Intramolecular and intermolecular enzymatic modulation of ion channels in excised membrane patches.

A calcium-activated potassium channel in posterior pituitary nerve terminals was modulated by phosphorylation and dephosphorylation. Nearly every patch of membrane containing this channel also contained both membrane bound protein phosphatase and membrane-bound protein kinase. By examining the statistical and kinetic nature of phosphorylation and dephosphorylation in excised patches, it was possible to evaluate two contrasting models for these enzymatic reactions. One of these models treated catalysis as an intermolecular process in which the enzyme and substrate are separate molecular species that diffuse and encounter one another during collisions. The second model treated catalysis as an intramolecular process in which the enzyme and substrate reside within a stable macromolecular complex. The study began with a Poisson analysis of the distribution of channel number in patches, and of the number of protein phosphatase-free and protein kinase-free patches. Subsequent kinetic analysis of dephosphorylation yielded an estimate of the mean number of protein phosphatase molecules per patch that was similar to the value obtained from Poisson analysis. Because these two estimates were independent predictions based on the intermolecular model, their agreement supported this model. Analysis of channel number in protein phosphatase-free patches and of the rarity of patches showing partial but incomplete rundown provided additional support for the intermolecular model over the intramolecular model. Furthermore, dephosphorylation exhibited monotonic kinetics with a rate well below the diffusion limit. Thus, several different lines of analysis support the intermolecular model for dephosphorylation, in which the protein phosphatase must encounter its substrate to effect catalysis. In contrast to the monotonic kinetics of dephosphorylation, the phosphorylation reaction exhibited sigmoidal kinetics, with a rate that depended on membrane potential. Voltage dependence is an unlikely property for a kinetic step involving encounters resulting from diffusion. Furthermore, the velocity of the phosphorylation reaction exceeded the diffusion limit, and this observation is inconsistent with the intermolecular model. Thus, both intermolecular and intramolecular enzymatic mechanisms operate in the modulation of the calcium-activated potassium channel of the posterior pituitary. These studies provide a functional characterization of the interactions between enzyme and substrate in intact patches of cell membrane.     

Modeling, simulation, and kinetic analysis of a heterogeneous reaction system for the enzymatic conversion of poorly soluble substrate.

We developed a kinetic model that describes a heterogeneous reaction system consisting of a solid substrate suspension for the production of D-amino acid using D-hydantoinase. As a biocatalyst, mass-produced free and whole cell enzymes were used. The heterogeneous reaction system involves dissolution of a solid substrate, enzymatic conversion of the dissolved D-form substrate, spontaneous racemization of an L-form substrate to D-form, and deactivation of the enzyme. In the case of using whole cell enzymes, transfer of the dissolved substrate and product through the cell membrane was considered. The kinetic parameters were determined from experiments, literature data, and by using Marquardt's method of nonlinear regression analysis. The model was simulated using the kinetic parameters and compared with experimental data, and a good agreement was observed between the experimental results and the simulation ones. Factors affecting the kinetics of the heterogeneous reaction system were analyzed on the basis of the kinetic model, and the efficiency of the reaction systems using free and whole cell enzymes was also compared.     

Scanning molecular sieve chromatography of interacting protein systems. III. Effect of kinetic parameters on the large zone boundary profiles for local equilibration between mobile and stationary phases.

Large zone reaction boundary profiles for molecular sieve chromatography as affected by kinetic parameters have been simulated for local equilibration between the mobile and stationary phases. Our studies of monomer-dimer and monomer-tetramer systems indicate that in a slowly equilibrating system, the kinetic controls operating between the mobile and stationary phases contribute most significantly to the overall boundary profile. In a rapidly equilibrating system, however, the kinetic parameters kij and kji operating in the mobile phase are the principal determinants of the reaction boundary, while the kinetic effects of kii and k-ii between the mobile and stationary phases are minimal.     

