Competition systems with periodic coefficients: A geometric approach

The classical two-species competition system is modified to include coefficients which are time-periodic with the same period. We show first that all (nonnegative) solutions converge to a periodic one, having the same period, thus excluding subharmonics. The global structure of the set of all periodic solutions is then investigated. This is accomplished by developing a geometric theory of the discrete dynamical system defined by the iterates of the period map T. It turns out, in particular, that periodic solutions appear which have no counterpart in the corresponding time-averaged system: thus oscillations in the environment may cause the two species to coexist in an oscillatory regime even if the corresponding averaged system would force either of the two species to extinction.     

Proton transfer at carbon

The viability of living systems requires that C--H bonds of biological molecules be stable in water, but that there also be a mechanism for shortening the timescale for their heterolytic cleavage through enzymatic catalysis of a variety of catabolic and metabolic reactions. An understanding of the mechanism of enzymatic catalysis of proton transfer at carbon requires the integration of results of studies to determine the structure of the enzyme-substrate complex with model studies on the mechanism for the non-enzymatic reaction in water, and the effect of the local protein environment on the stability of the transition state for this reaction. A common theme is the importance of electrostatic interactions in providing stabilization of bound carbanion intermediates of enzyme-catalyzed proton-transfer reactions.     

DFT study of the gas phase proton transfer in guanine assisted by water, methanol, and hydrogen peroxide

A computational study of hydrogen-bonded complexes between the oxo-/hydroxo-amino N7/9H tautomers of guanine and water, methanol, and hydrogen peroxide has been performed at the B3LYP/6-31+G(d) level of theory. The mechanisms of the water-, methanol-, and hydrogen peroxide-assisted proton transfers in guanine were studied and compared with the intramolecular proton transfer in guanine in the gas phase. It was found that the assisted proton transfers pass through about three times lower energy barriers than those found for isolated guanine tautomers. Figure DFT study of the gas phase proton transfer in guanine assisted by water, methanol and hydrogen peroxide     

Parameterization of Coulomb interaction in three-dimensional periodic systems

A simple method is proposed to calculate Coulomb interactions in three-dimensional periodic cubic systems. It is based on the parameterization of the interaction on polynomials and rational functions. The parameterized functions are compared to tabulation methods, to the Ewald calculations and cubic harmonic function fits found in the literature. Our parameterizations are computationally more efficient than, the use of tabulations at all cases and seem to be more efficient than the cubic harmonic parameterizations in the case of simultaneous potential energy and force calculations. In comparison to the Ewald method, it is feasible to use the parameterizations on small systems and on systems, where pair-wise additive short-range interactions are dominant. One also may prefer the parameterizations to the Ewald method for large systems, if limited accuracy is needed. The embedding of the method into existing molecular dynamics and Monte Carlo simulation codes is very simple. The presented investigation contains some numerical experimental data to support the correct theoretical partition of potential energy in periodic systems, as well.     

Proton transfer from exogenous donors in catalysis by human carbonic anhydrase II

In the site-specific mutant of human carbonic anhydrase in which the proton shuttle His64 is replaced with alanine, H64A HCA II, catalysis can be activated in a saturable manner by the proton donor 4-methylimidazole (4-MI). From 1H NMR relaxivities, we found 4-MI bound as a second-shell ligand of the tetrahedrally coordinated cobalt in Co(II)-substituted H64A HCA II, with 4-MI located about 4.5 A from the metal. Binding constants of 4-MI to H64A HCA II were estimated from: (1) NMR relaxation of the protons of 4-MI by Co(II)-H64A HCA II, (2) the visible absorption spectrum of Co(II)-H64A HCA II in the presence of 4-MI, (3) the inhibition by 4-MI of the catalytic hydration of CO2, and (4) from the catalyzed exchange of 18O between CO2 and water. These experiments along with previously reported crystallographic and catalytic data help identify a range of distances at which proton transfer is efficient in carbonic anhydrase II.     

