Maximum velocity, enzyme-catalyzed

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

The immobilization procedure may alter the behavior of the enzyme (compared to its behavior in homogeneous solution). For example, the apparent parameters of an enzyme-catalyzed reaction (optimum temperature or pH, maximum velocity, etc.) may all be changed when an enzyme is immobilized. Improved stability may also accrue from the minimization of enzyme unfolding associated with the immobilization step. Overall, careful engineering of the enzyme microenvironment (on the surface) can be used to greatly enhance the sensor performance. More information on enzyme immobilization schemes can be found in several reviews (7,8). 

Most biological reactions fall into the categories of first-order or second-order reactions, and we will discuss these in more detail below. In certain situations the rate of reaction is independent of reaction concentration hence the rate equation is simply v = k. Such reactions are said to be zero order. Systems for which the reaction rate can reach a maximum value under saturating reactant conditions become zero ordered at high reactant concentrations. Examples of such systems include enzyme-catalyzed reactions, receptor-ligand induced signal transduction, and cellular activated transport systems. Recall from Chapter 2, for example, that when [S] Ku for an enzyme-catalyzed reaction, the velocity is essentially constant and close to the value of Vmax. Under these substrate concentration conditions the enzyme reaction will appear to be zero order in the substrate. 

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... 

The quotient of rate constants obtained in steady-state treatments of enzyme behavior to define a substrate s interaction with an enzyme. While the Michaelis constant (with overall units of molarity) is a rate parameter, it is not itself a rate constant. Likewise, the Michaelis constant often is only a rough gauge of an enzyme s affinity for a substrate. 2. Historically, the term Michaelis constant referred to the true dissociation constant for the enzyme-substrate binary complex, and this parameter was obtained in the Michaelis-Menten rapid-equilibrium treatment of a one-substrate enzyme-catalyzed reaction. In this case, the Michaelis constant is usually symbolized by Ks. 3. The value equal to the concentration of substrate at which the initial rate, v, is one-half the maximum velocity (Lmax) of the enzyme-catalyzed reaction under steady state conditions. 

A plot of the rate constant, the initial velocity, the maximum velocity of a catalyzed reaction, or the ratio of an enzyme-catalyzed reaction (or the decadic logarithm of any of these quantities) as a function of the pH value of the solution, all other variables being held constant. See also pH Effects... 

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. 

For some enzyme-catalyzed reactions the equilibrium lies far to one side. However, many other reactions are freely reversible. Since a catalyst promotes reactions in both directions, we must consider the action of an enzyme on the reverse reaction. Let us designate the maximum velocity in the forward direction as Vf and that in the reverse direction as Vr There will be a Michaelis constant for reaction of enzyme with product Kmp, while Kms will refer to the reaction with substrate. 

Interpret, for each of the following cases, the curve showing measured initial velocity at constant substrate concentration (not maximum velocity) against pH for an enzyme-catalyzed reaction. 

Michaelis constant (ATm). The substrate concentration at which an enzyme-catalyzed reaction proceeds at one-half maximum velocity. 

We see that the rate of the enzyme-catalyzed reaction depends linearly on the enzyme concentration, and in a more complicated way on the substrate concentration. Thus, when [S] Km, (Eq. (2.41)) reduces to v = k2[E]0, and the reaction is zero order in [S], This means that there is so much substrate that all of the enzyme s active sites are occupied. It also means that [S] remains effectively unchanged, even though products are formed. This situation is known as saturation kinetics. The value k2[E]0 is also called the maximum velocity of the enzymatic reaction, and written as vmax. 

The Michaelis-Menten constant is a combination of rate constants and is independent of enzyme concentration under steady-state conditions. It is equal to the substrate concentration at which half the maximum velocity of the enzyme-catalyzed reaction is reached that is, when [S] = then v = V2. Vjnax- For the reaction illustrated in Equation 17.9, iiLM is described by Equation 17.11. 

Eor triose phosphate isomerase Albery and Knowles obtained a value of 4 x 10 M s so close to the diffusion controlled limit that these authors regard this enzyme as a nearly perfect catalyst, one that could not have evolved further because it is already catalyzing the reaction with substrate at almost the maximum velocity that is possible. " ... 

Each enzyme-catalyzed reaction has an optimal pH at which appropriate charges are present on both the enzyme and the substrate, and the velocity is at a maximum. 

Figure 2-16. The velocity of an enzyme-catalyzed reaction. (A) Velocity (v) versus substrate concentration ([S]). (6) Lineweaver-Burk plot. Note the points on each plot from which Vm and Km can be determined. Vm = maximum velocity, and Km = substrate concentration at 1/2 Vm.

C. The velocity of an enzyme-catalyzed reaction increases as the substrate concentration increases. It is highest when the enzyme is saturated with substrate. Then, v equals Vm, the maximum velocity. The velocity depends on Km. Enzymes have an optimal pH at which their activity is maximal. 

Simultaneous to the graph creation, kinetic properties in each vRxn are used to create the appropriate reaction rate equations (ordinary differential equations, ODE). These properties include rate constants (e.g., Michaelis constant, Km, and maximum velocity, Vmax, for enzyme-catalyzed reactions, and k for nonenzymatic reactions), inhibitor constants, A) and modes of inhibition or allosterism. The total set of rate equations and specified initial conditions forms an initial value problem that is solved by a stiff ODE equation solver for the concentrations of all species as a function of time. The constituent transforms for the each virtual enzyme are compiled by carefully culling the literature for data on enzymes known to act on the chemicals and chemical metabolites of interest. 

Figure 8-4 Michael is-Menten curve relating velocity (rate) of an enzyme-catalyzed reaction to substrate concentration. The value of Km is given by the substrate concentration at which one half of the maximum velocity is obtained.

Plot of substrate concentration versus initial velocity of an enzyme-catalyzed reaction. Segment A At low substrate concentration, the reaction follows first-order kinetics with respect to substrate concentration i.e., V — < [S], where k is a reaction rate constant. Segment B At high substrate concentration, maximum velocity (Umax) is attained (saturation kinetics), and any further increase in substrate concentration does not affect the reaction rate the reaction is then zero-order with respect to substrate but first-order with respect to enzyme. is the value of [S] corresponding to a velocity of j Vmax-... 

The cotton bollworm, Helicoverpa armigera, in Australia is of great economic importance and is cross-resistant to parathion-methyl and profenofos, but not to chlorpyrifos. It has an acetylcholinesterase with low sensitivity to paraoxon-methyl and profenofos, but the sensitivity to chlorpyrifos is unaltered. As Table 9.3 shows, the enzyme of the resistant insects is a little less efficient by having a slightly higher Km. (Km is the substrate concentration at which an enzyme-catalyzed reaction proceeds at one-half its maximum velocity.) This indicates a somewhat less efficient enzyme, but the difference is so slight that it does not cause any reduced fitness for the insects. The amount of and activity of acetylcholinesterase are almost always much higher than strictly necessary. 

Plot of the rate or velocity, P, of a reaction versus the concentration of substrate, [S], for (a) an uncatalyzed reaction and (b) an enzyme-catalyzed reaction. For an enzyme-catalyzed reaction the rate is at a maximum when all of the enzyme molecules are bound to the substrate. Beyond this concentration of substrate, further increases in substrate concentration have no effect on the rate of the reaction. 

The two important kinetic results obtained from studies of the steady state of enzyme-catalyzed reactions are the Michaelis constant Ku and the maximum velocity Fmax. These constants are determined from one of a number of graphical procedures relating the initial velocity To to the initial substrate concentration [(S]o over a range of [[Pg.285]

In this case, v is the velocity of the reaction, [S] is the substrate concentration, Vmax (also known as V or Vj ) is the maximum velocity of the reaction, and is the Michaelis constant. From this equation quantitative descriptions of enzyme-catalyzed reactions, in terms of rate and concentration, can be made. As can be surmised by the form of the equation, data that is described by the Michaelis-Menten equation takes the shape of a hyperbola when plotted in two-dimensional fashion with velocity as the y-axis and substrate concentration as the x-axis (Fig. 4.1). Use of the Michaelis-Menten equation is based on the assumption that the enzyme reaction is operating under both steady state and rapid equilibrium conditions (i.e., that the concentration of all of the enzyme-substrate intermediates (see Scheme 4.1) become constant soon after initiation of the reaction). The assumption is also made that the active site of the enzyme contains only one binding site at which catalysis occurs and that only one substrate molecule at a time is interacting with the binding site. As will be discussed below, this latter assumption is not always valid when considering the kinetics of drug metabolizing enzymes. 

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