Dynamics of ribosomes in mRNA translation under steady- and nonsteady-state conditions

Recent advances in DNA sequencing and fluorescence imaging have made it possible to monitor the dynamics of ribosomes actively engaged in messenger RNA (mRNA) translation. Here, we model these experiments within the inhomogeneous totally asymmetric simple exclusion process (TASEP) using realistic kinetic parameters. In particular, we present analytic expressions to describe the following three cases: (a) translation of a newly transcribed mRNA, (b) translation in the steady state and, specifically, the dynamics of individual (tagged) ribosomes, and (c) runoff translation after inhibition of translation initiation. In cases (b) and (c) we develop an effective medium approximation to describe many-ribosome dynamics in terms of a single tagged ribosome in an effective medium. The predictions are in good agreement with stochastic simulations.

Figure 1

Schematic of the three conditions that we study in the present work: (a) translation of a newly transcribed mRNA, (b) translation in the steady state, and (c) runoff translation after inhibition of initiation.

Figure 2

Schematic of the TASEP with ribosomes of size $\ell =10$ and codon-dependent elongation rates ${\omega }_i$. Here ribosomes occupy three codon positions only for demonstration.

Figure 3

Time evolution of the total ribosome density $\rho \left(t\right)$ for genes (a) sodA of E. coli, (b) YAL020C of S. cerevisiae, and (c) beta-actin of H. sapiens, obtained from stochastic simulations averaged over ${10}^6$ independent runs. The corresponding initiation rates are 1, $0.08617$, and $1/30$ initiations/s. Vertical dashed lines mark the average translation time $\langle T\rangle$ of the first round of translation.

Figure 4

Probability density function $p\left(T\right)$ for the translation time $T$ of the first, pioneering round of translation of the sodA gene. Vertical dashed line is at the mean value $\langle T\rangle$, and the dashed-dotted lines are at $\langle T\rangle \pm {(\langle T^2\rangle -{\langle T\rangle }^2)}^{1/2}$.

Figure 5

(a)–(f) Time evolution of the ribosome density ${\rho }_i\left(t\right)$ for genes sodA (left column), YAL020C (middle column), and beta-actin (right column) at two codon positions, $i=2$ (top row) and $i=100$ (bottom row). Symbols are from stochastic simulations averaged over ${10}^6$ independent runs. Dashed lines were computed using Eq. (14). Horizontal dashed line is the steady-state density ${\rho }_i^{*}$.

Figure 6

Time evolution of the ribosome density $\rho \left(t\right)$ for gene sodA of E. coli. Symbols are from stochastic simulations averaged over ${10}^6$ independent runs. Solid line was computed using Eq. (15). Horizontal dashed line is the steady-state density ${\rho }^{*}$.

Figure 7

Probability density function $p\left(T^{*}\right)$ of the translation time $T^{*}$ in the steady state for genes (a) sodA, (b) YAL020C, and (c) beta-actin. The histograms are the result of stochastic simulations averaged over ${10}^5$ independent runs. Dashed lines were computed using Eq. (19).

Figure 8

Time evolution of the ribosome density ${\rho }_i\left(t\right)$ for sodA gene at codon positions (a) $i=2$ and (b) $i=100$ after translation initiation inhibition at $t=0$. Symbols are from stochastic simulations averaged over ${10}^6$ runs. Solid line was computed from Eq. (30). Dashed horizontal line is the steady-state density ${\rho }_i^{*}$.

Figure 9

Time evolution of the total ribosome density $\rho \left(t\right)$ after translation initiation inhibition at $t=0$ for gene sodA. Symbols are from stochastic simulations averaged over ${10}^6$ runs. Solid line was computed from Eq. (31). Dashed horizontal line is the steady-state density ${\rho }^{*}$.