Modelling ribosome kinetics and translational control on dynamic mRNA

Abstract

The control of protein synthesis and the overall levels of various proteins in the cell is critical for achieving homoeostasis. Regulation of protein levels can occur at the transcriptional level, where the total number of messenger RNAs in the overall transcriptome are controlled, or at the translational level, where interactions of proteins and ribosomes with the messenger RNA determine protein translational efficiency. Although transcriptional control of mRNA levels is the most commonly used regulatory control mechanism in cells, positive-sense single-stranded RNA viruses often utilise translational control mechanisms to regulate their proteins in the host cell. Here I detail a computational method for stochastically simulating protein synthesis on a dynamic messenger RNA using the Gillespie algorithm, where the mRNA is allowed to co-translationally fold in response to ribosome movement. Applying the model to the test case of the bacteriophage MS2 virus, I show that the models ability to accurately reproduce experimental measurements of coat protein production and translational repression of the viral RNA dependant RNA polymerase at high coat protein concentrations. The computational techniques reported here open up the potential to examine the infection dynamics of a ssRNA virus in a host cell at the level of the genomic RNA, as well as examine general translation control mechanisms present in polycistronic mRNAs.

Fig 1. A model of ribosome kinetics on dynamic mRNAs.

(A) The transcriptome in the model consists of two types of mRNAs: background mRNAs which are considered as monocistronic with no secondary structure, and dynamic mRNAs which are polycistronic with secondary structure. Initiation rates at potential start codons (green bars, with red bars indicating stop codons) can vary in dynamic mRNAs depending on the current structure around the translation initiation region (TIR) while they are modelled as fixed in the background mRNAs. The movement of the ribosome during elongation is illustrated. (B) The transcriptome is modelled using the framework of the stochastic model in [10], with added RNA folding reactions on the dynamic mRNA.

Fig 2. Tree-representation of the bacteriophage MS2 coat protein gene.

(A) The inset gives a coarse-grained cartoon diagram of the full-nucleotide structure with explicit base-pairing, which is stored in the model. Bound ribosome is coloured yellow, with purple bases showing the location of the ribosome P-site. (B) The coarse-grained representation of the mRNA structure is translated into the rooted tree data structure shown, where each numbered node in the tree represents a coarse-grained helix in the cartoon diagram. Green arrows denote links to leaf nodes, while red arrows denote links to root nodes. Links to the main root node 0 denoting the 5’ end of the mRNA are not shown for simplicity. Black arrows between nodes show links in the linked list data structure which stores neighbour information for the tree.

Fig 3. Model of ribosome binding kinetics to a translation initiation region.

(A) Kinetic model of 30S:PIC binding to a TIR region of an mRNA via standby and direct pathways. TIR regions are considered as being hairpin only regions, possibly flanked by multi-loop helices. k_−F = 1/τ_u is the kinetic rate of TIR unfolding, while $k_1^B$ is the binding rate of 30S:PIC to the mRNA via ribosome protein S1. (B) Apparent 30S:PIC binding rate to TIR region at a cellular growth rate of μ = 0.7 doublings per hour.

Fig 4. The translational coupling and repression mechanisms in bacteriophage MS2 mRNA.

(A) Secondary structure cartoon of the bacteriophage MS2 coat and RdRp genes determined by phylogenetic analysis and enzymatic probing. (B) Translational repression of the RdRp gene occurs after synthesis of sufficient coat protein, which then binds to the translational repression (TR) hairpin that contains the start codon for the RdRp gene, blocking further ribosome initiations at this gene. (C) Diagram showing the translational coupling between the coat protein and RdRP genes. Synthesis of coat gene by the ribosome opens up a secondary TIR for the RdRp gene after melting of mRNA structure, allowing ribosome initiation at the RdRp start codon. Re-folding of the mRNA after translation of the coat gene hides the TIR for the RdRp gene.

Fig 5. Coat protein expression in bacteriophage MS2 for different hairpin mutants.

(A) Cartoon diagram of the secondary structure for the MS2 coat gene. Start codons for the various phage genes are indicated with a green bar, while stop codons are indicated with a red bar. The nucleotide sequence of the hairpin encompassing the coat gene start codon (dashed box in cartoon) is shown to the right. Mutants are labelled following [13]. (B) Best fit linear line of the experimental measurements from [13] to Eq 4. (C) Predicted MS2 coat protein synthesis rates are calculated from 30 min of ribosome kinetics at a growth rate of μ = 0.7 doublings per hour using hairpin unfolding times ranging from τ_u = 0.01 to τ_u = 10 seconds (black dots). The best fit of the data to the theoretical protein expression curve (Eq 2) is represented by the black line. (D) Fit of experimental relative coat protein expression data (red dots) to the theoretical expression curve (Eq 2).

Fig 6. Synthesis rates for Coat and RdRp proteins in Bacteriophage MS2.

(A) Temporal dynamics of coat protein and RdRp synthesis from bacteriophage MS2 mRNA in a bacterial cell over 30 minutes. Red dashed line corresponds to the initial synthesis rate of RdRp before coat protein binding to the TR stem-loop (c.f. Fig 4A) suppresses further synthesis. (B) Maximal Coat and RdRp synthesis rates from bacteriophage MS2 mRNA as a function of coat hairpin unfolding time. The curve is computed by varying τ_u explicitly in the program, with dots representing the results from simulations with specific mutant sequences. Blue dashed line shows the ratio of RdRp to Coat protein synthesis rates.