Enzymology Lecture 2 PDF

The following assumptions are made in deriving the Michaelis - Menten rate equation: 1. Relative concentrations of E and S: The concentration of substrate ([S]) is much greater than the concentration of enzyme ([E]), so that the percentage of total substrate bound by the enzyme at any one time is s...

The following assumptions are made in deriving the Michaelis - Menten rate equation: 1. Relative concentrations of E and S: The concentration of substrate ([S]) is much greater than the concentration of enzyme ([E]), so that the percentage of total substrate bound by the enzyme at any one time is small. 2. Steady-state assumption: ☆ [ES] does not change with time (the steady-state assumption), that is, the rate of formation of ES is equal to that of the breakdown of ES (to E + S and to E + P). 3. Initial velocity: ☆ Initial reaction velocities (Vo) are used in the analysis of enzyme reactions. ☆ This means that the rate of the reaction is measured as soon as enzyme and substrate are mixed. At that time, the concentration of product is very small and, therefore, the rate of the back reaction from P to S can be ignored  Michaelis–Menten Kinetic Theory of Enzyme Action Michaelis–Menten model accounts for the kinetic properties of some enzymes. It helps to describe many enzymatic reactions under the following assumptions: ►The reaction has only one substrate. ►The substrate concentration is much higher than that of the enzyme. ►Only the initial reaction velocity (Vo) is measured. More details about assumptions of Michaelis equation Why is it necessary to consider only the initial reaction rate?   At the beginning of the reaction the substrate alone, is present and the unoccupied active-sites of the enzyme molecule are free to bind them. Therefore, the substrate is rapidly converted to the product.  As the product concentration builds up and the substrate concentration falls, the reaction keeps getting slower and eventually stops at equilibrium (Fig. 6.7). Since it is impossible to consider this “changing” reaction rate, only the initial reaction-rate (Vo) is taken into account.  The relation between Vo and the substrate concentrate [S] is given by Michaelis–Menten equation: + The equation predicates a hyperbolic curve of Vo against [S]. Vo is measured at different substrate concentrations by incubating different amounts of the substrate with enzyme. The rate of disappearance of the substrate or the rate of appearance of the product during the first few minutes of the reaction only is taken into account. Vmax is the maximum velocity that can be reached by increasing the substrate concentration (Fig. 6.8). For any particular set of conditions it is a constant. It indicates a saturation state at which most enzyme active sites are occupied by the substrate molecules, and the reaction rate is no longer limited by substrate availability.  [S] is the substrate concentration at the initial phase of the reaction. This changes as the reaction proceeds, so the experimental data are taken, in the first few minutes of the reaction. Km is a special rate constant called the Michaelis constant. It is defined as the substrate concentration at which the reaction rate is half-maximal (Fig. 6.8). At this instance the enzyme is half-saturated with its substrate  Km has a characteristic value for a given enzyme substrate pair. In case of the enzyme which acts on more than one substrate, the value of Km is different for each of them. For example, Km of the enzyme hexokinase for fructose is 1.5 mM, whereas for glucose it is 0.05 mM (Table 6.6). Km reflects binding affinity: The Michaelis–Menten constant Reflects the binding affinity of the enzyme for its substrate. If affinity is more, less substrate is required to saturate the enzyme, so that Vmax is reached at a relatively low substrate concentration. Consequently, the substrate concentration corresponding to the half Vmax (i.e. Km) is relatively low. For this reason, high enzyme-substrate affinity implies a low Km value, and conversely, low-affinity implies high Km. Ex. Higher Km of glucose for glucokinase (10 mM) than that for hexokinase (0.05 mM) for example, indicates that hexokinase binds glucose with higher affinity than glucokinase. Finally note that : The Michaelis–Menten equation describes the relationship between initial reaction velocity and substrate concentration under steady state conditions. The Michaelis constant Km, defined as the substrate concentration at which the reaction velocity is half maximal, is related to the affinity of the enzyme for the substrate. The following inferences can be drawn from the Michaelis–Menten kinetics. Order of reaction: When the substrate concentration is relatively low (far below Km), most of the enzyme active sites are free. An increase in substrate concentration at this stage results in rapid occupancy of the available sites. Therefore, the reaction rate is related almost linearly, with the substrate concentration, and the reaction shows first order kinetics (Fig.5.10). With increasing substrate concentration, the reaction rate rises till a constant peak value (Vmax) is reached. Nearly all enzyme active sites are occupied by the substrate at this stage and further increase in substrate concentration has no effect on the reaction rate. The rate of reaction at this stage is in zero order with respect to the substrate. It implies that the reaction rate is independent of the substrate concentration (fig 5.10 ) Lineweaver–Burk plot:  The slope of the Michaelis–Menten curve is gradual and upwards giving it a hyperbolic shape.  From this shape, it is not possible to estimate the exact value of Vmax.  However, if reciprocal of the following parameters to give lineweaver burk plot, that was described by Hans Lineweaver and Dean Burk in 1934: Bisubstrate reactions: Heretofore, we have considered simple, single-substrate reactions, which obey Michaelis– Menten kinetics. Yet, far more common (60% of total) are the enzymatic reactions requiring multiple substrates and yielding multiple products. Indeed those involving two substrates mostly yield two products PLP = Pyridoxal phosphate Competitive Inhibition Mechanism: The inhibitor exhibits is a close structural resemblance with the actual substrate. It impairs substrate-binding to the enzyme, because it occupies the active site of the enzyme making it unavailable for the substrate.  