Maximal 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]. 

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. 

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. ... 

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)... 

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). 

A special numerical relationship arises from the Michaelis-Menten equation when the initial velocity is equal to half the maximal velocity, that, is VQ = (V2)Vmax. Equation 5.24 then reduces to Km = [S0]. This means that Km is equal to the substrate concentration in moles per liter at which the reaction velocity is half its maximum value. 

If we set up the same enzyme assay with a fixed amount of enzyme but vary the substrate concentration we will observe that initial velocity (va) will steadily increase as we increase substrate concentration ([S]) but at very high [S] the va will asymptote towards a maximal value referred to as the Vmax (or maximal velocity). A plot of va versus [S] will yield a hyperbola, that is, v0 will increase until it approaches a maximal value. The initial velocity va is directly proportional to the amount of enzyme—substrate complex (E—S) and accordingly when all the available enzyme (total enzyme or E j) has substrate bound (i.e. E—S = E i -S and the enzyme is completely saturated ) we will observe a maximal initial velocity (Pmax)- The substrate concentration for half-maximal velocity (i.e. the [S] when v0 = Vmax/2) is termed the Km (or the Michaelis—Menten constant). However because va merely asymptotes towards fT ax as we increase [S] it is difficult to accurately determine Vmax or Am by this graphical method. However such accurate determinations can be made based on the Michaelis-Menten equation that describes the relationship between v() and [S],... 

Ks is the dissociation constant for the enzyme substrate complex. It is important to remember that the Michaelis-Menten equation holds true not only for the mechanism as stated above, but for many different mechanisms that are not included in this treatment. In summary, ITm can be described as an apparent dissociation constant for all enzyme-bound species and, in all cases, it is the substrate concentration at which the enzyme operates at half-maximal velocity. 

Thus, Kn, the Michaelis constant, is a dynamic or pseudo-equilibrium constant expressing the relationship between the actual steady-state concentrations, rather than the equilibrium.concentrations. If Aj, is very small compared to A-i, reduces to K. A steady-state treatment of the more realistic reaction sequence E+ S ES EP E + P yields the same final velocity equation although now Km is a more complex function, composed of the rate constants of all the steps. Thus, the physical significance of K cannot be stated with any certainty in the absence of other data concerning the relative magnitudes of the various rate constants. Nevertheless, represents a valuable constant that relates the velocity of an enzyme-catalyzed reaction to the substrate concentration. Inspection of the Henri-Michaelis-Menten equation shows that Km is equivalent to the substrate concentration that yields half-maximal velocity ... 

The constant K in the above equation no longer equals the substrate concentration that yields half-maximal velocity (except when n = 1, when the equation reduces to the Henri-Michaelis-Menten equation). 

The equations of enzyme kinetics provide a quantitative way of desaibing the dependence of enzyme rate on substrate concentration. The simplest of these equations, the Michaelis-Menten equation, relates the initial velocity (Vj) to the concentration of substrate [S] and the two parametCTS and (Equation 9.1) The of the enzyme is the maximal velocity that can be achieved at an infinite concentration of substrate, and the of the enzyme for a substrate is the concentration of substrate required to reach Vz V iax- The Michaelis-Menten model of enzyme kinetics applies to a simple reaction in which the enzyme and substrate form an enzyme-substrate complex (ES) that can dissociate back to the free enzyme and substrate. The initial velocity of product formation, Vj, is proportionate to the concentration of enzyme-substrate complexes [ES]. As substrate concentration is increased, the concentration of enzyme-substrate complexes increases, and the reaction rate inaeases proportionately. 

The Michaelis-Menten equation describes several parameters, including the maximal velocity, and the Michaelis constant, K. ... 

Other concepts follow from the Michaelis-Menten equation. When the velocity of an enzymatic reaction is one-half the maximal velocity ... 

The kinetic parameters and Umax are estimated from the Michaelis-Menten equation and provide quantitative information regarding enzyme function. or the Michaelis constant is operationally defined as the concentration of substrate at which half-maximal velocity of the reaction is achieved (Fig. 4.1). With respect to the single substrate reaction scheme (Scheme 4.1), it should be realized that is equal to k + k2)lkx and thus is the amalgamation of several rate constants. With respect to affinity, unfortunately, is frequently (and incorrectly) used interchangeably with which is the substrate dissociation constant. Though may sometimes approximate the two do not have to be equal and numerous examples exist where these parameter values vary dramatically. 

