Michaelis initial velocity

The turnover number of an enzyme, is a measure of its maximal catalytic activity, is defined as the number of substrate molecules converted into product per enzyme molecule per unit time when the enzyme is saturated with substrate. The turnover number is also referred to as the molecular activity of the enzyme. For the simple Michaelis-Menten reaction (14.9) under conditions of initial velocity measurements, Provided the concentration of... 

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),... 

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 ... 

The Michaelis constant is numerically equal to the value of the initial substrate concentration that gives an initial velocity that is half that of the maximum. 

Cooperative enzymes show sigmoid or sigmoidal kinetics because the dependence of the initial velocity on the concentration of the substrate is not Michaelis-Menten-like but gives a sigmoid curve (Fig. 8-7). 

In 1913 invertase was again employed by Michaelis and Menten, this time in acetate buffer. Initial velocities were measured and an expression for the Michaelis constant and Vmax derived. [5] was assumed to be >[ ], so that ... 

Sometimes, however, initial velocities are needed. If measurements of the rate u, are made at the time t, simple division of Michaelis-Menten expressions yields for the initial velocity Oo... 

In Cleland nomenclature, the initial velocity and individual rate constants are designated by lower case italicized letters (e.g., v, k, k2, etc.). Dissociation, Michaelis, and equilibrium constants utilize an upper case italicized K with the appropriate unitalicized lower case subscript. For example, the equilibrium constant would be symbolized by whereas the Michaelis constant for substrate B would be designated by K. Dissociation constants for a Michaelis complex contain a subscript i and a letter for the dissociating ligand (e.g., for the EA binary complex, the dissociation constant would be Ki ). Maximum velocities are designated by a capital italicized V, usually with a subscript 1 or 2 depending on whether the forward or reverse reaction is referred to. (If the numerical subscript is not provided, the forward reaction is assumed. In most cases, the unitalicized subscript max is also provided.)... 

While this model explained the action of the brain enzyme on a number of hexose substrates and nonsubstrate inhibitory analogs, the mode had its weaknesses. It assumed that the other conformations of a hexose that are in equilibrium with the active conformer act as competitive inhibitors relative to this conformer. One cannot evaluate the effect of a competitive inhibitor which is present in a constant proportion relative to the active substrate by initial velocity measurements. Moreover, the use of apparent Michaelis constants may not provide accurate estimates of affinity, which is more directly related to a dissociation constant. The chief limitation of the model, however, is that an equally great number of experimental facts can be satisfactorily explained in terms of a simpler scheme involving the binding and phosphorylation of the Cl conformer. Furthermore, one can understand more directly how the enzyme can phosphorylate glucopyranose and fructofuranose equally well. 

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-... 

FIGURE 6-11 Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction. V max is extrapolated from the plot, because V0 approaches but never quite reaches /max. The substrate concentration at which V0 is half maximal is Km, the Michaelis constant. The concentration of enzyme in an experiment such as this is generally so low that [S] >> [E] even when [S] is described as low or relatively low. The units shown are typical for enzyme-catalyzed reactions and are given only to help illustrate the meaning of V0 and [S]. (Note that the curve describes part of a rectangular hyperbola, with one asymptote at /max. If the curve were continued below [S] = 0, it would approach a vertical asymptote at [S] = — Km.)... 

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. 

Key concept map for the enzymes. S = substrate, [S] = substrate concentration, P = product, E = enzyme, v0 = initial velocity, Vmax = maximal velocity, Kn, = Michaelis constant. 

Figure C1.1.1 Relationship between substrate concentration and initial velocity at fixed enzyme concentrations. The Michaelis constant, KM, is equal to the substrate concentration corresponding to one-half l/max.

Assume that an enzyme-catalyzed reaction follows Michaelis-Menten kinetics with a K"m of 1 /am. The initial velocity is 0.1 /AM/min at 10 mM substrate. Calculate the initial velocity at 1 mM, 10/am, and... 

The steady-state treatment of enzyme kinetics assumes that concentrations of the enzyme-containing intermediates remain constant during the period over which an initial velocity of the reaction is measured. Thus, the rates of changes in the concentrations of the enzyme-containing species equal zero. Under the same experimental conditions (i.e., [S]0 [E]0 and the velocity is measured during the very early stage of the reaction), the rate equation for one substrate reaction (uni uni reaction), if expressed in kinetic parameters (V and Ks), has the form identical to the Michaelis-Menten equation. However, it is important to note the differences in the Michaelis constant that is, Ks = k2/k1 for the quasi-equilibrium treatment whereas Ks = (k2 + k3)/k i for the steady-state treatment. 

The dynamics were run for several concentrations of substrate and variations in the Pc values. Initial velocities of the reaction were recorded. The Michaelis-Menten model was observed and characteristic Lineweaver-Burk plots were found from the model. Systematic variation of the lipophilicity of substrates and products showed that a lower affinity between a substrate and water leads to more of the S —> P reaction at a common point along the reaction progress curve. This influence is greater than that of the affinity between the substrate and the enzyme. The study created a model in which the more lipophilic substrates are more reactive. The water-substrate affinity appears... 

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. 

Kinetic Study of Hydrolysis. It is of great interest to know the nature of the high enantioselectivity of the Arthrobacter lipase. The initial velocity measurements were conducted for the purpose of knowing which is the main factor of the enantioselectivity, the apparent Michaelis constant K m or the catalytic constant k cat. 

Michaelis and Menten, and later Briggs and Haldane, used the scheme shown in Equation II-4 to derive a mathematical expression that describes the relation between initial velocity and substrate concentration. (Consult a biochemistry textbook for the step-by-step derivation of this relationship, because it is important to be aware of the assump-... 

Most enzymes react with two or more substrates. For this reason, the Michaelis-Menten equation is inadequate for a full kinetic analysis of these enzyme reactions. Nonetheless, the same general approach can be used to derive appropriate equations for two or more substrates. For example, most enzymes that react with two substrates, A and B, are found to obey one of two equations if initial velocity measurements are made as a function of the concentration of both A and B (with product concentrations equal to zero). These are... 

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],... 

The Michaelis—Menten equation relates initial velocity (z Q) to substrate concentration ([S]) thus ... 

The electron transfer from cytochrome c to O2 catalyzed by cytochrome c oxidase was studied with initial steady state kinetics, following the absorbance decrease at 550 nm due to the oxidation of ferrocyto-chrome c in the presence of catalytic amounts of cytochrome c oxidase (Minnart, 1961 Errede ci a/., 1976 Ferguson-Miller ei a/., 1976). Oxidation of cytochrome c oxidase is a first-order reaction with respect to ferrocytochrome c concentration. Thus initial velocity can be determined quite accurately from the first-order rate constant multiplied by the initial concentration of ferrocytochrome c. The initial velocity depends on the substrate (ferrocytochrome c) concentration following the Michaelis-Menten equation (Minnart, 1961). Furthermore, a second catalytic site was found by careful examination of the enzyme reaction at low substrate concentration (Ferguson-Miller et al., 1976). The Km value was about two orders of magnitude smaller than that of the enzyme reaction previously found. The multiphasic enzyme kinetic behavior could be interpreted by a single catalytic site model (Speck et al., 1984). However, this model also requires two cytochrome c sites, catalytic and noncatalytic. 

---