Perturbations equilibria

It is historically noteworthy that it was experiments with [2-D]-L-malate that led to the discovery of the equilibrium perturbation method (Section 7.1.4). As can be seen in Fig. 11.8 the perturbation is only a few [imolar although the isotope effect is quite sizable. 

Fig. 11.8 Equilibrium perturbation trace for deuterated L-malate reaction catalyzed by malic enzyme. The equilibrium perturbation technique is discussed in Section 7.1.4. The label on the ordinate, p,M has been recalculated from the change in absorbance of TPNH at 340 nm (Schimerlik, M. I., Rife, J. E. and Clcland, W. W. Biochemistry 14, 5347 (1975))...

Equilibrium perturbation with malic enzyme added to a pH 7.1 solution containing 0.419 mM malate-2-D, 0.079 mM NADPH, 20 mM potassium bicarbonate (3.8 mM carbon dioxide), 20 mM magnesium sulfate, 0.102 mM NADP+, and 3.83 mM pyruvate. NADPH initially disappears within the first 10 min, followed by its reappearance over the ensuing 60 min period. 

KINETIC ISOTOPE EFFECT EQUILIBRIUM PERTURBATION METHOD KINETIC ISOTOPE EFFECT SOLVENT ISOTOPE EFFECT EQUILIBRIUM THERMODYNAMIOS (Measurable Quantities)... 

This treatment makes the assumption that the equilibrium perturbation given by... 

The kinetic steady-state assumption implies that the equilibrium perturbation function [Pg.198]

For the reactivity parameters Y, n, a+ (but not a) andN+ the lack of curvature is not unexpected. This is because these parameters are defined with respect to the rate of some standard reaction (solvolysis of t-butyl chloride, substitution of methyl iodide, solvolysis of cumyl chlorides, combination reaction of nucleophiles with a standard electrophile). Therefore the resultant plot is of the type log k vs. log k, while the curvature shown in a typical Br nsted plot (Figure 5) results from a plot of log k vs. log K. This curvature is due to a gradual change from a reactant-like transition state, which is insensitive to a perturbation in the reactivity parameter, to a product-like transition state in which equilibrium perturbations are largely reflected in the transition state (and hence the rate). A log k — log k plot is not expected to show this effect and hence is not expected to show curvature. 

In fact, thermal equilibrium is not attained in the vapor phase osmometer, and the foregoing equations do not apply as written since they are predicated on the existence of thermodynamic equilibrium. Perturbations are experienced from heat conduction from the drops to the vapor and along the electrical connections. Diffusion controlled processes may also occur within the drops, and the magnitude of these effects may depend on drop sizes, solute diffusivity, and the presence of volatile impurities in the solvent or solute. The vapor phase osmometer is not a closed system and equilibrium cannot therefore be reached. The system can be operated in the steady state, however, and under those circumstances an analog of expression (3-6) is... 

The third method for measuring isotope effects is equilibrium perturbation (19). In this method, one adds enzyme to a reaction mixture calculated to be at equilibrium containing a labeled substrate and an unlabeled product. For a normal isotope effect, the unlabeled product reacts faster than the labeled substrate and causes a perturbation from equilibrium. As isotopic mixing takes place, however, the reaction comes back to chemical as well as isotopic equilibrium. The size of the perturbation is used to compute the isotope effect. This method is of intermediate precision, but can be used for isotope effects of 1.03 or greater. The isotope effect that is determined is similar to a V/K one. 

Cleland WW. Measurement of isotope effects by the equilibrium perturbation technique. Methods Enzymol. 1980 64 104-125. 

When a mobile phase is introduced to a column, its components undergo distribution until equilibrium is attained. Injection of a sample different from the mobile phase causes a small equilibrium perturbation at the column head. The equihbrium of each component of the mobile phase can be disturbed and, thereby, manifested... 

The equilibrium perturbed by the electrolytic process el) tries to be re-established. The compound C is replenished in the vicinity of the electrode by a chemical conversion of A with rate constant k[. In this way the amount of C that can undergo reduction at the surface of the electrode is increased and the wave becomes higher when compared with the conditions for a slowly established equilibrium (Fig. 18). The magnitude of this increase depends, for given experimental conditions, on the value of the formal rate constant k[, i.e. on the magnitude of ki and the concentration of the component B present in excess. 

