Blog post by Jordan Juritz

What do rush-hour traffic jams have to do with protein production? As we are all quite familiar with, congestion arises and the overall flow rate of cars decreases when many vehicles travel on a relatively small number of routes. In “

**Networks of ribosome flow models for modelling and analyzing intracellular traffic**”, Nanikashvili et al. present a model that describes this same phenomenon during protein translation.
The ribosome is the molecular machine responsible for piecing together amino acids to form proteins. mRNA, a long polymer molecule, serves as the working blueprint for the protein. The order in which the amino acids are added is encoded in the sequence of nucleotides on the mRNA. Much like a car on a road, the ribosome binds around the mRNA, and proceeds to synthesise the protein as it steps along the mRNA molecule, reading its instructions from the mRNA as it goes.

A typical yeast cell contains about 60,000 mRNA molecules and about 240,000 ribosomes at any given moment. Space is tight, and the competition for mRNA among ribosomes is very high. As a result, it is expected that there will be multiple ribosomes translating a single mRNA at any one time.

The authors of this paper have employed a network of “ribosome flow models with inputs and outputs (RFMIO)” to describe the precession of the ribosomes through this highly congested system.

A single RFMIO describes the dynamics of the probability density of ribosomes along a region of mRNA that encodes for a single protein. A single RFMIO describes the progression of a ribosome along a single section of protein-encoding mRNA. Within each RFMIO, the progression of the ribosome is bundled into an arbitrary number of steps. These steps can be fast or slow depending on the depending on the shape of the mRNA (is it straight or bundled up?) or the availability of the required resources, such as tRNAs. Therefore, the authors assign a unique rate to the transition between one step and the next, but only ever permit ribosomes to flow in the forward direction, just as cars can only drive one way down one side of the motorway. Cars travel much more slowly if there are many more cars bunched up ahead of them. Accordingly, in RFMIO models the flow of ribosomes to the next step is high (low) if the next state is free (full).

A single protein is produced once a ribosome has reached the end of an encoding region of mRNA, therefore, the outflow of ribosomes in an RFMIO model is interpreted as the protein production rate. Once a ribosome has reached the end of a single gene on an mRNA, it can stay attached to the mRNA to continue to translate another gene, or it can detach and diffuse back into solution.

The authors proved that after a long time has elapsed the probability distribution of ribosomes within a single RFMIO settles to a steady value. In this steady state, ribosomes produce proteins at a fixed, average rate. However, we know that living systems contain not just one, but many genes. Therefore, the authors considered networks of RFMIOs that enable ribosomes to be shared or recycled by many different genes. The authors proved that for arbitrary interconnection strengths the probability density of ribosomes still converges to a steady state across many different RFMIOs. As a result, many different proteins can be produced at steady rates, the ratios of which are determined by the strength and structure of the network. Crucially, outputs such as the total production rate or ribosome recycling rate are often convex functions of the interconnection parameters. The property of convexity implies that there exists an optimal protein production value that can be found easily (using efficient algorithms) even when the network of RFMIOs becomes very large. It’s like finding the highest point in a country with only one hill.

How do traffic jams arise in these systems? The figure below shows a simple network of two RFMIO connected in series. Both RFMIOs are arbitrarily made up of 3 internal substeps. In the first RFMIO, the rate at which ribosomes flow from internal step 2 to internal step 3 has been chosen to be very slow. As indicated in the corresponding graph, the probability densities after this bottle-neck are much lower than they were before, indicating a ribosome traffic jam has occurred in RFMIO 1! RFMIO 2 takes its input of ribosomes directly from RFMIO 1, therefore the slow transition in the first system has a long-range effect on the probability distribution and production rate of the second system. The implication of this is that, in the case that two genes are present on the same transcript mRNA, a bottle-neck in the ribosome flow on the first gene would reduce the production rate of the second protein.

**Figure 1:**A series of RMIOs. A bottleneck in the first RFMIO causes a low turnover of proteins in the second RFMIO.

This model can be used to do more than just simulate biological traffic jams. Consider the network of parallel RFMIOs shown in Figure 2. These two RFMIOs represent two genes that compete for a common pool of ribosomes, with a proportion “v” going into RFMIO 1 and proportion “1-v” going into RFMIO 2. “v” represents the binding strength of ribosomes with the starting point of the gene represented by RFMIO 1. This model can be solved to find the binding strengths that optimise the combined protein production rate, “y”. This class of models can be used to aid the design of synthetic biological circuits to tune the production rates of the system.

**Figure 2:**Two RFMIOs in parallel. The pair of systems compete for a share of the total ribosome pool. The protein production rate is maximised for the most efficient resource allocation.

An understanding of the properties of flowing traffic helps engineers to design more efficient transport systems, and the same is true for engineering projects within the cell. Bioengineers employ modelling techniques, such as these networks of RFMIOs, to aid in the design of smarter, more efficient nano-machines and biological systems. Bioengineering can give rise to novel medicines and technologies, and it helps us to understand just a little bit more about how nature solved these tricky problems in the first place.

**Figure 3:**A complex genetic regulatory pathway, introducing metabolites and enzyme concentrations. This system can be described by RFMIOs.

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