Chymotrypsin-catalyzed peptide synthesis. Kinetic analysis of the kinetically controlled peptide-bond formation

The kinetics of peptide-bond formation catalyzed by delta-chymotrypsin has been studied for a number of peptide products of different length using fixed concentrations of the acyl component (Ac-Phe-OMe, Ac-Ala-Ala-Phe-OMe, or Ac-Ala-Ala-Tyr-OMe) and varying concentration of the amino component (H-Ala-NH2 or H-Ala-Ala-NH2). The time course of the reactions was followed by monitoring ester consumption and peptide product formation by analytical HPLC. On the basis of a plausible four-centre mechanistic model, the theoretical time course of these reactions was calculated using rate and equilibrium constants determined by separate kinetic experiments. The excellent agreement observed between the theoretical and the experimental time courses supports the proposed mechanism and provides evidence for the validity of the present kinetic approach. By focusing attention on the rate constants which are critical for efficient synthesis, this mechanistic information constitutes a valuable basis for the use of the enzymatic peptide synthesis in preparative applications.     

General methods for analysis of sequential "n-step" kinetic mechanisms: application to single turnover kinetics of helicase-catalyzed DNA unwinding

Helicase-catalyzed DNA unwinding is often studied using "all or none" assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using "n-step" sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the "kinetic step size", m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using "n-step" sequential mechanisms has previously been limited by an inability to float the number of "unwinding steps", n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, f(ss)(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain f(ss)(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible, uncompetitive inhibitor.

We present a general kinetic analysis of enzyme catalyzed reactions evolving according to a Michaelis-Menten mechanism, in which an uncompetitive, reversible inhibitor acts. Simultaneously, enzyme inactivation is induced by an unstable suicide substrate, i.e. it is a Michaelis-Menten mechanism with double inhibition: one originating from the substrate and another originating from the reversible inhibitor. Rapid equilibrium of the reversible reaction steps involved is assumed and the time course equations for the reaction product have been derived under the assumption of limiting enzyme. The goodness of the analytical solutions has been tested by comparison with simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested.     

Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach

Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .     

Intermediates and transition states in thiamin diphosphate-dependent decarboxylases. A kinetic and NMR study on wild-type indolepyruvate decarboxylase and variants using indolepyruvate, benzoylformate, and pyruvate as substrates

The thiamin diphosphate (ThDP)-dependent enzyme indolepyruvate decarboxylase (IPDC) is involved in the biosynthetic pathway of the phytohormone 3-indoleacetic acid and catalyzes the nonoxidative decarboxylation of 3-indolepyruvate to 3-indoleacetaldehyde and carbon dioxide. The steady-state distribution of covalent ThDP intermediates of IPDC reacting with 3-indolepyruvate and the alternative substrates benzoylformate and pyruvate has been analyzed by (1)H NMR spectroscopy. For the first time, we are able to isolate and directly assign covalent intermediates of ThDP with aromatic substrates. The intermediate analysis of IPDC variants is used to infer the involvement of active site side chains and functional groups of the cofactor in distinct catalytic steps during turnover of the different substrates. As a result, three residues (glutamate 468, aspartate 29, and histidine 115) positioned perpendicular to the thiazolium moiety of ThDP are involved in binding of all substrates and decarboxylation of the respective tetrahedral ThDP-substrate adducts. Most likely, interactions of these side chains with the substrate-derived carboxylate account for an optimal orientation of the substrate and/or intermediate in the course of carbon-carbon ligation and decarboxylation supporting the suggested least-motion, maximum overlap mechanism. The active site residue glutamine 383, which is located at the opposite site of the thiazolium nucleus as the "carboxylate pocket" (formed by the Glu-Asp-His triad), is central to the substrate specificity of IPDC, probably through orbital alignment. The Glu51-cofactor proton shuttle is, conjointly with the Glu-Asp-His triad, involved in multiple proton transfer steps, including ylide generation, substrate binding, and product release. Studies with para-substituted benzoylformate substrates demonstrate that the electronic properties of the substrate affect the stabilization or destabilization of the carbanion intermediate or carbanion-like transition state and in that way alter the rate dependence on decarboxylation. In conclusion, general mechanistic principles of catalysis of ThDP-dependent enzymes are discussed.     

