Velocity Michaelis-Menten equation

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

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]. 

Equation (3-150) is the Michaelis-Menten equation, Vm is the maximum velocity (for the enzyme concentration ,), and is the Michaelis constant. 

The Michaelis-Menten equation (29) illustrates in mathematical terms the relationship between initial reaction velocity V and substrate concentration [S], shown graphically in Figure 8-3. 

The Michaelis constant is the substrate concentration at which is half the maximal velocity (V 3 /2) attainable at a particular concentration of enzyme. thus has the dimensions of substrate concentration. The dependence of initial reaction velocity on [S] and may be illustrated by evaluating the Michaelis-Menten equation under three conditions. 

The direct measurement of the numeric value of and therefore the calculation of often requires im-practically high concentrations of substrate to achieve saturating conditions. A linear form of the Michaelis-Menten equation circumvents this difficulty and permits and to be extrapolated from initial velocity data obtained at less than saturating concentrations of substrate. Starting with equation (29),... 

Most often the binding of inhibitors to enzymes is measured by their effects on the velocity of the enzyme catalyzed reaction. In the absence of inhibitor, the velocity is defined by the Michaelis-Menten equation (Chapter 2) ... 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

If [S] = Km, the Michaelis-Menten equation says that the velocity will be one-half of Vmax. (Try substituting [S] for Km in the Michaelis-Menten equation, and you too can see this directly.) It s really the relationship between Km and [S] that determines where you are along the hyperbola. Like most of the rest of biochemistry, Km is backward. The larger the Km, the weaker the interaction between the enzyme and the substrate. Km is also a collection of rate constants. It may not be equal to the true dissociation constant of the ES complex (i.e., the equilibrium constant for ES E + S). 

The Km is a landmark to help you find your way around a rectangular hyperbola and your way around enzyme behavior. When [S] < Km (this means [S] + Km = Km), the Michaelis-Menten equation says that the velocity will be given by v = CVnvdepends linearly on [S], Doubling [S] doubles the rate. 

At high substrate concentrations relative to Km ([S] Km), The Michaelis-Menten equation reduces to v = Vmax, substrate concentration disappears, and the dependence of velocity on substrate concentration approaches a horizontal line. When the reaction velocity is independent of the concentration of the substrate, as it is at Vmax, it s given the name zero-order kinetics. 

This is an assumption used to derive the Michaelis-Menten equation in which the velocity of ES formation is assumed to be equal to the velocity of ES breakdown. 

The phosphorylation of each substrate was monitored via a one- or two-substrate reaction in real time and the kinetic parameters (Vmca, Km, kcat, and kcJKm) were determined. Figure 6.54 shows the results of the evaluations of velocity with respect to substrate (Kemptide and CREBtide) concentrations. The data were fitted using the Michaelis-Menten equation to determine the kinetic parameters shown in Table 6.8. The V , of phosphor-Kemptide (105.57 pM/min) was approximately 4.3-fold larger than the V , for CREBtide (24.33 pM/min) although both peptide substrates had similar... 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

To achieve maximum velocity, a substrate concentration which is at least ten times greater than the Km value for the enzyme should be used. Although maximum velocity is only theoretically achieved at an infinite substrate concentration, it is possible using the Michaelis-Menten equation to calculate the percentage of maximum velocity given by any concentration of substrate. For a substrate concentration of ten times greater than the Km value the velocity (v) achieved will be ... 

The only rate-limiting factor in a coupled assay should be the concentration of the initial and linking products and all other reagents should be in excess. The role of the auxiliary and indicator enzymes is essentially that of a substrate assay system and under optimum assay conditions the rate of the indicator reaction should be equal to the rate of formation of the initial product. The indicator reaction must be capable of matching the different test reaction rates and its velocity can be defined by the Michaelis-Menten equation in the usual way ... 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

If it is assumed that ES is formed at the same rate at which it breaks down to E + P (a steady-state assumption), and that the concentration of S is much larger than the concentration of E, then the change in reaction velocity, v, relative to changes in [S], is described by the Michaelis-Menten equation ... 

Velocity data may be plotted in any one of a number of ways to illustrate the relation between v and [S], and plotting procedures are detailed later in this chapter. However, the Michaelis-Menten equation is an equation for a rectangular hyperbola, and plotting v versus [S] yields a hyperbolic curve, in the absence of cooperative or other unusual behaviors (O Figure 4-3). 

Thereafter, and V ax values for substrate turnover are determined in the absence (controls) and presence of several concentrations of the inhibitor of interest. It is recommended that substrate turnover in the presence of at least four concentrations of inhibitor are examined, at concentrations between 1/3 x IC50 and 4 x IC50. Velocity data are then plotted versus substrate concentration, yielding a control plot and plots at each of the concentrations of inhibitor assessed. Hyperbolic curves are then fitted to data with the Michaelis-Menten equation, or with whichever variation of the Michaelis-Menten equation was found to describe control enzyme behavior most appropriately (see Section 4.1.4 etseq.). In this way, a pattern of changes in Km and Vmax> or both, should become apparent with changing inhibitor concentration. 