Scanning molecular sieve chromatography of interacting protein systems. III. Effect of kinetic parameters on the large zone boundary profiles for local equilibration between mobile and stationary phases

Large zone reaction boundary profiles for molecular sieve chromatography as affected by kinetic parameters have been simulated for local equilibration between the mobile and stationary phases. Our studies of monomer-dimer and monomer-tetramer systems indicate that in a slowly equilibrating system, the kinetic controls operating between the mobile and stationary phases contribute most significantly to the overall boundary profile. In a rapidly equilibrating system, however, the kinetic parameters k(ij) and k(ji) operating in the mobile phase are the principal determinants of the reaction boundary, while the kinetic effects of k(ii) and k-(ii) between the mobile and stationary phases are minimal.     

Kinetics of the aspartate-aminotransferase reaction catalyzed by free and immobilized cells of E. coli]

The kinetics of the aspartate-aminotransferase reaction were studied, using free and immobilized cells of E. coli, strain 85 as an enzyme source. It was shown that the reaction is limited by mass transport of the reagents through the bacterial cell membrane even at high concentrations of the substrates in the surrounding solution. The polyacrylamide gel-incorporated cells of E. coli, strain 85 catalyze the aspartate-aminotransferase reaction more effectively as compared to free or destroyed cells. In the latter case the reaction is characterized by the following kinetic parameters: the effective values of the stationary rate of the product accumulation and its stationary efflux from the cell are equal to (15,37 +/- 0.4) . 10(-6) mole/s/mg of protein and (3,01 +/- 0,8) . 10(-20) mole/s per 1 cell. respectively. The steady-state constant for glutamate synthesis from aspartic acid is equal to 0,22--0,23.     

Fractal methods to analyze ion channel kinetics

We describe the traditional nonfractal and the new fractal methods used to analyze the currents through ion channels in the cell membrane. We discuss the hidden assumptions used in these methods and how those assumptions lead to different interpretations of the same experimental data. The nonfractal methods assumed that channel proteins have a small number of discrete states separated by fixed energy barriers. The goal was to determine the parameters of the kinetic diagram, which are the number of states, the pathways between them, and the kinetic rate constants of those pathways. The discovery that these data have fractal characteristics suggested that fractal approaches might provide more appropriate tools to analyze and interpret these data. The fractal methods determine the characteristics of the data over a broad range of time scales and how those characteristics depend on the time scale at which they are measured. This is done by using a multiscale method to accurately determine the probability density function over many time scales and by determining how the effective kinetic rate constant, the probability of switching states, depends on the effective time scale at which it is measured. These fractal methods have led to new information about the physical properties of channel proteins in terms of the number of conformational substates, the distribution of energy barriers between those states, and how those energy barriers change with time. The new methods developed from the fractal paradigm shifted the analysis of channel data from determining the parameters of a kinetic diagram to determining the physical properties of channel proteins in terms of the distribution of energy barriers and/or their time dependence.     

Hemolymph cholinesterase activity in the Mussel <Emphasis Type="Italic">Crenomytilus grayanus</Emphasis> (Dunker, 1853) that was exposed to adverse natural and anthropogenic conditions

The influence of habitat conditions on the activity, the structure of the substrate specificity (the ratio of the substrate hydrolysis rates), and the kinetic parameters of substrate hydrolysis due to the effect of hemolymph cholinesterase of the mussel Crenomytilus grayanus was studied. Mussels were collected from areas that are influenced by seasonal and stationary upwelling, as well as from a polluted area. Upwelling and anthropogenic pressure were shown to alter the structure of hemolymph cholinesterase substrate specificity in mussels, up to complete loss of the ability to catalyze the hydrolysis of propionyland butyrylthiocholine. It was established that during the seasonal upwelling the efficiency of the cholinergic process in mussels is provided by a wide range of effective concentrations of the substrates and by decreasing their affinity to the enzyme. Under the conditions of chronic anthropogenic pollution, the cholinesterase of the mussel hemolymph loses its ability to hydrolyze substrates other than acetylthiocholine.     

