C lets now imagine that time is discretized into a

Info icon This preview shows pages 2–3. Sign up to view the full content.

View Full Document Right Arrow Icon
(c) Let’s now imagine that time is discretized into a series of steps of length Δ t . At the initial instant, imagine that the channel is closed. What is the probability that in the next time interval Δ t that it will switch to open? What is the probability that in that same time interval Δ t that it will stay closed? Using those insights, now write an expression for the probability ( p closed ( t t ) that in the interval between t and t t the channel will switch from closed to open, having stayed closed the entire time until then. Make a corresponding derivation for p on ( t ). What can you say about the waiting time distributions? What are the time constants for the open and closed waiting time distributions? Using these distributions, compute the average time that the channel stays in each of the states. Make sure to compute this as an average and explain what integrals you write down and why. Given the nature of ion channel current traces, explain how you could go about determining these distributions and finding these average times. Hint: Remember that the exponential is characterized by the interesting property lim N →∞ (1 - x N ) N = e - x , (2) and use the fact that N = t/ Δ t . (d) Now we follow up on the results of part (c) to ask a more sophisticated question by considering the distribution of waiting times from one closed- open transition to the next closed-open transition. Start by sketching an ion channel current trace and show what is meant by the waiting time from one closed-open transition to the next. In particular, make a cogent argument that this waiting time distribution is given by p successive ( t ) = Z t 0 p open ( t - τ ) p closed ( τ ) dτ. (3) Then, using the results of part (c) for p open ( t ) and p closed ( t ), obtain an analytic form for this distribution and plot it and explain its features and significance.
Image of page 2

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern