As we discussed in class, a membrane can both conduct charge and store it, analogous to an RC circuit. The time-dependence of the membrane potential when it is perturbed from some initial membrane potential to a new membrane potential E can be described with the following differential equation: C dVm/dt + g(Vm - E) = 0. Where C is the membrane capacitance. Vm is the membrane potential, t is time, g is the conductance, and E is the newly-imposed membrane potential. Solve this equation for Vm(t). assuming that Vm(t=0) = 0. Write your final answer in terms of the characteristic time constant tau = C/g. Assume tau = 100 ms. Plot Vm(t) vs t for E = 20, 40, 60, 80, and 100 mV. By what factor would tau change if the membrane were made three times as ion-permeable, and why? Similarly, by what factor would tau change if the area of the plasma membrane was suddenly tripled without a change in total conductance? [Hint: Membrane capacitance is often expressed in mu F/cm? - think about what this tells you about the relationship between C and area]
Show transcribed image textAs we discussed in class, a membrane can both conduct charge and store it, analogous to an RC circuit. The time-dependence of the membrane potential when it is perturbed from some initial membrane potential to a new membrane potential E can be described with the following differential equation: C dVm/dt + g(Vm - E) = 0. Where C is the membrane capacitance. Vm is the membrane potential, t is time, g is the conductance, and E is the newly-imposed membrane potential. Solve this equation for Vm(t). assuming that Vm(t=0) = 0. Write your final answer in terms of the characteristic time constant tau = C/g. Assume tau = 100 ms. Plot Vm(t) vs t for E = 20, 40, 60, 80, and 100 mV. By what factor would tau change if the membrane were made three times as ion-permeable, and why? Similarly, by what factor would tau change if the area of the plasma membrane was suddenly tripled without a change in total conductance? [Hint: Membrane capacitance is often expressed in mu F/cm? - think about what this tells you about the relationship between C and area]