  Synthetic biology constructs often rely upon the introduction of "circuit"
genes into host cells, in order to express novel proteins and thus endow the
host with a desired behavior. The expression of these new genes "consumes"
existing resources in the cell, such as ATP, RNA polymerase, amino acids, and
ribosomes. Ribosomal competition among strands of mRNA may be described by a
system of nonlinear ODEs called the Ribosomal Flow Model (RFM). The competition
for resources between host and circuit genes can be ameliorated by splitting
the ribosome pool by use of orthogonal ribosomes, where the circuit genes are
exclusively translated by mutated ribosomes. In this work, the RFM system is
extended to include orthogonal ribosome competition. This Orthogonal Ribosomal
Flow Model (ORFM) is proven to be stable through the use of Robust Lyapunov
Functions. The optimization problem of maximizing the weighted protein
translation rate by adjusting allocation of ribosomal species is formulated and
implemented.
