfer information to other neurons.

Much computer modeling involves exploration and experimentation on the simulations. Through in silico experimentation, the researcher refines and studies these complex models. Different researchers make very different choices about which simplifications are justified and how best to analyze and study their networks. Therefore, a large variety of models exist. There is no single best way to do network modeling.

Glossary

Dynamics

The study of how a process changes over time.

ING

Interneuron network gamma – gamma oscillations generated by the activity of interneurons.

PING

Pyramidal interneuron network gamma – gamma oscillations generated by the interactions of pyramidal and inhibitory neurons.

Raster plot

Plot showing spiking of cells – vertical axis is cell identity and horizontal axis is time.