The parameter domain for which the quasi-steady state assumption is valid can be considerably extended merely by a simple change of variable. This is demonstrated for a variety of biologically significant examples taken from enzyme kinetics, immunology and ecology.

A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved.

The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other class...

Progress curves of enzyme-catalysed reactions are described by equations of a type that precludes direct calculation of the extent of reaction at any time. Previously, such equations have been solved by the Newton-Raphson method, but this procedure may fail when based upon the usual formulae. An alternative formulation is proposed that is both quicker and more robust.

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate...

The Fano factor, an observable quantifying fluctuations of product generation by a single enzyme, can reveal information about the underlying reaction scheme. A lower bound on this Fano factor that depends on the thermodynamic affinity driving the transformation from substrate to product constrains the number of intermediate states of an enzymatic cycle. So far, this bound has been proven only ...

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion ...

Molecular recognition is a central issue for nearly every biological mechanism. The analysis of molecular recognition to date has been conducted within the framework of classical chemical kinetics, in which the kinetic orders of a reaction have positive integer values. However, recent theoretical and experimental advances have shown that the assumptions inherent in this classical framework are ...