Quasi-Stationary Approximation of a Dynamical Model of microRNA Target Regulation. Part I. Establishment of Time Hierarchy in the Model Dynamics

Abstract

The Quasi-Steady-State Approximation (QSSA) theorem is considered as a basic approach for reduction of dimensionality of a dynamical model of microRNA target regulation. On the basis of previously determined parameters, seven ordinary differential equations of the model are written in a form appropriate to evaluate their terms for further reduction. In accordance with the terminology of the QSSA theorem, it is established that five of the system components are fast varying such that the corresponding kinetic equations form an attached system. The other two variables are slow varying and their kinetic equations form a degenerate system.

Keywords

• Ordinary differential equations
• QSSA theorem
• Reduction of dimensionality
• MicroRNA target regulation