Substrate concentration plotting reaction velocity versus

Figure 9.3 Plot of substrate concentration versus reaction velocity.

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-... 

A straight line whose perpendicular distance from a curve becomes progressively smaller as the distance from the origin at [0,0] becomes greater. For example, in a plot of velocity versus [Substrate Concentration] for an enzyme-catalyzed reaction, the asymptote reaches the maximal velocity when the enzyme molecules become saturated with substrate. 

One of the basic assumptions in kinetic studies of an enzyme-catalyzed reaction is that true initial rates are being measured. In such cases, a plot of the product concentration versus time must yield a straight line. (This behavior is only observed when the substrate is at or near its initial (or, r = 0) concentration. As time increases, product accumulation and substrate depletion will result in a curvature of this progress curve hence, the reaction velocity at these later times would be correspondingly lower.)... 

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-... 

Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for some allosteric enzymes, plots of V0 versus [S] (Fig. 6-29) produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non-regulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis-Menten relationship. Instead, the symbol [S]0 e or K0,5 is often used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6-29). 

If a plot of the reciprocal of the velocity of an enzyme catalyzed reaction versus the reciprocal of the substrate concentration yields a straight line, the intercept on the 1/V axis is ... 

The rate (v) of many enzyme-catalyzed reactions can be described by the Michaelis-Menten equation. For enzymes that exhibit Michaelis-Menten kinetics, plots of velocity versus substrate concentration are hyperbolic. 

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.

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. 

I 56. In the study of enzymes, a sigmoidal plot of substrate concentration ([S]) versus reaction velocity (V) may indicate... 

Some of the key features of the behaviour of enzymes can be demonstrated simply by incubating an enzyme with its substrate and measuring the amount of product formed in a given time. From such a measurement one can calculate the rate or velocity of the reaction, V (amount of product formed/time). If one performs this experiment several times with varying amounts of substrate, S, but the same amount of enzyme present, one can plot a graph of velocity versus substrate concentration (see Figure 11). Such a... 

A EXPERIMENTAL FIGURE 3-19 The and l/ ,ax for an enzyme-catalyzed reaction are determined from plots of the initial velocity versus substrate concentration. The shape of these hypothetical kinetic curves is characteristic of a simple enzyme-catalyzed reaction in which one substrate (S) is converted into product (P). The initial velocity is measured immediately after addition of enzyme to substrate before the substrate concentration changes appreciably, (a) Plots of the initial velocity at two different concentrations of enzyme [E] as a function of substrate concentration [S]. The [S] that yields a half-maximal reaction rate is the Michaelis constant K, a measure of the affinity of E for S. Doubling the enzyme concentration causes a proportional increase in the reaction rate, and so the maximal velocity 1/max is doubled the K, however, is unaltered, (b) Plots of the initial velocity versus substrate concentration with a substrate S for which the enzyme has a high affinity and with a substrate S for which the enzyme has a low affinity. Note that the 1/max is the same with both substrates but that is higher for S, the low-affinity substrate. 

From plots of reaction rate versus substrate concentration, two characteristic parameters of an enzyme can be determined the Michaelis constant K, a measure of the enzyme s affinity for substrate, and the maximal velocity V ax> a measure of its catalytic power (see Figure 3-19). 

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. 

Erom the plot of velocity versus substrate concentration shown in Figure 8-1, obtain the follotving parameters. (The amount of enzyme in the reaction mixture is 10 imol.)... 

FIGURE 8.1 Plot of reaction velocity versus substrate concentration. 

If a substrate were to have equal affinities for the R and T forms, the forms would be indistinguishable kinetically and the system would behave as if all the enzyme were present in a single form. Thus, Michaelis-Menten kinetics would apply, and a plot of the reaction velocity versus the substrate concentration would be hyperbolic. 

An another useful way to examine the experimental data is a plot of log [A] versus (Michaelis Menten, 1913). With the aid of such a plot, one ean examine the initial velocities of reaction in a very broad range of substrate concentrations and, although nonlinear, the plot becomes almost linear if the substrate concentrations are approximately O.3-3KA. 

Figure 1.9. Log-log plot of initial velocity versus initial substrate concentration used in determination of the reaction rate constant (kr) and the order of the reaction.

Figure 3.4. Initial velocity versus substrate concentration plot for an enzyme-catalyzed reaction. Notice the first- and zero-order regions of the curve, where the reaction velocity is, respectively, linearly dependent and independent of substrate concentration.

In what follows, we describe a t)q)ical analysis of velocity versus substrate concentration data set. Five replicates of reaction velocities were determined at each substrate concentration, and the data are shown in Table 3.1. It is good practice to start by constmcting a residual plot (Fig. 3.7). In this case, residuals refer to the difference between the mean of a set of data points (y,) and each individual data point j at a particular substrate concentration i ... 

Studies of enzyme kinetics involve measurements of initial velocity v of the reaction as a function of substrate concentration [S]. Values of the kinetic constants are determined by fitting the initial velocity and concentration data to the appropriate rate equations by the least-squares method. The maximal velocity and Michaelis constant are obtained from experimental data, usually from different methods of plotting the kinetic parameters, the most common of which is to plot llv versus... 

Comparison of hyperbolic and sigmoidal enzyme kinetics. The plot of velocity, rate of reaction, versus concentration of substrate or activator shows the response of a hyperbolic (Michaelis-Menten) reaction in black. The response of a sigmoidal reaction is shown by the purple curve. The shaded area indicates the range of physiological concentrations of substrate or activator. 

Fig. 9-5 Schematic plots of the reciprocal initial velocity, l/i , versus the reciprocal concentration of substrate A for a two-substrate reaction (a) successive binary complex formation between enzyme and substrates, Eq. (9-27) (b) ternary complex formation between both substrates and enzyme, Eq. (9-26). The concentrations of the second substrate, B, are such that Bi>B2>B3>B4.

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