Michaelis-Menten theory

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 ... 

Naidja, A., and Huang, P. M. (2002). Significance of the Henri-Michaelis-Menten theory in abiotic catalysis catechol oxidation by 8-Mn02. Surface Sci. 506, L243-L249. 

In order to understand why the malt a-amylase acts so slowly on a normal hexaose (Fraction PDXII) we have tried to apply the Michaelis-Menten theory and have determined the affinity constants of the enzyme-substrate compounds. If the concentration of starch and dextrin are expressed as moles of maltose per liter we find the affinity constant, K, between malt a-amylase and starch to be about 200 and for /3-amylase about 170. The affinity constant a-amylase to a-dextrin is so small that no values could be obtained. The constant certainly is smaller than 12. Thus, it is clear that the slow action of the malt a-amylase on the dextrin is due to a very low affinity of the enzyme to the substrate. In other words, the enzyme can readily attach itself to a long chain, but only with difficulty to chains shorter than a certain value. In the dextrinization period of the action of the enzyme on starch, a mixture of a-dextrins is produced with an average chain length of about 7 units. It can be assumed, therefore, that the enzyme readily attaches itself to chains that contain more than about 8 units provided that the chains are normal and contain no branchings or other anomalies. When anomalies occur these... 

According to the Michaelis-Menten theory, which is a widely accepted mechanism of an enzyme action, a substrate, S, is converted by an enzyme, E, to a product, P, through a reversible first step that leads to an intermediate enzyme-substrate complex, ES [3,4]. In other words, as shown in... 

These views, and the research on which they were based, were part of the mainstream of organic chemistry. The nature of enzyme action was also by this time an important topic for research in its own right. The developments which eventually led to the Michaelis-Menten theory were ones in which Adrian Brown, his elder brother Horace, and others from the group at Burton-on-Trent all played a major part (Boyde, 1980 Teich and Needham, 1992). Curiously, in their publications, the word catalysis itself is conspicuous by its absence. 

This might be considered the general equation for the kinetics of hydrolytic enzymes behaving according to the Michaelis-Menten theory. The total enzyme concentration, [Eo], has, for the purpose of this discussion, been kept constant. 

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. 

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 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. 

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. 

Substitution of Equation 4.8 into Equation 4.1 gives a new equation (Equation 4.9). According to Equation 4.1, the rate of the reaction increases with rising [ES], In theory, [ES] reaches a maximum when all enzyme molecules are bound with substrate, meaning [ES] equals [E(], If [ES] equals [Et], V will achieve V max (Equation 4.10). Combining Equations 4.9 and 4.10 affords Equation 4.11, the Michaelis-Menten equation. 

Receptor theories strive to explain how the various types of ligands give rise to a response. The variety of receptors and the signaling pathways to which they are linked pose a significant challenge to receptor theory. Receptor response pathways are far more complex than the activity of enzymes, and therefore the modeling of receptors is more complex than the Michaelis-Menten model seen in Chapter 4. 

At the start of this section, we derived Equation 5.8 to model dose-response relationships. This equation is elegantly simple and essentially identical to the Michaelis-Menten equation from our studies on enzymes. Receptors, however, are more diverse and more complicated than enzymes. Clark s straightforward equation models few receptors accurately, and Stephenson s equation (5.18) has emerged as the best available description of occupancy theory. While Stephenson s additions may result in a more accurate model, the simplicity of Clark s original theory remains attractive. Many receptor studies still rely on Clark s model and work around its deficiencies as best as possible. 

Payens (1976, 1977) realized that in order to derive an expression for the clotting time of milk, a kinetic description of the enzyme reaction must be combined with the kinetics of aggregation of destabilized colloidal particles. In early versions of his theory, the enzymatic reaction was described by Michaelis—Menten kinetics with the... 

Students should be able to describe the theory of Michaelis-Menten before entering the lab. 

Pharmacokinetic studies are in general less variable than pharmacodynamic studies. This is so since simpler dynamics are associated with pharmacokinetic processes. According to van Rossum and de Bie [234], the phase space of a pharmacokinetic system is dominated by a point attractor since the drug leaves the body, i.e., the plasma drug concentration tends to zero. Even when the system is as simple as that, tools from dynamic systems theory are still useful. When a system has only one variable a plot referred to as a phase plane can be used to study its behavior. The phase plane is constructed by plotting the variable against its derivative. The most classical, quoted even in textbooks, phase plane is the c (f) vs. c (t) plot of the ubiquitous Michaelis-Menten kinetics. In the pharmaceutical literature the phase plane plot has been used by Dokoumetzidis and Macheras [235] for the discernment of absorption kinetics, Figure 6.21. The same type of plot has been used for the estimation of the elimination rate constant [236]. 

Henderson-Hasselbalch equation lahn-Teller effect Lee-Yang-Parr method Lineweaver-Burk method Mark-Houwink plot Meerwein-Ponndorf theory Michaelis-Menten kinetics Stem-Volmer plot van t Hoff-Le Bel theory Wolff-Kishner theory Young-Laplace equation Ziegler-Natta-type catalyst... 

Promotion action of additives on biological growth in considered kinetic theory is taken into account by introduction into equation (22) in an explicit form of dependence of coefficients of birth b and chain propagation p on promoter concentration. This dependence may be approximated by equation of Mono type for organisms or Michaelis-Menten for fermentative catalysis. Equation (22) for x1=x2= k wi= 0 and f=2 is solved in relation to Ci(t). Theoretical curves qualitatively correctly (Figure 6) reflects acceleration of growth of cells of mouse embryo Balb/c 3T3 [22] with increase of serum concentration containing stimulators. 

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

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