General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: Application to kinetics of open complex formation between Eσ⁷⁰ RNA polymerase and λP(R) promoter DNA

A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Eσ⁷⁰ RNA polymerase (R)-λP(R) promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I₁, I₂), where the final product is an open complex RP(o). The kinetics of reversible and irreversible association (pseudofirst order, [R] >> [P]) to form long-lived complexes (RP(o) and I₂) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (k(a)), isomerization (k(i)), and dissociation (k(d)) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Eσ₇₀ RNA polymerase (R)- λP(R) promoter (P) open complex formation.