Rate constants for interconversion

If the rate constants for interconversion between M and ML are infinitesimally small (on the effective timescale of the experimental conditions), the complex does not contribute significantly to the supply of metal to the biosurface. The equilibrium equation (50) behaves as if frozen. In a biouptake process, the complex ML then does not contribute to the supply of metal towards the biosurface, and all the expressions given in Section 2 apply, with the only noteworthy point that the value of c"M to be used differs from the total metal concentration. In this case, the complexed metal is not bioavailable on the timescale considered, as metal in the complex species is absent from any process affecting the uptake. 

Uni-isouni pathway Typified by ligand-induced solute unfolding-folding phenomena at the stationary phase surface single elution zone observed but time-dependent loss of mass and bioactivity possible when the rate constants for interconversion, 21 > ki2. 

The Curtin-Hammett principle (see below) applies to this scheme when the rate constants for product formation K and 2 are small relative to rate constants for interconversion over the reactants and intermediates k, k k- and k-2 (in other words, when I j and 1 2 ate in rapid equilibrium). A kinetic analysis of such a process shows that the selectivity depends only upon the free-energy difference between the transition states [ZMSfl and [ -f f]. The ratio of the diastereoi-someric primary products is given by the same relationship as before ... 

Detailed experimental data on the rate constants associated adsorption/desorption kinetics or conformational interconversion of different forms of a protein chromatographed on -alkylsilicas are currently very sparse. The kinetics of de-naturation of several proteins on n-butyl-bonded silica surfaces have been reported. Fig. 18 for example, shows the dependence of peak area on the incubation time of lysozyme on the bonded phase surface, from which rate constants for interconversion on the stationary phase, i.e. were derived [63]. The graphical representations derived from quantitative numerical solutions of the probabihty distributions... 

C]-D-erythrose, unidirectional rate constants for interconversions of the species present were obtained. Assignments of the signals of D-psicose in solution, in which both furanose and pyranose species are present have been made by using differential isotope-shift measurements. 

Step 1. An enzymatic reaction is considered as a cyclic process that displays all the interconversions among the various enzyme forms involved. For each step in the reaction a rate constant is defined in terms of the product of the actual rate constant for that step and the concentration of free substrate involved in the step. Hence, the cyclic form of the reaction scheme given in Equations 17.6, 17.7, and 17.8 is represented by... 

The second and third relaxation processes were coupled, where the observed rate constants differed by a factor of 3 to 7 and the rate constant for each relaxation process varied linearly with the DNA concentration.112 This dependence is consistent with the mechanism shown in Scheme 2, where 1 binds to 2 different sites in DNA and an interconversion between the sites is mediated in a bimolecular reaction with a second DNA molecule. For such coupled kinetics, the sum and the product of the two relaxation rate constants are related to the individual rate constants shown in Scheme 2. Such an analysis led to the values for the dissociation rate constants from each binding site, one of the interconversion rate constants and the association rate constant for the site with slowest binding dynamics (Table 2).112 The dissociation rate constant from one of the sites was similar to the values that were determined assuming a 1 1 binding stoichiometry (Table 1). 

Simplifications ease the extraction of accurate values for the rate constants. For example, the keto, enol interconversion may sometimes be ignored, and k 2 > Xc, and Xtj > k are justifiable assumptions. ... 

The lability inherent in the planar, tetrahedral equilibria which nearly all involve Ni(II) requires that nmr line broadeningor photochemical perturbation methods be used for their kinetic resolution. First-order interconversion rate constants for... 

Rate and equilibrium constants have been determined for the aldol condensation of a, a ,a -trifluoroacetophenone (34) and acetone, and the subsequent dehydration of the ketol (35) to the cis- and fraw -isomeric enones (36a) and (36b)." Hydration of the acetophenone, and the hydrate acting as an acid, were allowed for. Both steps of the aldol reaction had previously been subjected to Marcus analyses," and a prediction that the rate constant for the aldol addition step would be 10" times faster than that for acetophenone itself is borne out. The isomeric enones are found to equilibrate in base more rapidly than they hydrate back to the ketol, consistent with interconversion via the enolate of the ketol (37), which loses hydroxide faster than it can protonate at carbon. 

Correlation functions are powerful tools in statistical physics, and in the above example they permit one to examine the behavior of a fluctuating system from a reference time back to previous times. Such fluctuations can occur in the concentration of two (or more) interconverting chemical species in dynamic equilibrium, and the technique of concentration correlation analysis permits one to determine the forward and reverse rate constants for their interconversion. See Concentration Correlation Analysis... 

The mechanism of an enzymatic reaction is ultimately defined when all the intermediates, complexes, and conformational states of the enzyme are characterized and the rate constants for their interconversion are determined. The task of the kineticist in this elucidation is to detect the number and sequence of these intermediates and processes, define their approximate nature (that is, whether covalent intermediates are formed or conformational changes occur), measure the rate constants, and, from studying pH dependence, search for the participation of acidic and basic groups. The chemist seeks to identify the chemical nature of the intermediates, by what chemical paths they form and decay, and the types of catalysis that are involved. These results can then be combined with those from x-ray diffraction and NMR studies and calculations by theoretical chemists to give a complete description of the mechanism. 

The enzyme has been shown to be specific for the (3 form by rapid reaction measurements on a time scale faster than that for the interconversion of the anomers, and also by determination of the activity toward model substrates that are locked in either of the configurations. By using sufficient enzyme to phos-phorylate all the active anomer of the substrate before the two forms can reequilibrate, it is found that 80% of the substrate reacts rapidly, and that the remaining 20% reacts at the rate constant for the anomerization. The kinetics were followed both by quenched flow using [y-32P]ATP10 and by the coupled spectrophotometric assay of equation 6.4.11 The other evidence comes from the steady state data on the following substrates 12... 

An extension of the simple mechanism in which ring forms are interconverted via a central, aldehydo intermediate includes direct pathways for the interconversion of the two pyranoses on one hand, and the two furanoses on the other. The existence of such direct pathways would permit a starting pyranose anomer to be converted rapidly to the other pyranose, as observed, even though the rate constant for the closure of the aldehydo form to the furanose ring were much greater than that for closure to the pyranose ring. 

Clearly, the data contain information about both the equilibrium constant and the rate constants for the conformational interconversion. In this instance, the quantitative analysis was based upon the cyclic voltammetric data. The points in Figure 16.3 are the background-corrected experimental data, and the curves were computed by digital simulation with values of the equilibrium and rate constants selected to achieve best agreement with the experimental data. A given set of parameters was found to account for the data at a variety of scan rates, a necessary condition if the kinetic model is to be judged adequate. 

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