Computational neuroscience of synapses and neurons

The fundamental unit of neuroscience is the neuron. Computer simulation of neurons depends on a series of transformations that provide different ways of looking at the same set of phenomena, from the biophysical concepts of ion flow and protein interactions, to the electrical concepts of resistance and capacitance, to differential equations and their numerical simulation, to information theory and systems engineering. Electronically, the neural membrane acts like a capacitor, while protein pores act as resistors. To this basic picture, many types of complexity can be added. Real neurons are not simply a single capacitor and resistor but rather many capacitors, resistors, and batteries, leading to the parallel conductance model and to multicompartment models. Using these models, given current concentrations of ions inside and outside the cell, one can calculate the voltage for a given neuron at a given point in time. However, voltages change with time and are the tip of a much more complex dynamical system. The voltage at any given time depends on the state of voltage and ligand-sensitive ion channels on the membrane, i.e., which pores are open and which are closed. Simulations can demonstrate how the neuron’s state evolves over time as a dynamical system. In this chapter, the genesis of the action potential and the spread of signals through the cell are explored.