115:412/508 Proteins & Enzymes spring 2002

Mechanism of Enzyme Action II

But many of the physical effects I have described also potentiate chemical catalysis by groups on the enzyme. We generally at least hope that the enzyme is not simply a template to which the substrates bind for ready reaction, but that groups on its surface - hydrophilic groups for sure - participate in catalysis. However, the amount of chemical participation varies widely among enzymes - the serine proteases have a lot of chemical participation, while tyrosyl tRNA synthetase has very little.

Very often the transition state of a reaction involves charge separation, which is energetically unfavorable. Any participation by a catalyst which spreads the charge more widely thus stabilizes the transition state and lowers the energy of activation. For instance, in the hydrolysis of an ester, the uncatalyzed reaction puts partial negative charge on the carbonyl, partial positive on the attacking H₂O. However, another electron-rich species, or base, can spread the charge more widely by pulling out a proton from the water, treating it as being part of the positive charge, which is neutralized by interaction with the electron-rich group.

Similarly the hydrolysis of an acetal, such as a glycoside, can be catalyzed by an acid which partially donates a proton to a leaving group which would otherwise be negatively charged: This sequence also shows how general base catalysis could be involved in the same reaction, by helping to pull off the proton which is removed from the water which attacks the carbonium ion intermediate. Those who know the mechanism of action of lysozyme will recognize that the role of general acid catalysts is there played by glu-35. Asp-52, however, probably acts by forming an ion pair with the carboxonium ion intermediate and thereby stabilizing it, rather than by removing the proton from attacking water. This is called electrostatic catalysis. It is not very important with model compounds, principally because of the shielding effect of a high-dielectric medium such as water, which lessens the energy of interaction between charges. However, the nonpolar portions of the amino acid side chains of proteins provide a low-dielectric medium, and when water is excluded between and around interacting charges, the energies of interaction are much higher, so that the stabilization of charge in the transition state can be very substantial and lower the activation energy greatly; it has been calculated that the interaction of the carboxonium ion in the transition state of lysozyme hydrolysis with asp-52 lowers the energy of activation by 9 kcal/mole, equivalent to a rate enhancement of 4x10⁶. (However, there are also claims that asp-52 actually forms a covalent acyl intermediate with the sugar; H₂O then attacks from above, displacing it.)

As I mentioned last time, besides this sort of general acid/base catalysis, in which a proton is transferred in going through the transition state, there is specific acid/base catalysis, in which the appropriate ions from water, H₃O⁺ or OH^-, fully donate or remove a proton, generally to form a true intermediate rather than a transition state. In general acid/ base catalysis any proton-donating (acidic) or proton-accepting (basic) species can aid any reaction where a proton must be transferred; these are likely to be much weaker acids or bases than H₃O⁺ or OH^-, but present in much greater concentration at neutral pH, and in enzymes they simply are there. The effectiveness of the catalyst, measured as the rate constant of the second order reaction involving substrate and catalyst, is generally proportional to the strength of the acid or base, i.e. its pK_a:

log k₂ = A - apK_a for general acid catalysis
log k₂ = A + bpK_a for general base catalysis
The term A is the rate of the uncatalyzed reaction (or as catalyzed by neutral H₂O), while a and b indicate the sensitivity of the reaction to catalysis. If a or b = 0, the reaction is not subject to acid or base catalysis; if a or b = 1, only specific catalysis by H₃O⁺ or OH^- is of importance. For ester hydrolysis b is 0.3 to 0.5.

I should mention here the principle of kinetic equivalence, which prevents distinguishing among some types of catalysis. For instance, a reaction might be catalyzed by A^-, or by HA and OH^-; both will show the same dependence on total A concentration and on pH, since [A^-] = [HA][OH^-] . The only way you can distinguish between the possibilities is when one would involve a second-order rate constant larger than the rate of diffusion of ions - if the reaction occurs fast enough at, say, pH 8.0, where [OH^-] = 10^-6 m, that a k₂ greater than 10⁸m^-1s^-1 would be necessary to achieve the observed rate. This is faster than the diffusion of the ion, and therefore impossible.

