Irreversible linear pathways in enzymatic reactions: analytical solution using the homotopy perturbation method

Abstract

In this work, the Homotopy Perturbation method is used for the first time to solve an irreversible linear pathway with enzyme kinetics. The enzymatic system has Michaelis–Menten kinetics and is modeled by a system of nonlinear ordinary differential equations. The analytical solution obtained with the method allow us to optimize several objectives: minimal time to reach a certain percent of final product, minimal amount of enzymes employed in the process, or even multiple objective optimization via Pareto front. We present an example to demonstrate the results.

Annex I: dataset

Table 1 shows, as explained in Eq. (67), the list of the maxima $M_{1,k}=\max |u_{1,k}(\tau )|$, $N_{1,k}=|v_{1,k}(\tau )|$, for $\tau \in [0,6]$, corresponding to the first stage of case (2) (i.e. Sect. 5.2).

Table 1 Convergence for the first stage of reaction (2)

Table 2 shows the same data for the second stage of the same reaction, $M_{2,k}=\max |u_{2,k}(\tau )|$, $N_{2,k}=|v_{2,k}(\tau )|$, for $\tau \in [1.55,6]$.

Table 2 Convergence for the first stage of reaction (2)