Stoichiometry and kinetics of transport vesicle fusion with Golgi membranes

The in vitro complementation assay established by Rothman and co-workers continues to be an important tool to study intra-Golgi transport. In this study, kinetic modeling is used to identify four main parameters that, together, explain the basic features of an assay that is a modification of the original assay. First, the assay signal depends on the ratio of Golgi membranes to transport intermediates in the assay. Secondly, an inactivation rate describes how the activity of transport intermediates decreases over time. Thirdly, the rate at which transport intermediates irreversibly bind to Golgi membranes is measured independently of membrane fusion, thus allowing a quantitative distinction between these two steps. Fourthly, a single rate constant describes the remaining reactions, which result in membrane fusion. This approach of kinetic modeling of experiments is generally applicable to other in vitro assays of cell biological phenomena, permitting quantitative interpretations and an increased resolution of the experiments.     

Reconstructing biochemical pathways from time course data

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.     

Formation of the "peroxy" intermediate in cytochrome c oxidase is associated with internal proton/hydrogen transfer

When dioxygen is reduced to water by cytochrome c oxidase a sequence of oxygen intermediates are formed at the reaction site. One of these intermediates is called the "peroxy" (P) intermediate. It can be formed by reacting the two-electron reduced (mixed-valence) cytochrome c oxidase with dioxygen (called P(m)), but it is also formed transiently during the reaction of the fully reduced enzyme with oxygen (called P(r)). In recent years, evidence has accumulated to suggest that the O-O bond is cleaved in the P intermediate and that the heme a(3) iron is in the oxo-ferryl state. In this study, we have investigated the kinetic and thermodynamic parameters for formation of P(m) and P(r), respectively, in the Rhodobacter sphaeroides enzyme. The rate constants and activation energies for the formation of the P(r) and P(m) intermediates were 1.4 x 10(4) s(-1) ( approximately 20 kJ/mol) and 3 x 10(3) s(-1) ( approximately 24 kJ/mol), respectively. The formation rates of both P intermediates were independent of pH in the range 6.5-9, and there was no proton uptake from solution during P formation. Nevertheless, formation of both P(m) and P(r) were slowed by a factor of 1.4-1.9 in D(2)O, which suggests that transfer of an internal proton or hydrogen atom is involved in the rate-limiting step of P formation. We discuss the origin of the difference in the formation rates of the P(m) and P(r) intermediates, the formation mechanisms of P(m)/P(r), and the involvement of these intermediates in proton pumping.     

Proton transfer in methylmalonyl-CoA epimerase from Propionibacterium shermanii. Studies with specifically tritiated (2R)-methylmalonyl-CoA as substrate.

(2R)-Methyl[2-3H]malonyl-CoA was used as the substrate for methylmalonyl-CoA epimerase from Propionibacterium shermanii, under conditions where the (2S)-methylmalonyl-CoA product was removed enzymically as fast as it was formed, and the fate of the label was monitored at different extents of reaction. Very little, if any, tritium is found attached to the C-2 position in the (2S)-epimer product (isolated as propionyl-CoA). Evidently, the hydrogen atom of the new C-H bond in the product is essentially solvent-derived. The rate of tritium release into the solvent is lower than the rate of product formation, and shows a primary kinetic tritium-isotope effect on kcat./Km of 2.3 +/- 0.1. The specific radioactivity of the remaining substrate rises slowly during the epimerase-catalysed reaction, and this provides an independent estimate of the primary kinetic tritium-isotope effect on kcat./Km of 1.6 +/- 0.5. These results, taken together, indicate that the mechanistic pathway of the epimerase-catalysed reaction resembles that established for proline racemase [Cardinale & Abeles, (1968) Biochemistry 7, 3970-3978], in which two enzyme bases are involved in catalysis. One base removes the proton from the substrate, the second provides the new proton, and there is no fast isotopic exchange between enzyme-bound intermediates and solvent protons.     

The photochemical cycle of bacteriorhodopsin.

