The 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).