Whole cell biophysical modeling of codon-tRNA competition reveals novel insights related to translation dynamics

Abstract

The importance of mRNA translation models has been demonstrated across many fields of science and biotechnology. However, a whole cell model with codon resolution and biophysical dynamics is still lacking. We describe a whole cell model of translation for E. coli. The model simulates all major translation components in the cell: ribosomes, mRNAs and tRNAs. It also includes, for the first time, fundamental aspects of translation, such as competition for ribosomes and tRNAs at a codon resolution while considering tRNAs wobble interactions and tRNA recycling. The model uses parameters that are tightly inferred from large scale measurements of translation. Furthermore, we demonstrate a robust modelling approach which relies on state-of-the-art practices of translation modelling and also provides a framework for easy generalizations. This novel approach allows simulation of thousands of mRNAs that undergo translation in the same cell with common resources such as ribosomes and tRNAs in feasible time. Based on this model, we demonstrate, for the first time, the direct importance of competition for resources on translation and its accurate modelling. An effective supply-demand ratio (ESDR) measure, which is related to translation factors such as tRNAs, has been devised and utilized to show superior predictive power in complex scenarios of heterologous gene expression. The devised model is not only more accurate than the existing models, but, more importantly, provides a framework for analyzing complex whole cell translation problems and variables that haven't been explored before, making it important in various biomedical fields.

Fig 1. Overview of the whole cell translation model.

Schematic visualization of the simulated elements at the cell level (A), at the mRNA level (B) and a simplified view of the state machines at the codon level (C), for initiation and elongation (the detailed state machines appear in F-G Figs in S1 File). At the cell level, a transcriptome of mRNA molecules with a finite pool of ribosomes and tRNAs is simulated, leading to a competition for these resources. At the mRNA level, we utilized a novel generalized deterministic TASEP model that incorporates both accurate dynamics at the codon level and dependence on cellular resources, which influences these dynamics. On the codon level, for each codon the dynamics are dictated by a state machine, an object that holds the state (e.g. “this codon is anticipating a tRNA”) and the rules of state transition order and conditions (see sub-section Generalized deterministic TASEP and state machines).

Fig 2. High correlation between the predictions of the MP-SMTM model and measured data for E. coli.

(A) Termination rate in steady state (predicted by the model) and protein abundance (empirical data); (B) Local initiation rate (as estimated for the model) and protein abundance (empirical data); (C) Mean ribo-seq read count and mean simulated occupancy. (D) Ribosomal density profiles for both simulation (average occupancy per codon) and ribo-seq (average read count per codon). In (A), (B) and (D) mRNAs with level lower than 0.2 were omitted from this analysis to avoid discretization errors of the simulation. In (A), (B) and (C) each point represents a single mRNA type. (All terms in this figure are defined in the Methods section, sub-sections System parameters, Prediction of protein synthesis rate and Additional terminology).

Fig 3. The effect of the codon order and composition on the total termination rate.

(A) Schematic illustration of the different randomization types. (B) Box plot for total simulated termination rate (i.e. the sum of termination rates of all mRNAs) distributions (10 values each) compared to the un-randomized scenario. The p-values shown are the result of a single-sample two-sided t-test.

Fig 4. The model promotes understanding and provides analysis framework for heterologous expression problems.

(A) Total E. coli and GFP genes termination rates for various GFP variants as heterologous genes. Two method were used for variant generation, as described in the sub section Heterologous expression in the Methods. The original variant is shown in orange. Smaller blue dots are related to variants in which one codon was chosen as substituted all synonymous codons (61 such variants in total). Other dots represent variants in which a single representing codon was chosen for each amino acid, according to some optimality score (either TDR, ESDR or inverse occupancy). (B) Two variants (marked with arrows in (A)) are compared in terms of ESDR. Codons for which the ESDR is different represent changes in supply and demand of associated tRNAs and allow to understand the results in (A). (C) Comparison of three optimization variants in terms of their ESDR, per codon, relative to the unoptimized variant (red represents a higher ESDR value). Some codons (such as CCC) exhibit an increase in ESDR in all variants, indicating that increasing the supply/demand for these codons can improve overall translational efficiency.

Fig 5. A multivariable regressor for predicting protein abundance (PA) and optical density (OD) of GFP variants.

(A) Pearson correlation between model prediction and the measured PA values of the GFP variants, as function of the number of feature selected for the train and the test sets. This graph demonstrates the approach taken for feature selection: For 100 times, a train (~67%) and test (~33%) sets were randomly selected. Each time, the next best feature was selected to be the one the increases R² the most in the test set (for more details, see sub-section 'Regressor features selection' in the Methods section). This result suggests that a model with more than ~10 features will show poor predictivity due to over-fitting. (B) After choosing the best features and sorting them, this figure shows the correlation between the predicted PA (blue) and OD (red) values and the measured ones, for increasing number of features. A features' set based on ESDR (continues line) was compared to a simpler metric of codon-count (dashed lines). In both cases (PA and OD) the ESDR-based model performed better and reached impressive correlation with empirical data, demonstrating the importance of our model (Data for this model was taken from Kudla et. al [34]).