Solutions to Cellular Biophysics Vol.2 by Thomas Fischer Weiss
By Thomas Fischer Weiss
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In fact, in a well-clamped cell, the speed can be so fast that the action potential occurs simultaneously at all points along the cell. For that reason, a space-clamped action potential is often called a membrane action potential. c. True. “Unclamped” is the normal condition for an axon. Therefore, action potentials occur in unclamped axons. 4 a. In general, at rest m is small and h is relatively large. For a large depolarization, the reverse is true — m is large and h is small. In both cases, the sodium conductance is small compared to the potassium conductance.
Thus, the potential difference between the remote electrode and the intracellular electrode is negative. Therefore, the answer is v7 (t). b. The stimulating electrode hyperpolarizes the membrane at the active recording electrode, and therefore, produces a positive potential at the active extracellular electrode. Thus, v(t) is a positive pulse and equals v3 (t). c. The stimulus current depolarizes the membrane as in part a. There is no difference of potential across the membrane at the remote voltage measuring electrode.
3 shows v(t ) for t ≥ 0 (provided Rs = 0 which was assumed implicitly in the derivation). Note that as the series resistance is decreased, the response approaches that for an ideal (zero series resistance) voltage source. The membrane potential follows the voltage step more faithfully in time and approaches a final value of 1. For example, if the series resistance is 1% of the membrane resistance, the final value of the voltage change across the membrane is 99% of the voltage step, and the time constant for the change in voltage is 1% of the membrane time constant.