Conductance Capacitance

 

Membrane Behavior Compared with an Electrical Current:

 

A membrane behaves electrically like a capacitance in parallel with a resistance.

 

Now, if we apply a pulse of current to the circuit, the current first charges up the capacitance, then changes the voltage.

 

 

 

The voltage V(t) approaches steady state along an exponential time course: V(t) = Vinf (1 - e up(- t/tc)

The steady-state value Vinf (also called the infinite-time or equilibrium value) does not depend on the capacitance; it is simply determined by the current I and the membrane resistance R:   Vinf= I.R .

 

This is just Ohm's law, of course; but when the membrane capacitance is in the circuit, the voltage is not reached immediately. Instead, it is approached with the time constanttc, given by tc = RC.

 

Thus, the charging time constant increases when either the membrane capacitance or the resistance increases.

Consequently, large cells, such as Xenopus oocytes that are frequently used for expression of genes encoding ion-channel proteins, and cells with extensive membrane invigorations, such as the T-system in skeletal muscle, have a long charging phase.