• MATHEMATICAL MODEL OF COUPLED TRANSCRIPTION, TRANSLATION AND DEGRADATION

Abstract

Synthesis of proteins is one of the most fundamental biological processes, which consumes a significant amount of cellular resources. Despite many efforts to produce detailed mechanistic mathematical models of translation, no basic and simple kinetic model of mRNA lifecycle (transcription, translation and degradation) exists. We present the approximate analytical solution the nonlinear differential equations that describe coupled transcription, translation and degradation. The simple and closed analytical expressions for the amount of  mRNA with translation initiation site not occupied by assembling ribosome, mRNA with translation initiation site occupied by assembling ribosome, ribosomes sitting on mRNA synthesizing proteins, proteins have been derived by using homotopy perturbation method for all values of parameter.  These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain.