Activation of skeletal muscle myosin light chain kinase by calcium(2+) and calmodulin

Many biological processes are now known to be regulated by Ca2+ via calmodulin (CM). Although a general mechanistic model by which Ca2+ and calmodulin modulate many of these activities has been proposed, an accurate quantitative model is not available. A detailed analysis of skeletal muscle myosin light chain kinase activation was undertaken in order to determine the stoichiometries and equilibrium constants of Ca2+, calmodulin, and enzyme catalytic subunit in the activation process. The analysis indicates that activation is a sequential, fully reversible process requiring both Ca2+ and calmodulin. The first step of the activation process appears to require binding of Ca2+ to all four divalent metal binding sites on calmodulin for form the complex, Ca42+-calmodulin. This complex then interacts with the inactive catalytic subunit of the enzyme to form the active holoenzyme complex, Ca42+-calmodulin-enzyme. Formation of the holoenzyme follows simply hyperbolic kinetics, indicating 1:1 stoichiometry of Ca42+-calmodulin to catalytic subunit. The rate equation derived from the mechanistic model was used to determine the values of KCa2+ and KCM, the intrinsic activation constants for each step of the activation process. KCa2+ and KCM were found to have values of 10 microM and 0.86 nM, respectively, at 10 mM Mg2+. The rate equation using these equilibrium constants accurately predicts the extent of enzyme activation over a wide range of Ca2+ and calmodulin concentrations. The kinetic model and analytical techniques employed herein may be generally applicable to other enzymes with similar regulatory schemes.     

Redox properties of protein disulfide isomerase (DsbA) from Escherichia coli.

The redox properties of periplasmic protein disulfide isomerase (DsbA) from Escherichia coli were analyzed by measuring the equilibrium constant of the oxidation of reduced DsbA by oxidized glutathione. The experiments are based on the finding that the intrinsic tryptophan fluorescence of DsbA increases about threefold upon reduction of the enzyme, which can be explained by the catalytic disulfide bridge quenching the fluorescence of a neighboring tryptophan residue. From the specific fluorescence of DsbA equilibrated in the presence of different ratios of reduced and oxidized glutathione at pH 7, an equilibrium constant of 1.2 x 10(-4) M was determined, corresponding to a standard redox potential (E'0) of DsbA of -0.089 V. Thus, DsbA is a significantly stronger oxidant than cytoplasmic thioredoxins and its redox properties are similar to those of eukaryotic protein disulfide isomerase. The equilibrium constants for the DsbA/glutathione equilibrium were found to be strongly dependent on pH and varied from 2.5 x 10(-3) M to 3.9 x 10(-5) M between pH 4 and 8.5. The redox state-dependent fluorescence properties of DsbA should allow detailed physicochemical studies of the enzyme as well as the quantitative determination of the oxidized protein by fluorescence titration with dithiothreitol and open the possibility to observe bacterial protein disulfide isomerase "at work" during catalysis of oxidative protein folding.     

Kinetic study of the reduction mechanism for Desulfovibrio gigas cytochrome c3.

The kinetic aspects of the reduction process in cytochrome c3 from Desulfovibrio gigas have been investigated over a wide range of pH values ranging between pH 5.8 and pH 9.8. The data have been analyzed in the framework of an I2H4 interaction network coupled to a proton-linked equilibrium between two tertiary structures (Cornish-Bowden, A. & Koshland, D.E. Jr (1970) J. Biol. Chem. 245, 6241-6250). The kinetic rate constants for the reduction of the four hemes for the two tertiary conformations have been characterized in the framework of the thermodynamic network obtained from the equilibrium analysis (Coletta, M., Catarino, T., LeGall, J.J. & Xavier, A.V. (1991) Eur. J. Biochem. 202, 1101-1106). The intrinsic reduction rate constants determined by reaction with sodium dithionite for two hemes (namely heme 4 and heme 1) are significantly faster than those for the other two heme residues. In view of the equilibrium redox properties, heme 4 (with the fastest reduction rate) may then work as the kinetic electron-capturing site for the electrons from sodium dithionite. The transfer to hemes 2 and 3 then occurs by virtue of their free-energy levels at equilibrium. At our experimental conditions, there is also transfer of electrons to hemes 2 and 3 from heme 1, which is reduced at a slower rate than heme 4, thus contributing to the biphasic kinetics observed for the overall process. The kinetic parameters obtained are discussed in terms of the mechanism proposed for the coupling between the electron and proton transfer, as induced by the heme/heme cooperativity network.     

Electron transfer between the two photosystems. II. Equilibrium constants

(1) The equilibrium constants for the redox reactions occurring between Photosystem (PS) I donors were measured on chloroplasts, dark-adapted in the presence of sodium ascorbate and 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea (DCMU) and then illuminated by d.c. light. The equilibrium constant for the electron transfer between plastocyanin and P-700 is close to 1 and the overall equilibrium constant between cytochrome f and P-700 is about 2.3. As these equilibrium constants do not depend upon the intensity of the d.c. beam, the low values we measured cannot be due to kinetic limitations. (2) The equilibrium constants were measured also in the absence of DCMU using chloroplasts in oxidizing conditions (ferricyanide or far red illumination) illuminated by a saturating flash. During the course of the reduction of PS I donors by plastoquinol molecules formed by the flash, the equilibrium constants are higher than in the preceding conditions: the value for plastocyanin to P-700 is close to 5, and that for cytochrome f to P-700 is about 25. (3) The variations of these equilibrium constants are tentatively interpreted as being due to mutual electrostatic interactions between cytochrome b and f which are included in the same complex. This model implies that the perturbation of the redox properties of cytochrome f by a positive charge located on cytochrome b is identical to the perturbation of the redox properties of cytochrome b by a positive charge located on cytochrome f.     

Inter-flavin electron transfer in cytochrome P450 reductase - effects of solvent and pH identify hidden complexity in mechanism

This study on human cytochrome P450 reductase (CPR) presents a comprehensive analysis of the thermodynamic and kinetic effects of pH and solvent on two- and four-electron reduction in this diflavin enzyme. pH-dependent redox potentiometry revealed that the thermodynamic equilibrium between various two-electron reduced enzyme species (FMNH*,FADH*; FMN,FADH2; FMNH2,FAD) is independent of pH. No shift from the blue, neutral di-semiquinone (FMNH*,FADH*) towards the red, anionic species is observed upon increasing the pH from 6.5 to 8.5. Spectrophotometric analysis of events following the mixing of oxidized CPR and NADPH (1 to 1) in a stopped-flow instrument demonstrates that the establishment of this thermodynamic equilibrium becomes a very slow process at elevated pH, indicative of a pH-gating mechanism. The final level of blue di-semiquinone formation is found to be pH independent. Stopped-flow experiments using excess NADPH over CPR provide evidence that both pH and solvent significantly influence the kinetic exposure of the blue di-semiquinone intermediate, yet the observed rate constants are essentially pH independent. Thus, the kinetic pH-gating mechanism under stoichiometric conditions is of no significant kinetic relevance for four-electron reduction, but rather modulates the observed semiquinone absorbance at 600 nm in a pH-dependent manner. The use of proton inventory experiments and primary kinetic isotope effects are described as kinetic tools to disentangle the intricate pH-dependent kinetic mechanism in CPR. Our analysis of the pH and isotope dependence in human CPR reveals previously hidden complexity in the mechanism of electron transfer in this complex flavoprotein.     

A new rapid and simple method to determine the kinetics of electrode reactions of biologically relevant compounds from the half-peak width of the square-wave voltammograms

A new method is introduced to determine the kinetic parameters of electron transfer reactions of biologically important compounds, based on the measurements of the half-peak width (DeltaE(p/2)) of the square-wave voltammograms. A simple surface (diffusionless) redox reaction, and a simple electrode reaction occurring from dissolved state are considered as model systems. In the region of quasireversible electron transfer, the half-peak widths of theoretical square-wave voltammograms are linear functions of the logarithm of the dimensionless kinetic parameter ln(K) that characterizes the rate of the electron transfer reaction. The dimensionless kinetic parameter K is defined as K=k(s)(fD)(-0.5) for the redox reaction taking place from dissolved state, whereas for the surface redox reaction K is defined as K=k(s)/f (k(s) is the standard rate constant of electron transfer, f is the SW frequency, and D is the diffusion coefficient). A set of linear regression equations for the dependences DeltaE(p/2)vs. ln(K) are derived, which can be used for rapid and precise determination of the charge-transfer kinetic parameters. The estimated values for the standard rate constants of various biologically relevant redox systems using this approach are in very good agreement with the experimental values determined by other square-wave voltammetric methods. The square-wave voltammetric half-peak width method can be used as a simple and reliable alternative to other voltammetric methods developed for the kinetic characterization of electron transfer rates.     

Stimulated and co-operative electron transfer in energy conversion and catalysis.

A new mechanism of electron transfer, stimulated electron transfer, is postulated, in which an electronic feedback is drastically increasing both the rate of electron transfer and the propagation of free energy along electron transferring molecular pathways. In principle, the idea of pushing a system far from equilibrium to achieve a high reaction rate and co-operative phenomena is applied to molecular electron transfer. The effect is calculated from a semiclassical kinetic model of a chain redox reaction with autocatalytic feedback on individual rate constants, where the steps have subsequently been minimized to obtain a continuous electron transfer pathway with electronic feedback. The influence of inhomogeneities and asymmetries in the electron transfer path and of vectorial components (electrical field, gradient of redox potential) are discussed as well as the acceleration of individual and multiple electron transfer as a function of feedback. Examples of autocatalytic feedback are provided including mechanisms involving electron transfer proteins and multi-centre electron transfer catalysts. Such a phenomenon can be described for molecular and interfacial electron transfer in analogy to stimulated and coherent light emission. The results suggest that autocatalytic or stimulated electron transfer may be a key to the understanding of efficient electron transfer and co-operative multi-electron transfer catalysis in biology and a challenge for fuel production mechanisms in artificial photosynthesis and fuel cycles.     

Modulation of the electron redistribution in mixed valence cytochrome C oxidase by protein conformational changes

The redistribution of two electrons in the four redox centers of cytochrome c oxidase following photodissociation of CO from the CO-bound mixed valence species has been examined by resonance Raman spectroscopy. To account for both the kinetic data, obtained from 5 micros to 2 ms, and the equilibrium results, a model is proposed in which the electron redistribution is modulated by a protein conformation transition from a nascent P(1) state to a relaxed P(2) state in a time window longer than 2 ms. In this model, all six possible two-electron reduced species are considered. The high population of species with a one-electron reduced binuclear center, in which the spectrum of heme a(3) is perturbed by the redox state of Cu(B), accounts for the significant residuals in the fitting of the kinetic data with four standard spectra derived from redox species with either zero or two electrons in the binuclear center. Under equilibrium conditions, the conformational change to the P(2) state destabilizes the redox states with only one electron in the binuclear center with respect to those with either zero or two electrons. As a result, the redox equilibrium is perturbed, and the electrons are redistributed. A simulation based on the new kinetics scheme, in which the electron redistribution is modulated by the protein conformation, gives reasonable agreement with both the equilibrium and the kinetic data, demonstrating the validity of this model.     

Steady-state redox behavior of cytochrome c, cytochrome a, and CuA of cytochrome c oxidase in intact rat liver mitochondria.

We have examined the steady-state redox behavior of cytochrome c (Fec), Fea, and CuA of cytochrome c oxidase during steady-state turnover in intact rat liver mitochondria under coupled and uncoupled conditions. Ascorbate was used as the reductant and TMPD (N,N,N',N'-tetramethyl-1,4-phenylenediamine) as the redox mediator. After elimination of spectroscopic interference from the oxidized form of TMPD, we found that Fea remains significantly more oxidized than previously thought. During coupled turnover, CuA always appears to be close to redox equilibrium with Fec. By increasing the amount of TMPD, both centers can be driven to fairly high levels of reduction while Fea remains relatively oxidized. The reduction level at Fea is close to a linear function of the enzyme turnover rate, but the levels at Fec and CuA do not keep pace with enzyme turnover. This behavior can be explained in terms of a redox equilibrium among Fec, CuA, and Fea, where Fea is the electron donor to the oxygen reduction site, but only if Fea has an effective Em (redox midpoint potential) of 195 mV. This is too low to be accounted for on the basis of nonturnover measurements and the effects of the membrane potential. However, if there is no equilibrium, the internal CuA----Fea electron-transfer rate constant must be slow in the time average (about 200 s-1). Other factors which might contribute to such a low Em are discussed. In the presence of uncoupler, this situation changes dramatically. Both Fec and CuA are much less reduced; within the resolution of our measurements (about 10%), we were unable to measure any reduction of CuA. Fea and CuA remain too oxidized to be in redox equilibrium with Fec during steady-state turnover. Furthermore, our results indicate that, in the uncoupled system, the (time-averaged) internal electron-transfer rate constants in cytochrome oxidase must be of the order of 2500 s-1 or higher. When turnover is slowed by azide, the relative redox levels at Fea and Fec are much closer to those predicted from nonturnover measurements. In presence of uncouplers, Fea is always more reduced than Fec, but in the absence of uncouplers, the two centers track together. Unlike the uninhibited, coupled system, the redox behavior here is consistent with the known effect of the electrical membrane potential on electron distribution in the enzyme. Interestingly, in these circumstances (azide and uncoupler present), Fea behaves as if it were no longer the kinetically controlling electron donor to the bimetallic center.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Detailed enzyme kinetics in terms of biochemical species: study of citrate synthase

The compulsory-ordered ternary catalytic mechanism for two-substrate two-product enzymes is analyzed to account for binding of inhibitors to each of the four enzyme states and to maintain the relationship between the kinetic constants and the reaction equilibrium constant. The developed quasi-steady flux expression is applied to the analysis of data from citrate synthase to determine and parameterize a kinetic scheme in terms of biochemical species, in which the effects of pH, ionic strength, and cation binding to biochemical species are explicitly accounted for in the analysis of the data. This analysis provides a mechanistic model that is consistent with the data that have been used support competing hypotheses regarding the catalytic mechanism of this enzyme.     

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.     

The dioxygen cycle. Spectral, kinetic, and thermodynamic characteristics of ferryl and peroxy intermediates observed by reversal of the cytochrome oxidase reaction.

The catalytic mechanism of O2 reduction by cytochrome oxidase was studied in isolated mitochondria and mitoplasts by partial reversal of the reaction. At a high redox potential (Eh) of cytochrome c, high pH, and a high electrochemical proton gradient (delta mu H+) across the inner mitochondrial membrane, the initial ferriccupric state (O) of the oxidized enzyme's bimetallic oxygen reaction center is converted to ferryl (F) and peroxy (P) intermediates, the optical spectroscopic properties of which are reported in detail. This is associated with reversed electron transfer from the bimetallic center to ferricytochrome c. The kinetics of reduction of ferricytochrome c by the reversed electron transfer process are compared with the kinetics of formation of F and P. The results are consistent with transfer of one electron from the ferric-cupric bimetallic center (O) to cytochrome c, yielding the F intermediate, followed by transfer of one electron from the latter to cytochrome c, yielding the P state. In the absence of an effective redox buffer, poising cytochrome c highly oxidized, these primary events are immediately followed by reoxidation of cytochrome c, which is ascribed to forward electron transfer to enzyme molecules still in the O state. This forward reaction also results in accumulation of the P intermediate. Kinetic stimulations of the data predict equilibrium constants for the reversed electron transfer steps, and Em,7 values of approximately 1.1 and 1.2 V may be calculated for the F/O and P/F redox couples, respectively, at delta mu H+ and delta psi equal to zero. Taken together with previously measured Em,7 values, these data indicate that it is the two-electron reduction of bound dioxygen to bound peroxide that is responsible for the irreversibility of the catalytic dioxygen cycle of cell respiration.     

