Membrane Capacitance and Conductance. For cells having simplemorphological shapes, the
intracellular voltage is nearly uniform throughout the cell suchthat any change in the membrane
potential acts equally on all parts of the membrane. If wehyperpolarize the cell or chemically block
excitable ionic conductances, the membrane potential vm ispassively related to the incoming current i
by:
Cm
dvm
dt
+Gm (vm - El ) = i (1)
where Cm is the whole-cell membrane capacitance, Gm is thewhole-cell membrane conductance, and
El is the leak potential. Most biological membranes have acapacitance of about 1 µF per square
centimeter of membrane area, which allows one estimate cell size bymeasuring capacitance.
a) One way to measure the capacitance is to inject a sinusoidalcurrent i = Ie j?t and to measure the
sinusoidal perturbation in the membrane potential vm = Ve j?t . Inthe frequency domain, both the
current I and the voltage V are complex-valued numbers. Derive aformula for the cell capacitance in
terms of I and V.
b) Another way to measure cell capacitance and conductance is touse a step current injection. In this
case, the current is suddenly increased to a constant i = Io andthe voltage responds with an exponential
form. Measurement of the voltage for a known current impulseprovides a means to estimate the
capacitance and conductance. Toward this aim, find the solution ofEq. 1 for a step increase in
current. Once you have this solution, how would you use the voltageand current measurements to
estimate the passive capacitance and conductance?
Membrane Capacitance and Conductance. For cells having simplemorphological shapes, the
intracellular voltage is nearly uniform throughout the cell suchthat any change in the membrane
potential acts equally on all parts of the membrane. If wehyperpolarize the cell or chemically block
excitable ionic conductances, the membrane potential vm ispassively related to the incoming current i
by:
Cm
dvm
dt
+Gm (vm - El ) = i (1)
where Cm is the whole-cell membrane capacitance, Gm is thewhole-cell membrane conductance, and
El is the leak potential. Most biological membranes have acapacitance of about 1 µF per square
centimeter of membrane area, which allows one estimate cell size bymeasuring capacitance.
a) One way to measure the capacitance is to inject a sinusoidalcurrent i = Ie j?t and to measure the
sinusoidal perturbation in the membrane potential vm = Ve j?t . Inthe frequency domain, both the
current I and the voltage V are complex-valued numbers. Derive aformula for the cell capacitance in
terms of I and V.
b) Another way to measure cell capacitance and conductance is touse a step current injection. In this
case, the current is suddenly increased to a constant i = Io andthe voltage responds with an exponential
form. Measurement of the voltage for a known current impulseprovides a means to estimate the
capacitance and conductance. Toward this aim, find the solution ofEq. 1 for a step increase in
current. Once you have this solution, how would you use the voltageand current measurements to
estimate the passive capacitance and conductance?
