Tunneling of intermediates in enzyme-catalyzed reactions

A fascinating group of enzymes has been shown to possess multiple active sites connected by intramolecular tunnels for the passage of reactive intermediates from the site of production to the site of utilization. In most of the examples studied to date, the binding of substrates at one active site enhances the formation of a reaction intermediate at an adjacent active site. The most common intermediate is ammonia, derived from the hydrolysis of glutamine, but molecular tunnels for the passage of indole, carbon monoxide, acetaldehyde and carbamate have also been identified. The architectural features of these molecular tunnels are quite different from one another, suggesting that they evolved independently.     

On the structure of flavin-oxygen intermediates involved in enzymatic reactions.

During the catalytic reactions of flavoprotein hydroxylases and bacterial luciferase, flavin peroxides are formed as intermediates [see Massey, V. and Hemmerich, P. (1976) in The Enzymes, 3rd edn (P. Boyer, ed.) pp. 421--505, Academic Press, New York]. These intermediates have been postulated to be C(4a) derivatives of the flavin coenzyme. To test this hypothesis, modified flavin coenzymes carrying an oxygen substituent at position C(4a) of the isoalloxazine ring were synthesized. They are tightly bound by the apoenzymes of D-amino acid oxidase, p-hydroxybenzoate hydroxylase and lactate oxidase; the resulting complexes show spectral properties closely similar to those of the transient oxygen adducts of the hydroxylases. The optical spectra of the lumiflavin model compounds were found to be highly dependent on the solvent environment and nature of the subsituents. Under appropriate conditions they simulate satisfactorily the spectra of the transient enzymatic oxygen adducts. The results support the proposal that the primary oxygen adducts formed with these flavoproteins on reaction of the reduced enzymes with oxygen are flavin C(4a) peroxides.     

Use of progress curves to investigate product inhibition in enzyme-catalysed reactions. Application to the soluble mitochondrial adenosine triphosphatase

1. Several methods of analysing progress curves of enzyme-catalysed reactions are discussed briefly in relation to their usefulness in a situation where a reaction product has a K(i) much lower than the K(m) for the substrate 2. A comparison is made of different methods of estimating initial rates in this situation. 3. The use of a computer curve-fitting routine capable of handling functions of more than one variable for the extraction of kinetic parameters from progress curves is described. 4. This method and that of fitting time as a polynomial in product concentration are applied to progress curves for the soluble mitochondrial adenosine triphosphatase and the results are compared with values obtained by more conventional methods.     

Dual-color fluorescence cross-correlation spectroscopy for monitoring the kinetics of enzyme-catalyzed reactions

Dual-color fluorescence correlation spectroscopy is a biophysical technique that enables precise and sensitive analyzes of molecular interactions. It is unique in its ability to analyze reactions in real time at nanomolar substrate concentrations and below, especially when applied to the monitoring of enzyme-catalyzed reactions. Furthermore, it offers a wide range of accessible reactions, restricted only by the prerequisite that a chemical bond or a physical interaction between two spectrally distinguishable fluorophores is established or broken. Recently, the optical setup of dual-color fluorescence correlation spectroscopy has been extended toward two-photon excitation, resulting in several advantages compared with standard excitation, such as lower fluorescence background, an even larger spectrum of potential fluorescence dyes to be used, as well as a more stable and simplified optical setup. So far, the method has been successfully employed to analyze the kinetics of nucleic acid and peptide modifications catalyzed by nucleases, polymerases, and proteases.     

Calculations of intrinsic isotope effects and the detection of tunneling in enzyme-catalyzed reactions

The equation of Northrop [1975, Biochemistry, 14, 2644] for calculating intrinsic isotope effects from observed deuterium and tritium isotope effects of V/K, in which hydrogen is the reference isotope, has been extended to experimental designs using either deuterium or tritium as a reference. Partial derivatives of the intrinsic equations allow calculation of the relative precision of the three referenced isotope effects and these favor the order deuterium > tritium > hydrogen. In comparisons of observed and calculated isotope effects when hydrogen tunneling is present, both the precision and the magnitude of the difference was greater for intrinsic calculations than for exponentiations based upon a breakdown in the Swain-Schaad relationship.     

