3D Kinetics, an Upgrade to the Classical Michaelis‐Menten Method

Abstract

Most of the kinetic data published nowadays are derived from different extensions of what Michaelis and Menten introduced to this field more than hundred years ago. The key assumption to Michaelis‐Menten kinetics is the steady state approximation where the change in the concentration of any enzyme‐substrate intermediate complex is assumed to be zero. This assumption has two underlying requirements with the first one being [S]≫[E] and the second being the limitation of the reaction time to the short initial linear region of the progress curve. The historical need for the steady state assumption was to simplify data treatment to such a degree that the analytical mathematics could be done without need for an abundance of computing power. However, with the computation power at our disposal today, none of the limiting assumptions are necessary anymore especially considering that many of these assumptions rarely hold true. The time course of aldehyde oxidase with one of it substrates, O6‐benzylguanine, is provided here as an example of the statement above. In addition to the obvious instant curvature in the time course plot which makes it difficult to identify the precise linear region, the simulation done on the ES complex based on the data further proves how the steady state approximation is a poor assumption to make especially during the shorter “linear” region of the progress curve as this region is the one in which the concentration of ES is changing the most (Figure 1). The easiest way to approach kinetic data today is to parameterize realistically complex kinetic reaction mechanisms through 3D kinetics. 3D numerical modeling uses the data derived from experiments that monitor the product formation as a function of both incubation time and substrate concentration. With this approach, scientists would be able to derive both the traditional Km and Vmax values as well as the micro‐rate constants related to each step of the enzymatic reaction (Figure 2).Support or Funding InformationThis work was supported by the National Institutes of Health grant: GM100874A‐1) Numerical fitting of product formation with two different models (A‐2 and A‐3) shows that Michaelis Menten (dashed line) does not fit the data well over longer period of time. B) Simulation of the ES complex through the A‐3 model shows a significant change in this species’s concentration over the initial period of the time course where it is assumed to be a constant in deriving the Michaelis‐Menten equation.Figure 1A) Numerical fitting of the product formation over time of different initial substrate concentrations with the kinetic model provided on the right side of the graph to solve for the micro‐rate constants k3‐k5. B) Classical kinetic parameters such as Km and Vmax can be obtained from the same data set by plotting the rate versus substrate concentration for each time point.Figure 2