Investigations of reaction kinetics for immobilized enzymes--identification of parameters in the presence of diffusion limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.     

A study of the allosteric kinetics of Phycomyces pyruvate kinase as judged by the effect of L-alanine and fructose 1,6-bisphosphate

The influence of fructose 1,6-bisphosphate and L-alanine on the kinetics of pyruvate kinase (ATP:pyruvate O2-phosphotransferase, EC 2.7.1.40) from Phycomyces blakesleeanus NRRL 1555 (-) was studied at pH 7.5. By addition of fructose 1,6-bisphosphate the sigmoid kinetics with respect to phosphoenol pyruvate and Mg2+ were abolished and the velocity curves became hyperbolic. In the presence of L-alanine the positive homotropic cooperativity with respect to phosphoenol pyruvate increased with Hill coefficient values close to 4, while the sigmoid kinetics with respect to Mg2+ became hyperbolic. Fructose 1,6-bisphosphate overcomes the inhibition produced by L-alanine, the antagonism between phosphoenol pyruvate and L-alanine also being evident. Inhibition has been found at high Mg2+ concentrations, compatible with the binding of the magnesium ions to an inactive conformational state of the enzyme. The data were analysed on the basis of the two-states concerted-symmetry model of Monod, Wyman and Changeux, and the parameters of the model were calculated. Phosphoenol pyruvate and fructose 1,6-bisphosphate appeared to show exclusive binding to the active conformational state (R), whereas magnesium ions bind preferentially, by a factor of 45, to the R state. L-Alanine binds more readily to the inactive T state of the enzyme.     

Allosteric interactions in phosphorylase B

An allosteric model of phosphorylase B is proposed based on the following assumptions. The enzyme consists of two sub-units and undergoes a concerted transition from the inactive T to the active R state. The binding of substrates, phosphate, and glycogen is regarded as exclusive, but the binding of the activator AMP is nonexclusive. The enzyme model is of the K, V type, i. e., the activator AMP is important, not only for the T-R transition and the substrates binding, but also for the formation of the active site. Therefore, it displays a big influence on the maximal reaction rate. Calculations based on this model lead to an equation containing 5 constants, which can be easily computed from kinetic data. All kinetic measurements fit the expressions derived from the model. Independent methods for the measurement of all the constants involved were developed. They are based on the study of binding of phosphorylase with the substrates and the activator. These measurements are in satisfactory agreement with the data obtained from enzyme kinetics.     

Allosteric regulation of rat testis mitochondrial aldehyde dehydrogenase by capronaldehyde and magnesium ion.

1. The influence of Mg2+ on the kinetic behaviour of mitochondrial aldehyde dehydrogenase from rat testis has been investigated using capronaldehyde as substrate. 2. The kinetic data, obtained by numerical analysis of the progress curves of aldehyde oxidation, were fitted to a modified version of the Monod-Wyman-Changeux model and the fitting procedure resulted in a good correspondence between theoretical and experimental reaction rates over a wide range of capronaldehyde and Mg2+ concentrations. 3. According to the model, the tetrameric enzyme is in equilibrium between two conformational states R and T which display comparable affinities for capronaldehyde (the dissociation constants are 0.17 and 0.3 microM, respectively), but different catalytic power (VT = 2VR). The T state can bind with lower affinity a second molecule of aldehyde (K = 2.5 microM). 4. Mg2+ stabilizes the T state (the dissociation constants for the R and T states are 2.2 and 0.12 mM, respectively) and acts as a strong activator of the R state, but as a weak inhibitor of the T state. In the absence of substrates and Mg2+, the R<-->T equilibrium favors the R state ([T]/[R] = 0.16). 5. The model is able to predict the kinetic behaviour also when the NAD+ concentrations are not saturating and when inhibitory effects by NADH are taken into account.     

