In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in...

F(1)-ATPase catalyses ATP hydrolysis and converts the cellular chemical energy into mechanical rotation. The hydrolysis reaction in F(1)-ATPase does not follow the widely believed Michaelis-Menten mechanism. Instead, the hydrolysis mechanism behaves in an ATP-dependent manner. We develop a model for enzyme kinetics and hydrolysis cooperativity of F(1)-ATPase which involves the binding-state cha...

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and en...

We studied fluctuations in the displacement of silica beads driven by single molecules of the motor protein kinesin, moving under low mechanical loads at saturating ATP concentrations. The variance in position was significantly smaller than expected for the case of stepwise movement along a regular lattice of positions with exponentially distributed intervals. The small variance suggests that t...

In a recent paper the authors hypothesized that the so called fractal-like enzyme kinetics of intracellular reactions may explain the preconditioning effect in biology (Vasilescu C, Olteanu M, Flondor P, Revue Roumaine de Chimie. 2011; 56(7): 751-7). Inside cells the reaction kinetics is very well described by fractal-like kinetics. In the present work some clinical implications of this model a...

This laboratory seeks to quantitatively determine glucose concentration in common beverages. The method employed is enzyme catalyzed oxidation of glucose, quantified by chronoamperometry. With an inexpensive patterned electrode and low cost glucose oxidase enzyme, an electrochemical sensor is constructed to selectively measure glucose in complicated beverages which can present as analytically c...

Multi-site enzymes, defined as where multiple substrate molecules can bind simultaneously to the same enzyme molecule, play a key role in a number of biological networks, with the Escherichia coli protease ClpXP a well-studied example. These enzymes can form a low latency 'waiting line' of substrate to the enzyme's catalytic core, such that the enzyme molecule can continue to collect substrate ...

This paper continues an earlier one [Hill, T.L. (1977) Proc. Natl . Acad. Sci. USA 74, 3632-3632] and presents further introductory examples. Most attention is devoted to a closed linear chain of two-state enzyme molecules with nearest-neighbor interactions. The one-dimensional Ising theory can be used here. The Bragg-Williams (mean field) approximation is introduced to deal with a one-, two-, ...

1. The kinetics of the reversible combination of one enzyme center with one molecule of a substrate or inhibitor is treated as a true bimolecular instead of a pseudomonomolecular reaction. The general equations describing such a reaction are presented and analyzed algebraically and graphically. 2. A new term, "specific concentration," is introduced to denote the concentration of reactants in un...

The concept of modulating enzymatic activity by exerting a mechanical stress on the enzyme has been established in previous work. Mechanical perturbation is also a tool for probing conformational motion accompanying the enzymatic cycle. Here we report measurements of the forward and reverse kinetics of the enzyme Guanylate Kinase from yeast (Saccharomyces cerevisiae). The enzyme is held in a st...