The dynamics of supply and demand in mRNA translation

Abstract

We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking "competition" effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system.

Figure 1. Schematic representation of the model including use and recharging of tRNAs.

Red particles represent ribosomes, and the lattice represents the mRNA. Ribosomes move from site to site with rates dependent on the size of a pool of aa-tRNAs. Every time a ribosome moves out of a site of type , a aa-tRNA is removed from the pool, and a tRNA is added to the corresponding pool of bare tRNAs. Bare tRNAs are recharged with a rate .

Figure 2. Supply

for each type of tRNA used in the simulations. These are based on the gene copy number for each tRNA in the Saccharomyces cerevisiae genome. The key for the label of each codon is available in the supporting information (Text S2).

Figure 3. mRNA A Supply and Demand.

Bar graphs showing (a) the supply of the codon at each site and (b) the occurrence frequency of each codon type on mRNA A.

Figure 4. Simulation results for mRNA A.

Plots (a) and (b) show how the current (protein production rate) and the mean density of ribosomes on the mRNA depend on the initiation rate , respectively. In (b) the points show the reader density and the crosses the coverage density . Plots (c) and (d) show ribosome density as a function of position for small () and large () initiation rate respectively. Black lines show the reader density and blue lines the coverage density . Red dots show the positions of codons of type , and the red bar indicates the width of the ribosomes. Bar graphs (e) and (f) show the steady state charging rate of each tRNA type. (e) shows and (f) , the same values as in (c) and (d).

Figure 5. Simulation results for mRNA A using the original TASEP model.

The tRNA charging rate is assumed to be infinite, and hence then numbers of aa-tRNAs are constant and based on gene copy numbers. In (b) the points show the reader density and the crosses the coverage density . Plots (c) and (d) show ribosome density as a function of position for small () and large () initiation rate respectively. Black lines show the reader density and blue lines the coverage density . Red dots show codons of type as in Fig. 4.

Figure 6. mRNA B Supply and Demand.

Bar graph showing (a) the supply of the codon at each site and (b) the occurrence frequency of each codon type on mRNA B.

Figure 7. Simulation results for mRNA B.

Subplots are as described in the caption for Fig. 4. Plots (c) and (d) show density for small () and large () initiation rate respectively. Red dots show the positions of codons of type , and the red bar indicates the width of the ribosomes. (e) and (f) show for the same as in (c) and (d).

Figure 8. The demand supply ratio.

Bar graphs showing the ratio for each codon type for mRNAs A and B.

Figure 9. Different reasons for queueing in a “designer mRNA”.

(a) Sketch of a designer mRNA with only two types of codon. All codons are the same except for the central one. (b) The solid curve shows the critical initiation rate beyond which queueing will be observed, as a function of . Which kind of queueing will be observed depends on , and the three regimes discussed in the text are separated with dotted lines. The inset shows a zoom around small .

Figure 10. Results for simulations containing mixtures of mRNAs A and B.

Plots (a)–(e) show results for a mixture in the ratio 50∶50 (by codon numbers). (a) and (b) show and as a function of for mRNAs of type A (black points) and type B (red crosses) (the same initiation rates are used for each species). The blue line shows , where blue labelled codons cause queueing. Plot (c) shows the charging levels of tRNAs for . (d) and (e) show the site dependent reader (pale lines) and coverage (dark lines) density for each mRNA type, again for . The codons corresponding to the first aa-tRNA to become depleted are highlighted with blue dots (), and those for the second in green (). Plots (f)–(j) show similar results for a mixture in the ratio 80∶20; results for a 20∶80 mixture are presented in the supporting information (Text S4).

Figure 11. The charging levels

of the first two aa-tRNAs to become depleted. Plot (a) shows results for the 20∶80 mixture of mRNAs A and B, plot (b) the 50∶50 mixture, and (c) the 80∶20 mixture. From left to right the abundance of mRNA A increases. Blue and green lines correspond to the codons labelled blue and green in Fig. 10, and dashed lines show .

Figure 12. Results for simulations containing mixtures of mRNAs C and D.

Plots (a)–(e) show results for a mixture in the ratio 50∶50 (by codon numbers). (a) and (b) show and as a function of for mRNAs of type C (black points) and type D (red crosses). The blue line shows , where blue labelled codons first become depleted. Plot (c) shows the charging levels of tRNAs for . (d) and (e) show the site dependent reader (pale lines) and coverage (dark lines) density for each mRNA type. The codons corresponding to the first aa-tRNA to become depleted are highlighted with blue dots (), and those for the second in green (). Plots (f)–(j) show similar results for a mixture in the ratio 20∶80; results for a 80∶20 mixture are presented in the supporting information (Text S4).

Figure 13. The charging levels

of the first two aa-tRNAs to become depleted. Plot (a) shows results for the 20∶50 mixture of mRNAs C and D, plot (b) the 50∶50 mixture, and (c) the 80∶20 mixture. From left to right the abundance of mRNA C increases. In each case the tRNA type labelled blue becomes depleted first. The inset in (c) is a zoom at small showing this more clearly. Dashed lines show .

Figure 14. Simulations of large numbers of mRNAs.

Results from two simulations containing 70 different species of mRNA (numbered 1 to 70 with full details being given in supplementary information S2). In both simulations the abundance of each of group II mRNAs (blue) are kept the same, but the abundance of group I mRNAs (red) are varied so as to match their abundance during the G1 and G2 phases of the cell cycle respectively. Plot (a) shows the charging levels for each tRNA, (b) the current for each mRNA and (c) the corresponding ribosome densities, each for G2 phase. Plots (d)–(f) show similar for G1 phase.