Substrate inhibition plots

Fig. 5.14. Substrate inhibition plots for batch system with top left comer showing the concentration of substrate inhibitor designated by [5 ] (Left Hanes-woolf Right Curve fit).

Figure 8. Substrate inhibition. Plot of Uq versus log [A], drawn according to Eq. (11.23), assuming that P, = = 1.

A useful graphical method for the estimation of kinetic parameters in substrate inhibition was described by Marmasse (1963). However, with substrate inhibition plots, even after a successful graphical analysis is completed, one should always fit the data to the appropriate equation with a computer program in order to estimate the kinetic constants. 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

Figure 8.11 Substrate inhibition. The enzyme L-amino acid oxidase (EC 1. 4. 3. 2) suffers substrate inhibition at concentrations of L-leucine above 3.0 mmol 1 1. A Lineweaver-Burk plot shows the characteristic bend to the usual straight line.

The value of A i oep was evaluated from results of separate experiments in which GR catalyzes the reduction of GSSG by NADPH in the presence of various concentrations of G6P as inhibitor. The procedure employed is described in Section 3.3.2, and the pertinent results, plotted as 1/T versus 1/[GSSG], are presented in Figure 4.60. It can be seen that whenever the inhibitor G6P is present, the lines bend upward as they approach the /V axis. This bend becomes more pronounced as the concentration of G6P increases. This behavior is usually associated with substrate inhibition [149] and perhaps the inhibitor G6P affects the substrate GSSG and the latter becomes inhibitory to the enzyme GR. However, this effect was not considered in the rate equations used in the experimental system. 

Double-reciprocal plots can be reasonably accurate if rate data can be obtained over a reasonable range of saturation, say from O.SVniax to O-SEmax- Any indication of a curved double-reciprocal plot necessitates consideration of substrate activation (downward curvature as one proceeds to higher (1/[S]) values), substrate inhibition (usually evident by upward curvature as one approaches the 1/v-axis), multiple binding of S, failure to measure true initial rates, or cooperativity. 

If a noncompetitive or an uncompetitive inhibitor were present with the substrate at constant ratio, then graphical analysis would suggest that the phenomenon of substrate inhibition is present. If an investigator analyzed the apparent substrate inhibition via a Marmasse plot, wrong estimates of both the K a and K s values would be reported and the investigator would be mislead with respect to the kinetic mechanism. If partial inhibitors or alternative substrates are present in constant ratio, depending on the relative sizes of the Ymax and values,... 

A. Effect of a competitive inhibitor on the reaction velocity (v0) versus substrate [S] plot. B. Lineweaver-Burke plot of competitive inhibition of an enzyme. 

A protein inhibitor has been extracted and partially purified from mouse liver by Lesca and Paoletti 45). This protein inhibits acid DNases from different tissues and species but not pancreatic or E. coli DNases. Very interestingly, V vs. substrate concentration plots become sigmoid in the presence of the inhibitor provided that pH is lower than 5.6. The existence of a DNase-inhibitor complex is suggested by sucrose-gradient results. An unusual feature of the inhibitor is its ability to reactivate acid DNase preparations treated with 8 M urea. 

A Lineweaver-Burk plot of the preceding data did not result in a straight line when the substrate concentration was high. To take into account the substrate inhibition effect, the following reaction mechanism was suggested ... 

Based on the result from the IC50 determination, determination of additional kinetic parameters such as Ki and the inhibition mode are useful (variation of the substrate concentration e.g. Km/4 1 Km with time). Transformation of the Michaelis-Menten equation are used both for calculation the Ki value as well as for graphical depiction of the type of inhibition (e.g. direct plot ([rate]/[substrate], Dixon plot [l/rate]/[inhibitor], Linewaver-Burk plot [l/rate]/[l/substrate] or Eadie-Hofstee plot [rate]/[rate/substrate]). 

Figure 9.2. Substrate inhibition manifested in (a) a saturation plot and (b) a Lineweaver-Burk plot of data.

What type of inhibition is taking place (2) Sketch the curves for no inhibition. competitive, uncompetitive, noncompetitive (mixed) inhibition, and substrate inhibition on a Woolf-Hanes plot and on an Eadie-Hofstee plot. 

A homotropic effect occurs when the binding of one substrate molecule perturbs the rate of catalysis of a second molecule of the same substrate. It is possible for the homotropic effect to be either positive, that is, to give rise to an increased rate of catalysis (homotropic activation, positive cooperativity, or autoactivation), or a negative, that is, causing a decreased rate of catalysis (homotropic inactivation, negative cooperativity, or substrate inhibition). These circumstances cannot be adequately modeled by the simple Michaelis-Menten equation, and neither do direct plots of v... 

