Cerebrospinal fluid in diseases of the nervous system: R. A. Fishman W. B. Saunders, London, 1980. p. 384, figs, and tables, £18,25, ISBN 7 2163 686 1

Abstract

We consider the equilibrium or steady-state noise power density spectrum in the quantity N = Σxi=0aiNi for an ensemble of independent and equivalent systems each of which can exist in the discrete set of states i = 0, 1, ···, x. Ni is the number of systems of the ensemble in state i and the ai's are constants. There is a transition rate constant αij for an arbitrary transition i →j; the kinetic equations are linear. There are possible applications to enzyme and biochemical kinetics generally, to membrane transport, muscle contraction, binding on macromolecules, etc. In each case, noise measurements would provide information about the kinetic scheme. The particular application considered here is to K+ channels or gates (one channel = one system) in the squid axon membrane: aiḡK is the K+ conductance of a channel in state i and the kinetic scheme is of the Hodgkin-Huxley type (HH). Here we allow an arbitrary set of ai's. This is a generalization of our treatment of K+ channel noise in an earlier paper. The theory is discussed and some calculations made using Fishman's recent experimental results on K+ channel noise as a guide. Preliminary indications are that the HH choice of ai's may be oversimplified and that a0 ≅ 0, a1 ≠a0, ax ≠ax-1. Quite possibly the ai's increase from a0 to ax, though the early ai's must be relatively small to give the observed induction behavior in gK(t). An increase in equal steps is unsatisfactory because this is essentially HH with x = 1 (no induction). More refined experiments may modify these tentative conclusions. In any case, it appears from Fishman's work that noise measurements will probably be very useful in distinguishing between rival models of K+ channels.