Enzyme Kinetics and Energy Metabolism

Enzyme kinetics and inhibition

Michaelis–Menten kinetics describes how the initial velocity of an enzyme-catalysed reaction depends on substrate concentration. For an enzyme of total concentration [E_t], the rate is v = k_{cat}[E_t][S]/(K_m + [S]), where K_m is the substrate concentration that gives half of V_{max} and k_{cat} is the turnover number, the number of substrate molecules one active site converts per second at saturation. Because V_{max} = k_{cat}[E_t], a single measured velocity is enough to solve for k_{cat} once K_m and [S] are known. The ratio k_{cat}/K_m, expressed in \mathrm{M^{-1}s^{-1}}, is the catalytic efficiency or specificity constant. It is the apparent second-order rate constant at low substrate concentration, and it is the standard basis for comparing two substrates for the same enzyme. Convert all concentrations to one unit before substituting, because a nM–µM mismatch changes the result by a factor of 1000. For example, an enzyme at 20 nM (0.02 \muM) with K_m = 4 \muM and [S] = 4 \muM that gives v = 1.0 \muM s^{-1} has k_{cat} = v(K_m+[S])/([E_t][S]) = 100 s^{-1}, and therefore k_{cat}/K_m = 2.5 \times 10^{7} M^{-1}s^{-1}. Inhibitors are classified by which kinetic parameters they change. A competitive inhibitor binds the free enzyme at the active site and competes with the substrate. It raises the apparent K_m but leaves V_{max} unchanged, because enough substrate can displace it. For this reason its action is reversed by excess substrate, which is the decisive test that separates it from the other classes. On a Lineweaver–Burk plot, the competitive pattern appears as lines that intersect on the y-axis. The combination of unchanged V_{max} with increased K_m therefore identifies competitive inhibition. Other classes behave differently. Uncompetitive inhibitors bind only the enzyme–substrate complex and lower both V_{max} and K_m. Non-competitive inhibitors bind a site away from the active site, lower V_{max} and leave K_m unchanged, and allosteric inhibitors alter enzyme conformation through a regulatory site. None of these is overcome by excess substrate. Irreversible inhibitors form covalent bonds with the enzyme, and non-specific inhibitors denature or modify it. 2-Deoxyglucose is a glucose analogue that lacks the 2-hydroxyl group. It is taken up by glucose transporters and phosphorylated by hexokinase, but the product, 2-deoxyglucose-6-phosphate, cannot be isomerised by glucose-6-phosphate isomerase. It therefore accumulates and inhibits both hexokinase and this isomerase at the early steps of glycolysis. Glucose-6-phosphate dehydrogenase belongs to the pentose phosphate pathway, and phosphofructokinase acts later in glycolysis, so neither is a primary target of this analogue.