Dynamical Analysis of the MicroRNA-Mediated Protein Translation Process

Mathematical modeling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate normalized procedure the system of seven nonlinear ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that two of the protein concentrations are “fast varying”, such that the corresponding kinetic equations form an attached system. The other four concentrations are “slow varying”, and form a degenerate system. Another variable appears to be a constant. Analytical relationships between the steady-state values of the fast varying concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of microRNAs on the protein translation process. Keywords-nonlinear dynamics; microRNA; protein translation; QSSA theorem