SynopsisThe kinetics of biopolymerizat.ion on nucleic acid templates is discussed. The model introduced allows for the simultaneous synthesis of several chains, of a given type, on a common template, e.g., the polyribosome situation. Each growth center [growing chain end plus enzyme(s)] moves one template site at a time, but blocks L adjacent sites.Solutions are found for the probability nj(t) that a template has a growing center t.hat occupies the sites j -L + I, . . . , j a t time t. Two special sets of solutions are considered, the uniform-density solutions, for which nj(t) = n, and the more general steadystate solutions, for which dnj(t)/dt = 0. I n the uniform-density case, there is an upper bound to the rauge of rates of polymerization that can occur. Corresponding to this maximum rate, there is one uniform solution. For a polymerization rate less than this maximum, there are two uniform solutions that give the same rate. In the steady-state case, only 1 , = 1 is discussed. For a steady-state polymerization rate less than the maximum uniform-density rate, the steadystate solutions consist of either one or two regions of nearly uniform density, with the density value(s) assumed in the uniform region(s) being either or both of the uniform-density solutions corresponding to that polymerization rate. For a steady-state polymerization rate eqital to or slightly larger than the maximum uniform-density rate, the steady-state solutions are nearly uniform to the single uniform-density solution for the maximum rate. The boundary conditions (rate of initiation and rate of release of completed chains from the template) govern the choice among the possible solutions, i.e., determine the region(s) of uniformity and the valu4s) assumed in the uniform region(s).

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.

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