Kinetic modeling of a bi-enzymatic system for efficient conversion of lactose to lactobionic acid

A model has been developed to describe the interaction between two enzymes and an intermediary redox mediator. In this bi-enzymatic process, the enzyme cellobiose dehydrogenase oxidizes lactose at the C-1 position of the reducing sugar moiety to lactobionolactone, which spontaneously hydrolyzes to lactobionic acid. 2,2'-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt is used as electron acceptor and is continuously regenerated by laccase. Oxygen is the terminal electron acceptor and is fully reduced to water by laccase, a copper-containing oxidase. Oxygen is added to the system by means of bubble-free oxygenation. Using the model, the productivity of the process is investigated by simultaneous solution of the rate equations for varying enzyme quantities and redox mediator concentrations, solved with the aid of a numerical solution. The isocharts developed in this work provide an easy-to-use graphical tool to determine optimal process conditions. The model allows the optimization of the employed activities of the two enzymes and the redox mediator concentration for a given overall oxygen mass transfer coefficient by using the isocharts. Model predictions are well in agreement with the experimental data.     

Thiol/disulfide exchange in the thioredoxin-catalyzed reductive activation of spinach chloroplast fructose-1,6-bisphosphatase. Kinetics and thermodynamics

Two kinetically and thermodynamically distinct thiol/disulfide redox changes are observed during the reversible thioredoxin fb-catalyzed reduction and oxidation of spinach chloroplast fructose-1,6-bisphosphatase by dithiothreitol. The two processes, which occur at different rates and with different equilibrium constants, can be observed independently in either the reduction (activation) or oxidation (inactivation) direction by assaying the enzyme activity at different magnesium and fructose-1,6-bisphosphate concentrations. The two processes, in both the reduction and oxidation directions, are kinetically zero-order in dithiothreitol concentration and first-order in thioredoxin fb concentration. The rate-limiting step in both directions is the reaction of fructose-1,6-bisphosphatase with thioredoxin. The more kinetically and thermodynamically favored reduction of fructose-1,6-bisphosphatase lowers the apparent Km for fructose-1,6-bisphosphate while the less favorable process lowers the Km for magnesium. Both of the thiol/disulfide redox changes reach equilibrium in redox buffers consisting of different ratios of reduced to oxidized dithiothreitol (Ered + DTTox in equilibrium Eox + DTTred). The equilibrium constants (Kox) are 0.12 +/- 0.02 and 0.39 +/- 0.08 for the fast and slow reduction processes at pH 8.0. The equilibrium constants for oxidation of the enzyme by glutathione disulfide (Ered + GSSG in equilibrium Eox + 2 GSH) can be estimated to be approximately 2400 and 7800 M, respectively. Thermodynamically the fructose-1,6-bisphosphatase/thioredoxin fb system is extremely sensitive to oxidation, comparable to disulfide bond formation in extracellular proteins.     