Allosteric regulation of beef liver arginase activity by L-ornithine

Inhibition of beef liver arginase by L-ornithine was investigated with two sets of independent experiments. Progress curves of the production of urea were simulated with two integrated Michaelis-Menten equations for competitive and non-competitive inhibition by ornithine. Both fitted the curves well, but failed to correctly predict the inhibition when the reaction was started with ornithine already present. Measurement of initial rates of reaction enabled an allosteric model to be built in accordance to Monod-Wyman-Changeux: arginine preferentially binds to the active state R and ornithine preferentially binds to the inactive state T. In the absence of both ligands, the R in equilibrium T equilibrium slightly favours the active state and both states bind ornithine more strongly than arginine. No great variation was observed in the 6 parameters of the model by assuming the enzyme to be a trimer or a tetramer. The model was able to predict not only the initial rate curves, from which it was derived, but also the progress curves independently obtained.     

Compared esterification kinetics of the lipase from Burkholderia cepacia either free or encapsulated in a silica aerogel

This paper presents an experimental comparison of the kinetics of esterification catalyzed with the lipase from Burkholderia cepacia, either free, or encapsulated in a silica aerogel dried by the supercritical CO₂ method. The operational characteristics, in terms of pre-equilibration at given water thermodynamic activity a_w, mass of enzyme in the gel, size of aerogel particles, are presented. The kinetic model known as BiBi Ping Pong with inhibition by both substrates has been found to fit relatively well with the experimental results, except when both substrate concentrations were high with the encapsulated enzyme. All kinetics constants were found to be increased by aerogel encapsulation. In particular V_max was increased by a factor of the order of 10 per mg of enzyme.     

Time evolution of the quaternary structure of Escherichia coli aspartate transcarbamoylase upon reaction with the natural substrates and a slow, tight-binding inhibitor

Here, we present a study of the conformational changes of the quaternary structure of Escherichia coli aspartate transcarbamoylase, as monitored by time-resolved small-angle X-ray scattering, upon combining with substrates, substrate analogs, and nucleotide effectors at temperatures between 5 and 22 °C, obviating the need for ethylene glycol. Time-resolved small-angle X-ray scattering time courses tracking the T → R structural change after mixing with substrates or substrate analogs appeared to be a single phase under some conditions and biphasic under other conditions, which we ascribe to multiple ligation states producing a time course composed of multiple rates. Increasing the concentration of substrates up to a certain point increased the T → R transition rate, with no further increase in rate beyond that point. Most strikingly, after addition of N-phosphonacetyl-l-aspartate to the enzyme, the transition rate was more than 1 order of magnitude slower than with the natural substrates. These results on the homotropic mechanism are consistent with a concerted transition between structural and functional states of either low affinity, low activity or high affinity, high activity for aspartate. Addition of ATP along with the substrates increased the rate of the transition from the T to the R state and also decreased the duration of the R-state steady-state phase. Addition of CTP or the combination of CTP/UTP to the substrates significantly decreased the rate of the T → R transition and caused a shift in the enzyme population towards the T state even at saturating substrate concentrations. These results on the heterotropic mechanism suggest a destabilization of the T state by ATP and a destabilization of the R state by CTP and CTP/UTP, consistent with the T and R state crystallographic structures of aspartate transcarbamoylase in the presence of the heterotropic effectors.     

Influence of nucleotide effectors on the kinetics of the quaternary structure transition of allosteric aspartate transcarbamylase

