Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process

Authors

  • Elena Nikolova Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  • Ivan Jordanov Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  • Nikolay Vitanov Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

DOI:

https://doi.org/10.11145/j.biomath.2012.10.071

Keywords:

microRNA, protein translation, QSSA theorem, driving reactions, control parameters

Abstract

Mathematical modelling 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 solutions, related to 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 dynamics.

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Published

2013-01-07

Issue

Section

Original Articles