Enhancement of nitroaromatic compounds anaerobic biotransformation using a novel immobilized redox mediator prepared by electropolymerization

Functionalized polypyrrole (PPy) composites were prepared by incorporation of a model redox mediator, anthraquinonedisulphonate (AQDS), as doping anion during the electropolymerization of pyrrole (Py) monomer on active carbon felt (ACF) electrode. Then, the resulting composite, ACF/PPy/AQDS as a novel immobilized redox mediator for catalyzing anaerobic biotransformation of the model nitroaromatic compounds (NACs), such as nitrobenzene (NB), 2,4- and 2,6-dinitrotoluene (DNT), were investigated in detail. The results showed that ACF/PPy/AQDS exhibited good catalytic activity and stability, and its addition effectively accelerated the NACs anaerobic reduction to the corresponding amino compounds. In order to estimate the relationship between community dynamics and the function of immobilized redox mediator, a combined method based on fingerprints (ribosomal intergenic spacer analysis, RISA) and 16S rRNA gene sequencing was used. The results indicated that the existence of ACF/PPy/AQDS made the potent AQDS-reducing bacteria keeping predominant in the catalytic systems. Based on the results above, it can be concluded that this novel immobilized redox mediator is feasible and potentially useful to enhance NACs anaerobic reduction.     

Modelling of the electron transfer reactions in Photosystem I by electron tunnelling theory: the phylloquinones bound to the PsaA and the PsaB reaction centre subunits of PS I are almost isoenergetic to the iron-sulfur cluster F(X)

Photosystem I is a large macromolecular complex located in the thylakoid membranes of chloroplasts and in cyanobacteria that catalyses the light driven reduction of ferredoxin and oxidation of plastocyanin. Due to the very negative redox potential of the primary electron transfer cofactors accepting electrons, direct estimation by redox titration of the energetics of the system is hampered. However, the rates of electron transfer reactions are related to the thermodynamic properties of the system. Hence, several spectroscopic and biochemical techniques have been employed, in combination with the classical Marcus theory for electron transfer tunnelling, in order to access these parameters. Nevertheless, the values which have been presented are very variable. In particular, for the case of the tightly bound phylloquinone molecule A(1), the values of the redox potentials reported in the literature vary over a range of about 350 mV. Previous models of Photosystem I have assumed a unidirectional electron transfer model. In the present study, experimental evidence obtained by means of time resolved absorption, photovoltage, and electron paramagnetic resonance measurements are reviewed and analysed in terms of a bi-directional kinetic model for electron transfer reactions. This model takes into consideration the thermodynamic equilibrium between the iron-sulfur centre F(X) and the phylloquinone bound to either the PsaA (A(1A)) or the PsaB (A(1B)) subunit of the reaction centre and the equilibrium between the iron-sulfur centres F(A) and F(B). The experimentally determined decay lifetimes in the range of sub-picosecond to the microsecond time domains can be satisfactorily simulated, taking into consideration the edge-to-edge distances between redox cofactors and driving forces reported in the literature. The only exception to this general behaviour is the case of phylloquinone (A(1)) reoxidation. In order to describe the reported rates of the biphasic decay, of about 20 and 200 ns, associated with this electron transfer step, the redox potentials of the quinones are estimated to be almost isoenergetic with that of the iron sulfur centre F(X). A driving force in the range of 5 to 15 meV is estimated for these reactions, being slightly exergonic in the case of the A(1B) quinone and slightly endergonic, in the case of the A(1A) quinone. The simulation presented in this analysis not only describes the kinetic data obtained for the wild type samples at room temperature and is consistent with estimates of activation energy by the analysis of temperature dependence, but can also explain the effect of the mutations around the PsaB quinone binding pocket. A model of the overall energetics of the system is derived, which suggests that the only substantially irreversible electron transfer reactions are the reoxidation of A(0) on both electron transfer branches and the reduction of F(A) by F(X).     

