Stochastic theory of protein synthesis and polysome: ribosome profile on a single mRNA transcript

The process of polymerizing a protein by a ribosome, using a messenger RNA (mRNA) as the corresponding template, is called {\it translation}. Ribosome may be regarded as a molecular motor for which the mRNA template serves also as the track. Often several ribosomes may translate the same (mRNA) simultaneously. The ribosomes bound simultaneously to a single mRNA transcript are the members of a polyribosome (or, simply, {\it polysome}). Experimentally measured {\it polysome profile} gives the distribution of polysome {\it sizes}. Recently a breakthrough in determining the instantaneous {\it positions} of the ribosomes on a given mRNA track has been achieved and the technique is called {\it ribosome profiling} \cite{ingolia10,guo10}. Motivated by the success of these techniques, we have studied the spatio-temporal organization of ribosomes by extending a theoretical model that we have reported elsewhere \cite{sharma11}. This extended version of our model incorporates not only (i) mechano-chemical cycle of individual ribomes, and (ii) their steric interactions, but also (iii) the effects of (a) kinetic proofreading, (b) translational infidelity, (c) ribosome recycling, and (d) sequence inhomogeneities. The theoretical framework developed here will serve in guiding further experiments and in analyzing the data to gain deep insight into various kinetic processes involved in translation.