Michaelis enzymatic analysis

The Henri-Michaelis-Menten Treatment Assumes That the Enzyme-Substrate Complex Is in Equilibrium with Free Enzyme and Substrate Steady-State Kinetic Analysis Assumes That the Concentration of the Enzyme-Substrate Complex Remains Nearly Constant Kinetics of Enzymatic Reactions Involving Two Substrates... 

The hyperbolic saturation curve that is commonly seen with enzymatic reactions led Leonor Michaelis and Maude Men-ten in 1913 to develop a general treatment for kinetic analysis of these reactions. Following earlier work by Victor Henri, Michaelis and Menten assumed that an enzyme-substrate complex (ES) is in equilibrium with free enzyme... 

Reliable enzymatic assays for SeMet are not available as specific SeMet metabolizing enzymes have not been identified and enzymes such as glutamine transaminase react with Met equally as well as with SeMet (Blazon et al., 1994). However, with some enzymes reaction rates for SeMet and Met differ sufficiently to be of some use in SeMet analysis. For example, SeMet is a better substrate than Met for the a,y-elimination by i.-methionine y-lyase of Pseudomonas putida (Esaki et al., 1979). The adenosyl methionine transferase from rat liver reacts with L-SeMet at 51% of the rate with L-Met, and with the corresponding D-isomers at only 13 and 10% of the rate of L-Met (Pan and Tarver, 1967). Other adenosyl methionine transferases, such as that from yeast, react with SeMet more rapidly and with higher stereoselectivity than with Met, providing an indirect means for SeMet determination (Mudd and Cantoni, 1957 Sliwkowski, 1984 Uzar and Michaelis, 1994). 

This analysis can be applied to enzymatic as well as to simple chemical transformations [9-11], for uni- and multi-substrate [12] reactions according to Eqs. (1) and (2). nNKM denotes the product of Michealis-Menten constants for all substrates. In this analysis one assumes that kinetics follow the Michaelis-Menten model, which is the case for most antibody-catalyzed processes discussed below. The kcat denotes the rate constant for reaction of the antibody-substrate complex, Km its dissociation constant, and kuncat the rate constant for reaction in the medium without catalytic antibody or when the antibody is quantitatively inhibited by addition of its hapten. In several examples given below there is virtually no uncatalyzed reaction. This of course represents the best case. 

For the sake of simplicity, we consider an enzymatic reaction where the Michaelis-Menten kinetics involves only the oxidized form of the enzyme as sketched in Sch. 1. As is often the case with redox enzymes, two electrons are exchanged in the reaction of the enzyme with one-electron cosubstrates. The subsequent analysis may be adapted with no difficulty to other reaction schemes. 

Finally, we end the chapter with a discussion of nature s catalysts enzymes. In fact, we allude to enzymes throughout the chapter. The general manner in which enzymes catalyze reactions is still a matter of debate, and so we present several theories. Our examination of enzymes is in preparation for a few specific enzymatic examples given in Chapters 10 and 11 as highlights for organic reaction mechanisms. Enzymes also provide an excellent setting in which to discuss Michaelis-Menton kinetics, the most common kinetic scenario used for catalysis. We also return to our analysis of the power of changing the thermodynamic reference state to examine reactivity, and show the manner in which an enzyme becomes "perfect". 

The effect of substrate concentration on enzymatic reaction was first put forward in 1903 (Henri, 1903), where the conversion into the product involved a reaction between the enzyme and the substrate to form a substrate-enzyme complex that is then converted to the product. However, the reversibility of the substrate-enzyme complex and its final breakdown into the substrate and free enzyme regeneration was generally ignored. In 1913, Michaelis and Menten took this into consideration and proposed the scheme shown in Equation 4.1 for a one-substrate enzymatic reaction. Experimental data, that is, the initial reaction rates, were collected to support their analysis. The reaction mechanism, which is one of the most common mechanisms in enzymatic reactions, was based on the assumption that only a single substrate and product are involved in the reaction. 

The reciprocal form of the equation produced a straight line with intercept values on the Y axis of 1/Vmax and on the X axis of -1/Km (Figure 2). This advancement in analysis of the Michaelis-Menten equation allowed for a simplified way of analyzing the effect of compounds that altered the catalytic activity of enzyme systems. Changes in enzymatic activity were observed to result from changes in the substrate affinity or maximum velocity (Lineweaver Burk 1934) resulting in the definition of inhibitory equations based on their effects on the kinetic constants of the Michaelis-Menten equation. 

Analysis This example demonstrated how to evaluate the parameters V m and Ky in the Michaelis-Menten rate law from enzymatic reaction data. Two techniques were used a Lineweaver-Burk plot and non-linear regression. It ras also shown how (he analysis could be carried out using Hanes-Woolf and Eadie-Hofstee plots. 

Analysis This example shows a straightforward Chapter 3 type calculation of the hatch reactor time to achieve a certain conversion X for an enzymatic-reaction with a Michaelis-Menten rate law. This batch reaction time is v y shml consequently, a continuous flow reactor would be better suited for this reaction. 

Worth noting that there is no monotonically form between 0 and 1 other that that of equation (1.35) to reproduce basic Michaelis-Menten term (1.34) when approximated for small x = [S t) K For instance, if one decides to use exp(-x then the unreactive probability will give 1/(1+x ) as the approximation for small x, definitely different of what expected in basic Michaelis-Menten treatment (1.34). This way, the physico-chemical meaning of Eq. (1.36) is that the Michaelis-Menten term (1.34) and its associated kinetics apply to fast enzymatic reactions, i.e., for fast consumption of [ S](t), which also explains the earlier relative success in applying linearization and graphical analysis to the initial velocity equation (1.18). 

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