Kinetics of the Transient Phase

Because of the difficulty of deriving useful and exact integrated rate equations for even relatively simple, one-substrate reversible mechanisms far from equilibrium (184), transient kinetic studies by the stopped-flow method have usually been interpreted qualitatively or on the basis of various simplified models (185,186). This lack of rigor may easily lead to unjustified conclusions, and a brief theoretical discussion on the basis of an ordered mechanism before discussion of the more interesting results may not be out of place. 

For several dehydrogenases, the time course of the formation of total enzyme-bound and free NADH, 2P, measured spectrophotometrically, can be described by the relation 

In this equation, Eo is the total enzyme active site concentration, and a is the steady-state specific rate of NADH formation, approached by a single exponential burst of amplitude with an apparent first-order rate constant A. is estimated by extrapolation of the steady-state portion of the progress curve to t = 0, and A is estimated by the usual logarithmic plot  

Some results show a biphasic exponential approach to the steady state 

Shore and H. Gutfreund, in Oxidation-Reduction Enzymes (A. Akeson and A. Ehrenberg, eds.), p. 755. Pergamon, Oxford, 1972. 

---

The kinetics of the transient phase of the hydrolysis of maltodextrin (average d.p. 11) by R. niveus glucoamylase have been studied using a fluorescent stopped-flow method. The fluorescence decreased rapidly on mixing solutions of the enzyme and the substrate, but slowly reappeared as the reaction proceeded the two phases are considered to represent the formation of an enzyme-substrate complex and the release of the free enzyme on breakdown of the complex into products. The importance of tryptophanyl residues at the subsite of R. niveus glucoamylase has been studied by modifying them with A-bromosuccinimide. ... 

The kinetic analysis of an enzyme mechanism often begins by analysis in the steady state therefore, we first consider the conclusions that can be derived by steady-state analysis and examine how this information is used to design experiments to explore the enzyme reaction kinetics in the transient phase. It has often been stated that steady-state kinetic analysis cannot prove a reaction pathway, it can only eliminate alternate models from consideration (5). This is true because the data obtained in the steady state provide only indirect information to define the pathway. Because the steady-state parameters, kcat and K, are complex functions of all of the reactions occurring at the enzyme surface, individual reaction steps are buried within these terms and cannot be resolved. These limitations are overcome by examination of the reaction pathway by transient-state kinetic methods, wherein the enzyme is examined as a stoichiometric reactant, allowing individual steps in a pathway to be established by direct measurement. This is not to say that steady-state kinetic analysis is without merit rather, steady-state and transient-state kinetic studies complement one another and analysis in the steady state should be a prelude to the proper design and interpretation of experiments using transient-state kinetic methods. Two excellent chapters on steady-state methods have appeared in this series (6, 7) and they are highly recommended. 

We show that transient metastable rotator phases occur on crystallization of octadecane (CH3 (CH2)j6 CH3) and other even chain-length alkanes into their tiiclinic phase from the supercooled melt. This was directly observed using time resolved x-ray scattering. The crystallization temperature (i.e. the limit of supercooling) is determined by the thermodynamic stabili of the transient phase with respect to the liquid. We explain the crystallization kinetics of the homologous series of n-alkanes in terms of a crossover from stability to long-lived metastability to transient metastability. Such metastable and transient phases are likely to have analogues in polymeric systems. 

These problems can be somewhat overcome by a study of reactions in solution where much greater densities are possible than in the gas phase and fast bimolecular reaction are diffusion limited [1,28,29]. However, since coordinatively unsaturated metal carbonyls have shown a great affinity for coordinating solvent we felt that the appropriate place to begin a study of the spectroscopy and kinetics of these species would be in a phase where there is no solvent the gas phase. In the gas phase, the observed spectrum is expected to be that of the "naked" coordinatively unsaturated species and reactions of these species with added ligands are addition reactions rather than displacement reactions. However, since many of the saturated metal carbonyls have limited vapor pressures, the gas phase places additional constraints on the sensitivity of the transient spectroscopy apparatus. 

Gas-phase Kinetics. A better appreciation of the experiments to be discussed later will be obtained after a review of some experimental aspects of the transient method. Here we deal with experiments at atmospheric pressure. A flow sheet for kinetic measurements is given in Fig. 1, a descendant of that first given by Bennett et al. (15). Chemical analysis of the gases during transients is ideally done by a mass spectrometer, although Kobayashi and Kobayashi (4 ) used a number of gas chromatographs in order to get samples sufficiently frequently. 

The transition-state theory (TST) provides the framework to derive accurate relationships between kinetic and thermochemical parameters. Consider the common case of the gas-phase bimolecular reaction 3.1, where the transient activated complex C is considered to be in equilibrium with the reactants and the products ... 

One of the widely used methods of analysis of kinetic data is based on extraction of the distribution of relaxation times or, equivalently, enthalpic barrier heights. In this section, we show that this may be done easily by using the distribution function introduced by Raicu (1999 see Equation [1.16] above). To this end, we use the data reported by Walther and coworkers (Walther et al. 2005) from pump-probe as well as the transient phase grating measurements on trehalose-embedded MbCO. Their pump-probe data have been used without modification herein, while the phase grating data (also reproduced in Figure 1.12) have been corrected for thermal diffusion of the grating using the relaxation time reported above, r,, and Equation (1.25). 

The H atoms formed by the methods mentioned above are highly reactive and unite with many elements to give hydrides. The reactions of H atoms in the gaseous phase and in solution have very extensively studied using kinetic methods because of the transient nature of this species. 

The apparent aqueous solubility of amorphous materials is much higher than that of their crystalline counterparts (Fig. 1). This is a kinetic phenomenon and, eventually, the solute in the supersaturated solution that is formed will begin to crystallize and the equilibrium solubility of the crystalline phase will be attained. The transient increase in solubility is often significant (>10x) and can be exploited to give markedly improved biopharma-ceutical performance. ... 

The kinetics of the initial stage of 3D Me-S bulk alloy formation process can be affected by nucleation and growth phenomena. A typical example is the formation of the fi phase of 3D Li-Al bulk alloy in the systems Al(polycrystalline)/molten Li, Cf and A1 (polycrystalline)/LP, 0104, propylene carbonate [3.345, 3.346]. In both systems, non-monotonous current transients were observed in the initial stage of alloy formation as shown in Fig. 3.66 [3.345]. 

Galvanostatic pulse excitation technique requires a fast E - i conversion device to switch from potentiostatic to galvanostatic conditions. The analysis of E(t) transients is rather complex since the nucleation and growth kinetics of the 3D Me bulk phase are changed continuously by the varying supersaturation. 

In most mechanisms these two phases of the overall reaction proceed at very different rates. As a result the examination of the kinetics of the achievement of a mechanistic steady state may well require observations at conversion levels and at clock times many orders of magnitude lower than those needed for the study of the initial rates in the main steady state reaction. The reactor and analytical procedures required for such transient studies are usually very different from those used in steady state investigations. 

Irradiation of o-nitrobenzaldehyde in benzene gives o-nitrosobenzoic acid ((/) 0.5) in a process that occurs via a triplet state having a lifetime of 0.6 ns, and the transient enol (49). A mechanism is proposed and this is outlined in Scheme 9. The kinetics of the photo-oxidation of benzaldehyde have been studied in the liquid phase and the rate constants extracted found to be in close agreement with those obtained from the photodecomposition of PhC020H. ... 

---