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In order to better understand the process of gene translation, the ribosomeflow model (RFM) with pool was introduced recently. This model describes themovement of several ribosomes along an mRNA template and simultaneouslycaptures the dynamics of the finite pool of ribosomes. Studying this systemwith respect to the number and stability of its equilibria was so far based onmonotone systems theory (Margaliot and Tuller, 2012). We extend the resultsobtained therein by using a geometric approach, showing that the equilibria ofthe system constitute a normally hyperbolic invariant submanifold.Subsequently, we analyze the Jacobi linearization of the system evaluated atthe equilibria in order to show that the equilibria are asymptotically stablerelative to certain affine subspaces. As this approach does not require anymonotonicity features of the system, it may also be applied for more complexsystems of the same kind such as bi-directional ribosome flows or time-varyingtemplate numbers.

Geometric stability considerations of the ribosome flow model with pool