Extension and Justification of Quasi-Steady-State Approximation for Reversible Bimolecular Binding

The quasi-steady-state approximation (QSSA) is commonly applied in chemical kinetics without rigorous justification. We provide details of such a justification in the ubiquitous case of reversible two-step bimolecular binding in which molecules as an intermediate step of the reaction form a transient complex. First, we justify QSSA in the regime that agrees with the results in the literature and is characterized by . Here, and are the initial concentrations of reacting receptor and ligand, respectively, and is the Michaelis constant. We also validate QSSA under an alternative condition that can be viewed as partially irreversible binding, and it does not require a tight bound on and but rather requires . Here, is the rate constant of decomposition of the transient complex to the ligand and the receptor, and and are the forward and the reverse rate constants of transformation of the complex to the product, respectively. Furthermore, we provide arguments that QSSA can also be accurate in a regime when and if . The derived conditions may be of practical use as they provide weaker requirements for the validity of QSSA compared to the existing results.