One Molecule Flipping Between Two Compartment Model

SantiUm, Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics, Lecture Notes on Mathematical Modelling in the Life Sciences, 

Another way of tackling this problem is to regard all the molecule positions within compartment I as single lumped state, and to do the same for compartment E. With this, the molecule can be seen as randomly flipping back and forth between states I and E. Assume that the transition probabilities from I. o E (kie), and from E io I kei), are constant. Then, the master equation governing the molecule stochastic dynamics is 

Consider the transition rates kie and kei. Intuitively, one expects that both rates are proportional to the channel area. On the other hand, it seems reasonable to assume that the larger a container is, the longer the molecule takes to scape from it. A very simple way to account for these two suppositions into account is to take 

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