We report the effects of allosteric effectors, ATP, CTP and UTP on the kinetics of the quaternary structure change of Escherichia coli ATCase during the enzyme reaction with physiological substrates. Time-resolved, small-angle, X-ray scattering of solutions allows direct observation of structural transitions over the entire time-course of the enzyme reaction initiated by fast mixing of the enzyme and substrates. In the absence of effectors, all scattering patterns recorded during the reaction are consistent with a two-state, concerted transition model, involving no detectable intermediate conformation that differs from the less active, unliganded T-state and the more active, substrate-bound R-state. The latter predominates during the steady-state phase of enzyme catalysis, while the initial T-state is recovered after substrate consumption. The concerted character of the structural transition is preserved in the presence of all effectors. CTP slightly shifts the dynamical equilibrium during a shortened steady state toward T while the additional presence of UTP makes the steady state vanishingly short. The return transition to the T conformation is slowed significantly in the presence of inhibitors, the effect being most severe in the presence of UTP. While ATP increases the apparent T to R rate, it also increases the duration of the steady-state phase, an apparently paradoxical observation. This observation can be accounted for by the greater increase in the association rate constant of aspartate, promoted by ATP, while the nucleotide produces a lesser degree of increase in the dissociation rate constant. Under our experimental conditions, using high concentrations of both enzyme and substrate, it appears that this very mechanism of activation turns the activator into an efficient inhibitor. The scattering patterns recorded in the presence of ATP support the view that ATP alters the quaternary structure of the substrate-bound enzyme, an effect reminiscent of the reported modification of PALA-bound R-state by Mg-ATP.     

Regulation by progesterone and pregnenolone of dimeric aldehyde dehydrogenase from rat testis cytoplasm

• 1.1. Aldehyde dehydrogenase from rat testis cytosol has been purified to electrophoretic homogeneity. With an isoelectric point of 9.5, the enzyme appears a dimer with a subunit molecular weight of 52,500.
• 2.2. The influence of pregnenolone and progesterone on the kinetic behaviour has been investigated using valeraldehyde as substrate.
• 3.3. The kinetic data were fitted to a modified version of the Monod-Wyman-Changeux model and the fitting procedure resulted in a good correspondence between theoretical and experimental reaction rates over a wide range of valeraldehyde concentrations.
• 4.4. According to the model, the dimeric enzyme is in equilibrium between two confonnational states R and T. The R state displays higher affinity for valeraldehyde, but lower catalytic power. In the absence of substrates and effectors the [T]/[R] ratio is near to 1.
• 5.5. Pregnenolone and progesterone activate the enzyme by stabilizing the more active state T and by increasing the catalytic power of the R state. The increase of activity is counteracted by the inhibition exerted by both steroids on the T state.

     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

Elementary steps in the reaction mechanism of chicken liver fatty acid synthase. pH dependence of NADPH binding and isotope rate effect for beta-ketoacyl reductase

The stopped flow method has been used to determine the pH dependence of the kinetics of the binding of NADPH to chicken liver fatty acid synthase over the pH range 6.0-8.5. The kinetics is consistent with a one-step binding mechanism, and the pH dependence of the second order rate constant indicates that an ionizable group either on the enzyme or on NADPH with a pK alpha of 6.1 is of importance in the binding process. The isotope rate effects have been determined for the steady state reaction with (S)- and (R)-[4-2H] NADPH as substrates and are very small. The pH dependence of the rate constant characterizing the reduction of acetoacetyl by NADPH on the enzyme (beta-ketoacyl reductase) and the isotope rate effects on this constant with (S)-[4-2H]NADPH as substrate also have been measured with the stopped flow method. A small pH-dependent isotope rate effect is found; these results suggest hydride transfer is not rate limiting for the beta-ketoacyl reductase reaction on the enzyme surface. The pH dependence of this rate constant is bell shaped and is very similar to that of the turnover number for the overall reaction; this suggests that the beta-ketoacyl reductase reaction may be partially rate limiting for the overall reaction when the enzyme is saturated with substrates.     

A mutant of Escherichia coli citrate synthase that affects the allosteric equilibrium.

