Rates and Equilibrium of CuA to heme a electron transfer in Paracoccus denitrificans cytochrome c oxidase

Intramolecular electron transfer between CuA and heme a in solubilized bacterial (Paracoccus denitrificans) cytochrome c oxidase was investigated by pulse radiolysis. CuA, the initial electron acceptor, was reduced by 1-methylnicotinamide radicals in a diffusion-controlled reaction, as monitored by absorption changes at 825 nm, followed by partial restoration of the absorption and paralleled by an increase in the heme a absorption at 605 nm. The latter observations indicate partial reoxidation of the CuA center and the concomitant reduction of heme a. The rate constants for heme a reduction and CuA reoxidation were identical within experimental error and independent of the enzyme concentration and its degree of reduction, demonstrating that a fast intramolecular electron equilibration is taking place between CuA and heme a. The rate constants for CuA --> heme a ET and the reverse heme a --> CuA process were found to be 20,400 s(-1) and 10,030 s(-1), respectively, at 25 degrees C and pH 7.5, which corresponds to an equilibrium constant of 2.0. Thermodynamic and activation parameters of these intramolecular ET reactions were determined. The significance of the results, particularly the low activation barriers, is discussed within the framework of the enzyme's known three-dimensional structure, potential ET pathways, and the calculated reorganization energies.     

Molecular Modelling of Chymotrypsin-Substrate Interactions: Calculation of Enantioselectivity

A method has been developed for the calculation of the enantioselectivity of chymotrypsin catalysed hydrolytic reactions using molecular mechanics and molecular dynamics. Nine different ester substrates, which are hydrolysed by the enzyme over a wide range of reaction rates have been studied. Models of the transition state of the ester hydrolysis were built using computer aided molecular modelling. The energies of the transition state models were calculated by molecular mechanics and molecular dynamics methods. The point charges of the substrates were modelled from known force field parameters and by semiempirical methods. The difference in free energy of activation between the enantiomers of each substrate were compared with experimental values. The calculations approximated the experimental results. The calculated structure of the transition state model of the chymotrypsin catalysed hydrolysis of acetyl-phenylalanine ester was virtually the same as the published crystal structure of a chymotrypsin-trifluoromethyl ketone inhibitor complex (Brady et al., Biochemistry 29: 7600-7607, 1990).     

A comparison of the reaction mechanisms of iron- and manganese-containing 2,3-HPCD: an important spin transition for manganese

Homoprotocatechuate (HPCA) dioxygenases are enzymes that take part in the catabolism of aromatic compounds in the environment. They use molecular oxygen to perform the ring cleavage of ortho-dihydroxylated aromatic compounds. A theoretical investigation of the catalytic cycle for HPCA 2,3-dioxygenase isolated from Brevibacterium fuscum (Bf 2,3-HPCD) was performed using hybrid DFT with the B3LYP functional, and a reaction mechanism is suggested. Models of different sizes were built from the crystal structure of the enzyme and were used in the search for intermediates and transition states. It was found that the enzyme follows a reaction pathway similar to that for other non-heme iron dioxygenases, and for the manganese-dependent analog MndD, although with different energetics. The computational results suggest that the rate-limiting step for the whole reaction of Bf 2,3-HPCD is the protonation of the activated oxygen, with an energy barrier of 17.4 kcal/mol, in good agreement with the experimental value of 16 kcal/mol obtained from the overall rate of the reaction. Surprisingly, a very low barrier was found for the O-O bond cleavage step, 11.3 kcal/mol, as compared to 21.8 kcal/mol for MndD (sextet spin state). This result motivated additional studies of the manganese-dependent enzyme. Different spin coupling between the unpaired electrons on the metal and on the evolving substrate radical was observed for the two enzymes, and therefore the quartet spin state potential energy surface of the MndD reaction was studied. The calculations show a crossing between the sextet and the quartet surfaces, and it was concluded that a spin transition occurs and determines a barrier of 14.4 kcal/mol for the O-O bond cleavage, which is found to be the rate-limiting step in MndD. Thus the two 83% identical enzymes, using different metal ions as co-factors, were found to have similar activation energies (in agreement with experiment), but different rate-limiting steps.     

