A stochastic model for simulating ribosome kinetics in vivo

Abstract

Computational modelling of in vivo protein synthesis is highly complicated, as it requires the simulation of ribosomal movement over the entire transcriptome, as well as consideration of the concentration effects from 40+ different types of tRNAs and numerous other protein factors. Here I report on the development of a stochastic model for protein translation that is capable of simulating the dynamical process of in vivo protein synthesis in a prokaryotic cell containing several thousand unique mRNA sequences, with explicit nucleotide information for each, and report on a number of biological predictions which are beyond the scope of existing models. In particular, I show that, when the complex network of concentration dependent interactions between elongation factors, tRNAs, ribosomes, and other factors required for protein synthesis are included in full detail, several biological phenomena, such as the increasing peptide elongation rate with bacterial growth rate, are predicted as emergent properties of the model. The stochastic model presented here demonstrates the importance of considering the translational process at this level of detail, and provides a platform to interrogate various aspects of translation that are difficult to study in more coarse-grained models.

Fig 1. Diagram of the ribosome kinetic model.

(A) Illustration of the reaction network that is simulated in the model. Aminoacylation of tRNAs (dashed boxes) indicate an area where there is limited knowledge of the biochemical kinetics and additional experimental work is needed. (B) Overview of the implementation steps. Specific mRNA sequences, and the concentration of ribosomes, are used as input parameters. The program determines the quantities of elongation factors, etc. that are expected from the number of ribosomes based on experimental data [19]. Examples of output data are shown in the final column.

Fig 2. Translational kinetics of ribosomes at different E. coli growth rates.

Time courses for the percentage of ribosomes (compared with total ribosomal mass) that are initiating (black), elongating (green), terminating (red), stalled (purple), or free 50S (blue) and free 30S:PIC (brown) are shown for growth rates of (A) μ = 0.7, (B) μ = 1.0, and (C) μ = 2.5 doublings per hour. The experimentally expected ratio of ribosome in elongating complexes (70S:EC—green line) to total ribosome is 0.80–0.85 for all growth rates [19], which matches with the model prediction. Time courses represent an average of three separate simulations.

Fig 3. Peptide chain elongation rates at different E. coli growth rates.

The peptide chain elongation rates (C_p) in amino acids per second are shown for the simulations at growth rates μ = 0.7,1.0, and 2.5 doublings per hour. Running averages of C_p over 1000 seperate protein syntheisis events are given by the red curves and reveal an average peptide chain elongation of C_p = 15,18, and 21 amino acids per second for μ = 0.7,1.0, and 2.5 doublings per hour, respectively. All model predictions of the peptide elongation rates match experimental estimates of [24].

Fig 4. Percentage of each tRNA in free ternary complex.

For each tRNA listed in Table K in S1 Text, the percentage of the tRNA that is in free ternary complex (TC) is computed by taking the ratio of the amount of the tRNA in free TC to the total amount of the tRNA. The average ratio for each tRNA (over the last 100 seconds of the translational simulation) is shown for for the T07 (black), T10 (red), and T25 (blue and T10a (green) transcriptomes. The tRNAs are ordered from lowest percentage to highest for each simulation separately.

Fig 5. Predicted codon decoding times and stalling frequency.

The average codon decoding times a stalling frequencies for each sense codon is calculated from the 215M individual decoding events that occur over the entire transcriptome in 1000s of simulation time. Blue and red bars indicate the T10 and T10a transcriptomes, respectively. Stalling events are computed as the frequency of ribosome stalling that occurs at the given codon.