Proton transport in carbonic anhydrase: Insights from molecular simulation

This article reviews the insights gained from molecular simulations of human carbonic anhydrase II (HCA II) utilizing non-reactive and reactive force fields. The simulations with a reactive force field explore protein transfer and transport via Grotthuss shuttling, while the non-reactive simulations probe the larger conformational dynamics that underpin the various contributions to the rate-limiting proton transfer event. Specific attention is given to the orientational stability of the His64 group and the characteristics of the active site water cluster, in an effort to determine both of their impact on the maximal catalytic rate. The explicit proton transfer and transport events are described by the multistate empirical valence bond (MS-EVB) method, as are alternative pathways for the excess proton charge defect to enter/leave the active site. The simulation results are interpreted in light of experimental results on the wild-type enzyme and various site-specific mutations of HCA II in order to better elucidate the key factors that contribute to its exceptional efficiency.     

The influence of hydrogen bonds on electron transfer rate in photosynthetic RCs

Hydrogen bonds formed between photosynthetic reaction centers (RCs) and their cofactors were shown to affect the efficacy of electron transfer. The mechanism of such influence is determined by sensitivity of hydrogen bonds to electron density rearrangements, which alter hydrogen bonds potential energy surface. Quantum chemistry calculations were carried out on a system consisting of a primary quinone Q_A, non-heme Fe²⁺ ion and neighboring residues_. The primary quinone forms two hydrogen bonds with its environment, one of which was shown to be highly sensitive to the Q_A state. In the case of the reduced primary quinone two stable hydrogen bond proton positions were shown to exist on [Q_A-His^M219] hydrogen bond line, while there is only one stable proton position in the case of the oxidized primary quinone. Taking into account this fact and also the ability of proton to transfer between potential energy wells along a hydrogen bond, theoretical study of temperature dependence of hydrogen bond polarization was carried out. Current theory was successfully applied to interpret dark P⁺/Q_A⁻ recombination rate temperature dependence.     

Theoretical study of the intermolecular H-bonding and intermolecular proton transfer between isocytosine tautomeric forms and <Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">S</Emphasis>-lactic acid

Eight H-bonded complexes between isocytosine (isoC) tautomeric forms and R/S-lactic acid (LA) have been studied at the B3LYP and HF levels of theory using 6–31+G(d) basis set. The energy barriers of the intermolecular proton transfers were also estimated as the results showed that they are several times lower than those of the intramolecular proton transfers of isoC in the gas phase. Furthermore, the energy barriers of the tautomerizations in which the carboxylic H-atom takes part are several times lower than those in which the LA OH group assists the proton transfer. Figure     

Energy transport mechanism in the form of proton soliton in a one-dimensional hydrogen-bonded polypeptide chain

The dynamics of protons in a one-dimensional hydrogen-bonded (HB) polypeptide chain (PC) is investigated theoretically. A new Hamiltonian is formulated with the inclusion of higher-order molecular interactions between peptide groups (PGs). The wave function of the excitation state of a single particle is replaced by a new wave function of a two-quanta quasi-coherent state. The dynamics is governed by a higher-order nonlinear Schrödinger equation and the energy transport is performed by the proton soliton. A nonlinear multiple-scale perturbation analysis has been performed and the evolution of soliton parameters such as velocity and amplitude is explored numerically. The proton soliton is thermally stable and very robust against these perturbations. The energy transport by the proton soliton is more appropriate to understand the mechanism of energy transfer in biological processes such as muscle contraction, DNA replication, and neuro-electric pulse transfer on biomembranes.     

Proton transfer in the photosynthetic reaction center of Blastochloris viridis

Photosynthetic reaction centers of Blastochloris viridis require two quanta of light to catalyse a two-step reduction of their secondary ubiquinone Q(B) to ubiquinol. We employed capacitive potentiometry to follow the voltage changes that were caused by the accompanying transmembrane proton displacements. At pH 7.5 and 20 degrees C, the Q(B)-related voltage generation after the first flash was contributed by a fast, temperature-independent component with a time constant of approximately 30 micros and a slower component of approximately 200 micros with activation energy (E(a)) of 50 kJ/mol. The kinetics after the second flash featured temperature-independent components of 5 micros and 200 micros followed by a component of 600 micros with E(a) approximately 60 kJ/mol.     

