In this and the following three videos, we present a canonical introduction to mRNA-protein system from systems biology 101. In the fourth video in this slide deck, we summarize the process of linear stability analysis that can be applied to systems of differential equations that can be expressed in the form of 2x2 matrix equations.
In this first video, we obtain the system of differential equations describing this model by presenting assumptions that mRNA molecules are transcribed and degraded and that copies of protein are translated and degraded.