Bacterial small RNAs (sRNA) are non-coding RNA molecules produced by bacteria. The role of sRNA in bacterial physiology is extremely diverse; they can either bind to protein targets, and modify the function of the bound protein, or bind to mRNA targets and regulate gene expression. Antisense sRNAs can be categorised as cis-encoded sRNAs, where there is an overlap between the antisense sRNA and the target gene, and trans-encoded sRNAs, where the antisense sRNA gene is separate from the target gene.

Relevant Biology

The model is based on sRNAs that bind to the chaperone protein, Hfq. Hfq binds to sRNA, forming a complex. This complex then binds to mRNA and promotes degradation of both the mRNA and sRNA in a stoichiometric manner. Mechanistically, the Hfq-mRNA-sRNA complex is broken down by a degradosome, a complex of proteins where the protein RNAse E is the centerpiece~\cite{aiba2007mechanism}. The important thing to note here is that the order is compulsory.

We can also assume that binding of mRNA to sRNA doesn't happen on its own, which Professor Scott and myself talked about. Some papers seem to suggest that it does, others note the requirement for Hfq.

In some cases Hfq is actually part of the degradosome, for example in SgrS regulation, and sometimes its not, in the case of RyhB. Both SrgS and RyhB are names for specific sRNA that regulate different metabolic pathways; RyhB is responsible for regulating iron metabolism in E. coli, SrgS is responsible for handling glucose-phosphate stress (a rapid increase in glucose-6-phosphate, a precursor to glycolysis). This changes the mechanism quite a bit, however, for the purposes of this model, I'm going to assume that our sRNA suppression style is more akin to RyhB - although we really should look into this.

Our previous models haven't considered the fact that sRNA gets degraded with the mRNA by the degradosome simultaneously. This new formulation is that assumptions' reckoning.

Model Formation

The model of chemical network is shown below. Before writing this out as a system of equations, I want to describe what's happening first. We are tracking the concentrations of seven species: s, m, M, h, H, Hs and Hms, representing the sRNA, the mRNA, the target protein, Hfq mRNA, Hfq, Hfq-sRNA complex, and Hfq-sRNA-mRNA complex respectively.

Production of a species, be it RNA or protein, is denoted with an α and a subscript indicating which species is being produced. Degradation is given by a β

Parameters

We identified parameters in the literature. The identified parameters and their sources are given in the table below.

sRNA sRNA Parameters from Literature

Sensitivity Analysis

To get a better handle on the dynamics of the system we ran a local sensitivity analysis. This determined what parameters the sRNA system is most sensitive to. The flux control coefficients for the sRNA system can be seen in the figure to the right.

The most notable of these are the flux control coefficients for the following parameters: β M(the degradation rate of YFP), αm (the transcription rate of the YFP mRNA transcript). These large flux control coefficient values demonstrate the system is highly sensitive to changes in these variables. So if we were able to influence these rates we would be able to dramatically change the level of flux through the system. In order for the sRNA system to be most efficient, we would want the flux of YFP through the system to be as low as possible. The most direct way to affect this would be to alter these values. Since we want to use this sRNA system to control a protein whose degradation rate and transcription rate we could not alter, we need to turn our gaze to some of the other factors at play.

Some other notable flux control coefficients are αS, αM, K-1. These rates are respectively the rate of transcription of sRNA, the rate of translation of YFP, and the rate of dissociation of Hfq-sRNa to Hfq and sRNA. These rates have the least impact on the system and are not good targets for optimization of sRNA.