Michaelis-Menten kinetics at high enzyme concentrations

The total quasi-steady state approximation (tQSSA) for the irreversible Michaelis-Menten scheme is derived in a consistent manner. It is found that self-consistency of the initial transient guarantees the uniform validity of the tQSSA, but does not guarantee the validity of the linearization in the original derivation of Borghans et al. (1996, Bull. Math. Biol., 58, 43–63). Moreover, the present rederivation yielded the noteworthy result that the tQSSA is at least roughly valid for any substrate and enzyme concentrations. This reinforces and extends the original assertion that the parameter domain for which the tQSSA is valid overlaps the domain of validity of the standard quasi-steady state approximation and includes the limit of high enzyme concentrations. The criteria for the uniform validity of the original (linearized) tQSSA are corrected, and are used to derive approximate solutions that are uniformly valid in time. These approximations overlap and extend the domains of validity of the standard and reverse quasi-steady state approximations.

[1]  G. Briggs,et al.  A Note on the Kinetics of Enzyme Action. , 1925, The Biochemical journal.

[2]  P. Maini,et al.  Enzyme kinetics at high enzyme concentration , 2000, Bulletin of mathematical biology.

[3]  S. Schnell,et al.  Closed Form Solution for Time-dependent Enzyme Kinetics , 1997 .

[4]  L. Segel,et al.  Extending the quasi-steady state approximation by changing variables. , 1996, Bulletin of mathematical biology.

[5]  L. A. Segel,et al.  The Quasi-Steady-State Assumption: A Case Study in Perturbation , 1989, SIAM Rev..

[6]  D. V. Slyke,et al.  THE MODE OF ACTION OF UREASE AND OF ENZYMES IN GENERAL , 1914 .

[7]  Lee A. Segel,et al.  Mathematics applied to deterministic problems in the natural sciences , 1974, Classics in applied mathematics.

[8]  H. Rabitz,et al.  Determination of approximate lumping schemes by a singular perturbation method , 1993 .

[9]  L. Segel,et al.  On the validity of the steady state assumption of enzyme kinetics. , 1988, Bulletin of mathematical biology.

[10]  Philip K. Maini,et al.  Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations , 2002 .

[11]  D. E. Atkinson.  Cellular Energy Metabolism and its Regulation , 1977 .

[12]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[13]  H. Gutfreund,et al.  Steps in the reactions of chymotrypsin with tyrosine derivatives. , 1959, Biochemical Journal.

[14]  Hanna Parnas,et al.  Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices. , 2002, Biophysical journal.

[15]  William C. Davidon,et al.  Mathematical Models in Physical Sciences , 1964 .

[16]  A. Sols,et al.  Concentrations of Metabolites and Binding Sites. Implications in Metabolic Regulation , 1970 .

[17]  On kinetic behavior at high enzyme concentrations , 1973 .