EcEoEb2kT5kTFigure 1:Consider a channel with energies Ecand Eofor the open and closed states, respectively. Let Eb− Eo= 5kT and Eb− Ec= 2kT ,where Ebis the energy of the barrier between states, and kT is a measure of thermal energy. For this energy diagram, Vm= +40mV.a. What is the equilibrium probability that a channel is open?b. Is the transition rate limited by the opening or closing of the channel?At a different potential, it is found that 1/4 of the channels are open. It is further found that the rate of opening, α, is unchanged.c. What are the new values of Eb− Ecand Eb− Eo?d. If the rate constant at Vm= +40 mV was τx= 10 msec, what is τxat Vm= 0 mV?1Figure 2:Consider the two-gate model shown above. The channel is conductive only when both gates are open (the right-hand position).a. If the rate constants for a single gate are α and β for the opening and closing reactions, respectively, what are the rate constantsfor the two transitions in the two-gate model?b. A step change in voltage is applied to this channel. The probability that a single gate is open is x0= 0 before the step, andx∞= 0.5 after. The time constant for this single gate is τx= 10 msec. Plot the open probability of this channel as a function oftime after the
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