End

Figure. 1.4-14 illustrates the behavior of the scaled JK and JNa as Vm is ramped up (depolarized) linearly from the -70 mV resting potential. Note that the initiation of rise in JNa does not have a crisp threshold and that the threshold depends on Vm as well as Vm. Also note that the specific ion channels responsible for JNa deactivate regardless of the depolarized Vm and Vm . The response of JK and JNa to step depolarizations in Vm is shown in Figure 1.4-15. The larger the depolarization, the larger JK, and the faster JNa responds, its peak coming earlier and decaying faster as Vm goes more positive. For Vm > 0, the peak in JNa actually decreases, and the steady-state JNa gets smaller. (Most full-featured, specialized neural modeling simulation programs, such as GENESIS, allow simulation of voltage clamping.)

Basic research on the molecular basis for neurophysiological phenomena has made enormous strides since the formulation of the dynamic model for nerve spike generation by Hodgkin and Huxley in 1952. Using the patch-clamp technique, which uses glass micropipette electrodes to isolate single ion gate proteins, it has been possible to characterize the conductance dynamics of five different kinds of potassium channel in bullfrog sympathetic ganglion cells, two types of voltage-gated sodium channel, three types of calcium channel, and a voltage-gated chloride channel (Yamada, Koch et al., 1989). Instead of subjecting the whole outside of a nerve axon membrane to a common potential, the patch-clamp technique isolates a single ionic channel on the outside of the membrane with the tip of the microelectrode, which is then made part of an electronic feedback system that forces a known potential across the isolated channel. The very small, specific ionic current of that channel is measured under conditions of known trans-channel potential and external ionic

FIGURE 1.4-14 Simulation of the voltage-clamped HH model with Simnon. Vm(t) in mV caused to ramp up (depolarize). HH model run with Euler integration; 8t = 0.00001, Cm = 1.0. Horizontal axis, time in milliseconds. Numbered traces are JNasc = JNa/10 |A/cm2; 1, 2, 3, 4 correspond to input voltage ramp slope Kr = -3, -6, -9, -12, respectively. Downward-curving traces are the scaled potassium ion current densities, JKsc = JK/10 | A/cm2, for the corresponding Vm ramps. Note that the JNas deactivate, even though Vm keeps depolarizing.

FIGURE 1.4-14 Simulation of the voltage-clamped HH model with Simnon. Vm(t) in mV caused to ramp up (depolarize). HH model run with Euler integration; 8t = 0.00001, Cm = 1.0. Horizontal axis, time in milliseconds. Numbered traces are JNasc = JNa/10 |A/cm2; 1, 2, 3, 4 correspond to input voltage ramp slope Kr = -3, -6, -9, -12, respectively. Downward-curving traces are the scaled potassium ion current densities, JKsc = JK/10 | A/cm2, for the corresponding Vm ramps. Note that the JNas deactivate, even though Vm keeps depolarizing.

FIGURE 1.4-15 In this simulation, the voltage clamp input forces Vm to have a stepwise change to levels of -50, -30, -10, +10, +30 mV. These levels correspond to the scaled sodium current density (JNasc) traces of 1, 2, 3, 4, and 5, respectively. The unnumbered, downward-curving traces are the scaled potassium current densities (outward flow) for the corresponding 5 Vm steps. (The steepest is for Vm = +30 mV.)

FIGURE 1.4-15 In this simulation, the voltage clamp input forces Vm to have a stepwise change to levels of -50, -30, -10, +10, +30 mV. These levels correspond to the scaled sodium current density (JNasc) traces of 1, 2, 3, 4, and 5, respectively. The unnumbered, downward-curving traces are the scaled potassium current densities (outward flow) for the corresponding 5 Vm steps. (The steepest is for Vm = +30 mV.)

composition (in the microelectrode). The patch-clamping technique provides a powerful tool for the electrical and pharmacological study of ion channel behavior.

By using the same notation as Section 1.4.1 for the HH equations, the five bullfrog potassium channel models can be written (Yamada et al., 1989):

1. The transient outward IK:

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