Mechanism of action of cAMP-dependent protein kinase. II. Solvolysis by additional nucleophilic agents

The reaction of the solvolysis of the phosphointermediate, formed in the course of the phosphotransferase reaction was studied using a number of non-specific nucleophilic agents. The methods of identification of the solvolysis products and determination of kinetic parameters were developed. The estimated dependence of the reaction of the reactivity of the nucleophilic agents versus their basicity allowed some conclusions about the transition state structure in the cases of enzyme's interaction with nucleophilic agents and protein substrate. The energy contribution of the specific interaction of the enzyme with histone H1 was evaluated.     

A hysteretic cycle in glucose 6-phosphate metabolism observed in a cell-free yeast extract

The dynamics of a partial glycolytic reaction sequence which converts glucose 6-phosphate to triose phosphates is described. The study was performed with cell-free extracts from baker's yeast harvested in the logarithmic and stationary growth phases. The experiments are based on a flow-through reactor supplied with the desalted cell-free extract as well as glucose 6-phosphate, ATP and phosphoenolpyruvate. In the reaction system the quasi-irreversible reactions catalyzed by 6-phosphofructo-1-kinase, pyruvate kinase, and fructose-1,6-bisphosphatase are involved. When substrate is supplied continuously, only stable stationary states can be observed. With transient perturbations of the substrate supply, multiple stationary states appear. Cyclic transitions between unique stable stationary states were induced by appropriate changes of the rate of substrate supply. A hysteretic cycle could then be demonstrated when, during reverse transitions, a parameter region of multistability was passed. The presence (in resting yeast) or absence (in growing yeast) of fructose-1,6-bisphosphatase did not significantly influence the dynamic capabilities of the investigated reaction sequence. The kinetic properties of the cell-free extracts fit mathematical models developed for in vitro systems reconstituted from purified enzymes.     

Investigation of kinetics of immobilized liver esterase by flow calorimetry

Flow calorimetry (FC) was shown to be a powerful tool for investigation of the kinetics of phenyl acetate hydrolysis catalyzed by pig liver carboxyl esterase. The enzyme was immobilized in alginate gel particles that were placed in a calorimetric flow column and the heat effect of enzyme reaction was followed in single flow and total recirculation conditions. It was shown that the registered temperature change was proportional to molar amount of substrate transformed in the column. A mathematical model describing the enzyme reaction, mass transfer, and heat effects in the calorimetric system was developed and used for the kinetic data evaluation. By combining data from single flow and recirculation modes true kinetic parameters were evaluated by the proposed mathematical procedure based on the model solution and successive approximations.

The kinetic data for carboxyl esterase showed a slide substrate inhibition by phenyl acetate. The obtained kinetic parameters were as follows: Michaelis constant K_m=2 mmol dm⁻³ and substrate inhibition constant K_i=42 mmol dm⁻³. The method can be applied to kinetic study of immobilized enzymes directly in the flow calorimeter without any requirement of an independent analytical technique.     

Model of calcium channel inactivation: a qualitative analysis

A simple model of calcium channel inactivation has been developed, based on the accumulation of calcium ions at the inner mouth of the channel and on their binding to a receptor which inactivates the channel. A qualitative analysis has shown that upon an appropriate choice of parameters corresponding to the cell structure and to kinetic properties of its components, the calcium dependent inactivation and that assumed to be voltage dependent can both be emulated. The model suggests that the supposed variety of calcium channels might be explained by quantitative differences in nonlinear interactions of the channels with other cell components.     

Role of induced fit in enzyme specificity: a molecular forward/reverse switch

Enzyme structures solved with and without bound substrate often show that substrate-induced conformational changes bring catalytic residues into alignment, alter the local environment, and position the substrate for catalysis. Although the structural data are compelling, the role of conformational changes in enzyme specificity has been controversial in that specificity is a kinetic property that is not easy to predict based upon structure alone. Recent studies on DNA polymerization have illuminated the role of substrate-induced conformational changes in enzyme specificity by showing that the rate at which the enzyme opens to release the bound substrate is a key kinetic parameter. The slow release of a correct substrate commits it to the forward reaction so that specificity is determined solely by the rate of substrate binding, including the isomerization step, and not by the slower rate of the chemical reaction. In contrast, fast dissociation of an incorrect substrate favors release rather than reaction. Thus, the conformational change acts as a molecular switch to select the right substrate and to recognize and disfavor the reaction of an incorrect substrate. A conformational switch may also favor release rather than reverse reaction of the product.     