Determination of the optimum operating time for batch isothermal performance of enzyme-catalyzed multisubstrate reactions

This communication consists of a mathematical analysis encompassing the maximization of the average rate of monomer production in a batch reactor performing an enzymatic reaction in a system consisting of a multiplicity of polymeric substrates which compete with one another for the active site of a soluble enzyme, under the assumption that the form of the rate expression is consistent with the Michaelis-Menten mechanism. The general form for the functional dependence of the various substrate concentrations on time is obtained in dimensionless form using matrix terminology; the optimum batch time is found for a simpler situation and the effect of various process and system variables thereon is discussed. The reasoning developed here emphasizes, in a quantitative fashion, the fact that the commonly used lumped substrate approaches lead to nonconservative decisions in industrial practice, and hence should be avoided when searching for trustworthy estimates of optimum operation.List of Symbols O 1/s row vector of zeros - a 1/s row vector of rate constants k _i(i = 2,...,N) - A 1/s matrix of rate constants k _i and k_–i (i=2,...,N) - b 1/s row vector of rate constant k ₂ and zeros - C mol/m³ molar concentration of S - C mol/m³ vector of molar concentrations of C _i (i=0, 1, 2, ..., N) - C ₀ mol/m³ column vector of initial molar concentrations of C _i(i=0, 1, 2,.., N) - C _–01 mol/m³ column vector of initial molar concentrations of C _i(i=2,..., N) - C _{E, tot} mol/m³ total molar concentration of enzyme molecules - C _i mol/m³ molar concentration of S _i (i=0,1,2,...,N) - C _{i, o} mol/m³ initial molar concentration of S _i(i=0, 1, 2, ..., N) - E enzyme molecule - I identity matrix - K 1/s matrix of lumped rate constants - k _i 1/s pseudo-first order lumped rate constant associated with the formation of S _i -1 (i=1, 2, ...,N) - k _{cat, i} 1/s first order rate constant associated with the formation of S _i-1 (i=1, 2, ..., N) - K _m mol/m³ Michaelis-Menten constant - L number of distinct eigenvalues - M _i multiplicity of the i-th eigenvalue - N maximum number of monomer residues in a single polymeric molecule - r ₁ mol/m³ s rate of formation of S ₀ - r _i mol/m³ s rate of release of S _i -1 - r _opt maximum average dimensionless rate of production of monomer S₀ - S lumped, pseudo substrate - S₁ inert moiety - S _i substrate containing i monomer residues, each labile to detachment as - S₀ by enzymatic action (i=1,2,...,N) - t s time elapsed since startup of batch reaction - t _lag s time interval required for cleaning, loading, and unloading the batch reactor - t _opt s time interval leading to the maximum average rate of monomer production - v _ij s^1-j eigenvectors associated with eigenvalue imi (i=1, 2, ..., L; j =1, 2, ..., M_i) Greek Symbols _ij mol/m³ arbitrary constant associated with eigenvalue _i (i=1, 2, ..., L; j=1, 2, ..., M _i ) - 1/s generic eigenvalue - _i 1/s i-th eigenvalue     

An on-line method for the collection and analysis of quasi-steady-state kinetic data for enzyme-catalyzed reactions.

A special mixing device for initiating enzyme-catalyzed reactions is used to rapidly achieve an unperturbed quasi-steady state. An on-line computer is employed to sample the initial conditions, the mixing time, and concentrations that change as a function of time during this quasi-steady state phase. A statistical method for estimating initial, quasi-steady state rates from the time course of the enzyme-catalyzed reaction is described. Practical considerations for using this parameter estimation system lead to the conclusion that for the enzyme-catalyzed reaction tested, the extent overall reaction should be above .2% for high initial substrate concentrations, and above 1% for initial substrate concentrations in the range of the Michaelis constant. Application of this method to a typical enzyme-catalyzed reaction suggests that objective estimates of initial rates from a given set of concentrations and corresponding times can be obtained with a standard error in the range of 2–3%, but that reproducibility is not better than about 10%. When this procedure was used to estimate initial rates for the glycerol dehydrogenase-catalyzed oxidation of glycerol by NAD, it was found that this enzyme did not behave according to the classical “Michaelis-Menten” mechanism of enzyme action.     

