Protein . nucleic-acid reaction kinetics. Theoretical analysis of the binding reaction between DNA and RNA polymerase

This paper presents methods developed in order to analyze experimental results concerning the binding of Escherichia coli DNA-dependent RNA polymerase to DNA at high and at low DNA concentrations, using the filter retention assay. The basis hypotheses, under which the mathematical expressions for describing the kinetics of binding are derived, are as follows. (a) At low DNA concentration: equivalence and independence of the specific binding sites; first-order dependence of the binding reaction on both DNA and protein concentration. (b) At high DNA concentration: equivalence and independence of the non-specific binding sites; no direct transfer or one-dimensional sliding of the protein along the DNA. Comparison between theoretical predictions and experimental results at high DNA concentration will allow one to determine the relative value of the rates of binding of RNA polymerase to different promoters (between 1 and 2 in T5 DNA). Binding experiments performed at low DNA concentration are reported in this paper: these results and the analysis which is reported allow one to determine the value of the rate constant of formation of non-filterable complexes for the system fd DNA (replicative form) . RNA-polymerase (kappa a = 3.3 X 10(8) M-1 s-1 in 0.1 M NaCl, 0.01 M MgCl2).