We describe a mutant of Escherichia coli citrate synthase, CS R319L, in which the arginine residue at position 319 of the sequence has been replaced by leucine. In this mutant, saturation by the substrate acetyl-CoA is changed from sigmoid (Hill parameter = 1.75 +/- 0.2) to hyperbolic (Hill parameter = 1.0 +/- 0.1) and dependence on the activator KCl is greatly reduced. Further mutations at this site and at position 343 (which model building predicts is close enough to allow a side-chain interaction with position 319) are also described. In the wild-type enzyme, the model suggests the possibility of a salt-bridge interaction between Arg-319 (located on the P helix in the small domain) and Glu-343 (in the Q helix in the same domain), but mutation of Glu-343 to Ala (CS E343A) produced a much smaller difference in the kinetic properties than the ARg-319 to Leu mutation did. Small changes in kinetic properties were also obtained with an Arg-319----Glu (CS R319E) mutation. In CS R319L, oxaloacetate, the first substrate to bind, induces an ultraviolet difference spectrum which is obtained with wild-type enzyme only in the presence of KCl. To account for these observations we postulate that wild-type E. coli citrate synthase exists in two conformational states, T and R, which are equilibrium; T state binds NADH, the allosteric inhibitor, while R state binds substrates and can be converted to another substrate-binding state, R', by KCl.(ABSTRACT TRUNCATED AT 250 WORDS)     

The role of intersubunit interactions for the stabilization of the T state of Escherichia coli aspartate transcarbamoylase

Homotropic cooperativity in Escherichia coli aspartate transcarbamoylase results from the substrate-induced transition from the T to the R state. These two alternate states are stabilized by a series of interdomain and intersubunit interactions. The salt link between Lys-143 of the regulatory chain and Asp-236 of the catalytic chain is only observed in the T state. When Asp-236 is replaced by alanine the resulting enzyme exhibits full activity, enhanced affinity for aspartate, no cooperativity, and no heterotropic interactions. These characteristics are consistent with an enzyme locked in the functional R state. Using small angle x-ray scattering, the structural consequences of the D236A mutant were characterized. The unliganded D236A holoenzyme appears to be in a new structural state that is neither T, R, nor a mixture of T and R states. The structure of the native D236A holoenzyme is similar to that previously reported for another mutant holoenzyme (E239Q) that also lacks intersubunit interactions. A hybrid version of aspartate transcarbamoylase in which one catalytic subunit was wild-type and the other had the D236A mutation was also investigated. The hybrid holoenzyme, with three of the six possible interactions involving Asp-236, exhibited homotropic cooperativity, and heterotropic interactions consistent with an enzyme with both T and R functional states. Small angle x-ray scattering analysis of the unligated hybrid indicated that the enzyme was in a new structural state more similar to the T than to the R state of the wild-type enzyme. These data suggest that three of the six intersubunit interactions involving D236A are sufficient to stabilize a T-like state of the enzyme and allow for an allosteric transition.     

Cooperativity and high pressure: stabilization of the R conformation of the allosteric aspartate transcarbamylase under the influence of pressure.

The allosteric enzyme aspartate transcarbamylase (ATCase) from E. coli shows homotropic cooperative interactions between its six catalytic sites for the binding of the substrate aspartate. This cooperativity is explained by the transition of the enzyme from a conformation which has a low affinity for aspartate (T state) to a conformation with high affinity (R state). The crystallographic structures of these two conformations are known to a resolution of 2.5 A and 2.1 A, respectively, and they reveal an important difference in the quaternary structure of the protein. Enzyme kinetics under high pressure were used to study the transition between the two states. It appears that in the presence of a low concentration of aspartate, conditions under which the enzyme is essentially in the T state, pressure promotes the transition to the R state, the maximal effect being observed at 120 MPa. This transition is accompagnied by a significant deltaV. This observation is in accordance with the change in the protein surface exposed to the solvent, and with the increased number of water molecules bound to the protein. Since the partial specific volume of the enzyme does not change significantly during the T to R transition, the negative deltaV is only related to the change in hydration of the protein. This result emphasizes a significant role of the protein-solvent interactions in this important regulatory conformational change.     

Kinetic properties of crystalline enzymes. Carboxypeptidase A.

