Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 14B / iv / Solution

Integrating the density, and using ${\lambda }_{+}+{\lambda }_{-}=A$ and ${\lambda }_{+}{\lambda }_{-}=k_1{k}_2$, givesThe same result follows from first-step analysis: the enzyme waits on average $1/k_1$ to bind, and each complex either produces or returns to the initial enzyme state.