A Maximum Entropy Model for tRNA Abundances Initiating Protein Synthesis

Abstract

We investigate the role of relative tRNA availabilities in limiting the rate of amino acid incorporation during the translation stage of protein synthesis. Although an extensive literature focuses on maximizing the incorporation rate, the physical importance of having only finite amounts of information to control tRNA abundances has not been similarly addressed. This project quantifies the existing tradeoff between the protein synthesis rate and available information by maximizing the system's entropy, and defines the minimum information required to achieve a given mean synthesis rate. The resulting model predicts the distribution of likely sets of tRNA abundances required to produce the essential proteins of a given cell type for an initial set of codon frequencies. Numerical methods and Monte Carlo simulations then characterize and manipulate the selectivity of the model's solution space for tRNA abundance sets of E. coli under several experimental settings, demonstrating the feasibility of achieving the predicted minimum incorporation time. At the localization limit, we show that the optimal solutions involve largely mid-range concentrations but are distinctly nonuniform, with individual tRNAs varying by the importance of the corresponding cognate codon. The findings demonstrate the types of analyses possible with the model, but more accurate data about tRNA abundances under various conditions could usefully fine-tune the parameters. The model provides a plausible mechanism by which, given a set of weighted codon frequencies, one can predict the optimal tRNA availability and directly determine the cell's state at a given point on the information tradeoff continuum.