Model reduction for non-linear protein translation pathways using slow and fast subsystems

الملخص EN

This paper reviews the mechanisms of miRNA model where mathematical models of miRNA translation are suggested to describe the dynamics of protein synthesis.

In this regard, we use the idea of quasi steady state approximation (QSSA) for separating model equations into slow and fast subsystems.

This separation is based on a proper scaling that we have used in this study.

The suggested technique provides one to minimize the model elements and gives some analytical approximate solutions.

Accordingly, the equation of slow manifold can be calculated from the simplified model.

The slow manifold is sufficiently close to the analytical solutions when the slow-fast parameter becomes smaller.

We apply three types of model coefficient analysis including, elasticity coefficients, flux control coefficients and concentration control coefficients.

These techniques have three main goals.

The first goal quantifies the sensitivity of reaction rates to the change of concentrations or parameters.

The second goal is to measure the change of a flux along model pathways in response to a change in model reaction rates.

The third goal is to calculate the change of concentrations while responding to a change in reaction rates.