quasisteadystate

Quasi-steady state, often abbreviated as QSSA, is a concept used in chemical kinetics and related disciplines to describe a situation in which an intermediate species in a reaction network maintains a nearly constant concentration over the timescale of interest. In such cases, the rate of formation of the intermediate roughly balances its rate of consumption, so its concentration changes only slowly compared with other species in the system.

In enzyme kinetics, the quasi-steady-state approximation is a classical and widely cited application. For the reaction sequence E + S ⇌ ES → E + P, the intermediate complex ES is assumed to reach a quasi-steady state: d[ES]/dt ≈ 0. This leads to an expression for the ES concentration and, subsequently, to the Michaelis–Menten rate law: v = Vmax [S] / (Km + [S]), where Km = (k−1 + k2)/k1 and Vmax = k2[E0]. The QSSA thus provides a reduced description of a system with fast intermediate dynamics and a slower overall progression to product.

The approximation is not universal. It is most reliable when the enzyme concentration is small relative to the substrate, and the formation and conversion of the intermediate are faster than the overall reaction progress. There are variations, such as the rapid-equilibrium approximation (which assumes fast pre-equilibrium of E and S) and the total quasi-steady-state approximation (tQSSA), which extends the idea to more complex networks with multiple intermediates.

Beyond biochemistry, quasi-steady-state reasoning is employed in reaction engineering, atmospheric chemistry, and systems biology to simplify models that involve fast and slow timescales, enabling tractable analyses of large kinetic networks.