10.6 12 Generality of MM kinetics In this problem you'll see that the MM formula is really more generally applicable than the discus- sion in the text may have made it seem. The enzyme chymotrypsin catalyzes the hydrolysis of peptides (short protein fragments). We will denote the enzyme's original state as EOH to emphasize one key hydroxyl group on one of its residues. We will also represent a peptide generically by the symbol RCONHR', where the central atoms CONH indicate one particular peptide bond (see Figure 2.15 on page 43) and R, R' denote everything to the left and right respectively of the bond in question. The enzyme operates as follows: A noncovalent complex (EH-RCONHR") forms rapidly be- tween the enzyme EOH and the peptide substrate RCONHR', which we will call S. Next EOH gives up a hydrogen and bonds covalently to one half of the peptide, breaking the bond to the other half, which is released. Finally, the remaining enzyme-peptide complex splits a water molecule to restore EOH to its original form and release the other half of the peptide: eg Kes EOH + S + H2O EOH.S+H20 * EOCOR+NH R' +H2O kg EOH+RCO2H + NH R'. Assume as shown that the last step is irreversible. Assume that the first reaction is so fast that it's practically in equilibrium, with equilibrium constant csKeq,s. Apply the steady-state assumption to CEOCOR to show that the overall reaction velocity of the scheme described above is of Michaelis-Menten form. Find the effective Michaelis constant and maximum velocity in terms of Keq,s, the rate constants k2, kz, and the total concen- tration CE, tot of enzyme