The reaction cycle of bacteriorhodopsin in the purple membrane isolated from Halobacterium halobium has been studied by optical absorption spectroscopy using low-temperature and flash kinetic techniques. After absorption of light, bacteriohodopsin passes through at least five distinct intermediates. The temperature and pH dependence of the absorbance changes suggests that branch points and/or reversible steps exist in this cycle. Flash spectroscopy in the presence of a pH-indicating dye shows that the transient release of a proton accompanies the photoreaction cycle. The proton release occurs from the exterior and the uptake is on the cytoplasmic side of the membrane, as required by the function of bacteriorhodopsin as a light-driven proton pump. Proton translocating steps connecting release and uptake are indicated by deuterium isotope effects on the kinetics of the cycle. The rapid decay of a light-induced linear dichroism shows that a chromophore orientation change occurs during the reaction cycle.     

Constant-ratio alternative substrate approach for differentiation of enzyme mechanisms

A new kinetic approach using alternative substrates as a tool for studying enzyme mechanisms is described. In this method the substrate to alternative substrate ratio is maintained constant and the common product (or summation of product analogs) is measured. The double-reciprocal plots so obtained at several constant ratios generate different patterns for various mechanisms, thus permitting a choice of kinetic model. In some cases, secondary intercept plots are utilized as a diagnostic aid. Another feature of this approach is that most of the resultant plots are linear. The graphical patterns for four cases of two-substrate, two-product reactions are presented as examples. These patterns allow one to differentiate several mechanisms which are not distinguishable by conventional alternative substrate, competitive inhibitor, or product inhibition studies alone. When used in combination with other methods, various mechanisms involving isomerization and abortive complex formation can be differentiated even if only one alternative substrate is available.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.     

Deriving reaction mechanisms from kinetic spectroscopy. Application to late rhodopsin intermediates.

A general algebraic approach to the kinetic analysis of time-dependent absorption data is presented that allows the calculation of possible kinetic schemes. The kinetic matrices of all possible reaction mechanisms are calculated from experimental eigenvalues and eigenvectors derived from the decay constants and amplitude spectra (b-spectra) of the global exponential fit to the time-dependence of the absorption data. The eigenvalues are directly related to the decay constants, and the eigenvectors are obtained by decomposing the b-spectra into spectral components representing the intermediates. The analysis method is applied to the late intermediates (lumi, meta I, meta I-380, and meta II) of the rhodopsin photoreaction. The b-spectra are decomposed into lumi, meta I, meta-380, and rhodopsin spectra. The meta-380 component is partitioned into isospectral meta I-380 and meta II components based on physical criteria. The calculated kinetic matrices yield a number of reaction mechanisms (linear scheme with back reactions, branched schemes with equilibrium steps, and a variety of square models) consistent with the photolysis data at 25 degrees C. The problems associated with isospectral intermediates (meta I-380 and meta II) are treated successfully with this method.     

NMR analysis of covalent intermediates in thiamin diphosphate enzymes

Enzymic catalysis proceeds via intermediates formed in the course of substrate conversion. Here, we directly detect key intermediates in thiamin diphosphate (ThDP)-dependent enzymes during catalysis using (1)H NMR spectroscopy. The quantitative analysis of the relative intermediate concentrations allows the determination of the microscopic rate constants of individual catalytic steps. As demonstrated for pyruvate decarboxylase (PDC), this method, in combination with site-directed mutagenesis, enables the assignment of individual side chains to single steps in catalysis. In PDC, two independent proton relay systems and the stereochemical control of the enzymic environment account for proficient catalysis proceeding via intermediates at carbon 2 of the enzyme-bound cofactor. The application of this method to other ThDP-dependent enzymes provides insight into their specific chemical pathways.     

Efficient maximum likelihood estimation of kinetic rate constants from macroscopic currents

A new method is described that accurately estimates kinetic constants, conductance and number of ion channels from macroscopic currents. The method uses both the time course and the strength of correlations between different time points of macroscopic currents and utilizes the property of semiseparability of covariance matrix for computationally efficient estimation of current likelihood and its gradient. The number of calculation steps scales linearly with the number of channel states as opposed to the cubic dependence in a previously described method. Together with the likelihood gradient evaluation, which is almost independent of the number of model parameters, the new approach allows evaluation of kinetic models with very complex topologies. We demonstrate applicability of the method to analysis of synaptic currents by estimating accurately rate constants of a 7-state model used to simulate GABAergic macroscopic currents.     

