Gene length as a regulator for ribosome recruitment and protein synthesis: theoretical insights

Abstract

Protein synthesis rates are determined, at the translational level, by properties of the transcript's sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we propose transcript length as a further key determinant of translation efficiency. Based on a physical model that considers the kinetics of ribosomes advancing on the mRNA and diffusing in its surrounding, as well as mRNA circularisation and ribosome drop-off, we explain how the transcript length may play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. According to our results, the proximity of the 3' end to the ribosomal recruitment site of the mRNA could induce a feedback in the translation process that would favour the recycling of ribosomes. We also demonstrate how this process may be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.

Figure 1

Ribosome density vs CDS length for different datasets. Blue diamonds (mice) and fuchsia down triangles (P. falciparum ) are individual genes, while yellow circles (HEK293T), green squares (S. cerevisiae ) and red triangles (S. cerevisiae ) are length-binned data for the entire genome, with the error bars representing the standard deviation for each bin. The grey line indicates the behaviour of a power law with exponent −1.

Figure 2

Sketch of the translation process and models. The three-steps of the translation process (A): initiation (in the model approximated by a one-step process with rate α), elongation and termination (β). In the standard exclusion process (B) particles can enter the beginning of the lattice with a rate α, move from one site to the next one with rate p (provided that it is not occupied by another particle), and then exit on the last site with rate β. In this study we consider a more refined version of the model (C) in which ribosomes cover $\ell$ sites (codons), advance one site at a time, and the unidimensional lattice is placed in a three-dimensional environment. R represents the end-to-end distance between the 5′and the 3′ region, and a is the radius of the reaction volume for initiation. The dashed grey line represents a possible diffusive trajectory of the ribosomal subunits leaving the transcript and being re-absorbed (recycled) in the reaction volume around the first site of the lattice.

Figure 3

Comparison between theory and experimental ribosome densities in yeast (A,B)^, and human embryonic kidney cells (C). The symbols and datasets correspond to the ones of Fig. (1). The grey lines represent the best fit of the model (the parameter values are written in each panel), while the shadow areas correspond to the regions spanned within the margin of error of the estimated ${\overline{\alpha }}_{\infty }$. Orange circles are the outcome of stochastic simulations used to test the numerical solution of the equation using the parameters obtained from the best fit.

Figure 4

Model with ribosome drop-off. Green lines correspond to the Arava dataset, while red ones correspond to the Mackay dataset Symbols of experimental points in yeast correspond to the ones of Fig. 1, while dashed lines represent the solutions of the model described in the previous section with the same parameters used in panels A and B of Fig. 3. The continuous lines are the outcome of simulations of our model including ribosome drop-off at a rate of 10⁻³ s⁻¹, and the grey line shows the outcome of the simulations with drop-off only.

Figure 5

Model with mRNA circularisation. Sketches of the two possible mRNA conformations, open and circularised, whose transitions depend on the free energy gap ΔG (A). In blue and yellow we have represented the interacting proteins (e.g. PABP and eIF4F) bound at the 3′ and 5′ ends; the black line is the end-to-end distance that is equal to d in the circularised state. We have fixed d = 5 nm in our calculation. Ribosome density computed taking into account mRNA circularisation (continuous line) is then compared to experimental data (triangles, cfr. symbols used in Fig. 1) and the previous model neglecting circularisation (dashed line) (B). The fitted parameters are ${\overline{\alpha }}_{\infty }\mathrm{=(4.7}\pm \mathrm{0.6)}{10}^{-3}$ s⁻¹, λ = 7.0 ± 0.6 nm and ε = − 8.3 ± 0.4 (k _B T). End-to-end distance (blue curve, right axis) and calculated probabilities P _c and P _o = 1 − P _c as a function of the CDS length L (C).

Figure 6

Effects of competition for resources (ribosomes) on the protein production rate. The ribosome density depends on the overall ribosome concentration c _∞. We show the ribosome density as a function of the transcript length for different concentrations of available ribosomes c _∞ (A). The curve denoted with c _∞ in the legend is built starting from the same parameters of Fig. 3A. We change c _∞ as described in the legend for the other curves. Short transcripts are less affected by changes in c _∞, as we also show in (B) where we plot the relative expression of transcripts η (defined in the text) as a function of c _∞. We used transcript with three different lengths (here L = 100, 500 and 2500). According to these results, ribosomal proteins that are short should be relatively more expressed under high ribosome competition regimes compared to other types of proteins.