Determination of inhibition constants, I50 values and the type of inhibition for enzyme-catalyzed reactions

A procedure is proposed for determining whether an inhibitor of an enzyme-catalyzed reaction is competitive, noncompetitive, or uncompetitive with respect to the substrate. The method is based on fitting the equation for noncompetitive inhibition to data obtained by measuring the rate of the reaction over a range of substrate and inhibitor concentrations. The results of this fit may suggest that the inhibition may be either competitive or uncompetitive, whereupon the data are reanalyzed using the appropriate equation. Comparison of this second fit with the first using an F test permits a statistical decision to be made on the type of inhibition. The chosen fit yields values and standard errors for the Michaelis-Menten parameters (maximum velocity and Michaelis constant), as well as the inhibition constant(s). From these values it is then possible to predict the I50, and its standard error, at any chosen substrate concentration, thereby facilitating comparison with results obtained with similar inhibitors, for homologous enzymes, or in other laboratories.     

Carbocyclic analogues of dTTP and UTP: properties in polymerase enzyme-catalyzed reactions

Racemic carbocyclic analogues of dTTP [(+/-)-C-dTTP] and its ribo counterpart, 5-methyl-UTP [(+/-)-C-m5UTP] were synthesized and examined, in comparison with dTTP and UTP (and m5UTP), as potential substrates of E. coli DNA and RNA polymerases, respectively. Unexpectedly, only a very low (terminal) incorporation of C-dTMP into DNAs of different structure was observed, C-dTTP did not serve as a substrate for chain elongation by the Klenow DNA polymerase. Inhibition of DNA replication was, however, observed in the presence of (+/-)-C-dTTP. The UTP analogue, (+/-)-C-m5UTP proved neither a substrate nor an inhibitor of the RNA polymerase enzyme.     

A potential role for isothermal calorimetry in studies of the effects of thermodynamic non-ideality in enzyme-catalyzed reactions

Attention is drawn to the feasibility of using isothermal calorimetry for the characterization of enzyme reactions under conditions bearing greater relevance to the crowded biological environment, where kinetic parameters are likely to differ significantly from those obtained by classical enzyme kinetic studies in dilute solution. An outline of the application of isothermal calorimetry to the determination of enzyme kinetic parameters is followed by considerations of the nature and consequences of crowding effects in enzyme catalysis. Some of those effects of thermodynamic non-ideality are then illustrated by means of experimental results from calorimetric studies of the effect of molecular crowding on the kinetics of catalysis by rabbit muscle pyruvate kinase. This review concludes with a discussion of the potential of isothermal calorimetry for the experimental determination of kinetic parameters for enzymes either in biological environments or at least in media that should provide reasonable approximations of the crowded conditions encountered in vivo.     

Estimation of the initial velocity of enzyme-catalysed reactions by non-linear regression analysis of progress curves.

Most methods for studying the kinetic properties of an enzyme involve the determination of initial velocities. When the reaction progress curve shows significant curvature due to depletion of the substrate, accumulation of inhibitory products or instability of the enzyme, estimation of the initial velocity is a subjective and inexact process. Two methods have been suggested [Cornish-Bowden (1975) Biochem. J. 144, 305-312; Boeker (1982) Biochem J. 203, 117-123] that attempt to eliminate this subjective element. The present study offers a third alternative, which is based on fitting a reparameterized form of the integrated Michaelis-Menten equation to the progress curves by non-linear regression. This method yields estimates and standard errors of the initial velocity and of the time to reach 50% reaction. No prior knowledge of the apparent product concentration at zero time or infinite time is required, since both of these quantities are also estimated from the data. It is shown that this method yields reliable estimates of the initial velocity under a wide range of circumstances, including those where the two previously published methods perform poorly.     

Analysis of progress curves for enzyme-catalysed reactions. Automatic construction of computer programs for fitting integrated rate equations.

