CBS Computational Biology Services

Cornish-Bowden, A. and Hofmeyr, J.-H. (2005) Kinetic characterization of enzymes for systems biology. The Biochemist, 27, 11-14.

With the rapid growth of the use of computational models, there is a need for quantitative data regarding the biochemical reactions occurring in the living cell. Nearly all of the kinetic information that is available was obtained in a test tube under conditions that are far from those occurring in the living cell. Although, the experimental paradigm of studying an isolated enzyme in a test tube was very useful to address mechanisms of enzyme action, including allosteric and cooperative behaviors, this approach misses much of the kinetics occurring in the living system. One serious problem is that for reasons of simplification studies are carried out in absence of products, i.e., under conditions of irreversibility. This is so because kinetic equations for reversible reactions are much more complicated than for irreversible reactions, and the number of parameters that needs to be determined increases a lot. Of course, in vivo reactions occur under reversible conditions. Presently, there are only a few enzymes for which reversible kinetics is known, and usually this is obtained in absence of regulatory metabolites. True, inhibitors and activators are studied but only one at a time, while in vivo they maybe present all simultaneously.

Cornish-Bowden and Hofmeyr propose an alternative concept for enzyme kinetics in the context of mathematical modelling: kinetics should be measured under reversible conditions, but the knowledge of exact kinetics is not required, instead only a good approximation around a steady-state in vivo is necessary. In other words, an exact kinetic equation that gives exact rates for all range of substrate and product concentrations is replaced by a simplified equation that gives approximate rates that are adequate in the range of concentrations that are physiological relevant, i.e., in the neighborhood of the in vivo steady-state. For example, for an irreversible reaction obeying a compulsory-order ternary-complex mechanism the exact reversible equation is:

where

This equation can be replaced by the approximate form:

Note that, for example K_A, K_B, K_Q, K_P are not true Michaelis-Menten constants because they are not determined at saturating concentrations, but instead they are determined at concentrations chosen to be representative of the in vivo steady-state. A similar strategy for modeling of biochemical systems is at the core of the development of Biochemical Systems Theory, by Mike Savageau. In the Generalized Mass Action approach (GMA), all kinetic steps are simply approximated by a generalized mass action law, and under this approach equation (1) would be simply approximated by:

in which the kinetic parameters would be determined in the neighborhood of the steady-state of interest. Of course, the higher the number of parameters the better the approximation.

On a positive note about mathematical modeling, Cornish-Bowden and Hofmeyr rightly point that in a model not all parameters are equally important, and actually the sensitivity of the behavior of the model to errors in the estimations of many parameters is low.