These have been mechanisms which involve lowering the activation energy of an already existing pathway. The alternative is to generate a basically different pathway, involving a new, generally covalent intermediate whose formation and breakdown both have a lower activation energy than the classical mechanism. The classical case is the hydrolysis of esters catalyzed by imidazole:

Imidazole is a better attacking nucleophile than water and a better leaving group than even p-nitrophenol, so that the overall reaction is faster than the uncatalyzed reaction in water. It should be noted that imidazole can also act as a general base catalyst, and indeed probably thus catalyzes the attack of another imidazole. One can distinguish nucleophilic alternate-pathway catalysis from general base catalysis in the following ways:

If an intermediate compound, such as acylimidazole, can actually be isolated, it is proof positive of nucleophilic catalysis. Less directly, the intermediate may react with alternate second attacking molecules, such as methanol and phosphate in stead of H₂O, to an extent not seen for the uncatalyzed reaction. Such partitioning is also evidence for an intermediate compound.

On the other hand, general acid or base catalysis necessarily involves transfer of a proton in the transition state. This is more difficult if the hydrogen ion to be transferred is actually a deuteron ²H⁺, or triton ³H⁺, because the zero-point energy of the bond to hydrogen is lower and the ∆G^* consequently higher; thus when proton transfer occurs in the transition state the reaction is slower for a deuteron, theoretically 7 fold but for other reasons anywhere betwen 2 and 15-fold. Such an isotope effect will be seen using deuterated or tritiated substrate if the proton is transferred in the rate-limiting step from a carbon atom, or using D₂O as solvent if the proton is exchangeable, being on an oxygen, nitrogen or sulfur. On the other hand no primary hydrogen isotope effect will be seen in nucleophilic catalysis.

Small secondary isotope effects are seen when the deuterium substitution is at a position adjacent to where reaction occurs and the transition state has carbonium ion character, because the C-H substrate will more readily go into sp² hybridization than the C-D substrate. The maximum effect expected is a k_h/k_d ratio of 1.38, and ratios of 1.1 to 1.2 are accepted as indicating considerable carbonium ion character for an intermediate; the value is 1.11 for lysozyme acting on a substrate with a D on C-1, but only 1.01 for b-glucosidase.

Somewhat similar but much smaller effects can be observed using ¹³C, ¹⁵N and ¹⁸O substrates; an isotope effect on the overall reaction indicates that breakage of a bond involving the heavy atom, rather than some other step, is largely rate-limiting. These isotope effects are not measured as direct effects on the rate - they are of the order of 1 or 2% - but by measuring the heavy-atom enrichment of the product using mass spectrometry; if there is an isotope effect, the product will be depleted in the heavy isotope, because substrate with the heavy atom reacted less.

Metal ions can act as catalysts in a number of ways. The most obvious is electrostatic: as a stable positive charge, in the significant cases a divalent cation, they can stabilize negative charges in the transition state. Mg⁺⁺ and Ca⁺⁺, which can interact with only four ligands, generally do nothing fancier than that, and indeed act largely as 'bridges' in binding negatively charged groups - for instance ATP nearly always reacts as its Mg⁺⁺ complex. Zinc is the most often used as a strong positive charge which polarizes compounds coordinated to it and favors a negatively charged transition state, as in liver alcohol dehydrogenase.

A less obvious but related means for metal ions to catalyze reactions is to polarize a coordinated water molecule, which then attacks the substrate. For instance, Zn in carbonic anhydrase is coordinated to three histidines which attach it to the protein, but the fourth ligand is a water molecule which is believed to have a pK_a of 7 rather than 15.74 (K_w = 10^-14 divided by 55 m). Metal-bound OH^-, though with a far lower pK_a than free water, reacts nearly as well as free OH^- - for instance, H₂O bound to Co(NH₃)₅⁺⁺⁺ has a pK_a of 6.6, 9 pH units below that of free H₂O, but is only 40 fold less effective than an equimolar concentration of free OH^- in catalyzing the hydration of CO₂, though this rather disagrees with the Brønsted relationships for organic bases and acids, where effectiveness in catalysis follows pK_a rather well, i.e. if log k₂ = A + bpK_a and b is 0.5, a decrease of pK_a by 9 units should mean a 4.5-fold decrease in log k₂ and thus a 30,000 fold decrease in rate.

The really catalytic metal ions are usually the transition metals, Mn⁺⁺, Fe⁺⁺, Co⁺⁺, Cu⁺⁺ and Zn⁺⁺ - partly because they have a smaller ionic radius than Ca⁺⁺ or Mg⁺⁺, more because they have more unfilled orbitals to coordinate ligands, hold them close while they work on them. Cu and Fe also can act as redox catalysts, shifting back and forth between different oxidation states, in the course of a reaction in which substrates are oxidized and reduced; in some cases oxidation states not seen free in solution, such as Cu⁺⁺⁺ and Fe⁺⁴, seem to be involved.