Question

1. lon channel opening. Consider an ion channel that is initially open at $t = 0$, and opens and closes with probabilities per unit time $\alpha$ and $\beta$ respectively: Let the probabilities of the ion channel being closed or open be $p_0$ and $p_1$ respectively. a) List the parameters of this system. List the variables of this system. b) Write down an ordinary differential equation, describing the rate of change of the open probability $p_1$. Express the right-hand side in terms of $p_1$ and the parameters of the system. c) Solve the ordinary differential equation to obtain $p_1(t)$. Assume the channel is initially closed, such that the system satisfies the following initial conditions $p_1(0) = 0$. d) At long times, i.e. when $t \to \infty$, write down an expression for the probability of the channel being open as a function of system parameters. e) What is the time at which the system reaches half its steady-state value?

Name: 1 lon channel opening consider an ion channel that is initially open at t 0 and opens and closes with probabilities per unit time alpha and beta respectively let the probabilities of the ion 56544
Uploaded: 2019-07-20T20:27:00-08:00
Duration: 4 min 31 s
Channel: Gideon Idumah
Description: 1 lon channel opening consider an ion channel that is initially open at t 0 and opens and closes with probabilities per unit time alpha and beta respectively let the probabilities of the ion 56544

          1. lon channel opening. Consider an ion channel that is initially open at $t = 0$, and opens and closes with probabilities per unit time $\alpha$ and $\beta$ respectively:

Let the probabilities of the ion channel being closed or open be $p_0$ and $p_1$ respectively.

a) List the parameters of this system. List the variables of this system.
b) Write down an ordinary differential equation, describing the rate of change of the open probability $p_1$. Express the right-hand side in terms of $p_1$ and the parameters of the system.
c) Solve the ordinary differential equation to obtain $p_1(t)$. Assume the channel is initially closed, such that the system satisfies the following initial conditions $p_1(0) = 0$.
d) At long times, i.e. when $t \to \infty$, write down an expression for the probability of the channel being open as a function of system parameters.
e) What is the time at which the system reaches half its steady-state value?

1 lon channel opening consider an ion channel that is initially open at t 0 and opens and closes with probabilities per unit time alpha and beta respectively let the probabilities of the ion 56544

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