The preferred pathway mechanism also provides one hypothesis for substrate activation or inhibition 6,39). It is simply a limiting case of a nonequilibrium random mechanism which can be formally reconciled with linear primary plots over wide reactant concentrations. However, with sufficiently large concentrations of B, net reaction through EB may become significant, and cause deviations from Eq. (1) toward lower or higher activity, depending upon whether k > ki or ki < ki [Eq. (10)]. This and other mechanisms for substrate inhibition and activation will be discussed in Section II,F,1. 

When Rudolph and Fromm used thionicotinamide adenine dinucleotide (thio-DPN) as an alternate substrate for NAD+ and varied the concentration of ethanol with liver alcohol dehydrogenase [following the reaction at 342 nm, the isosbes-tic point for thio-DPN and reduced thio-DPN (thio-DPNH)], they saw what appeared to be concave upward reciprocal plots with partial substrate inhibition in the presence of thio-DPN (38). However, the asymptote intercepts appeared to decrease with increased thio-DPN concentration, which is not what the above equations predict for a case where a minimum is present in the curve. There must have been other interactions that caused the substrate inhibition by ethanol in the presence of thio-DPN. 

These Lineweaver-Burk plots showed apparent substrate inhibition at concentrations greater than 0.05M. 

Lineweaver-Burk plots provide a good illustration of competitive inhibition and pure noncompetitive inhibition (Fig. 9.18). In competitive inhibition, plots of 1/v vs 1/[S] at a series of inhibitor concentrations intersect on the ordinate. Thus, at infinite substrate concentration, or 1/[S] = 0, there is no effect of the inhibitor. In pure noncompetitive inhibition, the inhibitor decreases the velocity even when [S] has been extrapolated to an infinite concentration. However, if the inhibitor has no effect on the binding of the substrate, the is the same for every concentration of inhibitor, and the lines intersect on the abcissa. 

FIGURE 4.7 Representative plot depicting substrate inhibition kinetics. 

FIGURE 4.9 Eadie-Hofstee plots useful to diagnose the type of kinetics occurring in a reaction for (a) hyperbolic (Michaelis-Menen) kinetics, (b) Sigmoidal kinetics, (c) Biphasic kinetics with no saturation of second phase, and (d) Substrate inhibition kinetics. 

FIGURE 13.2 Biochemical plots for the enz5me kinetic characterizations of biotransformation, (a) Direct concentration-rate or Michaelis-Menten plot (b), Eadie-Hofstee plot (c), double-reciprocal or Lineweaver-Burk plot. The Michaelis-Menten plot (a), typically exhibiting hyperbolic saturation, is fundamental to the demonstration of the effects of substrate concentration on the rates of metabolism, or metabolite formation. Here, the rates at 1 mM were excluded for the parameter estimation because of the potential for substrate inhibition. Eadie-Hofstee (b) and Lineweaver-Burk (c) plots are frequently used to analyze kinetic data. Eadie-Hofstee plots are preferred for determining the apparent values of and Umax- The data points in Lineweaver-Burk plots tend to be unevenly distributed and thus potentially lead to unreliable reciprocals of lower metabolic rates (1 /V) these lower rates, however, dictate the linear regression curves. In contrast, the data points in Eadie-Hofstee plot are usually homogeneously distributed, and thus tend to be more accurate. 

Notes It is recommended that statistical and computer analysis of kinetic data should be carried out to evaluate kinetic parameters (Cleland, 1967 Cornish-Bowden, 1995), however these linear plots may still retain their diagnostic values. The linear plots indicate the compliance to die Michaelis-Menten kinetics whereas nonlinear plots imply multiple substrate addition, substrate inhibition or homotropic allosterism. 

We shall turn now to much more realistic cases of bisubstrate reactions. The proper way to study a substrate inhibition in bisubstrate reactions is to vary a noninhibitory substrate, at differing high levels of the inhibitory one and see whether the slopes, intercepts, or both of reciprocal plots show the inhibitory effects (Cleland, 1979). These cases are then called competitive, uncompetitive, and noncompetitive substrate inhibition, respectively. 

A direct plot of Uo versus [B] is not hyperbolic anymore, but has an unusual shape, characteristic for substrate inhibition (Fig. 1). 

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