Gene Expression Deterministic Description

Another interested example that we shall not address here due to the complexity of the mathematics involved is that in which the promoter is regulated. However, the interested readers can study it in the specialized literature. 

The average number of RNA and protein molecules can be computed from the respective probability distributions as follows  

From these definitions we can derive the differential equations governing the dynamics of NmO) and Np(t) as 

Given that the master equation for P tiM, t) is the same for the two models studied in the previous section, substitution ofEq. (8,36) into the expression oxdNu t)/dt gives 

However, we know that Eq. (8.37) is not the best approximation because it relies on an assumption not supported by experimental evidence. To avoid this problem let us consider Eq. (8.43) instead. However, before doing so it is convenient to rewrite this equation as 

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