The reduction in concentration of reactants, enzymes, and solute molecules can provide important information about kinetic systems. For example, one can readily differentiate a first-order process from a second-order process by testing whether the period required to reduce a reactant concentration to 50% of its initial value depends on dilution. First-order processes and intramolecular processes should not exhibit any effect on rate by diluting a reactant. In terms of enzyme-catalyzed processes, the Michaelis-Menten equation requires that the initial reaction velocity depends strictly on the concentration of active catalyst. Dilution can also be used to induce dissociation of molecular complexes or to promote depolymerization of certain polymers (such as F-actin and microtubules). 

Also referred to as the Hanes-Hultin plot and the Hanes-Woolf (or, Woolf-Hanes) plot, the method is based on a transformation of the Michaelis-Menten equation i.e., the expression for the Uni Uni mechanism) [A]/v = (i a/ max) + ([A]/Umax) whcrc U ax IS the maximum forward velocity and is the Michaelis constant for A. In the Hanes plot, the slope of the line is numerically equal to Umax, the vertical intercept is equivalent to, ... 

GRAPHICAL REPRESENTATION. The above expression represents the equation of a hyperbola (i.e., f(x) = axl(b + x) where a and b are constants) and a plot of the initial velocity as a function of [S] will result in a rectangular hyperbola. Another way for representing the Michaelis-Menten equation is by using the doublereciprocal (or, Lineweaver-Burk ) transformation ... 

An enzyme is said to obey Michaelis-Menten kinetics, if a plot of the initial reaction rate (in which the substrate concentration is in great excess over the total enzyme concentration) versus substrate concentration(s) produces a hyperbolic curve. There should be no cooperativity apparent in the rate-saturation process, and the initial rate behavior should comply with the Michaelis-Menten equation, v = Emax[A]/(7 a + [A]), where v is the initial velocity, [A] is the initial substrate concentration, Umax is the maximum velocity, and is the dissociation constant for the substrate. A, binding to the free enzyme. The original formulation of the Michaelis-Menten treatment assumed a rapid pre-equilibrium of E and S with the central complex EX. However, the steady-state or Briggs-Haldane derivation yields an equation that is iso-... 

A kinetic parameter, introduced by Koshland, to indicate the ratio of substrate concentrations needed to achieve reaction velocities equal to Q.f max and 0.9Fniax-For an enzyme obeying the Michaelis-Menten equation, o.9/ o.i equals 81, indicating that such enzymes exhibit modest sensitivity of reaction rate relative to changes in the substrate concentration. Many positively cooperative enzymes have So.g/So.i values between five and ten, indicating that they can be turned on or off over a relatively narrow substrate concentration range. 

Symbol for maximal velocity of an enzyme-catalyzed reaction, usually expressed as the molarity change in product per unit time (usually, second). Fmax must not be confused with or specific activity the former has dimensions of time, and the latter is usually expressed as micromol product per unit time per milligram of protein. See Michaelis-Menten Equation Enzyme Rate Equations (1. The Basics)... 

Referring to reactions in which the reaction velocity is independent of the reactant under consideration. For example, for the reaction A + B C, if the empirical rate expression is v = A [B], the reaction is first order with respect to B but zero order with respect to A. See Chemical Kinetics Rate Saturation Michaelis-Menten Equation... 

C. The Michaelis-Menten equation describes the velocity, z , as a function of the substrate concentration, [S], for an enzyme-catalyzed reaction. 

D. Although it may seem from Point B in Figure 3-3 that the can be determined from this representation of the velocity data, in practice, it is more accurate to use the Lineweaver-Burk equation, a modified form of the Michaelis-Menten equation, for estimation of and (Figure 3-4). 

Two characteristics, the Michaelis constant KM and the maximal velocity V are the most important numeric data. The well-known Michaelis-Menten equation describes the relationship between the initial reaction rate and the substrate concentration with these two constants. The actual form of the rate equation of an enzymic process depends on the chemical mechanism of the enzymic transformation of the substrate to product (Table 8.1). 

This is the Michaelis-Menten equation, the rate equation for a one-substrate enzyme-catalyzed reaction. It is a statement of the quantitative relationship between the initial velocity V0, the maximum velocity Vnmx, and the initial substrate concentration [S], all related through the Michaelis constant Km. Note that Km has units of concentration. Does the equation fit experimental observations Yes we can confirm this by considering the limiting situations where [S] is very high or very low, as shown in Figure 6-12. 

Relation between Reaction Velocity and Substrate Concentration Michaelis-Menten Equation (a) At... 

The Michaelis-Menten equation describes how reaction velocity varies with substrate concentration ... 

The initial reaction velocity, vQ, of an enzyme-catalyzed reaction varies with the substrate concentration, [S], as shown in Figure E5.1. The Michaelis-Menten equation has been derived to account for the kinetic properties of enzymes. (Consult a biochemistry textbook for a derivation of this equation and for a discussion of the conditions under which the equation is valid.) The common form of the equation is... 

The important kinetic constants, V and Ku, can be graphically determined as shown in Figure E5.1. Equation E5.2 and Figure E5.1 have all of the disadvantages of nonlinear kinetic analysis. Kmax can be estimated only because of the asymptotic nature of the line. The value of Ku, the substrate concentration that results in a reaction velocity of Vj /2, depends on Kmax, so both are in error. By taking the reciprocal of both sides of the Michaelis-Menten equation, however, it is converted into the Lineweaver-Burk relationship (Equation E5.3). 

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