Application of the law of mass action results in \[\begin{aligned} \frac{d C_{1}}{d t} &=k_{1} S E+\left(k_{-3}+k_{4}\right) C_{2}-\left(k_{-1}+k_{2}+k_{3} S\right) C_{1} \\[4pt] \frac{d C_{2}}{d t} &...Application of the law of mass action results in \[\begin{aligned} \frac{d C_{1}}{d t} &=k_{1} S E+\left(k_{-3}+k_{4}\right) C_{2}-\left(k_{-1}+k_{2}+k_{3} S\right) C_{1} \\[4pt] \frac{d C_{2}}{d t} &=k_{3} S C_{1}-\left(k_{-3}+k_{4}\right) C_{2} \end{aligned} \nonumber \] Applying the quasi-equilibrium approximation \(\dot{C}_{1}=\dot{C}_{2}=0\) and the conservation law \(E_{0}=E+C_{1}+C_{2}\) results in the following system of two equations and two unknowns: \[\begin{align} \left(k_{-1}+k_{2}…
Rational functions often play a role in biochemistry. Here we discuss two such examples and the contexts in which they appear. In both cases, we consider the initial rise of the function as well as it...Rational functions often play a role in biochemistry. Here we discuss two such examples and the contexts in which they appear. In both cases, we consider the initial rise of the function as well as its eventual saturation.
