Substrate inhibition velocity constants

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

Another kinetic profile, substrate inhibition, occurs when the velocity from ESS is lower than that of ES (Fig. 5). In this case, the saturation curve will increase to a maximum and then decrease before leveling off at Vm2. For the P450 enzymes, Vm2 is usually not zero when sub-millimolar concentrations of substrate are involved. This observation suggests that ESS still has some activity. If substrate inhibition occurs at very high substrate concentrations, non-active-site interactions should be suspected. Substrate inhibition profiles are easily identified, provided that the observed concentration range is appropriate and Kmi is not much smaller than Km2 (Fig. 5). However, determining the kinetic constants in Eq. (10) requires... 

The determination of kinetic mechanisms requires more than just initial velocity patterns, and inhibition studies are usually required. Several types of inhibitors are useful. The products are substrates in the reverse reaction and thus have some affinity for the enzyme and will give inhibition unless their inhibition constants exceed their solubility. Dead-end inhibitors are molecules that play musical chairs with the substrates for open portions of the active site but do not react. Substrates may act as dead-end inhibitors by combining at points in the mechanism where they are not intended and thus cause substrate inhibition. The inhibition patterns caused by these inhibitors are useful in distinguishing between different kinetic mechanisms. 

The first is the simplest case.. Assuming that the end-products do not inhibit the enzyme, the reaction is represented hy y — Vt, where y is the amount of substrate transformed in the time t, and F is the velocity constant of the reaction. If tne end-products inhibit the enzyme, as is usual, then V decreases with the time in a manner depending on the affinity of the particular enzyme, and expressed by various empirical equations. 

As stated earlier, the velocity terms are dependent on the concentration of substrate, relative to KM, used in the activity assay. Likewise in an activity assay the free fraction of enzyme is also in equilibrium with the ES complex, and potentially with an ESI complex, depending on the inhibition modality of the compound. To account for this, we must replace the thermodynamic dissociation constant Kt with the experimental value K-pp. Making this change, and substituting Equations (7.4) and (7.6) into Equation (7.7), we obtain (after canceling the common E T term in the numerator and denominator)... 

This is not a completely true statement. As you may see later on, the velocity of an enzyme-catalyzed reaction depends on the concentration of substrate only when the substrate concentration is near the Km. If we start out with a concentration of substrate that is 1000 times the Km, most of the substrate will have to be used up before the velocity falls because of a decrease in substrate concentration. If the product of the reaction does not inhibit and the enzyme is stable, the velocity will remain constant for much more than 1 to 5 percent of the reaction. It s only when we re near the Km that substrate depletion during the assay is a problem. 

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. 

This linearization of the tight-binding scheme allows the investigator the opportunity to calculate values for [Etotai] and Ki, the dissociation constant for the inhibitor. In the Henderson plot, [Itotai]/(l v/Vo) is plotted as a function of vjv where Vq is the steady-state velocity of the reaction in the absence of the inhibitor. The slope of the line is the apparent dissociation constant for the inhibitor. Secondary plots (from repeating the inhibition experiment at different substrate concentrations) will yield the Ki value. The vertical intercept is equal to [Etotai]- Hence, repeating the experiment at a different concentration of enzyme will produce a parallel line. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

Inhibition kinetics are included in the second category of assay applications. An earlier discussion outlined the kinetic differentiation between competitive and noncompetitive inhibition. The same experimental conditions that pertain to evaluation of Ku and Vmax hold for A) estimation. A constant level of inhibitor is added to each assay, but the substrate concentration is varied as for Ku determination. In summary, a study of enzyme kinetics is approached by measuring initial reaction velocities under conditions where only one factor (substrate, enzyme, cofactor) is varied and all others are held constant. 

The dependence of the kinetic constants (Table I) upon the concentration of Ca2t, pH, and ionic strength is not the same for all the synthetic substrates shown on Table I. In general, however, with all these substrates the maximal velocities are achieved between pH 9 and 11, maximal affinity for substrate occurs between pH 7.5 and 8.5 (Fig. 4), and inhibition of enzymic activity is observed with NaCl concentrations greater than 0.1 N. Similar dependence upon these parameters is seen when activities are measured with DNA and RNA (3). 

The assay was performed by first preincubating selected experimental agents and the enzyme for 10 minutes. Thereafter, the assay was initiated by adding the substrate to obtain a final volume of 100 p,l. The initial velocity of chromogenic substrate hydrolysis was measured by the change in absorbance at 405 nm at 25°C during the linear portion of the time course. Inhibition constants, K, for factor Xa are summarized in Table 1. 

The first term on the right represents the inhibition effect, while the second term is the net reaction excluding the inhibition. KltX is the equilibrium dissociation constant (in mM), and indicates the ratio (El - ] )/(Eh ), when the binding relaxes to equilibrium. Here, A stands forX0, A, . orX4, and (/ ., - X]) is the concentration of the enzyme-substrate X1 complex, and A, A, is the product of the concentrations of the free enzyme E, and the free substrate Xx. The reaction velocities. /rir and. /rlh are the maximal rates of forward and backward rates of catalysis (in mM/min), respectively. As seen from Eq. (11.65), the rate is a nonlinear function of the concentrations of metabolites. 

In this case the maximal velocity Vmax is reduced, but KM is unaffected the inhibitor binding constant can be evaluated from the dependence of Vmax on inhibitor concentration C/.This form of non-competitive inhibition, characterised by independent binding of substrate and inhibitor, and complete lack of activity when enzyme is bound to inhibitor, represents a simple limiting case. 

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