X-Message-Number: 3915 From: Ralph Merkle <> Subject: The rate of change of membrane potentials Date: Mon, 27 Feb 1995 10:56:06 PST To quote from "Principles of Neural Science," Third edition, by Kandel, Schwartz and Jessell, page 97: The capacitance of the membrane has the effect of reducing the rate at which the membrane potential changes in response to a current pulse (Figure 7-2a) [7-2a shows a gradual rise of voltage in respone to a current pulse]. If the membrane had only resistive properties, a step pulse of outward current passed across it would change the membrane potential instantaneously (Figure 7-3, line a) [which shows a square wave step]. On the other hand, if the membrane had only capacitive properties, the membrane potential would change slowly, in a ramp-like manner, in response to the same step pulse of current (Figure 7-3, line b) [which shows a straight line of moderate slope]. Because the membrane has *both* capacitive and resistive properties in parallel, the actual change in membrane potential resulting from a rectangular current pulse combines features of the two pure responses. Thus the initial slope of Vm as a function of time is the same as that for a purely capacitive element, whereas the final slope and amplitude are the same as those for a purely resistive element (Figure 7-3, line c) [which shows a curve gradually approaching a limiting value]. The rising phase of the potential change shown in Figure 7-2A can be described by the following equation: delta Vm(t) = Im R(1 - e**(-t/tau)) [Vm is the membrane voltage, Im is the membrane current, t is time]. where e, which has the value of 2.72, is the base of the system of natural logarithms, and tau equals RC, the product of the resistance and capacitance of the membrane. The parameter tau, called the *membrane time constant*, can be measured experimentally. For the response of the membrane to a rectangular step of current (Figure 7-3), tau is the time that it takes Vm to move 63% of the way toward its final value (1-1/e x 100). The time constants of different neurons typically range from 1 to 20 ms. The effect of the time constant on integration of synaptic input is especially important. Most synaptic potentials are caused by brief synaptic currents triggered by the opening of ligand-gated channels. The time course of the rising phase of a synaptic potential is determined by both active and passive properties of the membrane, but the falling phase is purely a passive process. Its time course is a function of the membrane time constant. The longer the time constant, the longer the duration of the synaptic potential. When synaptic potentials overlap in time, they add together in a process known as *temporal summation.* In this way individual excitatory postsynaptic potentials that alone might be too small to trigger an action potential can sum to reach threshold. If a postsynaptic cell has a long membrane time constant, the synaptic potential lasts longer and there is more chance for temporal summation (Figure 7-4). [which shows various pre-synaptic spike trains, and the variation in the time course of the post synaptic membrane voltages as tau is varied]. Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=3915