  In order to better understand the process of gene translation, the ribosome
flow model (RFM) with pool was introduced recently. This model describes the
movement of several ribosomes along an mRNA template and simultaneously
captures the dynamics of the finite pool of ribosomes. Studying this system
with respect to the number and stability of its equilibria was so far based on
monotone systems theory (Margaliot and Tuller, 2012). We extend the results
obtained therein by using a geometric approach, showing that the equilibria of
the system constitute a normally hyperbolic invariant submanifold.
Subsequently, we analyze the Jacobi linearization of the system evaluated at
the equilibria in order to show that the equilibria are asymptotically stable
relative to certain affine subspaces. As this approach does not require any
monotonicity features of the system, it may also be applied for more complex
systems of the same kind such as bi-directional ribosome flows or time-varying
template numbers.

Subcellular Processes;Dynamical Systems