Enzymes kinetic partitioning

Cleland introduced the net rate constant method to simplify the treatment of enzyme kinetic mechanisms that do not involve branched pathways. This method can be applied to obtain rate laws for isotope exchange, isotope partitioning, and positional isotope exchange. Since the net-rate constant method allows one to obtain VraaJKra and in terms of the individual rate constants, this method has greatest value for the characterization of isotope effects on and Kj. Because only... 

Johnson and Fierke Hammes have presented detailed accounts of how rapid reaction techniques allow one to analyze enzymic catalysis in terms of pre-steady-state events, single-turnover kinetics, substrate channeling, internal equilibria, and kinetic partitioning. See Chemical Kinetics Stopped-Flow Techniques... 

Rose, I.R. (1995) Partition analysi detection enzyme reactions cycle intermediates, in Purich, D. L. (eds.), Methods in Enzymology, 249, Enzyme Kinetics and Mechanisms, Part D, Acad. Press, San-Diego, 315-340. 

Incubation of AChE with onchidal resulted in the production of acetate, demonstrating that onchidal was a substrate for AChE, and approximately 3250 mol of onchidal was hydrolyzed/mol of enzyme irreversibly inhibited. Organophosphate and carbamate inhibitors of AChE have partition ratios (mol of toxin hydrolyzed/mol of enzyme irreversibly inhibited) that approach unity. Therefore, the relatively high partition ratio for onchidal suggests that the mechanism of inhibition utilized by onchidal may be distinctly different from other irreversible inhibitors (Walsh, 1984). The rate of hydrolysis of onchidal (Acat) was 325 min this value is relatively slow suggesting that onchidal is not a very good substrate. The ability of AChE to hydrolyze onchidal raised the question of whether inhibition of enzyme activity resulted from onchidal itself or from a product of the enzymatic hydrolysis of onchidal. Enzyme kinetics revealed that onchidal was unable to completely inhibit higher concentrations of AChE. From the experiments performed by Abramson et al. (1989), onchidal was in molar excess and was completely hydrolyzed. Thus,... 

When considering enzyme kinetics in a reversed micellar system it is critical to recognize that there are two volumes upon which to base concentration dependent constants and variables, the total or observed reaction volume and the micellar or aqueous water pool volume (111. Additionally, the partitioning of the substrate between the hulk organic solvent mixture and the reversed micelles... 

The kinetic partitioning of enzyme intermediates is an important principle, and the rules governing kinetic partitioning are quite simple. The fractional yield of a given reaction is given simply as the rate of the desired reaction divided by the sum of the rates of all reactions involving the intermediate. For example, consider the forked reaction pathway in Scheme XXI. 

For a sequential bisubstrate enzyme, the rate of dissociation of the hrst substrate can be estimated by substrate trapping methods. The rationale for this experimental approach is shown in Scheme XXII. The enzyme is first preincubated with radiolabeled substrate A and is then mixed with an excess of unlabeled substrate A and substrate B to initiate the reaction. The recovery of radio-labeled product is a function of the kinetic partitioning of the enzyme-bound substrate between dissociation to yield free S and forward reaction with substrate B to yield product P. 

When an enzyme is entrapped, it is necessary to consider the combined effects of mass transport, partition, and reaction within the film and enzyme kinetics to understand processes that determine the overall response. These interactions can be quite complex, although some progress has been made toward developing models for these systems. ... 

The bridge that divides in vitro and in vivo transporter correlation remains wide. Unlike direct enzyme kinetic correlations where a clear product is generated when substrate is added to enzyme, transporter outcomes are affected by many parameters. The physicochemical properties of compounds, such as lipophilicity, pKa, permeability, solubility, and partitioning coefficient,... 

Cleland WW (1975) Partition analysis and the concept of net rate constants as tools in enzyme kinetics. Biochemistry 14, 3220-3224. 

Fig. 6.70 Substrate and product profiles in an immobilized enzyme system as a consequence of partition and mass transfer limitations. (From A. Illanes, R. Femandez-Lafuente, JM Guisan, L. Wilson, Heterogeneous enzyme kinetics, in A. Illanes (Ed.), Enzyme Biocatalysis, Springer, 2008, pp. 155-203. Copyright 2008 Springer).

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

With a 3,3-heterodihalogeno substitution of the (3-lactam ring, a selective interaction of each enantiomer of the chiral azetidinone with the enzyme active site is expected. The enantiomer 3R of the 3F, 3Br derivative indeed has a more favorable kinetic parameter k-JK, than the enantiomer 3S.33 The partition ratio kCA /kt (=k3/k4, Eq. 11.1) for the inactivation is also higher. Therefore, enantiomer 3R is a better suicide substrate for HLE since a lower partition ratio corresponds to abetter suicide substrate.20... 

The concentrations of Q and P are normalized to the values they would have if the film were exposed to a concentration of Q or P equal to the bulk concentration of cosubstrate, Cp, taking into account the two partition coefficients, Kp and kq. The kinetic parameter A measures the competition within the enzyme film between diffusion represented by the term 8qD/1 and the rate term The current is normalized toward the parameters of the diffusional transport of the cosubstrate in the solution in the solution. The set of equations listed in Table 6.10 ensues. 

In addition to the TDI experiment, the partition ratio measures the TDI efficiency. Specifically, the partition ratio is the number of inactivation kinetic events (k nact) versus the number of substrate turnover events per unit enzyme (kcat) [161], Thus, the most potent partition ratio is zero. The most common experimental setup for determining the partition ratio is the titration method that increases the inhibitor concentration relative to a known amount of enzyme. After the incubations, a secondary incubation containing a probe substrate similar to the TDI experiment is used to define the remaining activity. For accurate determination of the partition ratio from the titration method, it is assumed that the inhibitor is 100% metabolized ... 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

If the overall reaction rate is controlled by step three (k3) (i.e. if that is the rate limiting step), then the observed isotope effect is close to the intrinsic value. On the other hand, if the rate of chemical conversion (step three) is about the same or faster than processes described by ks and k2, partitioning factors will be large, and the observed isotope effects will be smaller or much smaller than the intrinsic isotope effect. The usual goal of isotope studies on enzymatic reactions is to unravel the kinetic scheme and deduce the intrinsic kinetic isotope effect in order to elucidate the nature of the transition state corresponding to the chemical conversion at the active site of an enzyme. Methods of achieving this goal will be discussed later in this chapter. 

Rose and co-workers first demonstrated that a proteo-lyzed form of hexokinase forms a sticky (or sluggishly dissociable) complex with glucose. The generalized application of this approach to the kinetic characterization of multisubstrate enzymes has been treated in detail. See also Partition Coefficient Radiospecific Activity Stickiness... 

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