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Single Channel

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Single Channel Model

Description | Equations | Implementation | Examples | Discussion

Equations

Let there be N relevant conformational states of a single channel, let's denote them by A₁, A₂, ..., A_N. Many of these conformation can have exactly same ion conductance. The kinetics of the channel is stochastic, and thus be characterized by a distribution function P i (t): the probability of the channel being in state i at time t. Let q i j be the rate constant for reaction Ai -> Aj. Then the equation for the stochastic kinetics is 

d P _i (t) / d t = Sum_j ( P_j q _{j i} - P _i q _{i j})

This equation gives the probability distribution of a channel at a particular time. One can also run a Monte Carlo simulation to see the stochastic jumping process of the single molecule. There will be no differential equation for this, but it can be best presented by a short computer code. Let x be the state of the protein (x=1,2,...N) 
t = 0
x = k
q_k = q_k1+q_k2+...+q_kN
t = dt 
r = ran(iseed) 
If (r .le. exp(-qk*dt)) then x = k 
else r = ran(iseed)
if (r .le. qk1/qk) x = 1
if ((r .gt. q_k1/q_k) .and. (r .le. (q_k1+q_k2)/q_k) x = 2
...
if (r .gt. (q_k1+...q_kN)/q_k) x = N
End if

4-2-1-1-2..

Contact Hong Qian for comments or questions.