Investigation of the intermolecular proton transfer in the supersystems adenine-methanol/ethanol/i-propanol: MP2 and DFT levels study

Twelve H-bonded supersystems constructed between the adenine tautomers and methanol, ethanol, and i-propanol were studied at the B3LYP and MP2 levels of theory using 6-311G(d,p) and 6-311++G(d,p) basis functions. The thermodynamic parameters of the complex formations were calculated in order to estimate the exact stability of the supersystems. It was proven that the calculated energy barriers of the alcohol-assisted proton transfers are about 60% lower than those of the intramolecular proton transfers in adenine found earlier (Gu and Leszczynski in J Phys Chem A 103:2744–2750, 1999). Figure H-bonded complex between i-propanol and adenine     

Proton transfer function of carbonic anhydrase: Insights from QM/MM simulations

Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are briefly reviewed. The topics include a preliminary analysis of nuclear quadrupole coupling constant calculations for the zinc ion and more detailed analyses of microscopic pK_a of the zinc-bound water and free energy profile for the proton transfer. From a methodological perspective, our results emphasize that performing sufficient sampling is essential to the calculation of all these quantities, which reflects the well solvated nature of CAII active site. From a mechanistic perspective, our analyses highlight the importance of electrostatics in shaping the energetics and kinetics of proton transfer in CAII for its function. We argue that once the pK_a for the zinc-bound water is modulated to be in the proper range (~ 7.0), proton transfer through a relatively well solvated cavity towards/from the protein surface (His64) does not require any major acceleration. Therefore, although structural details like the length of the water wire between the donor and acceptor groups still may make a non-negligible contribution, our computational results and the framework of analysis suggest that the significance of such “fine-tuning” is likely secondary to the modulation of pK_a of the zinc-bound water. We encourage further experimental analysis with mutation of (charged) residues not in the immediate neighborhood of the zinc ion to quantitatively test this electrostatics based framework; in particular, Φ analysis based on these mutations may shed further light into the relative importance of the classical Grotthus mechanism and the “proton hole” pathway that we have proposed recently for CAII.     

Different types of biological proton transfer reactions studied by quantum chemical methods

Different types of proton transfer occurring in biological systems are described with examples mainly from ribonucleotide reductase (RNR) and cytochrome c oxidase (CcO). Focus is put on situations where electron and proton transfer are rather strongly coupled. In the long range radical transfer in RNR, it is shown that the presence of hydrogen atom transfer (HAT) is the most logical explanation for the experimental observations. In another example from RNR, it is shown that a transition state for concerted motion of both proton and electron can be found even if the donors are separated by a quite long distance. In CcO, the essential proton transfer for the OO bond cleavage, and the most recent modelings of proton translocation are described, indicating a few remaining major problems.     

Correlation Effects in the Double Proton Transfer of the Formic Acid Dimer

The role of correlation effects in the potential energy hypersurface for the double proton transfer in the hydrogen bond of the formic acid dimer has been studied at the non-empirical level. The calculations were performed in different large as well as for the first time in complete basis set at the correlation level. The possible reasons of incorrect results of quantum chemical calculations are considered.     

Kinetics and thermodynamics of proton transfer to CpRu(dppe)H: Via dihydrogen bonding and (η-H2)-complex to the dihydride

The interaction between Cp^∗RuH(dppe) and a series of proton donors (HA) of increasing strength: CFH₂CH₂OH (MFE), CF₃CH₂OH (TFE), (CF₃)₂CHOH (HFIP), p-nitrophenol, CF₃COOH and HBF₄ has been investigated spectroscopically by variable-temperature IR, UV-Vis, and NMR spectroscopy in solvents of differing polarity (n-hexane, dichloromethane and their mixture). The low-temperature IR study shows the establishment of a hydrogen-bond which involves the hydride ligand as the proton accepting site. The basicity factor E_j for the hydride was found to be 1.39. All techniques indicate that an equilibrium exists between the dihydrogen-bonded complex and the cationic dihydrogen complex, [Cp^∗Ru(η²-H₂)(dppe)]⁺, the formation of which is shown here for the first time. The proton transfer from HFIP is characterized by ΔH^° = −8.1 ± 0.6 kcal mol⁻¹ and ΔS^° = −17 ± 3 eu. The activation parameters for the subsequent irreversible isomerization leading to the classical dihydride complex, [Cp^∗Ru(H)₂(dppe)]⁺, are ΔH^‡ = 20.9 ± 0.8 kcal mol⁻¹ and ΔS^‡ = 9 ± 3 eu as determined from ¹H NMR spectroscopy for protonation by HBF₄. Computational results at the DFT/B3PW91 level confirm the experimentally observed hydride basicity increase on descending the Group from iron to ruthenium and also the formation of the non-classical complex as an intermediate, prior to the thermodynamically favored dihydride.     

