The Effect of Codon Translation Rates on Cotranslational Protein Folding Mechanisms of Arbitrary Complexity

Abstract

Bacterial cells use the naturally occurring variability in the rate at which different codons are translated to guide the folding of nascent proteins into ordered, biologically-active structures during their synthesis by the ribosome. Predicting how codon translation rates effect cotranslational protein folding mechanisms is therefore of fundamental biological interest. Here, we demonstrate that cotranslational folding mechanisms sampling an arbitrarily large number of states can be accurately modeled by treating this problem using the Markov chain formalism. This allows a general equation to be derived that describes the probability that a nascent protein is in any one of these conformational or thermodynamic states as a function of translation rates of individual codons in an mRNA molecules' open reading frame, which we show is accurate in modeling molecular dynamics simulations of cotranslational folding. Using this framework we demonstrate that there exists scenarios in which, contrary to conventional wisdom, fast-translating codons can actually increase the amount of cotranslational folding that occurs. This approach can be applied to the cotranslational folding of cytosolic and membrane proteins, and possibly the processing of nascent chains by auxiliary factors such as chaperones and enzymes.