Entropic contributions to rate accelerations in enzymic and intramolecular reactions and the chelate effect

It is pointed out that translational and (overall) rotational motions provide the important entropic driving force for enzymic and intramolecular rate accelerations and the chelate effect; internal rotations and unusually severe orientational requirements are generally of secondary importance. The loss of translational and (overall) rotational entropy for 2 --> 1 reactions in solution is ordinarily on the order of 45 entropy units (e.u.) (standard state 1 M, 25 degrees C); the translational entropy is much larger than 8 e.u. (corresponding to 55 M). Low-frequency motions in products and transition states, about 17 e.u. for cyclopentadiene dimerization, partially compensate for this loss, but "effective concentrations" on the order of 10(8) M may be accounted for without the introduction of new chemical concepts or terms.

On the attribution and additivity of binding energies

It can be useful to describe the Gibbs free energy changes for the binding to a protein of a molecule, A-B, and of its component parts, A and B, in terms of the "intrinsic binding energies" of A and B, DeltaG(A) (i) and DeltaG(B) (i), and a "connection Gibbs energy," DeltaG(s) that is derived largely from changes in translational and rotational entropy. This empirical approach avoids the difficult or insoluble problem of interpreting observed DeltaH and TDeltaS values for aqueous solutions. The DeltaG(i) and DeltaG(s) terms can be large for binding to enzymes and other proteins.

Thiazolium C(2)-proton exchange: structure-reactivity correlations and the pKa of thiamin C(2)-H revisited

Rate constants for C(2)-proton exchange from thiamin, N(1')-methylthiamin, and several 3-substituted-4-methylthiazolium ions catalyzed by D2O and deuterioxide ion were determined by 1H NMR at 30 degrees C and ionic strength 2.0 M. Values of pKa for the thiazolium ions, including thiamin itself, were found to be in the range pKa = 17-19; the pKa values for N(1')-protonated thiamin and free thiamin C(2)-H in H2O are 17.7 and 18.0, respectively. The pKa value for N(1')-protonated thiamin was calculated from the observed rate constant for the pD-independent reaction with D2O after correction for a secondary solvent deuterium isotope effect of kH2O/kD2O = 2.6. The pKa value for free thiamin was calculated from the rate constant for catalysis by OD- after correction by a factor of 3.3 = 8/2.4 for an 8-fold negative deviation of kOD from the Brønsted plot of slope 1.0 for general base catalysis and a secondary solvent isotope effect of kOD/kOH = 2.4. Values of k-a = 2 X 10(10) and 3 X 10(9) M-1 s-1 were assumed for diffusion-controlled protonation of the C(2) ylide in the reverse direction by H3O+ and H2O, respectively. The Hammett rho I value for the exchange reaction catalyzed by deuterioxide ion or D2O is 8.4 +/- 0.2. There is no positive deviation of the rate constants for free or N(1')-substituted thiamin analogues in either Hammett correlation. This shows that the aminopyrimidinyl group does not provide significant intramolecular catalysis of nonenzymic C(2)-proton removal in the coenzyme.

Alkaline phosphatase is an almost perfect enzyme

The second-order rate constant, kcat/km, for catalysis of the hydrolysis of 4-nitrophenyl phosphate by alkaline phosphatase decreases with increasing viscosity in the presence of sucrose or arabinose, with a slope of delta[kcat/Km)0/(kcat/Km)]/delta(eta/eta 0) = 1.4 at pH 8.0, 25 degrees C. This is consistent with rate-limiting diffusional encounter of the substrate with active enzyme and indicates that alkaline phosphatase is a "perfect enzyme". However, the reported second-order rate constants of kcat/Km = 6.6 x 10(6) to 4.6 x 10(7) M-1 s-1 are smaller than the diffusional limit; this shows that only approximately 0.1-1% of the diffusional encounters are productive. The first-order rate constant, kcat, for rate-limiting hydrolysis of the phosphoenzyme intermediate at pH = 6 with saturating substrate concentration is independent of viscosity in aqueous sucrose solutions. This shows that sucrose does not destabilize the transition state for phosphoenzyme hydrolysis. However, at pH 8.0 product dissociation is rate limiting and kcat decreases with increasing viscosity in the presence of sucrose, with slopes of delta(k0/kobsd)/delta(eta/eta 0) = 1.2 in 0.04 M Mops buffer, 1.0 in 0.1 M Tris, and 1.2 in 0.67 M Tris buffer. This is consistent with rate-limiting diffusional separation of inorganic phosphate and of Tris phosphate from the enzyme. In contrast, glycerol causes a large decrease in kcat/Km at pH 8.0 and also decreases kcat at pH 6. This shows that glycerol decreases the rate by a solvent effect on the catalytic activity of the enzyme, as well as by increasing the viscosity.

Sequential dissociation of Ca2+ from the calcium adenosinetriphosphatase of sarcoplasmic reticulum and the calcium requirement for its phosphorylation by ATP

The kinetics for dissociation of the stable enzyme-calcium complex of the sarcoplasmic reticulum calcium ATPase, cE.Ca2, were followed by assay with simultaneous addition of [32P]ATP and EGTA, which gives 70% phosphorylation of cE.Ca2 with k = 300 s-1 (25 degrees C, pH 7.0, 5 mM MgSO4, 0.1 M KCl). The binding of ATP to cE.Ca2 is described by kATP = 1.0 X 10(7) M-1 s-1, k-ATP = 120 s-1, and Kdiss = 12 microM; ATP binding is partially rate limiting for phosphorylation at less than 100 microM ATP. The sequential dissociation of Ca2+ from cE.Ca2 is described by k-2 = 55-60 s-1 for the first, "outer" Ca2+, k-1 = 25-30 s-1 for the second, "inner" Ca2+, and K0.5 = 3.4 microM, n = 1.9 (from Kdiss = 7.4 X 10(-7) M for Ca.EGTA). Dissociation of the inner Ca2+ is inhibited by external Ca2+, with K0.5 = k-1/k2 = 0.7 microM. This confirms the conclusion that dissociation of the two Ca2+ ions is sequential. The ability of cE.Ca2 to catalyze phosphorylation by ATP disappears in the presence of EGTA with k = 50-55 s-1, the same as k-2 for dissociation of the outer Ca2+ ion. This result, and the absence of the induction period that would occur if both cE.Ca2 and cE.Ca1 were catalytically competent, shows that both Ca2+ ions are required for phosphorylation. This conclusion is confirmed by the stoichiometry of 1.4/0.7 = 2.0 for the ratio of Ca2+ internalized to phosphoenzyme formed after simultaneous addition of ATP and EGTA. Phosphorylation of cE.Ca2 in the presence of 45Ca gives 0.15, not 0.3, 45Ca internalized, which corresponds to exchange of only 1 Ca2+ and is in agreement with this conclusion. The requirements for binding of two Ca2+ for catalytic specificity toward ATP and loss of two Ca2+ from E approximately P.Ca2 for specificity toward water account for the stoichiometry of Ca2+ transport and provide a possible reason for the two steps in the phosphorylation of cE.Ca2.ATP.

Catalysis of the hydrolysis of phosphorylated pyridines by Mg(OH)+: a possible model for enzymatic phosphoryl transfer

The second-order rate constants for reaction of the Mg2+ complexes of phosphorylated pyridine monoanions with Mg(OH)+ are 10(4)-10(6)-fold larger than the second-order rate constants for their reaction with water (25 degrees C, ionic strength 1.5). Of the 10(6)-fold rate enhancement with the phosphorylated 4-morpholinopyridine/Mg2 complex, approximately 10(4)-fold is attributed to the greater nucleophilicity of Mg(OH)+ compared with water. The remaining catalysis of approximately 10(2)-fold is attributed to induced intramolecularity from positioning of the hydroxide ion and phosphoryl group by the Mg2+ ions. This reaction may provide a model for the role of a metal ion in increasing the concentration of the anions of enolpyruvate and serine and holding the nucleophile in the correct position for phosphoryl transfer in the reactions catalyzed by pyruvate kinase and alkaline phosphatase, for example. Some mechanisms that can provide catalysis of phosphoryl transfer through a metaphosphate-like transition state are reviewed briefly.