Proton pumping in cytochrome c oxidase: Energetic requirements and the role of two proton channels

Cytochrome c oxidase is a superfamily of membrane bound enzymes catalyzing the exergonic reduction of molecular oxygen to water, producing an electrochemical gradient across the membrane. The gradient is formed both by the electrogenic chemistry, taking electrons and protons from opposite sides of the membrane, and by proton pumping across the entire membrane. In the most efficient subfamily, the A-family of oxidases, one proton is pumped in each reduction step, which is surprising considering the fact that two of the reduction steps most likely are only weakly exergonic. Based on a combination of quantum chemical calculations and experimental information, it is here shown that from both a thermodynamic and a kinetic point of view, it should be possible to pump one proton per electron also with such an uneven distribution of the free energy release over the reduction steps, at least up to half the maximum gradient. A previously suggested pumping mechanism is developed further to suggest a reason for the use of two proton transfer channels in the A-family. Since the rate of proton transfer to the binuclear center through the D-channel is redox dependent, it might become too slow for the steps with low exergonicity. Therefore, a second channel, the K-channel, where the rate is redox-independent is needed. A redox-dependent leakage possibility is also suggested, which might be important for efficient energy conservation at a high gradient. A mechanism for the variation in proton pumping stoichiometry over the different subfamilies of cytochrome oxidase is also suggested. This article is part of a Special Issue entitled: 18th European Bioenergetic Conference.     

The kinetics of a weakly electron-coupled proton transfer in azurin

The thermodynamics and kinetics of the weakly electron-coupled proton transfer of Pseudomonas aeruginosa azurin have been studied and quantitatively determined using fast scan cyclic voltammetry (CV), in which the protein is adsorbed on two types of electrode (pyrolytic graphite ‘edge’ (PGE) or 1-decanethiol modified gold). Electron transfer is coupled to a slow protonation of His35, which is not a ligand to the copper ion but is located approximately 8 Å away. Protonation of His35 produces small changes in the reduction potential of the copper site, which are time-resolved within the scan rate range 0.01-100 V s⁻¹.     

Proton Transfer in Liquid Water II; A Semiempirical Method to Describe Chemical Reactions

Abstract

A new semiempirical method is developed to deal with the proton transfer in liquid water. In the previous work, we have shown that two- and three-body charge transfer interactions and electrostatic interactions are the most important factors to describe the potential energy surfaces (PES) of the proton transfer in liquid water [Chemical Physics 180, 239–269, 1994], In order to take account of these factors, we develop a semiempirical method imposing the principle of electronegativity equalization to the Atoms in Molecule (AIM) method. The method is free from the well-known discrepancy of the traditional AIM methods, that is, the fractional molecular charges at large molecular separation, and thus can be applied to the charge transfer reactions. Intra- and intermolecular physical quantities, such as total energies, force vectors, dipole moment vectors and intermolecular charge transfer, obtained by the present method are found to be in good agreement with those by ab initio calculation.     

Proton transfer reactions in aqueous solutions of pyridoxamine phosphate

UV-visible and ¹³C NMR measurements described in the literature and our ³¹P NMR measurements support the following mechanism of proton transfer reactions in aqueous solutions of pyridoxamine phosphate: Only the tautomeric equilibrium between neutral form, A _N, and zwitterion, A _Z, which is analogous to the tautomeric equilibrium of 3-hydroxypyridine in aqueous solution, is important, and that equilibrium does not change upon the dissociation of the second phosphate proton. With these simplifying assumption, we have simulated the relaxation spectrum of the proton transfer reactions of pyridoxamine phosphate in water using parameters from analogous reactions and compared it with our ultrasound and temperature jump measurements. We have found that the relaxation process measured by the temperature jump experiment is mainly caused by the overall reaction A _N=A _Z (or A _N ^- =A _Z ^- ) and the ultrasound absorption at the isoelectric point between pK₂ and pK₃ is mainly caused by the overall reaction .