Concerning the kinetics of polypeptide synthesis on polyribosomes

Abstract

SynopsisThe kinetics of biosynthesis of polypeptides on polyribosomes is analyzed in accordance with a simple mathematical model. Each ribosome is assumed to block L adjacent (m-RNA) template sites but to move a distance of one, and only one, template site (nucleotide triplet) upon the addition of each monomer unit to the growing polypeptide chain bound to it. Solutions are sought for the probability, n&), thrtt a template possesses, at time t, a polypeptide chain that has reached degree of polynlerization j.Several classes of steady-state solutions are obtained via machine computation. These correspond to various choices of relative rates of initiation, polymerization along templates, and termination (release of completed chains from templates).Experimental data available from radioactive pulse labeling experiments are discussed. The data obtained by Dintzis, and by Winslow and Ingram, in studies of the synthesis of the a chain of rabbit hemoglobin and human hemoglobin, respectively, are consistent with steady-state solutions obtained from the current theoretical calculations when the rates of initiation and termination are of comparable magnitude and ratedetermining. In this case, a (relatively) small number of chains are polymerized at a (relatively) fast rate each near the beginning of the template, and there exists a transition to a situation near the end of the template in which a (relatively) large number of chains are polymerized a t a (relatively) slow rate each. For this solution the situat,ion near the end of the template is entirely analogous to a traffic jam in automobile traffic.

Stochastic kinetics of ribosomes: Single motor properties and collective behavior

“…[46] where the dwell time distribution was not derived. By making one-to-one correspondence beween the mechano-chemical cycle in their generic model for cytoskeletal motors and that in our model of ribosome, we find that the MM-like equation reported by Bustamante et al [46] reduces to the MMlike equation (24).…”

“…We refer to such collective movement of ribosomes on a mRNA strand as ribosome traffic because of its superficial similarity with vehicular traffic [22]. In most of the earlier theoretical studies of ribosome traffic, individual ribosomes have been modelled as hard rods and their steric interactions have been captured by mutual exclusion [23,24,25,26,27,28,29,30,31,32]. Thus, all those models may be regarded as totally asymmetric simple exclusion process (TASEP) for hard rods [33,34].…”

“…In the earlier TASEP-type models of ribosome traffic [23,24,25,26,27,28,29,30,31,32] , the phase diagrams were plotted in a two-dimensional plane spanned by α and β, which determine the rates of initiation and termination. In this paper we plot the three-dimensional phase diagrams of our model of ribosome traffic [36] in spaces spanned by three parameters which, for different diagrams, are selected from α, β, the availability of amino acid monomers and the rate of GTP hydrolysis.…”

A mathematical modelling framework for elucidating the role of feedback control in translation termination

“…Kinetic models of biopolymerization on nucleic acid templates were developed early on (MacDonald et al, 1968), (MacDonald and Gibbs], 1969).…”

Phase transitions in nonequilibrium systems

“…This is clearly a direct consequence of the fact that the dynamics is a nonequilibrium one. The model and many variants of it have been a subject of extensive studies in recent years [21][22][23][24][25][26][27][28][29][30].…”