Homework Help is Here – Start Your Trial Now!
Math
Probability
a)Write the transition matrix. Is this an Ergodic Markov chain? Explain your answer b)Starting from a group of nAChR's where 34% are in the C1 state, 42% in the C2 state and 24% in the O state, calculate the probability of finding channels in open state after 4 microseconds. Show all of your work. c)Find the fixed vector of this matrix (show your work)

a)Write the transition matrix. Is this an Ergodic Markov chain? Explain your answer b)Starting from a group of nAChR's where 34% are in the C1 state, 42% in the C2 state and 24% in the O state, calculate the probability of finding channels in open state after 4 microseconds. Show all of your work. c)Find the fixed vector of this matrix (show your work)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

a)Write the transition matrix. Is this an Ergodic Markov chain? Explain your answer

b)Starting from a group of nAChR's where 34% are in the C1 state, 42% in the C2 state and 24% in the O state, calculate the probability of finding channels in open state after 4 microseconds. Show all of your work.

c)Find the fixed vector of this matrix (show your work)

d)Starting with the initial probability distribution of C1=0.24; C2=0; O=0.76, predict what fraction of ion channels will be in each state after 1000 time steps (hint: the probability distribution converges after about 100 time steps)

7. Ion channels are trans-membrane proteins with a hollow channel running through the interior that allows polar ions to traverse the nonpolar lipid bilayer. The channels may exist in several conformations (shapes), which may either allow or block passage of ions through the channel. Transitions between the conformational states are random (as is everything on the molecular scale), but they may be induced by external events, such as binding of another molecule, or a change in membrane potential. In this section we will analyze a simple model of nicotinic acetylcholine receptor (NACHR), which is an important ion channel involved in transmission of signals between neurons. The opening of the channel is induced by binding of the neurotransmitter acetylcholine (Ach). The Markov chain model has three states: closed (C1), closed with Ach bound (C2), and open (O). Suppose that at a certain concentration of Ach, the transition probabilities between the different states per two microsecond are as follows: 0.04 (from C1 to C2), 0.07 (from C2 to C1), 0.12 (from C2 to O) and 0.02 (from O to C2); the other transition probabilities between different states are 0.
Transcribed Image Text:7. Ion channels are trans-membrane proteins with a hollow channel running through the interior that allows polar ions to traverse the nonpolar lipid bilayer. The channels may exist in several conformations (shapes), which may either allow or block passage of ions through the channel. Transitions between the conformational states are random (as is everything on the molecular scale), but they may be induced by external events, such as binding of another molecule, or a change in membrane potential. In this section we will analyze a simple model of nicotinic acetylcholine receptor (NACHR), which is an important ion channel involved in transmission of signals between neurons. The opening of the channel is induced by binding of the neurotransmitter acetylcholine (Ach). The Markov chain model has three states: closed (C1), closed with Ach bound (C2), and open (O). Suppose that at a certain concentration of Ach, the transition probabilities between the different states per two microsecond are as follows: 0.04 (from C1 to C2), 0.07 (from C2 to C1), 0.12 (from C2 to O) and 0.02 (from O to C2); the other transition probabilities between different states are 0.
Expert Solution
steps

Step by step

Solved in 6 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Paths and Circuits
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS