Enzyme reactions maximum velocity

Immunoassay standard curves. Immunosensors were prepared as described. Sample, standards, and conjugate were added sequentially to the respective cells to start the competitive assay. After a 10 min incubation, the solution was discarded and a proprietary buffer was added to each cell. A sufficient concentration of glucose was then added to each cell to drive the enzyme reaction to maximum velocity. As in the qualification tests, the hydrogen... 

Kinetics is the branch of science concerned with the rates of chemical reactions. The study of enzyme kinetics addresses the biological roles of enzymatic catalysts and how they accomplish their remarkable feats. In enzyme kinetics, we seek to determine the maximum reaction velocity that the enzyme can attain and its binding affinities for substrates and inhibitors. Coupled with studies on the structure and chemistry of the enzyme, analysis of the enzymatic rate under different reaction conditions yields insights regarding the enzyme s mechanism of catalytic action. Such information is essential to an overall understanding of metabolism. 

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. 

In none of the cases mentioned were substrates that were polymerized to different degrees used at equimolar concentrations, so that, in some cases, it is not clear to what extent the differences in the rate of cleavage reflect the effective concentration of the terminal bonds (as assumed by Mill154) and to what extent they reflect the differences in the enzyme reaction-mechanism. More satisfactory information would be obtainable by comparing the values of the maximum velocities. 

Probably the most important variable to consider in defining optimal conditions or standard conditions is the initial substrate concentration. Most enzymes show a hyperbolic curve as relation between initial reaction velocity and substrate concentration, well known now as the Michaelis-Menten curve. With increasing substrate concentration (S) the velocity (o) rises asymptotically to a maximum value (V) (Fig. 3), according to the expression ... 

Figure 8.7 The kinetic effects of a non-competitive inhibitor. The effect of a noncompetitive inhibitor is not reversed by high concentrations of substrate and the enzyme reaction shows a reduced value for the maximum velocity. The enzyme remaining is unaltered and gives the same value for the Michaelis constant as originally shown by the uninhibited enzyme.

Lineweaver-Burk plot (Figure 8.11). In such cases the chosen substrate concentration must give the highest reaction velocity possible. It is important, when describing any enzyme assay, to report the percentage maximum velocity which the method will give. 

Equation (18) is the Henri-Michaelis-Menten equation, which relates the reaction velocity to the maximum velocity, the substrate concentration, and the dissociation constant for the enzyme-substrate complex. Usually substrate is present in much higher molar concentration than enzyme, and the initial period of the reaction is examined so that the free substrate concentration [S] is approximately equal to the total substrate added to the reaction mixture. 

Reaction velocity as a function of substrate concentration for a first-order enzymic reaction (left) and for a cooperative enzyme with fourth-order kinetics (right). Substrate concentration is expressed as [S]/[S0.s] and velocity as a fraction of maximum velocity. At a [S]/ [S0.5] value of l the substrate concentration is equal to [S0.5] and the reaction velocity is half of the maximum velocity. Note the much greater rate of increase over the same interval for the cooperative enzyme. 

The parameter B2 is chosen for this project in order to gain some insight into possible consequences of varying the capability of the acetylcholinesterase to hydrolyze the neurotransmitter. Imbalances in this capability give rise to devastating diseases such as Alzheimer s and Parkinson s. The enzyme activity is included in the grouped parameter B2, which includes the maximum reaction velocity in reaction 2. The parameter B2 itself includes the enzyme activity together with three constants for the enzyme system, namely the concentration of acetylcholinesterase in compartment (II), the volume V2 of compartment (II), and the flow rate q. 

For a high value of substrate concentration, the reaction velocity reaches its maximum (saturation). Under those conditions, all the available enzyme Ej is bound in the complex with the substrate. Thus... 

It can be shown that Km equals the concentration of the substrate at which the reaction velocity is one half of its maximum. The Michaelis-Menten constant is an important figure of merit for the enzyme. It is the measure of its activity. Although it describes a kinetic process, it has the physical meaning of dissociation constant, that is, a reciprocal binding constant. It means that the smaller the Km is, the more strongly the substrate binds to the enzyme. 

In this equation, a hyperbolic saturation curve is described by two constants, Vm and Km. In the simple example in Figure IB, v is velocity, Vm is simply [EJ and Km is (k2 + 23) 12- Umax (or Vm) is the reaction velocity at saturating concentrations of substrate, and Km is the concentration of the substrate that achieves half the maximum velocity. Although the constant Km is the most useful descriptor of the affinity of the substrate for the enzyme, it is important to note the difference between Km and Kh. Even for the simplest reaction scheme (Fig. IB), the Km term contains the rate constant for conversion of substrate to product ( 23) If the rate of equilibrium is fast relative to k23, then Km approaches Kh. 

The catalytic efficiency of an enzyme is indicated by its kcatIKM value, the value combining the effectiveness of both the productive substrate binding and the subsequent conversion of substrate molecules into product (Copeland, 2000). This value is the apparent second-order rate constant for enzyme action under conditions in which the binding site of the enzyme is largely unoccupied by substrate. The kcatIKM value is the index for comparing the relative rates of cleavage of alternative, competing substrates. The KM is the Michaelis constant, an apparent dissociation constant and hence a measure of substrate affinity. This value equals the concentration of substrate needed to reach half maximum velocity of the enzyme reaction. 

The effect of different water activities on the initial reaction velocitiy Uj is summarized in figure 5. Experiments were carried out at 100 bar and 50°C. Unlike Marty et al. (1992) we did not experience a maximum in the reaction velocity but a steady decrease as the water activity increased. At an aw of 0.27, corresponding to a water content of the enzyme preparation of 3% (w/w), the residual activity was as low as 9 pmol h lg l enzyme (i.e. 4.5% of the activity at aw= 0.03). Since there is no decrease in activity at low water activity, we conclude, that, in the case of esterase EP10, SC-CO2 does not strip essential water from the enzyme. This makes esterase EP10 a very easy to use catalyst, since the water content of the SC-CO2 has merely to be kept very low to ensure maximum activity. 

Vmax is the maximum rate of an enzyme reaction when the substrate is present in saturating amounts. Vmax is derived fiom the Michaelis-Menten equation, where v is the initial velocity and P is the product of the reaction. v-V [S]/(Km+[S]=d [P]/dl. 

Enzymes in skin and eye lotions, immobilized in foams and on tissues for skin and eye decontamination (Gordon et al, 2003), or in topical skin protectants (Braue et al, 2002), act under conditions where local OP concentrations can be very high. In these cases, enzyme reaction order in [OP] tends to zero, so that reaction rate is close to maximum velocity ... 

MichaeUs-Menten kinetics predict that as the concentration of the substrate increases, the rate increases hyperbolically. However, some enzymes exist in which a maximum velocity is obtained at low substrate concentration, but further increases in the substrate concentration lead to a decrease in velocity. This effect is known as substrate inhibition and can eventually lead to complete enzyme inhibition or partial enzyme inhibition. It is thought that substrate inhibition occurs if two substrate molecules bind to the enzyme simultaneously in an incorrect orientation and produce an inactive E S S complex, analogous to that discussed for uncompetitive inhibition. The rate of the enzyme reaction that undergoes substrate inhibition is given by Equation 17, where K represents the... 

For a given amount of enzyme, the maximum reaction velocity (Vjnax) is reached when all of the enzyme is saturated with substrate (i.e., [ES] = [Et]) and therefore, V ,ax = 2 X [Et]. Substituting this in equation (6) gives... 

To measure enzyme activity reliably, all the factors that affect the reaction rate-other than tlie concentration of active enzyme—must be optimized and rigidly controlled. Furthermore, because the reaction velocity is at or near its maximum under optimal conditions, a larger analytical signal is obtained that can be more accurately and precisely measured than a smaller signal obtained under suboptimal conditions. Much effort has therefore been devoted to determining optimal conditions for measuring the activities of enzymes of clinical importance. 

The reaction rate is directly proportional to the concentration of the enzyme if an excess of free substrate molecules is present. Thus, enzyme-substrate interactions obey the mass-action law. For a given enzyme concentration, the reaction velocity increases initially with increasing substrate concentration. Eventually, a maximum is reached, and further addition of substrate has no effect on reaction velocity (v) (Figure 6-4). The shape of a plot of V versus [S] is a rectangular hyperbola and is characteristic of all nonallosteric enzymes (Chapter 7). At low substrate concentrations, the reaction rate is proportional to substrate concentration, with the reaction following first-order kinetics in terms of substrate concentration. 

Figure 5. Saturation kinetics the dependence of enzyme catalysis on the concentration of substrate. Reaction velocity represents the rate at which product is formed. (A) shows a hyperbolic saturation curve for two hypothetical enzymes. One binds its substrate more tightly than the other and reaches saturation at lower substrate concentration. This enzyme has a lower value, the substrate concentration where the reaction is half of maximum. The other binds the substrate more loosely and reaches the same velocity but requires higher substrate concentrations. (B) shows hypothetical velocities for cooperative enzymes. Although more complex, these enzymes also show the phenomenon of saturation.

Figure 2.22 (a) a plot of reaction velocity V agains substrate concentration [S] for an enzyme that obeys Michaelis-Menten kinetics. is the maximum reaction velocity and is the Michaelis constant (b) Chemical reactions prohles for catalysed ( ) and uncatalysed reactions (-). 

The velocity of an enzyme reaction increases as [S] increases. When [S] becomes much larger than AM, the velocity approaches a constant, that is, as [S] , VO Ernax. Hence, fin ax is the maximum velocity that can be achieved with a given total enzyme concentration and it can be measured as the limiting (maximum) velocity obtained as [S] is increased fin ax is proportional to enzyme concentration. Thus, fin ax is a property of the enzyme and its substrate and also depends on enzyme concentration and on the conditions of temperature, pH, and ionic strength in the solution. 

In competitive inhibition the inhibitor, I, binds reversibly to the active site of the enzyme. Consequently, the inhibitor competes with the substrate for the active site. As more substrate is added, at constant inhibitor concentration, the inhibitor is displaced and the reaction rate approaches the same maximum value as in the absence of inhibitor. However, more substrate is required to achieve any given reaction velocity in the presence of inhibitor than in its absence. The amount of inhibition depends on the inhibitor constant, Kl, which is also the dissociation constant for the binding of the inhibitor to the enzyme ... 

Maximum velocity of enzyme reaction (cm/s) Root-mean-square velocity (cm/s)... 

SCFs [14,18-21]. Figure 4.9-3 shows how kinetic parameters can be obtained from a Lineweaver-Burk plot. The example is from the esterification of ibu-profen with propanol in SCCO2 using Mucor miehei lipase (Scheme 4.9-1) [22]. In this case the Michaelis constant was = 2.8 mmol ester per mole of mixture and the maximum reaction velocity V ax = 360 g ester per kg enzyme per hour. The kinetic parameters are specific to the reaction system, reactor type, enzyme and substrate concentrations as well as to reaction conditions. 

This constant, K , is variously called the half-velocity constant, the Michaelis-Menten constant, and is indicative of the strength of the bond between enzyme and substrate. The lower the value of K, the greater is the affinity between enzyme and substrate. Values of for single substrate-enzyme reactions are generally between 10 and 10 M. The significance of this range of values is that it only requires 10" to 10 M of substrate to allow an enzyme to operate at half of its maximum rate. 

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. 

The time required to reach steady-state potential reading is dependent on the enzyme layer thickness because of the diffusion parameter for the substrate to reach the active sites of the enzyme and of the electroactive species to diffuse through the membrane to the sensor. A mathematical model relating the thickness of the membrane, d, the diffusion coefficient, D, the Michaelis constant, K, and the maximum velocity of the enzyme reaction, Vmax, has been developed ... 

Figure 30.2 shows an initial velocity versus substrate concentration curve. The reaction velocity (v) increases in proportion to increasing concentration of substrate [5] until aU the catalytic sites of the enzyme are working as fast as they can and maximum reaction velocity (V )... 

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