Non-linear biochemical reactions with fluctuations

Comparing Equations (11.21) and (4.5), we see that is exactly equal to J in Equation (4.6). The above derivation also indicates that if the enzyme has only one unbound state, then the mean waiting time will always have the double reciprocal formofa/[S] +b. 

4 The CME models for non-linear biochemical reactions with fluctuations 

For unimolecular reaction systems described by mass-action kinetics, the kinetic equations are always linear. Hence they are called linear reaction systems. For stochastic unimolecular systems, the key is to understand the multi-state kinetics of a single molecule, as we have seen. If N is the number of states of amolecule, and there are M number of identical, independent molecules, then the probability of having 

For non-linear systems, closed form solutions usually do not exist and it is necessary to simulate their behavior. 

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A non-linear biochemical reaction system with concentration fluctuations... 

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