A definitive mechanism for chorismate mutase

In previous research presentations, we have described the important features of the chorismate --> prephenate reaction using molecular dynamics (MD) and thermodynamic integration studies. This investigation of the reaction in Escherichia coli and water involves QM/MM procedures (SCCDFTB/MM two-dimensional reaction coordinates to identify transition state structures in the water, enzyme, and gas phase followed by B3LYP/6-31+G* single-point computations which allow the determination of activation energies in water and in the E. coli enzyme). Computed activation energies of 11.3 kcal/mol in enzyme and 20.3 kcal/mol in water may be compared to the experimental values of 12.7 and 20.7 kcal/mol, respectively. The transition state structures in the gas phase, water, and enzyme are much the same. The transition states are characteristic of a concerted pericyclic rearrangement. The very small differences in the partial charges of O13 in NAC and TS support only a small preferential (10%) electrostatic stabilization of TS. The free energy of NAC formation in water exceeds that in enzyme by 8.5 kcal/mol, and it is this favored formation of NAC that provides the major kinetic advantage to the enzymatic reaction. These findings compare most favorably with those previous observations of this laboratory employing molecular dynamics and thermodynamic integrations. A definitive mechanism for the chorismate mutase enzymes is provided.     

The binding of triazine herbicides to the photosynthetic reaction center of Rhodopseudomonas viridis. Energy minimization studies.

The binding of six herbicides of the triazine family to the photosynthetic reaction center of Rhodopseudomonas viridis was investigated with energy-minimization techniques, in order to correlate experimental with calculated data. The inhibitors were modeled in the active site according to the X-ray structure analysis of the complex formed between the triazine terbutryn (2-ethylamino-4-t-butylamino-6-methylthio-s-triazine) and the reaction center of R. viridis [Michel, H., Epp. O. & Deisenhofer, J. (1986) EMBO J. 5, 2445-2451]. 40 different energy minimizations were carried out with varying cutoff radii, partial charges on inhibitor atoms and dielectric constants, i.e. 10 different combinations of these were tested. The impact of these parameters on the calculated binding and interaction energy was either examined for all protein/triazine complexes or, in the case of the dielectric constant, a smaller sample was used. The calculated energies are dominated by van der Waals interactions, which change by up to 20% when extending the cutoff radius from 0.8 nm to 1.5 nm. The use of uniform or distance-dependent dielectric constant or partial charges on the inhibitor atoms does not severely influence the resulting structures, but shows a great impact on the calculated energies. In the two groups of triazines, each containing three inhibitors with methoxy or methylthio substituents, correlations of biological and calculated data were found quite often, but only once with all six triazines. The energy-minimized structures were compared and analysed. A third hydrogen bond, not seen in the X-ray analysis of the reaction center/tertubryn complex, was found between the t-butylamino moiety of terbutryn (and equivalent moieties in the other triazines) and the carbonyl oxygen of TyrL222.     

Reaction-path energetics and kinetics of the hydride transfer reaction catalyzed by dihydrofolate reductase

We have studied the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase (DHFR) and the coenzyme nicotinamide adenine dinucleotide phosphate (NADPH); the substrate is 5-protonated 7,8-dihydrofolate, and the product is tetrahydrofolate. The potential energy surface is modeled by a combined quantum mechanical-molecular mechanical (QM/MM) method employing Austin model 1 (AM1) and a simple valence bond potential for 69 QM atoms and employing the CHARMM22 and TIP3P molecular mechanics force fields for the other 21 399 atoms; the QM and MM regions are joined by two boundary atoms treated by the generalized hybrid orbital (GHO) method. All simulations are carried out using periodic boundary conditions at neutral pH and 298 K. In stage 1, a reaction coordinate is defined as the difference between the breaking and forming bond distances to the hydride ion, and a quasithermodynamic free energy profile is calculated along this reaction coordinate. This calculation includes quantization effects on bound vibrations but not on the reaction coordinate, and it is used to locate the variational transition state that defines a transition state ensemble. Then, the key interactions at the reactant, variational transition state, and product are analyzed in terms of both bond distances and electrostatic energies. The results of both analyses support the conclusion derived from previous mutational studies that the M20 loop of DHFR makes an important contribution to the electrostatic stabilization of the hydride transfer transition state. Third, transmission coefficients (including recrossing factors and multidimensional tunneling) are calculated and averaged over the transition state ensemble. These averaged transmission coefficients, combined with the quasithermodynamic free energy profile determined in stage 1, allow us to calculate rate constants, phenomenological free energies of activation, and primary and secondary kinetic isotope effects. A primary kinetic isotope effect (KIE) of 2.8 has been obtained, in good agreement with the experimentally determined value of 3.0 and with the value 3.2 calculated previously. The primary KIE is mainly a consequence of the quantization of bound vibrations. In contrast, the secondary KIE, with a value of 1.13, is almost entirely due to dynamical effects on the reaction coordinate, especially tunneling.     

Activation Energies from Transition Path Sampling Simulations

We derive an new expression for the calculation of activation energies within the framework of transition path sampling. Using this expression one can determine activation energies without knowledge of the reaction mechanism, which is often unavailable for processes occurring in complex systems. Since in this method activation energies are calculated directly from path averages, no computationally expensive calculation of reaction rate constants is necessary. As an illustrative example, we determine the activation energy for the isomerization of a model diatomic immersed in a bath of repulsive soft particles.     

Mechanism for folate-independent aldolase reaction catalyzed by serine hydroxymethyltransferase

Serine hydroxymethyltransferase catalyzes the cleavage of β-hydroxyamino acids into glycine and aldehydes in the absence of tetrahydrofolate. The enzyme accepts various β-hydroxyamino acids as the substrate of this reaction. The reaction rate varies depending on the substituent and stereochemistry at the Cβ atom: the erythro forms and the β-phenyl substituent are preferred over the threo forms and the β-methyl substituent, respectively. Although several mechanisms have been proposed, what determines the substrate preference remains unclear. We first performed quantum mechanical calculations to assess the validity of the reaction mechanisms. The results indicate that the retro-aldol mechanism starting with abstraction of the proton from the β-hydroxyl group is plausible. This also suggests that Cα-Cβ bond cleavage is the rate-limiting step. We next measured the dependence of the rate constants on temperature with four representative substrates and calculated the activation energies and pre-exponential factors from the Arrhenius plots. The activation energies of the erythro forms were lower than those of the threo forms. The β-phenyl substituent lowered the activation energy in the threo form, whereas it did not alter the activation energy but increased the pre-exponential factor in the erythro form. We present a unified model to explain the origin of the substituent and stereochemical preferences by combining the theoretical and experimental results. A possible biological role of the tetrahydrofolate-independent activity in thermophiles is also discussed.     

Electron transfer rates and equilibrium within cytochrome c oxidase.

Intramolecular electron transfer (ET) between the CuA center and heme a in bovine cytochrome c oxidase was investigated by pulse radiolysis. CuA, the initial electron acceptor, was reduced by 1-methyl nicotinamide radicals in a diffusion-controlled reaction, as monitored by absorption changes at 830 nm. After the initial reduction phase, the 830 nm absorption was partially restored, corresponding to reoxidation of the CuA center. Concomitantly, the absorption at 445 nm and 605 nm increased, indicating reduction of heme a. The rate constants for heme a reduction and CuA reoxidation were identical within experimental error and independent of the enzyme concentration. This demonstrates that a fast intramolecular electron equilibration is taking place between CuA and heme a. The rate constants for CuA --> heme a ET and the reverse (heme a --> CuA) process were found to be 13 000 s-1 and 3700 s-1, respectively, at 25 degrees C and pH 7.4. This corresponds to an equilibrium constant of 3.4 under these conditions. Thermodynamic and activation parameters of the ET reactions were determined. The significance of these results, particularly the observed low activation barriers, are discussed within the framework of the known three-dimensional structure, ET pathways and reorganization energies.     

