Taylors’ Technique for Solving Delay Equations of Gene Expression Model with Competitive and Non- Competitive Mechanisms

Abstract

In this paper, the delay differential equations of Gene expression models with mechanisms of signal-dependent transcription regulation are solved and studied in two cases: When there is (i) competition and (ii) without competition(non-competition) for Deoxy ribo Nucleic Acid (DNA) regulatory binding sites in a cell. Also, we studied the effect of both increasing the inhibitor or decreasing the abundance of the activator (inhibition mechanism), and decreasing the inhibitor or increasing the abundance of the activator (activator mechanism) on the steady-state of the solutions. A new analytical approximation approach derived from Taylor series expansion is used for solving the delay differential equations of gene expression models. From the analytical approximate solutions of gene expression models that are resulting from using the proposed method, we found  that the behavior of the solution in the activation mechanisms whether in the competitive or non-competitive model is more stable than the abundance of the activator increases, while the inhibition mechanisms are less stable. We also noticed that the convergence of these solutions is achieved with a few iterations.

Keywords: Taylors’ technique, activator, inhibitor, Gen,  mRNA, protein, convergence analysis.

DOI: 10.7176/MTM/12-1-01

Publication date: January 31^st 2022