Michaelis enzyme kinetics

Hamilton, S. D. Pardue, H. L. (1982). Kinetic method having a linear range for substrate concentration that exceed Michaelis-Menten constants. Clinical Chemistry, vol. 28, no.l2, (December 1982), pp.2359-2365, ISSN 0009-9147 Hasinoff, B. B. (1985). A convenient analysis of Michaelis enzyme kinetic progress curves based on second derivatives. Biochimica et Biophysica Acta (BBA) - General Subjects, Vol. 838, no. 2, (February 1985), pp. 290-292, ISSN 0304-4165 Kahn, K. Tipton, P.A. (1998). Spectroscopic characterization of intermediates in the urate oxidase reaction. Biochemistry, vol. 37, no. (August 1998), pp. 11651-11659, ISSN 0006-2960. 

Leonor Michaelis and Maud Menten laid the foundation for enzyme kinetics as early as 1913 by proposing the following scheme ... 

Michaelis-Menten kinetics Kineties of eonversion of substrates in enzyme-eatalyzed reaetions. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

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 ... 

FIGURE 15.8 Sigmoid versus [S] plot. The dotted line represents the hyperbolic plot characteristic of normal Michaelis-Men ten-type enzyme kinetics. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The values of the Michaelis-Menten kinetic parameters, Vj3 and C,PP characterise the kinetic expression for the micro-environment within the porous structure. Kinetic analyses of the immobilised lipase in the membrane reactor were performed because the kinetic parameters cannot be assumed to be the same values as for die native enzymes. 

The initial reaction rate (v0) obtained from each substrate concentration was fitted to Michaelis-Menten kinetics using enzyme kinetics. Pro (EKP) Software (ChemSW product,... 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

Solution Most enzyme reactors use such high concentrations of water that the fluid density is constant. Applying Michaelis-Menten kinetics to the component balance for a steady-state CSTR gives... 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

The initial condition for [SE] assumes that the enzyme was charged to the reactor in pristine condition. It makes no difference whether the enzyme is free or immobilized provided the reaction follows Michaelis-Menten kinetics. 

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. ... 

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 ... 

The reaction rate for this enzyme kinetics example is expressed by the Michaelis-Menten equation and with product inhibition. 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

Quite often the asymptotic behavior of the model can aid us in determining sufficiently good initial guesses. For example, let us consider the Michaelis-Menten kinetics for enzyme catalyzed reactions,... 

Pyruvate kinase (PK) is one of the three postulated rate-controlling enzymes of glycolysis. The high-energy phosphate of phosphoenolpyruvate is transferred to ADP by this enzyme, which requires for its activity both monovalent and divalent cations. Enolpyruvate formed in this reaction is converted spontaneously to the keto form of pyruvate with the synthesis of one ATP molecule. PK has four isozymes in mammals M, M2, L, and R. The M2 type, which is considered to be the prototype, is the only form detected in early fetal tissues and is expressed in many adult tissues. This form is progressively replaced by the M( type in the skeletal muscle, heart, and brain by the L type in the liver and by the R type in red blood cells during development or differentiation (M26). The M, and M2 isozymes display Michaelis-Menten kinetics with respect to phosphoenolpyruvate. The Mj isozyme is not affected by fructose-1,6-diphosphate (F-1,6-DP) and the M2 is al-losterically activated by this compound. Type L and R exhibit cooperatively in... 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

Microbial Biotransformation. Microbial population growth and substrate utilization can be described via Monod s (35) analogy with Michaelis-Menten enzyme kinetics (36). The growth of a microbial population in an unlimiting environment is described by dN/dt = u N, where u is called the "specific growth rate and N is microbial biomass or population size. The Monod equation modifies this by recognizing that consumption of resources in a finite environment must at some point curtail the rate of increase (dN/dt) of the population ... 

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

An exponential function that describes the increase in product during a first-order reaction looks a lot like a hyperbola that is used to describe Michaelis-Menten enzyme kinetics. It s not. Don t get them confused. If you can t keep them separated in your mind, then just forget all that you ve read, jump ship now, and just figure out the Michaelis-Menten description of the velocity of enzyme-catalyzed reaction—it s more important to the beginning biochemistry student anyway. 

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 ... 

MODELS OF ENZYME KINETICS 10.2.1 Michaelis-Menten Model... 

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