The Membrane Equation
The Membrane Equation
Any physical or biophysical mechanism instantiating an information processing system that needs to survive in the real world must obey several constraints: (1) it must operate at high speeds, (2) it must have a rich repertoire of computational primitives, with the ability to implement a variety of linear and nonlinear, high-gain, operations, and (3) it must interface with the physical world—in the sense of being able to represent sensory input patterns accurately and translate the result of the computations into action, that is motor output (Keyes, 1985). The membrane potential is the one physical variable within the nervous system that fulfills these three requirements: it can vary rapidly over large distances (e.g., an action potential changes the potential by 100 mV within 1 msec, propagating up to 1 cm or more down an axon within that time), and the membrane potential controls a vast number of nonlinear gates—ionic channels—that provide a very rich substrate for implementing nonlinear operations. These channels transduce visual, tactile, auditory, and olfactory stimuli into thanges of the membrane potential, and such voltage changes back into the release of neurotransmitters or the contraction of muscles. This is not to deny that ionic fluxes, or chemical interactions of various substances with each other, are not crucial to the working of the brain. They are, and we will study some of these mechanisms in Chap. 11. Yet the membrane potential is the incisive variable that serves as primary vehicle for the neuronal operations underlying rapid computations—at the fraction of a second time scale—in the brain. We will introduce the reader in a very gentle manner to the electrical properties of nerve cells by starting off with the very simplest of all neuronal models, consisting of nothing more than a resistance and a capacitance (a so-called RC circuit). Yet endowed with synaptic input, this model can already implement a critical nonlinear operation, divisive normalization and gain control. As a starting point, we choose a so-called point representation of a neuron. Here, the spatial dependency of the neuron is reduced to a single point or compartment.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.