I was going through the GRN modelling from Chemical and enzyme kinetics by D. Gonze & M. Kaufman (PDF). The gene has 2 sites for activator/repressor. It say the DNA $D_0$ combines with activator/repressor at one of the sites leading to $D_1$ and then $D_1$ combines with $X$ again leading to $D_2$. It says then then total DNA is conserved in the reaction leading to $D_{Total} = D_0 + 2D_1 + D_2$. I want to ask why is there "2" with $D_1$ shouldn't it be $D_{Total} = D_0 + D_1 + D_2$. What I am talking about is given on page 49 of the document. $$D_0 + X \leftrightarrow D_1$$ $$D_1 + X \leftrightarrow D_2$$ For first chemical reaction the rates are $k_1$ and $k_{-1}$. For the second reaction the chemical reaction rates are $\alpha k_1$ and $k_{-1}$. Also, what will be the rate of the reaction for $D_2+X\rightarrow D_3$ when the DNA has 3 sites instead of 2.


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