The 1-exp function as an alternative model of non-linear saturable kinetics

Non-linear saturation kinetics can be described through a potency function, a trigonometric function, a logarithmic function, a hyperbolic function, or an exponential function. Saturable enzyme reaction kinetics can be alternatively formulated as a 1-exp function without the limitations of a steady-state assumption (d[C]/dt = 0, where C is the enzyme-substrate complex). The time-dependent substrate conversion (-d[S]/dt = V(max) [1-exp(-Ka [S])]) depends on the maximum velocity (V(max)), the association constant (Ka) and substrate concentration [S]. In contrast to the classical Michaelis-Menten equation, the 1-exp function has an explicit solution for the substrate concentration [S] in an integrated form. [S] = (1/Ka) ln[1-exp(Ka [S]o)) exp(- Ka V(max) t)] A deceleration term must be introduced to describe enzyme reaction kinetics realistically. The 1-exp function with deceleration term can also be expanded to describe the three inhibition types of enzyme reaction kinetics.