### Stochastic mechano-chemical kinetics of translation: translocation and
missense error

10 March 2017

Debashish Chowdhury

Department of Physics

Indian Institute of Technology, Kanpur

#### Abstract

The rate of transition from one state to another on the network of discrete mechano-chemical states is the inverse of the corresponding mean first-passage time (FPT). For example, the average rate of elongation of a protein by a ribosome is the inverse of the ribosome's mean dwell time at a codon which is essentially a FPT. Based on the calculation of FPT, we develop a theoretical formalism that connects conclusions drawn from experiments using static, ensemble techniques with those of kinetic, single molecule experiments. We present an application of this formalism by analyzing the results of cryo-electron microscopy and smFRET on bacterial ribosomal pre-translocation complex. We then extend the stochastic model capturing the possibilities of both mis-reading of mRNA codon and mis-charging of tRNA within a unified theoretical framework. The exact analytical expression for the average rate of elongation of a nascent protein, that we obtain by using the formalism of FPT, is a generalization of the Michaelis-Menten formula for the average rate of enzymatic reactions.

(Work done in collaboration with Ajeet Sharma, Colin Kinz-Thompson, Joachim Frank, Ruben Gonzalez Jr. and Annwesha Dutta).

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