Enzyme equilibria solute effects

Kurz and Frieden in 1977 and 1980 determined -secondary kinetic isotope effects for the unusual desulfonation reaction shown in Table 1, both in free solution and with enzyme catalysis by glutamate dehydrogenase. The isotope effects (H/D) were in the range of 1.14-1.20. At the time, the correct equilibrium isotope effect had not been reported and their measurements yielded an erroneous value... 

But where there is an equilibrium among two or more conformations of the enzyme in solution, crystallization may select out only one of the conformations. a-Chymotrypsin has a substantial fraction of an inactive conformation present under the conditions of crystallization, but only the active form of the enzyme crystallizes. An allosteric effector molecule that changes the conformation of the protein in solution may have no effect on the crystalline protein, as, for example, with phosphorylase b.5A The enzyme is frozen in one conformation, with the crystal lattice forces preventing any conformational change. On the other hand, the addition of an effector to phosphorylase a causes the crystals first to crack and then to anneal, giving crystals of the enzyme in a second conformation. 

The majority of the many methods used to study the composition of equilibrium solutions of carbohydrates examine the mixture without separating the individual components. With the discovery that the anomeric forms of sugars could be readily separated by gas chromatography of their tri-methylsilyl ethers, a new approach to the problem was found. A protocol was developed for the direct gas chromatographic analysis of the amount of each anomer present in an aqueous solution. The protocol can be used on the micro scale and can be used in enzyme assays such as that for mutarotase. The method has been made more effective by combining gas chromatography with mass spectrometry. It is shown how mass spectral intensity ratios can be used to discriminate anomers one from another. The application of these methods to the study of complex mutarotations is discussed. 

Attempts to imply that dynamical effects are associated with the so-called nonequilibrium solvation effects125 have been shown to be very problematic (see Ref. 4). Furthermore, it has been clearly demonstrated that the difference between the non-equilibrium solvation effects in enzyme and solution is an integral part of the difference between the corresponding activation barriers.4... 

The differences in the motion of the two loops seen in the simulations appeared to originate from differences between the two subunits in the crystal structure that made the closing of the loop in subunit II less probable than in subunit I. These seemed to hinder full relaxation of all the bonds and angles in the loop in subunit II to their equilibrium values, so that, during much of the simulation time, only 9 residues moved in subunit II, whereas 11 moved in subunit I. This discrepancy appears to arise from crystal contacts, which keep the loop in subunit II in a defined open conformation in the crystal structure, whereas the loop in subunit I is disordered and exposed to solvent. Sulfate and phosphate ions are able to bind in the active site of subunit I but not subunit II in the crystal. These differences suggest that the loop in subunit I may undergo motions that are more representative of those of the active enzyme in solution than the loop in subunit II, which exists in a somewhat artificial state that restricts its motion. Therefore, the effect of gating on the rate constant of the reaaion was estimated from the motion of the loop in subunit I. 

The effect of pH on the response comes from two effects. Firstly, enzymatic activity is a function of pH and, secondly, pH may affect a dissociation equilibrium of the product, and only one form will be detectable by the transducer (Figure 4.10). The loss of activity due to the pH can be compensated by increasing the enzyme concentration in the membrane. The conversion of substrate can then be maintained at its maximal level and the enzyme sensor will have very little dependence on pH. The pH-dependence curve is then broader and flatter than that of the same enzyme in solution. 

Solution in 0.1 M acetate buffer, pH 3.5, resulted in an enzymically active species (8n) of 240,000 daltons (46). Tanis and Naylor (47) have reported that at low concentration of protein the 18 S form predominated above pH 5.3 and the 12 S form below pH 4.8. Between these pH values a rapid equilibrium of the 12 S and 18 S species was observed The dissociation behavior of urease at low pH depends on the buffer used. In 0.1 M potassium phosphate buffer, adjusted to pH 2.0 with HC1, a heterogeneous mixture of dissociated forms was obtained (d) with an Mw of about 150,000. In acetate buffer at pH 3.5 dissociation into a 120,000 molecular weight species (4n) was observed (48). In 34% acetic acid at pH 2.2 there is effected a dissociation to subunits (n) of 30,000 daltons (7). This same value was obtained for urease ultracentrifuged in 8 M urea -f- 0.5 M thiol and in performic acid oxidized urease (48). 

The effect of an uncompetitive inhibitor on the Km of a substrate deserves some commentary. A lower Km implies that an enzyme has been inhibited by increasing the enzyme s affinity for its substrate. This seemingly counterintuitive statement can be made clearer by examining the equilibria in Scheme 4.14. By binding the enzyme-substrate complex, the inhibitor forces some free enzyme to bind substrate in order to maintain equilibrium concentrations of all species in solution. The inhibitor does indeed increase the affinity of the enzyme for its substrate (i.e., decrease Km). 

It would be instructive to examine the effect of the product on the initial forward velocity. For example, suppose we have a solution containing a certain concentration of S and a certain concentration of P. In the absence of an appropriate enzyme, the reaction does not occur at a measurable rate. Now we add an enzyme catalyzing the reversible reaction S P. In which direction and at what rate will the reaction progress The direction of the reaction will depend on the ratio of [P]/[S] relative to K. An equation for the net velocity can be derived quite easily from rapid equilibrium assumptions (where K g = Ks, and K f = Kv). 

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