Slope ˜ 4.6 MegaOhms Linear range Upward deviation due to activation of Na conductance 1.0 0.0 –1.0 –1.0 –0.5 0.0 0.5 1.0 •Fig. 5.1 (A) Voltageresponsesofanaxontorectangularpulsesofhyperpolarizingcurrent(negativenumbers)ordepolarizingcurrent(positivenumbers)asinjectedandrecordedfromanintracellularelectrode.Thechangesintransmembranepotentialaremirrorimagesofthesmallamplitudepulses.Atthethresholdlevel(current= 1.0),thereisa50:50chanceofreturningtorestingpotentialorofgeneratinganactionpotential.Forclarity,onlytherisingphaseoftheactionpotentialisshown.B, Current-voltage(I-V)plotderivedfromdatainA.Currentpulseamplitudeisplottedonthex-axis,andvoltageresponse(measuredatdottedline)isplottedonthey-axis.Notethedeviationfromlinearitywithlargedepolarizations,whichisduetoactivationofvoltage-gatedconductances.(RedrawnfromHodgkinAL,RushtonWAH:Theelectricalconstantsofacrustaceannervefibre.Proc R Soc Lond B Biol Sci. 1946;133:444-479.) pulses) or hyperpolarizing (downward-going pulses) current across its cell membrane. The injection of positive charge is depolarizing because it makes the cell less negative (i.e., decreases the potential difference across the cell membrane). Conversely, the injection of negative charge makes the membrane potential more negative, and this change in potential is called hyperpolarization. The larger the current that is injected, the greater the change in the membrane potential will be. The responses to hyperpolarizing and small-amplitude depolarizing current pulses (see
Fig. 5.1A ) all have the same fundamental shape because of the passive properties of the membrane. In contrast, the shapes of the responses to the larger depolarizing stimulus pulses differ from those to hyperpolarizing and small-amplitude depolarizing current pulses because the larger stimuli activate nonpassive elements in the membrane.
For the responses to hyperpolarizing current pulses, once a long enough time has elapsed from the start of the current pulse to allow the membrane voltage to plateau (essentially several times τ), virtually all of the injected current is flowing through the membrane resistance. If the difference between the initial and steady-state voltages is plotted against the amplitude of the current pulse (see
Fig. 5.1B ), a linear relationship is observed for the hyperpolarizing pulses, which is exactly what is expected from Ohm’s law (V = I *
R) for current flowing through a resistor. The slope of this line (ΔV/ΔI) is referred to as the input resistance of the cell (Rin) and is determined experimentally, exactly as just described. Rin is related to the membrane resistance (rm) of the cell, but the exact relationship depends on the geometry of the cell and is complex in most cases.
Next, note that although the current is injected as rectangular pulses, with vertical rising and falling edges, the shape of the membrane voltage responses just after the starts and ends of the pulses have slower rises and falls. Moreover, with regard to only the responses to hyperpolarizing and small-amplitude depolarizing current pulses (see
Fig. 5.1A ), the fall and rise in the membrane voltage have exponential shapes. This shows that the membrane is responding to these current pulses as a parallel RC circuit would; that is, the stimulus causes no change in membrane resistance or capacitance (cm), and thus the time course of the rise and fall in voltage is the same in all cases because it is governed by the same membrane time constant (τ).