Figure 5.15 Equilibrium perturbation. Absorbance changes at 250 nm consequent upon the addition of E. coli purine nucleoside phosphorylase (ISOpg in 5 iL) to a solution (3mL) containing [l - H]inosine (1.99mM), hypo-xanthine (O.lOOmM), ribose-1-phosphate (O.SOmM) and inorganic phosphate (ll.SmM) in 0.2 M glycine-HCl buffer, pH 9.4, in a 1cm pathlength cuvette. ...

For the investigation of adsorption/desorption kinetics and surface diffusion rates, SECM is employed to locally perturb adsorption/desorption equilibria and measure the resulting flux of adsorbate from a surface. In this application, the technique is termed scanning electrochemical induced desorption (SECMID) (1), but historically this represents the first use of SECM in an equilibrium perturbation mode of operation. Later developments of this mode are highlighted towards the end of Sec. II.C. The principles of SECMID are illustrated schematically in Figure 2, with specific reference to proton adsorption/desorption at a metal oxide/aqueous interface, although the technique should be applicable to any solid/liquid interface, provided that the adsorbate of interest can be detected amperometrically. 

One of the first uses of the SECM was as a fabrication tool to form dissolution channels and growth hillocks on materials at the micrometer to submicrometer level. This area is dealt with in greater detail in Chapter 13. For these studies, the feedback mode of the device was predominantly utilized. Because the purpose was only to alter the topographical features of a substrate, little information was provided on the rates or nature of the dissolution processes. In this section we describe how the equilibrium perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the... 

A method for obtaining very precise multiple hydrogen kinetic isotope effects was developed in order to determine whether alanine racemase catalyzes a concerted or a stepwise process [21]. The method employs an equilibrium perturbation-type... 

The entire scheme for a deuterium washout equilibrium perturbation is described in Fig. 7.7A. The two reactants initially present are boxed. The starting substrates for the perturbation are ] H]-D-Ala (lower manifold) and ] H]-L-Ala (upper manifold). All hydrons on the upper manifold are considered to have the same identity as solvent. An equilibrium perturbation-type washout of the ] H]-D-Ala in H2O proceeds by abstraction of Ca deuteron by a protiated enzyme (lower manifold), followed by donation of a proton, to yield the protiated L-isomer. The enzyme rapidly and irreversibly exchanges the deuteron for proton, moving from the lower to the upper manifold. The contemporaneous racemization of the r-isomer on the upper manifold occurs more rapidly than the racemization from the lower manifold. This transient accumulation of the slower species (in this case o-isomer) produces the perturbation in the optical signal, from which (V/K) for the d l direction may be determined. 

Figure 7.8. Equilibrium perturbation-type solutions were pD 8.90, which gives enzyme in...

Knowles and coworkers also performed competitive deuterium washouts (i.e., an equilibrium perturbation-type washout experiments), using deuterated substrates in H2O solutions, which yielded the (V/K) values for both directions [85]. Further confirmation of these KIE values was validated by a double competitive deuterium washout experiment, in which both substrates are Ca deuterated, which yielded a ratio of the two (V/K) values. The authors were also able to perform competitive deuterium washout experiments where direct proton exchange between free enzyme forms is rate-limiting (i.e., at high substrate concentration the lower manifold of Fig. 7.16 is dominant). This experiment indicated that interconversion of free enzyme forms is very similar to the racemization manifold, in that loss of proton from one form yields the other free enzyme form, with water acting as the catalyst. Fig. 7.16. 

The constants Cf and Cr in Eqs. (84) and (85) are commitments in the forward and reverse directions and represent partition ratios for the complexes that undergo the isotope-sensitive step in the forward and reverse directions, respectively. Thus, Cf is the ratio of the rate constant for the isotope-sensitive step to the net rate constant for release of a substrate back off of the enzyme. The substrate involved in this calculation is the variable one in a direct comparison study, the perturbant in an equilibrium perturbation study, or the labeled substrate in an internal competition experiment. These need not be the same substrate, and thus... 

---