Equation (3.9) is the fundamental equation of enzyme kinetics, generally known as the Michaelis-Menten equation, the constant value Ka as the Michaelis constant and the constant value Vmax as the maximal velocity of reaction. 

Integrated rate equation an equation which represents the concentration of the substrate or product as a function of time. The corresponding plots are called the progress curves, which can also be obtained by direct measurement (see Enzyme kinetics). By integrating the Michaelis-Menten equation, one obtains for example, with (Sj - S) = P, the integrated velocity equation P(t) = V t + K lnS/, where P is the product concentration, S the substrate concentration, Sg the substrate concentration at t = 0, and and are the maximal velocity and Michaelis constant, respectively. 

This is the Michaelis-Menten equation which contains two constants and K. The latter is known as the Michaelis constant and is defined as the molar substrate concentration at which the velocity of the reaction is half-maximal. This can be shown by substituting the values V J2 for V[ in the equation as follows ... 

The Michaelis-Menten equation (32) is a rectangular hyperbola which can only be drawn accurately with a large number of experimental points. The Michaelis constant Km), although situated in an easily accessible part of the curve, can only be calculated after the maximal velocity has been determined by extrapolation to infinite substrate concentration. 

This equation, illustrating the curves of Figure 14 (for values of n = 1 — 4), calls to mind the Michaelis-Menten equation (32). V here represents the maximal velocity n the number of sites binding the substrate K replaces Km. If n = 1, the equation becomes identical with the Michaelis-Menten equation (32) and, in this case, K = K ... 

When activator is not present in the system, i.e. [A]=0 M, the above equation attain the form of well known Michaelis-Menten equation. If the activator is present in the system at any concentration, the reaction rate is defined as apparent so the maximal velocity and dissociation constants too ... 

The oxidation rate was also dependent on the concentration of hypotaurine in the incubation medium. The reaction appeared to obey simple Michaelis-Menten kinetics (Fig. 2). The kinetic constants were estimated from a linear transformation of the Michaelis-Menten equation in a t against v/s plot. The apparent Michaelis constant ( ) was about 0.2 ramol/1 and the maximal velocity (F) about 0.1 ymol/s X kg. In our crude liver homogenate the apparent for hypotaurine oxidation was of the same order of magnitude as for the partially purified L-cysteine sulphinate decarboxylase (Jacobsen et al., 1964), the preceding enz3nne in the biosynthesis pathway. 

Equation (19.7) assumes that the system is at equilibrium. To make sense of it, think about a few different values for [ligand]. When [ligand] = 0, the fractional occupancy equals zero. When [ligand] is very, very high (i.e., many times the KD), the fractional occupancy approaches 100%. When [ligand] = KD, fractional occupancy is 50% (just as the Michaelis-Menten constant Km describes the concentration of enzyme substrate that gives half-maximal velocity). 

Michaelis-Menten kinetics in 1913 L. Michaelis and M. Menten realized that the rate of an enzymatic reaction differed from conventional chemical reactions. They postulated a scheme whereby the reaction of a substrate plus enzyme yields enzyme plus substrate and placed it into the form of the equation reaction velocity = (maximal velocity of the reaction x substrate concentration)/(concentration of substrate + a fitting constant Km). The Km (referred to as the Michaelis-Menten constant) is the concentration of the substrate at which the reaction rate is half the maximal value it also characterizes the tightness of the binding between substrate and enzyme. 

The basis of the operational model is the experimental finding that the experimentally obtained relationship between agonist-induced response and agonist concentration resembles a model of enzyme function presented in 1913 by Louis Michaelis and Maude L. Menten. This model accounts for the fact that the kinetics of enzyme reactions differ significantly from the kinetics of conventional chemical reactions. It describes the reaction of a substrate with an enzyme as an equation of the form reaction velocity = (maximal velocity of the reaction x substrate concentration)/(concentration of substrate A a... 

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