Michaelis process

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

Baird, D.G. and Collias, D.I. Polymer Processing, Butterwoith-Heinemann, Newton, USA (1995). Michaeli, W. Polymer Processing, Hanser, Munich (1992). 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

This form is worthwhile to note, in that many catalytic processes utilize dual substrates. The equation contains an apparent Michaelis constant, given by... 

Atlanta, Ga., 26th-30th April 1998, p.2942-5. 012 FEEDSTOCK RECYCLING OF POLYMETHYL METHACRYLATE (PMMA) BY DEPOLYMERISING IN A REACTIVE EXTRUSION PROCESS Breyer K Michaeli W IKV (SPE)... 

The functioning of enzymes produces phenomena driving the processes which impart life to an organic system. The principal source of information about an enzyme-catalyzed reaction has been from analyses of the changes produced in concentrations of substrates and products. These observations have led to the construction of models invoking intermediate complexes of ingredients with the enzyme. One example is the Michaelis-Menten model, postulating an... 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

It has been demonstrated spectroscopically that Ce(IV) - and V(V) perchlorates and Ce(IV) nitrate form complexes with alcohols of composition [ROH Ce(IV)] and [ROH V(OH)3]. The agreement between the determined formation constant and the Michaelis-Menten constant for Ce(IV) oxidation is good evidence for the role of these complexes in the oxidation process. The oxidations by Co(iri) and V(V) perchlorates have kinetics... 

On the other hand, the macrolides showed unusual enzymatic reactivity. Lipase PF-catalyzed polymerization of the macrolides proceeded much faster than that of 8-CL. The lipase-catalyzed polymerizability of lactones was quantitatively evaluated by Michaelis-Menten kinetics. For all monomers, linearity was observed in the Hanes-Woolf plot, indicating that the polymerization followed Michaehs-Menten kinetics. The V, (iaotone) and K,ax(iaotone)/ m(iaotone) values increased with the ring size of lactone, whereas the A (iactone) values scarcely changed. These data imply that the enzymatic polymerizability increased as a function of the ring size, and the large enzymatic polymerizability is governed mainly by the reachon rate hut not to the binding abilities, i.e., the reaction process of... 

Michaelis and Henglein [131] investigated formation process of Pd-core/Ag-shell bimetallic nanoparticles by UV-Vis spectroscopy. As shown in Figure 10, the Pd/Ag bimetallic nanoparticles possess a surface plasmon absorption band close to 360 nm when more than 10 monolayers of Ag are deposited. The plasmon absorption band, however, is located at shorter wavelength when the shell thickness is less than 10 monolayers, while the band disappears when the thickness of the shell is below about three-atomic layers. 

An additional problem arises when the exchange processes are rate-limited. This may be caused by enzymes that become saturated when all their active sites are occupied by the drug, or it may be due to adsorbing proteins that have a limited binding capacity. In such cases, one obtains a type of Michaelis-Menten kinetics of the form ... 

We now consider the case of a competitive inhibitor which has been added to the above reaction at the fixed concentration of 40 mM [15]. The following initial velocities of the competitively inhibited Michaelis-Menten process are observed at the same substrate concentrations as above ... 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

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 sol-gel-entrapped microbial cells have shown excellent tolerance to different alcohols [99], The immobilized E. coli cells followed the Michaelis-Menten equation when quantified with the (3-glucosidase activity via the hydrolysis of 4-nitrophenyl-(3-D-galactopyranosdie [142], The sol-gel matrices doped with gelatin prevented the cell lysis, which usually occurs during the initial gelation process [143], Microorganisms are now widely used in the biosorption of different pollutants and toxicants. Bacillus sphaericus JG-A12 isolated from uranium mining water has been entrapped in aqueous silica nanosol for the accumulation of copper and uranium [144], Premkumar et al. [145] immobilized recombinant luminous bacteria into TEOS sol-gel to study the effect of sol-gel conditions on the cell response (luminescence). The entrapped and free cells showed almost the same intensity of luminescence (little lower), but the entrapped cells were more stable than the free cells (4 weeks at 4°C). This kind of stable cell could be employed in biosensors in the near future. 

Additional advances have been made in the use of leaving groups other than halide for the nonphosphorus component of the Michaelis-Arbuzov reaction. The sensitive species 3,5-d i-t-b u ty I -4-hydroxybenzyl acetate has been noted to undergo efficient reaction (75-85% isolated yields) with a series of trialkyl phosphites upon heating at relatively low temperature (95°C) without the use of excess phosphite or additional catalyst.138 Chromatographic analysis of the reaction mixture indicates virtually quantitative conversion in the process. 

For example, in the instance of 9-chloroacridine, the attachment of the halogen (leaving group) at a suitably electrophilic carbon site allows the occurrence of a replacement reaction, presumably occurring via an addition-elimination procedure for phosphorus attachment, followed by the common nucleophilic displacement (ester cleavage) of the Michaelis-Arbuzov process (Figure 6.1).4... 

The use of transition metals for the facilitation of substitution reactions on vinylic carbon has proven to be quite successful. For example, vinylic chlorides in the presence of nickel(II) chloride react with trialkyl phosphites to substitute phosphorus for the halide (Figure 6.17j.71-72 While reminiscent of a direct Michaelis-Arbuzov reaction, including final dealkylation by a chloride ion, the reaction actually involves an addition-elimination process. It appears that chloride provides a more facile reaction than bromide, a characteristic noted in several reaction systems. 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

In the steady-state approach (equations (35) and (36)), no attempt is made to isolate the adsorption step from the internalisation of solutes. In this case, a Langmuir adsorption via membrane carriers is coupled to an irreversible and rate-limiting internalisation of the solute carrier complex [186], The process can be described by the Michaelis-Menten equation ... 

As discussed in Section 5.1, for saturable uptake of a trace metal, the steady-state process is most commonly described by Michaelis-Menten uptake kinetics [265] ... 

It is perhaps wise to begin by questioning the conceptual simplicity of the uptake process as described by equation (35) and the assumptions given in Section 6.1.2. As discussed above, the Michaelis constant, Km, is determined by steady-state methods and represents a complex function of many rate constants [114,186,281]. For example, in the presence of a diffusion boundary layer, the apparent Michaelis-Menten constant will be too large, due to the depletion of metal near the reactive surface [9,282,283], In this case, a modified flux equation, taking into account a diffusion boundary layer and a first-order carrier-mediated uptake can be taken into account by the Best equation [9] (see Chapter 4 for a discussion of the limitations) or by other similar derivations [282] ... 

---