# Markov chain transition Matrix for Ion channels in Python

I was working to code for a markov chain transition matrix for potassium channels. Potassium channels conists of 4 gates 1,2,3,4. the potassium ions antransition from 1->2 or 1->1, 2->1,2->2,2->3 etc. I want to make a transition matrix for this given the transition rates for different transitions betwee the states. Eg: transition rate from state1 to state 2(i.e 1->2) is given by 4*alpha_n(V) where alpha_n(V) = (0.01*(10.0 - V))/(exp(1.0 - (0.1*V)) - 1.0). i.e alpha is dependent on voltage. Similarly for transition rate from state 2 to state1(i.e 2->1) is given by beta_n(V) where beta_n(V) = 0.125*exp(-V/80.0) i.e beta is dependent on voltage. I am not able to decipher ow to make a probability transition matrix for this. Can someone help me?