The 1-exp Function as an Alternative Model of Non-Linear Saturable Kinetics

Abstract

Summary: 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]/df = K max {1 -exp(-AT a [S])}) depends on the maximum velocity (F max ), the association constant (K a ) 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.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.

Fluorescent peptomer substrates for differential degradation by metalloproteases

“…When substrate concentration is well below K M (a condition verified to be true at 0.5 μM) the catalytic reaction is effectively first-order in rate, providing an estimation of the proportion of k cat to K M . 55,56…”

“…Progress curves were fit to the following equation: where P is the concentration of product (cleaved substrate), S 0 is initial substrate concentration, and k obs is the exponential fitting parameter. 55 At low substrate concentrations ([S]<<K M ), when the Michaelis-Menten equation is in the first-order reaction phase k obs is proportional to the catalytic efficiency as follows: where E 0 is enzyme concentration (determined by active site titration), k cat is the turnover number, K M is the Michaelis constant, and the ratio of k cat to K M is catalytic efficiency. 56 Progress curves at 10 μM and 0.5 μM were both used for parameter estimations in the R code.…”

“…where P is the concentration of product (cleaved substrate), S0 is initial substrate concentration, and kobs is the exponential fitting parameter. 55 At low substrate concentrations ([S]<<KM), when the Michaelis-Menten equation is in the first-order reaction phase kobs is proportional to the catalytic efficiency as follows:…”

“…When substrate concentration is well below KM (a condition verified to be true at 0.5 µM) the catalytic reaction is effectively first-order in rate, providing an estimation of the proportion of kcat to KM. 55,56 Table 1: Kinetic parameter estimates for MMP-2. Kinetic parameters calculated using the tQSSM and the low substrate concentration approximation for catalytic efficiency.…”

Exposure-response modeling improves selection of radiation and radiosensitizer combinations

“…Since TD 50 is a typical measure of radiation sensitivity, we propose to let the radiosensitizer modulate this parameter and thereby increase the risk of complications. Assuming an exponential sigmoidal modulation function gives a new definition of t , where I ( C ) is an exponential inhibitory function with parameter k s [ 34 ]: …”