Qssa

Quasi-Steady-State Approximation (QSSA) is a method in chemical kinetics and systems biology used to simplify reaction networks by assuming that certain reactive intermediates rapidly reach a steady state.

Origin: The concept emerged in the early 20th century in work by Briggs and Haldane on enzyme kinetics.

In a simple enzyme-catalyzed reaction E + S ⇌ ES → E + P, the rate equations yield d[ES]/dt = k1[E][S] - (k-1 + k2)[ES]. Under QSSA, d[ES]/dt ≈ 0, giving [ES] = (E0 [S])/(Km + [S]), with Km = (k-1 + k2)/k1 and E0 = [E] + [ES]. The product formation rate is v = d[P]/dt = k2[ES] = Vmax[S]/(Km + [S]), where Vmax = k2 E0. QSSA relies on separation of timescales: the ES complex forms and dissipates faster than product accumulation.

Variants include the standard (sQSSA) and the total (tQSSA) formulations; the latter uses total enzyme concentration to express all species and is more robust when enzyme and substrate are of comparable magnitudes.

Limitations: not valid if substrate concentration is comparable to enzyme concentration, in cases with slow ES relaxation, or when feedback and allosteric effects invalidate the steady-state assumption; also less accurate for multi-substrate or networked reactions without clear timescale separation.

Applications: enzyme kinetics analysis, metabolic pathway modeling, and systems biology; used to derive Michaelis-Menten type rate laws and to reduce complex reaction networks for simulation.