Michaelis–Menten kinetics

Abstract: Nearly 100 years ago Michaelis and Menten published their now classic paper (Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333−369) in which they showed that the rate of an enzyme- catalyzed reaction is proportional to the concentration of the enzyme−substrate complex predicted by the Michaelis− Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information. Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather Vmax/Km, the specificity constant times the enzyme concentration (kcat/Km × E0).

Abstract: The kinetics of the activation of Glu-plasminogen and Lys-plasminogen (P) by a two-chain form of human tissue plasminogen activator (A) were studied in purified systems, and in the presence of fibrinogen (f) and of fibrin films (F) of increasing size and surface density. The activation in the purified systems followed Michaelis-Menten kinetics with a Michaelis constant of 65 p~ and a catalytic rate constant of 0.06 s-' for Glu-plasminogen as compared to 19 p~ and 0.2 s" for Lysplasminogen. In the presence of fibrinogen plots of l/u uersus 1/[P] or l/u uersus l/[fl yielded straight lines with an apparent Michaelis constant at infinite [fl of 28 PM and a catalytic rate constant of 0.3 s-' for Gluplasminogen as compared to 1.8 p~ and 0.3 s-' for Lysplasminogen. In the systems with fibrin, plasmin was estimated from the rate of release of '"I from "'I-labeled fibrin films. The initial rate of activation (u) was calculated and Lineweaver-Burk plots of l/u uersus 1/ [PI or l/u uersus l/[F] yielded straight lines. Activation occurred with an intrinsic Michaelis constant of 0.16 PM and a catalytic rate constant of 0.1 s-' for Gluplasminogen as compared to 0.02 PM and 0.2 s" for Lysplasminogen. The kinetic analysis suggested that the activation in the presence of fibrin occurs through binding of an activator molecule to the clot surface and subsequent addition of plasminogen (sequential ordered mechanism) to form a cyclic ternary complex. The low Michaelis constant in the presence of fibrin allows efficient plasminogen activation on a fibrin clot, while its high value in the absence of fibrin prevents efficient activation in plasma.

Abstract: Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual b-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.

Abstract: Oxidoreductases, such as glucose oxidase, can be electrically wired to electrodes by electrostatic complexing or by covalent binding of redox polymers so that the electrons flow from the enzyme, through the polymer, to the electrode. We describe two materials for amperometric biosensors based on a cross-linkable poly(vinylpyridine) complex of (Os-(bpy){sub 2}Cl){sup +/2+} that communicates electrically with flavin adenine dinucleiotide redox centers of enzymes such as glucose oxidase. The uncomplexed pyridines of the poly(vinylpyridine) are quaternized with two types of groups, one promoting hydrophilicity (2-bromoethanol or 3-bromopropionic acid), the other containing an active ester (N-hydroxysuccinimide) that forms amide bonds with both lysines on the enzyme surface and with an added polyamine cross-linking agent (tri-ethylenetetraamine, trien). In the presence of glucose oxidase and trien this polymer forms rugged, cross-linked, electroactive films on the surface of electrodes, thereby eliminating the requirement for a membrane for containing the enzyme and redox couple. The glucose response time of the resulting electrodes is less than 10 s. The glucose response under N{sub 2} shows an apparent Michaelis constant, K{sub m}{prime} = 7.3 mM, and limiting current densities, j{sub max}, between 100 and 800 {mu}A/cm{sup 2}. Currents are decreased by 30-50% in air-saturated solutions because of competitionmore » between O{sub 2} and the Os(III) complex for electrons from the reduced enzyme. Rotating ring disk experiments in air-saturated solutions containing 10 mM glucose show that about 20% of the active enzyme is electrooxidized via the Os(III) complex, while the rest is oxidized by O{sub 2}. These results suggest that only part of the active enzyme is in electrical contact with the electrode.« less