Quasi-steady-state approximation

When enzyme complexes relax much faster than substrate concentrations, the quasi-steady-state approximation sets the time derivatives of the fast complexes to zero and solves their algebraic balance equations.

It approximates the fast intermediate by a steady state balance without requiring the entire chemical system to be at equilibrium.

A quasi-steady-state approximation for enzyme-substrate complexes can remain useful when total enzyme and initial substrate concentrations are comparable. The relevant parameter can involve the sum $s_0+K_m$, rather than $s_0$ alone. In a mechanism-based inhibition model with $s_0/K_m=O(\epsilon )$, bounded intermediate decay rates and an inactivation rate of order $\epsilon$, the fast complexes adjust in a layer of scaled width $O(\epsilon )$. On bounded slow-time intervals the main complex follows the substrate, the later complex and accumulated inactivated enzyme remain $O(\epsilon )$, and the substrate has leading exponential depletion. An outer algebraic complex concentration does not satisfy the unbound initial condition inside that initial layer.

For sequential binding with dimensionless parameters $\alpha ,\beta ,\gamma$, the reduced product rate has the formIt is quadratic at low substrate concentration and saturates at high concentration.