Initial velocities plotting substrate concentration versus

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 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. 

If an approximate Km value for the enzyme-substrate combination of interest is known, a full-scale kinetic assay may be done immediately. However, often an approximate value is not known and it is necessary first to do a range finding or suck and see preliminary assay. For such an assay, a concentrated substrate solution is prepared and tenfold serial dilutions of the substrate are made so that a range of substrate concentrations is available within which the experimenter is confident the Km value lies. Initial velocities are determined at each substrate concentration, and data may he plotted either hyperholically (as V versus [S]) or with [S] values expressed as logio values. In the latter case, a sigmoidal curve is fitted to data with a three parameter logistic equation (O Eq. 4) ... 

A graphical procedure for characterizing isomerization mechanisms . The protocol uses data from product inhibition, and l/[v[p]=o vpjo] is plotted versus 1/[P] at various constant concentrations of the substrate (where Vp=o is the initial velocity in the absence of product and V[p]o is the initial velocity in the presence of product). Secondary and ternary replots allows one to characterize the mechanism . This procedure requires very accurate estimation of initial rates. 

A graphical procedure " for plotting enzyme initial rate data as v versus v/[S] (also known as the Woolf-Au-gustinsson-Hofstee plot), where the initial velocity v is the so-called (y)-axis variable and v divided by the initial substrate concentration [S] is the so-called (v)-axis variable, such that the vertical-axis intercept equals Vmax, the slope equals and the horizontal-axis intercept is V IK... 

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.)... 

For example, Bachelard used [Mgtotai]/[ATPtotai ] = 1 in his rate studies, and he obtained a slightly sigmoidal plot of initial velocity versus substrate ATP concentration. This culminated in the erroneous proposal that brain hexokinase was allosterically activated by magnesium ions and by magnesium ion-adenosine triphosphate complex. Purich and Fromm demonstrated that failure to achieve adequate experimental control over the free magnesium ion concentration can wreak havoc on the examination of enzyme kinetic behavior. Indeed, these investigators were able to account fully for the effects obtained in the previous hexokinase study. ... 

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-... 

Fig. 3. A schematic plot of the steady-state initial velocity v, versus the substrate concentration S, illustrating a hyperbolic saturation isotherm (--), positive cooperativity (---), and...

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],... 

Equation 6 describes an intersecting initial velocity pattern where 1/v is plotted versus 1/A at different values of B, whereas Equation 6 describes the pattern where 1/v is plotted versus 1/B at different values of A (Fig. 1). Both the slopes and the intercepts of the reciprocal plots are functions of the other substrate concentration, and replots of slopes or intercepts versus the reciprocal of the other substrate concentration allow determination of all kinetic constants. 

The Henri-Michaelis-Menten equation describes the curve obtained when initial velocity is plotted versus substrate concentration. The curve shown in Figure 4-7 is a right rectangular hyperbola with limits of and - K . The curvature is fixed regardless of the values of and V mxx- Consequently, the ratio of substrate concentrations for any two fractions of Vj m is constant for all enzymes that obey Henri-Michaelis-Menten kinetics. For example, the ratio of substrate required for 90% of Vmat to the substrate required for... 

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. 

The enzymatic activity of AChE from electric eel is inhibited by monosulfonate tetraphenyl porphyrin (TPPSi) the structure of which can be seen in Figure 12.1 with Rj = SO3, R2 = no substituent group, and no metal incorporated [36]. A Lineweaver-Burk plot of enzymatic rates in the absence/presence of TPPSj determines the type of inhibition resulting from the presence of the porphyrin. The Lineweaver-Burk plot is the plot of the double-reciprocal form of the initial enzymatic rate versus the substrate concentration. Intersection of the lines generated in the absence and presence of inhibitor at the y-axis shows no change in maximal velocity but a change in the Michaelis constant K j, an indication of the substrate binding affinity, and indicates competitive inhibition by the porphyrin. Competitive inhibition involves competition of the inhibitor for occupation of the active site of the enzyme. 

Fig. 9-1 Schematic plot of initial velocity versus substrate concentration for a mechanism involving one substrate.

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.

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. 

In such cases, it is important that the data cover both high and low concentrations of substrate so that the initial velocities fall within several orders of magnitude. In substrate inhibition, graphical analysis precedes statistical analysis, and data are usually plotted in the form of Vo versus log [A] (Fig. 7) from such plots, the initial estimate of can be obtained by graphical methods (Section 11.2.7). 

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.

Figure 4.1. Initial velocity versus substrate concentration plot for fumarase in the absence and presence of the reversible inhibitor succinate.

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... 

FIGURE 6.7 Graphical procedures for the estimation of V and K . (a) Plot of initial velocity versus substrate concentration. 

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