Michaelis’ theory

D. A. Micha. Theory of Chemical Reaction Dynamics, Vol. II, chapter Rearrangement in molecular collisions A many-body approach, page 181. CRC Press, Boca Raton, Florida, 1985. 

Chance (78) has discussed this experimental data in terms of the extended Michaelis theory which accounts for the similar peroxidatic action of peroxidase, the only difference being that with peroxidase the main reaction can proceed via the secondary complexes, whereas with catalase these complexes are inactive and the main reaction proceeds via the primary complexes. Representing the primary complexes by FeOOH and FeOOR he suggests the various reactions are ... 

Catalase and peroxidase do not follow the simple Michaelis theory and the theory is extended (7) to take into account the reaction of the enzyme-substrate complex and a hydrogen or electron donor (AH ) ... 

Chance (16a) recently demonstrated the formation of an intermediate compound of catalases and hydrogen peroxide. The compound had many properties in common with the intermediate compound of hydrogen peroxide and peroxidase. The spectrum could be determined in the region of the Soret band showing a small shift of the band toward the red. The rate of formation of this compound was 3 X lO liter mole sec, exceeding the value required by the Michaelis theory for catalase activity. Without the addition of acceptor the compound decomposed slowly at about the same rate as the peroxidase-peroxide compound. The catalase activity increases the equilibrium constant to 1 X 10 mole liter h The inter-... 

Lenore Michaelis and Maud L. Menten proposed a general theory of enzyme action in 1913 consistent with observed enzyme kinetics. Their theory was based on the assumption that the enzyme, E, and its substrate, S, associate reversibly to form an enzyme-substrate complex, ES ... 

David A. Micha Quantum Theory Project University of Florida Gainesville, Florida 32611-8435, USA... 

David A. Micha (317), Quantum Theory Project, University of Florida, Gainesville, Florida 32611... 

Enzyme-Catalyzed Batch Reactions. Michaelis-Menten theory assumes equih-brium between occupied and unoccupied sites ... 

The Michaelis-Menten theory assumes that k-2 is sufficiently small that the second step in the process does not affect the equilibrium formation of the ES complex [61]. At steady state the rates of formation and breakdown of ES are equal ... 

The general theory of enzyme kinetics is based on the work of L. Michaelis and M. L. Menten, later extended by G. E. Briggs and J. B. S. Haldane.la The basic reactions (E = enzyme, S = substrate, P = product) are shown in equation 2.1 ... 

Km is the Michaelis constant. In some cases such as hydrolases or lactic dehydrogenases (T2), the velocity may fall again with higher substrate concentrations, so that there is an optimum substrate concentration which approximates the theoretical value V, the maximal velocity, following the theory of Michaelis and Menten... 

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

The search for models of biological membranes among porous membranes continued in the twenties and thirties. Here, Michaelis [67] and Sollner (for a summary of his work, see [90] for development in the field, [89]) should be mentioned. The existence and characteristics of Donnan membrane equilibria could be confirmed using this type of membrane [20]. The theory of porous membranes with fixed charges of a certain sign was developed by Teorell [93], and Meyer and Sievers [65]. 

MICHAELIS-MENTEN KINETICS PREEXPONENTIAL FACTOR ARRHENIUS EQUATION COLLISION THEORY TRANSITION-STATE THEORY ENTROPY OF ACTIVATION PRENYL-PROTEIN-SPECIFIC ENDOPEP-TIDASE... 

A key point should be to identify the rate-limiting step of the polymerization. Several studies indicate that the formation of the activated open monomer is the rate-limiting step. The kinetics of polymerization obey the usual Michaelis-Menten equation. Nevertheless, all experimental data cannot be accounted for by this theory. Other studies suggest that the nature of the rate-limiting step depends upon the structure of the lactone. Indeed, the reaction of nucleophilic hydroxyl-functionalized compounds with activated opened monomers can become the rate-limiting step, especially if stericaUy hindered nucleophilic species are involved. 

Ac, acetyl AONs, antisense oligonucleotides B, boat Bn, benzyl Bz, benzoyl C, chair CD, circular dichroism CO, carbon monoxide ConA, concanavalin A DAST, diethylaminosulfur trifluoride DFT, density functional theory DMDO, dimethyldiox-irane DMT, dimethoxytriphenylmethyl DNA, deoxyribonucleic acid dsDNA, double-stranded DNA E, envelope Fmoc, fluorenylmethyloxycarbonyl GlcNAc, /V-acetylglucosamine ITC, isothermal titration calorimetry kcat, catalytic rate constant Aa, association constant K, inhibition constant KM, Michaelis constant LiSPh, lithium thiophenolate LPS, lipopolysaccharide pM, micromolar MMT,... 

If enzymes are described under tbe aspect of reaction mechanisms, the maximal rate of turnover Vmax. the Michaelis and Menten constant Km, the half maximal inhibitory concentration ICso, and tbe specific enzyme activity are keys of characterization of the biocatalyst. Even though enzymes are not catalysts in a strong chemical sense, because they often undergo an alteration of structure or chemical composition during a reaction cycle, theory of enzyme kinetics follows the theory of chemical catalysis. 

The basic kinetic model for enzyme catalysed conversions in water and in w/o-microemulsions is based on the theory of MichaeHs and Menten [83]. Although the Michaelis-Menten-model is often sufficient to describe the kinetics, the bi-bi-models (e. g. random bi-bi, orderedbi-bi or ping-pongbi-bi), which describe the sequences of substrate bindings to the enzyme are the more accurate kinetic models [84]. 

The ES complex is the key to understanding this kinetic behavior, just as it was a starting point for our discussion of catalysis. The kinetic pattern in Figure 6-11 led Victor Henri, following the lead of Wurtz, to propose in 1903 that the combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis. This idea was expanded into a general theory of enzyme action, particularly by Leonor Michaelis and Maud Menten in 1913. They postulated that the enzyme first combines reversibly with... 

The simple theory outlined above has to be modified to account for the pH dependence of the catalytic parameters in mechanisms more complicated than the basic Michaelis-Menten. 

In 1913, L. Michaelis and M. L. Menten developed the theories of earlier workers and proposed the following scheme ... 

The theory predicts that unless there is a change of rate-determining step with pH, the pH dependence of kcJKM for all non-ionizing substrates should give the same pKa that for the free enzyme. With one exception, this is found (Table 5.2). At 25°C and ionic strength 0.1 M, the pKa of the active site is 6.80 0.03. The most accurate data available fit very precisely the theoretical ionization curves between pH 5 and 8, after allowance has been made for the fraction of the enzyme in the inactive conformation. The relationship holds for amides with which no intermediate accumulates and the Michaelis-Menten mechanism holds, and also for esters with which the acylenzyme accumulates. 

Michaelis and Menten developed a kinetic theory of enzyme action. 

D. A. Micha. Dynamics of Molecular Collisions, Vol. IA, chapter Optical models in molecular collision theory, page 81. Plenum Press, New York, 1976. 

D A Micha. Quantum theory of reactive molecular collisions. Adv. Chem. Phys., 30 7, 1975. 

D. A. Micha. Density matrix theory and computational aspects of quantum dynamics in an active medium. Intern. J. Quantum Chem., 80 394, 2000. 

Z. Yi, D. A. Micha, and J. Sund. Density matrix theory and calculations of nonlinear yields of CO photodesorbed from Cu(001) by light pulses. J. Chem. Phys., 110 10562, 1999. 

---