Spectrochemical probes have demonstrated that the conformations of carboxypeptidase A differ in solution and in the crystalline state. Detailed kinetic studies of carboxypeptidase A crystals and solutions now show that the physical state of the enzyme is also a critical parameter that affects this enzyme's function. Thus, for all substrates examined, crystallization of the enzyme markedly reduces catalytic efficiency, kcat, from 20- to 1000-fold. In addition, substrate inhibition, apparent in solution for some di- and depsipeptides, is abolished with crystals, while longer substrates with normal kinetics in solution may exhibit activation with the crystals. The physical state of the enzyme also affects the mode of action of known modifiers of peptidase activity of the enzyme. In solution, addition of benzoylglycine or cinnamic acid markedly increases the rate of hydrolysis of CbzGly-Phe, but, with the crystalline enzyme, their addition hardly alters the activity. This is in accord with the weakening or absence of inhibitory enzyme-substrate binding modes. Kinetic studies on crystals were carried out over a range of enzyme concentrations, substrate concentrations, and crystal sizes, and in all instances the results are in good agreement with the theory developed by Katchalski for enzymes insolubilized by other means. Importantly, these kinetic parameters are determined under conditions which obviate artifacts due to diffusion limitation of substrates or products. The differences in the kinetic behavior of carboxypeptidase crystals, on the one hand, and of their solutions, on the other hand, bear importantly on efforts to interpret the function of the enzyme in structural terms. Hypothetical modes of substrate-enzyme interaction, generated by superimposing substrate models on the crystal structure of carboxypeptidase to stimulate kinetics in solution, have failed to detect all of these changes which affect inhibitory or activating binding modes.     

Large differences are observed between the crystal and solution quaternary structures of allosteric aspartate transcarbamylase in the R state

Solution scattering curves evaluated from the crystal structures of the T and R states of the allosteric enzyme aspartate transcarbamylase from Escherichia coli were compared with the experimental x-ray scattering patterns. Whereas the scattering from the crystal structure of the T state agrees with the experiment, large deviations reflecting a significant difference between the quaternary structures in the crystal and in solution are observed for the R state. The experimental curve of the R state was fitted by rigid body movements of the subunits in the crystal R structure which displace the latter further away from the T structure along the reaction coordinates of the T→R transition observed in the crystals. Taking the crystal R structure as a reference, it was found that in solution the distance between the catalytic trimers along the threefold axis is 0.34 nm larger and the trimers are rotated by 11° in opposite directions around the same axis; each of the three regulatory dimers is rotated by 9° around the corresponding twofold axis and displaced by 0.14 nm away from the molecular center along this axis. Proteins 27:110–117 © 1997 Wiley-Liss, Inc.     

Evolution of allosteric models for hemoglobin

We compare various allosteric models that have been proposed to explain cooperative oxygen binding to hemoglobin, including the two-state allosteric model of Monod, Wyman, and Changeux (MWC), the Cooperon model of Brunori, the model of Szabo and Karplus (SK) based on the stereochemical mechanism of Perutz, the generalization of the SK model by Lee and Karplus (SKL), and the Tertiary Two-State (TTS) model of Henry, Bettati, Hofrichter and Eaton. The preponderance of experimental evidence favors the TTS model which postulates an equilibrium between high (r)- and low (t)-affinity tertiary conformations that are present in both the T and R quaternary structures. Cooperative oxygenation in this model arises from the shift of T to R, as in MWC, but with a significant population of both r and t conformations in the liganded T and in the unliganded R quaternary structures. The TTS model may be considered a combination of the SK and SKL models, and these models provide a framework for a structural interpretation of the TTS parameters. The most compelling evidence in favor of the TTS model is the nanosecond - millisecond carbon monoxide (CO) rebinding kinetics in photodissociation experiments on hemoglobin encapsulated in silica gels. The polymeric network of the gel prevents any tertiary or quaternary conformational changes on the sub-second time scale, thereby permitting the subunit conformations prior to CO photodissociation to be determined from their ligand rebinding kinetics. These experiments show that a large fraction of liganded subunits in the T quaternary structure have the same functional conformation as liganded subunits in the R quaternary structure, an experimental finding inconsistent with the MWC, Cooperon, SK, and SKL models, but readily explained by the TTS model as rebinding to r subunits in T. We propose an additional experiment to test another key prediction of the TTS model, namely that a fraction of subunits in the unliganded R quaternary structure has the same functional conformation (t) as unliganded subunits in the T quaternary structure.