# A state model of sodium channels

I am studying by myself Human Physiology. I have encountered the following question:

In the following given model of sodium channel with 3 states open closed blocked (which I assume means inactivated), the rates of going from state to stated are given in the picture below.

a. Write matrix $Q$ for the system and find it's eigenvalues. b. What does these values represent?

If anyone has an idea what is the required matrix I will be grateful. Thanks!

• Interesting question, looks like homework but i won't give you a minus. Can you describe full description, i mean, what these numbers mean. Suppose it is charge need to be possessed to change the state, if so, i can do that, it looks like simple matrix model if we add some probabilities of generating charge. I also suppose that you need to get eigenvalues just to find stable system state and that's good. – dshulgin Apr 26 '16 at 11:51
• I think Q is supposed to be an adjacency matrix that represents the graph in your diagram. Take a look here: en.wikipedia.org/wiki/Adjacency_matrix and here: cs.elte.hu/~lovasz/eigenvals-x.pdf – Justas Apr 26 '16 at 22:49
• This is a homework question. You should at least make some attempt at the answer. – WYSIWYG Apr 27 '16 at 8:37
• Thank you all. It is from HW I found in the net. So, no other information valid for me. I usually, of course, make a lot of self effort. But, sometimes, like in this case, even though you know you have the right tools, you just don't know where to start, especially, if not all the definitions are given... So, Thanks for your help and comments! – user135172 Apr 27 '16 at 14:25

$$\begin{array}{|l|c|c|c|} \hline & A & B & C \\\hline A & 0 & 10 & 0 \\\hline B & 100 & 0 & 50 \\\hline C & 5 & 0 & 0 \\\hline \end{array}$$