Principles of Computational Modelling in Neuroscience

The membrane potential of a neuron varies widely across the spatial extent of a neuron. The membrane may have spatially distinct distributions of ion channels and synaptic inputs arrive at different dendritic locations and propagate to the cell body. The membrane potential varies along axons, as the action potential propagates. We therefore need neuron models that include spatial, as well as temporal, dimensions. The most common approach is compartmental modelling in which the spatial extent of a neuron is approximated by a series of small compartments, each assumed to be isopotential. In limited cases of simple neuron geometry, analytical solutions for the membrane potential at any point along a neuron can be obtained through the use of the cable theory. We describe both modelling approaches here. Two case studies demonstrate the power of compartmental modelling: (1) action potential propagation along axons; and (2) synaptic signal integration in pyramidal cell dendrites.