Some characteristics of the kinetics of enzymatic reactions based on the example of catalase]

A method of kinetic analysis for quickly acting enzymes, which are characterized with substrate inhibition, on the catalase model is proposed. Catalase kinetics was shown to be full described, considering changes in the maximal reaction rate and Michaelis constant, by four parameters instead of two usual ones (Vmax, Km equals const.). The method described makes possible to calculate the change the Michaelis constant in time and to estimate real dependencies of the reaction rate on time and on the substrate concentration. Moreover, the enzyme concentration and its inactivation rate at any reaction moment can be calculated under saturation conditions. It is supposed that experimental dependencies of Km on t and of Vmax on t are the results of residual conformation changes accumulated by the enzyme in the reaction process.     

Hysteresis, alternative stationary states and auto-oscillations in an open futile cycle one of the reactions of which is substrate inhibited]

In connection with the problem of regulation of futile (energy-dissipating) cycles in cell metabolism, a kinetic model has been investigated of an open cycle S1 (see article) S2, in which one of the enzymes (E-) is inhibited by the excess of its substrate S2. The quasi-stationary net velocity of the utilization of substrate S1 in the cycle as a function of its concentration is shown to be of a hysteretic character. Owing to this the alternative stationary states and self-oscillations may occur in the cycle. Under certain conditions the transition from one alternative state to another may reverse the direction of the net flux of conversion from S1 to S2 or vice versa. The self-oscillations are associated with a periodical change in the net flux direction. It is suggested the participation of glycogen (starch) in the self-oscillatory mechanism of the futile cycle formed by the phosphofructokinase and fructose bisphosphatase reactions may give rise to oscillations with the period of 10(3)-10(4) min, which may serve as the basis for the cell clock.     

Morpholinecarbonyl-Rhodamine 110 based substrates for the determination of protease activity with accurate kinetic parameters

Commonly used fluorogenic substrate analogues for the detection of protease activity contain two enzyme-cleavable bonds conjugated to the fluorophore. Enzymatic cleavage follows a two-step reaction with a monoamide intermediate. This intermediate shows fluorescence at the same wavelength as the final product complicating the kinetic analysis of fluorescence-based assays. Fluorogenic substrate analogues for α-chymotrypsin with one cleavable peptide bond have been prepared from morpholinecarbonyl-Rhodamine 110 (MC-Rh110). A comparison of their kinetic properties with the corresponding (peptide)(2)-Rh110 derivatives revealed that these frequently used double-substituted substrate analogues yield only apparent K(m) and k(cat) values that are quite different from the kinetic parameters obtained from the monosubstituted MC-Rh110 based substrate analogues. Although both the monoamide intermediate and MC-Rh110 are monosubstituted Rhodamine 110 derivatives, they show different spectroscopic properties. The data from the spectroscopic analysis clearly show that these properties are directly related to the electron structure of the fluorophore and not to the previously proposed equilibrium between the lactone form and the open ionic form of the fluorophore. This knowledge about the determinants of the spectroscopic properties of monosubstituted Rhodamine 110 introduces a way for a more systematic development of new fluorogenic protease substrate analogues.     

The active site and mechanism of action of recombinant acetohydroxy acid synthase from tobacco

Acetohydroxy acid synthase (AHAS) is one of several enzymes that require thiamine diphosphate and a divalent cation as essential cofactors. Recently, the three-dimensional structure of the enzyme from yeast has been determined [Pang et al., J. Mol. Biol. 317 (2002) 249-262]. While this structure sheds light on the binding of the cofactors and the reaction mechanism, the interactions between the substrates and the enzyme remain unclear. We have studied the pH dependence of kinetic parameters in order to obtain information about the chemical mechanism in the active site. Data are consistent with a mechanism in which substrate selectively catalyzed to the enzyme with an unprotonated base having a pK of 6.48, and a protonated group having a pK of 8.25 for catalysis. The temperature dependence of kinetic parameters was pH-dependent, and the enthalpies of ionization, DeltaH(ion), calculated from the slope of pK(1) and pK(2) are both pH-independent. The solvent perturbation of kinetic parameters was pH-dependent, and the pK(1) from the acidic side and the pK(2) from the basic side were shifted down 0.4 pH units and shifted up 0.6 units as water was replaced by 15% ethanol, respectively. The data are discussed in terms of the acid-base chemical mechanism.     