The regulatory GTPase cycle of turkey erythrocyte adenylate cyclase.

It has recently been suggested that adenylate cyclase activity is controlled by a regulatory cycle consisting of two reactions: a hormone induced formation of the active adenylate cyclase-GTP complex, and a subsequent turn-off reaction in which hydrolysis of the bound nucleotide reverts the system to the inactive state. To test this model each of the two reactions was measured separately and their rate constants were used to estimate the steady state adenylate cyclase and GTPase activities. The first order rate constants were kon = 3 min-1 for the activation reaction and koff = 15 min-1 for the turn-off reaction. Substitution of these rate constants in the steady state equation of the regulatory cycle gave values of hormone stimulated adenylate cyclase and GTPase activities similar to those determined by direct measurements. Treatment of the adenylate cyclase with cholera toxin caused a decrease of 96% in the rate constant of the turn-off reaction. In this case too the activities calculated from the steady state equation were in good agreement with those determined directly.     

Kinetic studies on the successive reaction of neuronal nitric oxide synthase from L-arginine to nitric oxide and L-citrulline

Rat neuronal nitric oxide synthase (nNOS) was heterologously expressed in Escherichia coliand purified. The conversion of L-arginine to N(omega)-hydroxy-L-arginine and further to L-citrulline in one cycle of the reaction of the purified nNOS was measured with the reaction rapid quenching method using (3)H-L-arginine as the substrate. It was found that most of the produced (3)H-N(omega)-hydroxy-L-arginine was successively hydroxylated to (3)H-L-citrulline without leaving the enzyme. From the analysis of time courses, the rate constants for each reaction step, and also for the dissociation of the intermediate, were estimated at various temperature in which the rates for the first and the second reactions were not much different each other but the rate for the dissociation of (3)H-N(omega)-hydroxy-L-arginine from the enzyme was significantly slow. Under the steady-state reaction condition, almost all of the nNOS was estimated to be active from the amount of burst formation of L-citrulline in the pre-steady state. The rate constant for the dissociation of the product L-citrulline from nNOS was calculated from the combination of results of the rapid quenching experiments and the metabolism of L-arginine in the presence of an excess amount of substrate, which was the smallest among all the rate constants in one cycle of the nNOS reaction. The activation energies for all the reaction steps were determined from the temperature dependence of the rate constants, which revealed that the rate-determining step of the nNOS reaction in the steady state was the dissociation of the product L-citrulline from the enzyme.     

Free energy of transition for the individual alkaline conformers of yeast iso-1-cytochrome c

Direct protein electrochemistry was used to obtain the thermodynamic parameters of transition from the native (state III) to the alkaline (state IV) conformer for untrimethylated Saccharomyces cerevisiae iso-1-cytochrome c expressed in E. coli and its single and multiple lysine-depleted variants. In these variants, one or more of the lysine residues involved in axial Met substitution (Lys72, Lys73, and Lys79) was mutated to alanine. The aim of this work is to determine the thermodynamic affinity of each of the substituting lysines for the heme iron and evaluate the interplay of enthalpic and entropic factors. The equilibrium constants for the deprotonation reaction of Lys72, 73, and 79 were computed for the minimized MD average structures of the wild-type and mutated proteins, applying a modified Tanford-Kirkwood calculation. Solvent accessibility calculations for the substituting lysines in all variants were also performed. The transition enthalpy and entropy values within the protein series show a compensatory behavior, typical of a process involving extensive solvent reorganization effects. The experimental and theoretical data indicate that Lys72 most readily deprotonates and replaces M80 as the axial heme iron ligand, whereas Lys73 and Lys79 show comparably higher pKa values and larger transition free energies. A good correlation is found within the series between the lowest calculated Lys pKa value and the corresponding experimental pKa value, which can be interpreted as indicative of the deprotonating lysine itself acting as the triggering group for the conformational transition. The triple Lys to Ala mutant, in which no lysine residues are available for heme iron binding, features transition thermodynamics consistent with a hydroxide ion replacing the axial methionine ligand.     

