When introducing a new (synthetic/circuit) gene into a cell, the new gene competes for resources with all of the existing (host) genes in the cell. Some of these resources include ribosome, DNA polymerase, RNA polymerase, and amino acids. In some extreme cases, the synthetic genes could hog the resources and not leave enough for the host genes, thus shutting down cell function and killing the cell. One method to try and reduce this competition for ribosomes is to create “orthogonal ribosomes,” which are ribosomes that only translate the circuit gene (and the circuit gene does not attract host ribosomes). This project uses the Ribosomal Flow Model (RFM) to form a dynamical model for orthogonal ribosome competition.

The RFM is a nonlinear tridiagonal dynamical system used in queuing theory that can represent a single strand of mRNA. Each cite (codon) has a probability of a ribosome being present (value x of the state). The flux from one codon to the next in the sequence is proportional to the current site’s occupancy times the next site’s vacancy.

A 5-codon RFM at 2 seconds through its dynamics.

The steady-state of the 5-codon RFM.

A set of mRNA strands (genes) may be connected to a common pool of ribosomes.

Left: The top strand has a bottleneck between the third and fourth codon, and holds many of the ribosomes in the network. This globally depresses the translation rate. Right: This problematic link is faster, and all strands have a higher protein translation rate. All images are at steady state.

Orthogonal ribosomes may be introduced to translate the circuit genes. The host ribosomes (with host 16s rRNA) and circuit ribosomes (with mutated 16s rRNA) may each dissociate into and be created from ‘neutral’ribosomes by mass action, which abstract out the protein backbone of the ribosome. The Orthogonal Ribosomal Flow Model (ORFM) is stable and has a unique solution when codon occupancies are in [0, 1]. In the following figures, the host ribosomes are in blue, the circuit ribosomes are in red, and the ‘neutral’ ribosomes are in purple.

Left: There are no circuit genes, but circuit ribosomes are still created. Right: There are a large number of circuit genes.

An nonconex optimization problem can be constructed to maximize a linear functional of the protein output rates by adjusting the creation rate of host and circuit ribosomes from the neutral ribosomes.

We also consider a self-inhibiting feedback controller that ensures orthogonal ribosomes are only created if they are needed. The golden circuit mRNA strand produces a protein which inhibits the formation of circuit ribosomes.

Left: The feedback controller winds down the creation of orthogonal ribosomes. Right: The feedback controller competes with other genes, and its inhibitive effect is blunted.

The ORFM model assumes a perfect rejection: host ribosomes will never translate circuit genes (and vice versa). The cross-talk RFM model allows for a varying-but-nonzero initiation rate between ribosomal species. Empirically the crosstalk ORFM model appears stable, but proving its stability remains an open question.

mRNA strands access both types of ribosomes.

Relevant Publications

Journal Articles

LCSS
Mediating Ribosomal Competition by Splitting Pools

Miller, Jared, Al-Radhawi, Muhammad Ali, and Sontag, Eduardo Daniel

IEEE Control Systems Letters 2021

Abs Bib HTML PDF Code Slides

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.
@article{miller2020ribosome, author = {Miller, Jared and Al-Radhawi, Muhammad Ali and Sontag, Eduardo Daniel}, journal = {IEEE Control Systems Letters}, title = {{Mediating Ribosomal Competition by Splitting Pools}}, year = {2021}, volume = {5}, number = {5}, tag = {ribosome}, pages = {1555-1560}, doi = {10.1109/LCSYS.2020.3041213}, abbr = {LCSS}, url = {https://ieeexplore.ieee.org/document/9483415}, html = {https://ieeexplore.ieee.org/document/9483415}, pdf = {mediating_ribosomes.pdf}, code = {https://gitlab.com/jarmill/Ribosomes}, bibtex_show = {true}, slides = {ACC_Ribosome_3.pptx} }