Biophysical Journal 13: 1276-1295 (1973)
© 1973 the Biophysical Society

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Fluctuations and Noise in Kinetic Systems

Application to K⁺ Channels in the Squid Axon

ABSTRACT

We consider the equilibrium or steady-state noise power density spectrum in the quantity N = ^x_i=0 a_iN_i for an ensemble of independent and equivalent systems each of which can exist in the discrete set of states i = 0, 1, ···, x. N_i is the number of systems of the ensemble in state i and the a_i's are constants. There is a transition rate constant _ij 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: a_iK 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 a_i'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 a_i's may be oversimplified and that a₀ 0, a₁ a₀, a_x a_x-1. Quite possibly the a_i's increase from a₀ to a_x, though the early a_i's must be relatively small to give the observed induction behavior in g_K(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.