Theoretical investigation on the mechanism and kinetics of the ring-opening polymerization of ε-caprolactone initiated by tin(II) alkoxides

A theoretical investigation of the ring-opening polymerization (ROP) mechanism of ε-caprolactone (CL) with tin(II) alkoxide, Sn(OR)₂ initiators (R?=?n-C₄H₉, i-C₄H₉, t-C₄H₉, n-C₆H₁₃, n-C₈H₁₇) was studied. The density functional theory at B3LYP level was used to perform the modeled reactions. A coordination-insertion mechanism was found to occur via two transition states. Starting with a coordination of CL onto tin center led to a nucleophilic addition of the carbonyl group of CL, followed by the exchange of alkoxide ligand. The CL ring opening was completed through classical acyl-oxygen bond cleavage. The reaction barrier heights of ε-caprolactone with different initiators were calculated using potential energy profiles. The reaction of ε-caprolactone with Sn(OR)₂ having R?=?n-C₄H₉ has the least value of barrier height compared to other reactions. The rate constants for each reaction were calculated using the transition state theory with TheRATE program. The rate constants are in good agreement with available experimental data.     

Temperature effects upon the time course of contraction and re-extension in Stentor coeruleus

A double-flash microphotographic technique has been used to follow the variation with temperature of the following kinetic parameters related to the contraction and re-extension of the ciliate Stentor coeruleus, namely the rate of contraction, the initiation time before contraction, the rate of re-extension and the initiation time before re-extension, all described by first order kinetics. Activation enthalpies, entropies and free energies related to the above mentioned parameters were calculated from the variation of the rate constants with temperature. The enthalpies and entropies appear to be of minor interest compared to the free energies. For the contraction and the initiation of contraction the delta G transition state values obtained were 14 and 15 kcal/mole, respectively, while the re-extension and the initiation of re-extension both were represented by a value of delta G transition state about 19 kcal/mole. These results are compared to activation parameters for different motile systems and for the formation and breakdown of ATP-myosin complexes. A model for the contraction and re-extension processes is proposed in accordance with the results measured.     

Mechanism of the physiological reaction catalyzed by tryptophan synthase from Escherichia coli

The physiological synthesis of L-tryptophan from indoleglycerol phosphate and L-serine catalyzed by the alpha 2 beta 2 bienzyme complex of tryptophan synthase requires spatial and dynamic cooperation between the two distant alpha and beta active sites. The carbanion of the adduct of L-tryptophan to pyridoxal phosphate accumulated during the steady state of the catalyzed reaction. Moreover, it was formed transiently and without a lag in single turnovers, and glyceraldehyde 3-phosphate was released only after formation of the carbanion. These and further data prove first that the affinity for indoleglycerol phosphate and its cleavage to indole in the alpha subunit are enhanced substantially by aminoacrylate bound to the beta subunit. This indirect activation explains why the turnover number of the physiological reaction is larger than that of the indoleglycerol phosphate cleavage reaction. Second, reprotonation of nascent tryptophan carbanion is rate limiting for overall tryptophan synthesis. Third, most of the indole generated in the active site of the alpha subunit is transferred directly to the active site of the beta subunit and only insignificant amounts pass through the solvent. Comparison of the single turnover rate constants with the known elementary rate constants of the partial reactions catalyzed by the alpha and beta active sites suggests that the cleavage reaction rather than the transfer of indole or its condensation with aminoacrylate is rate limiting for the formation of nascent tryptophan.     

