General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: Application to kinetics of opencomplex formation between E sigma(70) RNA polymerase and lambda P-R promoter DNA

A novel analytical method based on the exact solution of equations of kinet ics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of E sigma(70) RNA polymerase (R)-lambda P-R pro moter (P) open complex formation, which is described by the minimal three-s tep mechanism with two kinetically significant intermediates (I-1, I-2), [GRAPHICS] where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] much greater than [P]) to form long-lived complexes (RPo and I-2) and the kinetics of dissociatio n of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating ob served rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereb y provides a basis for interpreting the composite rate constants of associa tion (k(a)), isomerization (k(i)), and dissociation (k(d)) obtained from ex periment for this or any other sequential mechanism of any number of steps. in subsequent papers, we apply this formalism to analyze kinetic data obta ined in the reversible and irreversible binding regimes of E sigma(70) RNA polymerase (R)-lambda P-R promoter (P) open complex formation.