Estimation of kinetic parameters by progress curve analysis for the synthesis of (R)-mandelonitrile by Prunus amygdalus hydroxynitrile lyase

Consistent sets of kinetic parameters were estimated for the synthesis of (R)-mandelonitrile, catalyzed by Prunus amygdalus hydroxynitrile lyase, at 5 and 25 degrees C and pH 5.5 by progress curve analysis. The rate constants and equilibrium constants of the nonenzymatic reaction were determined separately to reduce the number of parameters to be estimated simultaneously. At a lower temperature the equilibrium is much more favorable and the formation of rac-mandelonitrile by the nonenzymatic reaction is suppressed. The estimated kinetic parameters were used to identify that the rate determining step in the catalytic cycle is the release of (R)-mandelonitrile from the ternary complex.     

Modelling of the electron transfer reactions in Photosystem I by electron tunnelling theory: The phylloquinones bound to the PsaA and the PsaB reaction centre subunits of PS I are almost isoenergetic to the iron-sulfur cluster FX

Photosystem I is a large macromolecular complex located in the thylakoid membranes of chloroplasts and in cyanobacteria that catalyses the light driven reduction of ferredoxin and oxidation of plastocyanin. Due to the very negative redox potential of the primary electron transfer cofactors accepting electrons, direct estimation by redox titration of the energetics of the system is hampered. However, the rates of electron transfer reactions are related to the thermodynamic properties of the system. Hence, several spectroscopic and biochemical techniques have been employed, in combination with the classical Marcus theory for electron transfer tunnelling, in order to access these parameters. Nevertheless, the values which have been presented are very variable. In particular, for the case of the tightly bound phylloquinone molecule A₁, the values of the redox potentials reported in the literature vary over a range of about 350 mV. Previous models of Photosystem I have assumed a unidirectional electron transfer model. In the present study, experimental evidence obtained by means of time resolved absorption, photovoltage, and electron paramagnetic resonance measurements are reviewed and analysed in terms of a bi-directional kinetic model for electron transfer reactions. This model takes into consideration the thermodynamic equilibrium between the iron-sulfur centre F_X and the phylloquinone bound to either the PsaA (A_1A) or the PsaB (A_1B) subunit of the reaction centre and the equilibrium between the iron-sulfur centres F_A and F_B. The experimentally determined decay lifetimes in the range of sub-picosecond to the microsecond time domains can be satisfactorily simulated, taking into consideration the edge-to-edge distances between redox cofactors and driving forces reported in the literature. The only exception to this general behaviour is the case of phylloquinone (A₁) reoxidation. In order to describe the reported rates of the biphasic decay, of about 20 and 200 ns, associated with this electron transfer step, the redox potentials of the quinones are estimated to be almost isoenergetic with that of the iron sulfur centre F_X. A driving force in the range of 5 to 15 meV is estimated for these reactions, being slightly exergonic in the case of the A_1B quinone and slightly endergonic, in the case of the A_1A quinone. The simulation presented in this analysis not only describes the kinetic data obtained for the wild type samples at room temperature and is consistent with estimates of activation energy by the analysis of temperature dependence, but can also explain the effect of the mutations around the PsaB quinone binding pocket. A model of the overall energetics of the system is derived, which suggests that the only substantially irreversible electron transfer reactions are the reoxidation of A₀ on both electron transfer branches and the reduction of F_A by F_X.     

Stepwise Kinetic Equilibrium Models of Quantitative Polymerase Chain Reaction

ABSTRACT: BACKGROUND: Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. RESULTS: Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of initial target concentration. Model 1 was found to be slightly more robust than model 2 giving better estimates of initial target concentration when estimation of parameters was done for qPCR curves with very different initial target concentration. Both models may be used to estimate the initial absolute concentration of target sequence when a standard curve is not available. CONCLUSIONS: It is argued that the kinetic approach to modeling and interpreting quantitative PCR data has the potential to give more precise estimates of the true initial target concentrations than other methods currently used for analysis of qPCR data. The two models presented here give a unified model of the qPCR process in that they explain the shape of the qPCR curve for a wide variety of initial target concentrations.