In epithelial cells isolated from rat small intestine, we have studied the influence of vasoactive intestinal peptide (VIP), a neurotransmitter which markedly increases enterocyte cyclic AMP, and of two cyclic AMP analogues (8-bromo cyclic AMP and N6,2'-O-dibutyryl cyclic AMP) on the rate of glycolysis, fructose 2,6-bisphosphate concentration and 6-phosphofructo-2-kinase activity, as well as on the rate of 3-O-methyl-D-[14C]glucose uptake. Our results show that, without affecting the rate of 3-O-methyl-D-[14C]glucose accumulation, VIP and cyclic AMP analogues were able to inhibit glucose consumption and L-lactate formation by isolated rat enterocytes. These effects occurred parallel to a significant decrease in the cellular concentration of fructose 2,6-bisphosphate and to a partial inactivation of 6-phosphofructo-2-kinase. These findings support the hypothesis that VIP inhibits glycolysis in rat enterocytes through a cyclic AMP-dependent mechanism.     

Strategy for the simulation of batch reactors when the enzyme-catalyzed reaction is accompanied by enzyme deactivation

The balance equations pertaining to the modelling of batch reactors performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. The functional form of the solution for the general situation where both the rate of the enzyme-catalyzed reaction and the rate of enzyme deactivation are dependent on the substrate concentration is obtained, as well as the condition that applies if a maximum conversion of substrate is sought. Finally, two examples of practical interest are explored to emphasize the usefulness of the analysis presented.List of Symbols C _E mol/m³ concentration of active enzyme - C _E,O mol/m³ initial concentration of active enzyme - C _S mol/m³ concentration of substrate - C _S,O mol/m³ initial concentration of substrate - C _S,min mol/m³ minimum value for the concentration of substrate - k 1/s first order rate constant associated with conversion of enzyme/substrate complex into product - k ₁ 1/s first order deactivation constant of enzyme (or free enzyme) - k ₂ 1/s first order deactivation constant of enzyme in enzyme/substrate complex form - K _m mol/m³ Michaelis-Menten constant - p mol/(m³s) time derivative of C _S - q mol/m³ auxiliary variable - t s time elapsed after reactor startup Greek Symbols 1/s univariate function expressing the dependence of the rate of enzyme deactivation on C _S - mol/m³ dummy variable of integration - mol/m³ dummy variable of integration - 1/s univariate function expressing the dependence of the rate of substrate depletion on C _S - m³/(mol s) derivative of with respect to C _S     

Starting D-optimal designs for batch kinetics studies of enzyme-catalyzed reactions in the presence of enzyme deactivation.

This paper describes a strategy for the starting experimental design of experiments required by general research in the field of biochemical kinetics. The type of experiments that qualify for this analysis involve batch reactions catalyzed by soluble enzymes where the activity of the enzyme decays with time. Assuming that the catalytic action of the enzyme obeys a Michaelis-Menten rate expression and that the deactivation of the enzyme follows a first-order decay, the present analysis employs the dimensionless, integrated form of the overall rate expression to obtain a criterion (based on the maximization of the determinant of the derivative matrix) that relates the a priori estimates of the parameters with the times at which samples should be withdrawn from the reacting mixture. The analysis indicates that the initial concentration of substrate should be as large as possible, and that the samples should be taken at times corresponding to substrate concentrations of approximately 2/3, 1/4, and I/epsilon of the initial concentration (where epsilon should be as large as possible).     

pH-activity curves for enzyme-catalysed reactions in which the hydron is a product or reactant.

A reaction in which the hydron [International Union of Pure and Applied Chemistry (1986) Chem. Int. 8 (4), 21] is a reactant will have a more acidic pH optimum than the reverse reaction in which it is a product. Simple mechanistic models, made by postulating various ways in which the hydron is supplied for the forward reaction, lead to the prediction that the pK that characterizes the fall in activity on the alkaline side for the forward reaction will be equal to that characterizing the fall on the acid side for the reverse reaction. It is not possible to identify what is responsible for this pK without additional information; as is well known, different possible dispositions of hydrons in transition states cannot usually be distinguished solely by kinetics.