Stochastic models of ribosome kinetics

The translation mechanism that synthesizes proteins based on mRNA sequences is a fundamental process of the living cell. Since most of the antibiotics work on this level, the understanding of this process can help us in the developing of new medicines. Also, we can find optimal protein encodings according to different criteria which can be used to efficiently produce those proteins in genetic engineering.

Conceptually, an mRNA can be seen as a string of codons, each coding for a specific amino acid. The codons of an mRNA are sequentially read by a ribosome, where each codon is translated using an amino acid specific transfer-RNA (aa-tRNA), building one-by-one a chain of amino acids, i.e. a protein. In this setting, aa-tRNA can be interpreted as molecules containing a so-called anticodon, and carrying a particular amino acid. Dependent on the pairing of the codon under translation with the anticodon of the aa-tRNA, plus the stochastic influences such as the changes in the conformation of the ribosome, an aa-tRNA, arriving by Brownian motion, docks into the ribosome and may succeed in adding its amino acid to the chain under construction. Alternatively, the aa-tRNA dissociates in an early or later stage of the translation.

Using probabilistic model checking, a computer science technique originally developed for showing correctness of software and hardware, we analyse ribosome kinetics. We compute different parameters of the model, like probabilities of translation errors and average insertion times per codon. Our models predict strong correlation to the quotient of the concentrations of the so-called cognate and near-cognate tRNAs, in accord with experimental findings and other studies. We show that probabilistic model checking is a viable alternative to the stochastic techniques, like Gillespie-style simulations.