Malate dehydrogenases. The lack of evidence for dissociation of the dimeric enzyme in kinetic analyses

The kinetic parameters of beef heart cytoplasmic and pig heart mitochondrial malate dehydrogenases have been examined over a wide range of enzyme concentration. No significant changes are observed in these properties. In conjunction with active enzyme sedimentation and sedimentation equilibrium experiments, it is concluded that there is no evidence for dissociation of the dimeric enzyme at any enyzme level in the kinetic analyses. Thus, if dissociation occurs, it must be too slow to be of significance in determining the kinetic properties of the enzyme. It is shown that unless a subunit and its dimeric form have identical kinetic and substrate binding characteristics, the kinetic parameters should change as a function of enzyme concentration.     

Evaluation of intrinsic immobilized kinetics in hollow fiber reactor systems.

Immobilized cell and enzyme hollow fiber reactors have been developed for a variety of biochemical and biomedical applications. Reported mathematical models for predicting substrate conversion in these reactors have been limited in accuracy because of the use of free-solution kinetic parameters. This paper describes a method for determining the intrinsic kinetics of enzymes immobilized in hollow fiber reactor systems using a mathematical model for diffusion and reaction in porous media and an optimization procedure to fit intrinsic kinetic parameters to experimental data. Two enzymes, a thermophilic beta-galactosidase that exhibits product inhibition and L-lysine alpha-oxidase, were used in the analysis. The intrinsic kinetic parameters show that immobilization enhanced the activity of the beta-galactosidase while decreasing the activity of L-lysine alpha-oxidase. Both immobilized enzymes had higher Km values than did the soluble enzyme, indicating less affinity for the substrate. These results are used to illustrate the significant improvement in the ability to predict substrate conversion in hollow fiber reactors.     

Structural basis for substrate specificity differences of horse liver alcohol dehydrogenase isozymes

A structure determination in combination with a kinetic study of the steroid converting isozyme of horse liver alcohol dehydrogenase, SS-ADH, is presented. Kinetic parameters for the substrates, 5beta-androstane-3beta,17beta-ol, 5beta-androstane-17beta-ol-3-one, ethanol, and various secondary alcohols and the corresponding ketones are compared for the SS- and EE-isozymes which differ by nine amino acid substitutions and one deletion. Differences in substrate specificity and stereoselectivity are explained on the basis of individual kinetic rate constants for the underlying ordered bi-bi mechanism. SS-ADH was crystallized in complex with 3alpha,7alpha,12alpha-trihydroxy-5beta-cholan -24-acid (cholic acid) and NAD(+), but microspectrophotometric analysis of single crystals proved it to be a mixed complex containing 60-70% NAD(+) and 30-40% NADH. The crystals belong to the space group P2(1) with cell dimensions a = 55.0 A, b = 73.2 A, c = 92.5 A, and beta = 102.5 degrees. A 98% complete data set to 1.54-A resolution was collected at 100 K using synchrotron radiation. The structure was solved by the molecular replacement method utilizing EE-ADH as the search model. The major structural difference between the isozymes is a widening of the substrate channel. The largest shifts in C(alpha) carbon positions (about 5 A) are observed in the loop region, in which a deletion of Asp115 is found in the SS isozyme. SS-ADH easily accommodates cholic acid, whereas steroid substrates of similar bulkiness would not fit into the EE-ADH substrate site. In the ternary complex with NAD(+)/NADH, we find that the carboxyl group of cholic acid ligates to the active site zinc ion, which probably contributes to the strong binding in the ternary NAD(+) complex.