A molecular dynamics study of gating in dioxolane-linked gramicidin A channels.

The gating transition of the RR and SS dioxolane ring-linked gramicidin A channels were studied with molecular dynamics simulations using a detailed atomic model. It was found that the probable reaction path, describing the transition of the ring from the exterior to the interior of the channel where it blocked the permeation pathway, involved several steps including the isomerization of the transpeptide plane dihedral angle of Val1. Reaction coordinates along this pathway were defined, and the transition rates between the stable conformers were calculated. It was found, in good accord with experimental observations, that the calculated blocking rate for the RR-linked channel was 280/s with a mean blocking time of 0.04 ms, whereas such blocking did not occur in the case of the SS-linked channel. An important observation is that the resulting lifetime for the blocked state of the RR-linked channel was in good accord with the experimental observations only when the calculations were performed in the presence of a potassium ion inside the channel.     

Effect of temperature on the acidolysis of N-acyl-N,alpha,alpha-trialkyl glycine amides as related to the nature of substituents.

The C-terminal amide bond of N-acyl-N,alpha,alpha-trialkyl glycine amides is labile to acid and this has been currently assigned to steric crowding within the amino acid residue. However, our previous work has shown that in the acidolysis of some of these compounds steric hindrance seems to play a less important role than what one would expect. Thus, the cleavage of two sets of such compounds bearing different degrees of crowding was investigated at five different temperatures in order to clarify the effect of structure on reactivity in terms of enthalpy and entropy of activation. The compounds exhibited an Arrhenius-type behaviour, and both enthalpies and entropies of activation were calculated by taking advantage of the transition state theory. In addition, the kinetic data were analysed in terms of isokinetic relationships in order to find evidence to support that the compounds react under the same mechanism. The changes in the reaction rate are governed by the changes in both the enthalpy and the entropy of activation, which are related to bond energy and steric hindrance, respectively. In general, the entropies of activation are very negative for all compounds investigated, which reflects large steric constrictions associated with the formation of the transition state. In addition, they are very sensitive to the structure of the substrates.     

Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Density functional studies of the substituent effect on absorption and emission properties of 1, 8-naphthalimide derivatives

Using TD-PBE1PBE/6-31G* and TD-B3LYP/6-31G* approaches, we calculated the absorption and emission spectra of 1,8-naphthalmide derivatives in gas-phase. The geometric structures optimized by HF/6-31G* and B3LYP/6-31G* models and the absorption and emission maxima were in good agreement with existed experimental measurements. It was also found that the lowest singlet states corresponded mainly to the electronic transition from the highest occupied orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). Intramolecular charge transfer occurred between substituents and naphthalimic rings. Study also showed that most compounds with low absorption excitation energies had low vertical ionization potentials. Finally, the delocalization electronic energies between substituents and naphthalimic rings of isomers were investigated to obtain further sight into their stability.     

Kinetic analysis of the thermal stability of the photosynthetic reaction center from Rhodobacter sphaeroides

The temperature-induced denaturation of the photosynthetic reaction center from Rhodobacter sphaeroides has been studied through the changes that occur in the absorption spectrum of the bound chromophores on heating. At elevated temperatures, the characteristic absorbance bands of the bacteriochlorins bound to the polypeptides within the reaction center are lost, and are replaced by features typical of unbound bacteriochlorophyll and bacteriopheophytin. The kinetics of the spectral changes cannot be explained by a direct conversion from the functional to the denatured form of the protein, and require the presence of at least one intermediate. Possible mechanisms for the transformation via an intermediate are examined using a global analysis of the kinetic data, and the most likely mechanism is shown to involve a reversible transformation between the native state and an off-pathway intermediate, coupled to an irreversible transformation to the denatured state. The activation energies for the transformations between the three components are calculated from the effect of temperature on the individual rate constants, and the likely structural changes of the protein during the temperature-induced transformation are discussed.