Transient state kinetic investigation of 5-aminolevulinate synthase reaction mechanism

5-Aminolevulinate synthase (ALAS), a pyridoxal 5'-phosphate-dependent enzyme, catalyzes the first, and regulatory, step of the heme biosynthetic pathway in nonplant eukaryotes and some bacteria. 5-Aminolevulinate synthase is a dimeric protein having an ordered kinetic mechanism with glycine binding before succinyl-CoA and with aminolevulinate release after CoA and carbon dioxide. Rapid scanning stopped-flow absorption spectrophotometry in conjunction with multiple turnover chemical quenched-flow kinetic analyses and a newly developed CoA detection method were used to examine the ALAS catalytic reaction and identify the rate-determining step. The reaction of glycine with ALAS follows a three-step kinetic process, ascribed to the formation of the Michaelis complex and the pyridoxal 5'-phosphate-glycine aldimine, followed by the abstraction of the glycine pro-R proton from the external aldimine. Significantly, the rate associated with this third step (k(3) = 0.002 s(-1)) is consistent with the rate determined for the ALAS-catalyzed removal of tritium from [2-(3)H(2)]glycine. Succinyl-CoA and acetoacetyl-CoA increased the rate of glycine proton removal approximately 250,000- and 10-fold, respectively, supporting our previous proposal that the physiological substrate, succinyl-CoA, promotes a protein conformational change, which accelerates the conversion of the external aldimine into the initial quinonoid intermediate (Hunter, G. A., and Ferreira, G. C. (1999) J. Biol. Chem. 274, 12222-12228). Rapid scanning stopped-flow and quenched-flow kinetic analyses of the ALAS reaction under single turnover conditions lend evidence for two quinonoid reaction intermediates and a model of the ALAS kinetic mechanism in which product release is at least the partially rate-limiting step. Finally, the carbonyl and carboxylate groups of 5-aminolevulinate play a major protein-interacting role by inducing a conformational change in ALAS and, thus, possibly modulating product release.     

Analyzing a kinetic titration series using affinity biosensors

The classical method of measuring binding constants with affinity-based biosensors involves testing several analyte concentrations over the same ligand surface and regenerating the surface between binding cycles. Here we describe an alternative approach to collecting kinetic binding data, which we call "kinetic titration." This method involves sequentially injecting an analyte concentration series without any regeneration steps. Through a combination of simulation and experimentation, we show that this method can be as robust as the classical method of analysis. In addition, kinetic titrations can be more efficient than the conventional data collection method and allow us to fully characterize analyte binding to ligand surfaces that are difficult to regenerate.     

Analysis of progress curves for a highly concentrated Michaelian enzyme in the presence or absence of product inhibition.

Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.     

Hunting oxygen complexes of nitric oxide synthase at low temperature and high pressure

The reaction of nitric oxide synthase (NOS) with oxygen is fast and takes place within several steps, separated by ephemeral intermediates. The use of extreme experimental conditions, such as low temperature and high pressure, associated to rapid kinetic analysis, has proven to be a convenient tool to study this complex reaction. Stopped-flow experiments under high pressure indicated that oxygen binding occurred in more than one step. This was further corroborated by the detection of two short-lived oxy-compounds, differing in their spectral and electronic properties. Oxy-I resembles the ferrous oxygen complex known for cytochrome P450, whereas oxy-II appears to be locked in the superoxide form. Subzero temperature spectroscopy, together with an analytical separation method, revealed that the subsequent one-electron reduction of the oxygen complex is carried out by the NOS cofactor tetrahydrobiopterin (BH4). The low-temperature stabilized oxidation product of BH4 was found to be a protonated BH3 radical. Finally, work in the presence of a BH4 analog indicated that proton transfer to the activated oxygen complex is a second essential function of BH4.