Occupancy of the enzyme active site by the inhibitor yields (EI) complex. Since the formation of (EI) depends upon the concentration of the inhibitor (just as the formation of ES is dependent on the substrate concentration), the inhibition is strictly dependent upon the relative concentrations of the inhibitor and the substrate at fixed concentration of the enzyme. Effect on enzyme kinetics: The Km shows an apparent increase in the presence of the inhibitor (Table 6.7). This reflects decreased affinity of the substrate with the\ enzyme active site. The decreased affinity is because the substrate must now compete with the inhibitor for the active site. This is depicted in a double reciprocal plot as a shift in the x- intercept (–1/Km) and in the slope of the line (Km/Vmax) (Fig. 5.12). Vmax (the measure of fastest possible rate) remains unchanged because the binding of inhibitor is reversible; and at infinite concentration of the substrate (obtained by extrapolation) the inhibitor can be completely displaced from the enzyme active site. Statin drugs as examples of competitive inhibitors: * This group of antihyperlipidemic agents competitively inhibits the first committed step in cholesterol synthesis. * This reaction is catalyzed by hydroxymethylglutaryl–CoA reductase (HMG-CoA reductase). * Statin drugs, such as atorvastatin (Lipitor) and pravastatin (Pravachol), are structural analogs of the natural substrate for this enzyme, and compete effectively to inhibit HMG-CoA reductase. * By doing so, they inhibit cholesterol synthesis, thereby lowering plasma cholesterol levels (Figure 13) Some examples of competitive inhibitors are : (a) Malonate ions inhibit the succinate dehydrogenase reaction of Kreb’s cycle. (b) Acetazolamide causes competitive inhibition of carbonic anhydrase. Inhibition of the succinate dehydrogenase reaction by malonate anions is a classical example of competitive inhibition (Fig. 6.11). Malonate is a structural analog of succinate, the actual substrate of the enzyme succinate dehydrogenase. It occupies the active site of the enzyme, thus preventing it from acting on succinate Some more of competitive inhibitors (of therapeutic significance) are given in the next section (see Table) Non-competitive Inhibition Mechanism: In this type, the enzyme inhibitor is structurally unrelated to the structure of substrate and binds the enzyme at a site distinct from the enzyme active site. Occupancy of this site by the inhibitor alters the shape of the enzyme such that its catalytic activity is reduced or lost. The substrate is still able to bind the enzyme, but the enzyme cannot catalyze the reaction when inhibitor is bound. Thus, the non-competitive inhibitor does not block active site of the enzyme, but behaves as though it was removing active enzyme from the solution. Evidently, unlike competitive inhibition, increasing the substrate concentration does not reverse the inhibition. Effect on enzyme kinetics: The non-competitive inhibitor  Does not block the active site of the enzyme. Therefore, the Km (indicating enzyme-substrate affinity) remains unaffected.  Increasing the concentration of the substrate does not affect binding of the inhibitor to the enzyme.  This is because the shape of the enzyme is different when the inhibitor is bound to it, and hence it does not matter how much substrate is present; the enzyme will always be less effective due to this shape change.  This is reflected in decreased Vmax, and is seen graphically on the double reciprocal plot where both the slope and the y- intercept are changed Some examples of non-competitive inhibitors are: (a) Heavy-metal ions, such as Hg, Ag, and Pb; they react reversibly with thiol groups (SH) of enzymes. The thiol group participates in maintenance of the three- dimensional conformation of the enzyme proteins. (b) Chelating agents such as ethylene-diaminetetra-acetic acid (EDTA). EDTA can chelate metals required for the activity of some enzymes. Provided that the inhibitor has not reacted covalently with the enzyme, the non-competitive inhibition can often be reversed by exhaustive dialysis of the inhibited enzyme. Other examples for non –competitive inhibitors :- * Ferrochelatase, an enzyme that catalyzes the insertion of Fe2+ into protoporphyrin (a precursor of heme) is an example of an enzyme sensitive to inhibition by lead. * Other examples of noncompetitive inhibition are certain insecticides, whose neurotoxic effects are a result of their covalent binding at the catalytic site of the enzyme acetylcholinesterase (an enzyme that cleaves the neurotransmitter, acetylcholine). Uncompetitive Inhibition:- The inhibitor binds with only the ES form of the enzyme to form the enzyme-substrate-inhibitor (ESI) complex. Binding may occur at a site distant from the active site, or at a site overlapping with the active site. In either case, the result is lowering of both: the catalytic efficiency of the enzyme and its apparent binding affinity for the substrate. These result in changes in Km and Vmax (both decreases). As a result, in the double reciprocal plot a line parallel to that of the uninhibited enzyme (slope remains unchanged), but with altered intercepts on both, the x and the y axis (Fig. 6.13).  The uncompetitive inhibition is uncommon in single substrate reactions. But a noteworthy example in clinical enzymology is the inhibition of intestinal alkaline phosphatase by L- phenylalanine. It is more commonly observed in two-substrate reactions with a double displacement reaction mechanism. However, the interpretation is complex in the later case and will not be considered further Note: The types of inhibitions presented here are extreme cases. Actually, however, one may come across mixed types of inhibitions. For instance, the binding of an inhibitor to a site other than the active site may not only change the shape of the enzyme, but also affect the binding of the substrate at the active site, so that Km as also Vmax is altered Finally we conclude that :