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Consider the reaction scheme:

$$\ce{S + E ->[k_1] C1} \qquad \ce{C1 ->[k_2] E + P} \qquad \ce{S + C1 <=>[k_3][k_4] C2}$$

where $\ce{S}$ is the substrate, $\ce{E}$ is the enzyme, $\ce{P}$ is the product, $\ce{C1}$ and $\ce{C2}$ are enzyme substrate complexes. Let $[\ce{S}] = s$, $[\ce{E}] = e$, $[\ce{C1}] = c_1$, $[\ce{C2}] = c_2$ and $[\ce{P}] = p$ be the concentrations of each respective chemical. I have used the law of mass reaction to convert this reaction into a system of differential equations:

\begin{align} \frac{\mathrm{d}s}{\mathrm{d}t} &= -k_1se-k_3sc_1+k_4c_2\\ \frac{\mathrm{d}e}{\mathrm{d}t} &= -k_1se+k_2c_1\\ \frac{\mathrm{d}c_1}{\mathrm{d}t} &= k_1se-k_2c_1-k_3sc_1+k_4c_2\\ \frac{\mathrm{d}c_2}{\mathrm{d}t} &= k_3sc_1-k_4c_2\\ \frac{\mathrm{d}p}{\mathrm{d}t} &= k_2c_1 \end{align}

I notice that

$$\frac{d}{dt}(e+c_1+c_2) = 0.$$

Hence $e+c_1+c_2 = const.$ Now is this a conservation equation? Also how do I use this equation to simplify the system?

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