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PubMed2006

The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies.

The metabolism of a cell can be viewed as a weighted sum of elementary modes. Due to the multiplicity of modes the identification of the individual weights represents a non-trivial problem. To enable the determination of weighting factors we have identified and implemented two gene deletions in combination with defined growth conditions that limit the metabolism from 4374 original elementary modes to 24 elementary modes for a non-PHB synthesizing control and 40 modes for a PHB synthesizing strain. These remaining modes can be further grouped into five families that have the same overall stoichiometry. Thus, the complexity of the problem is significantly reduced, and weighting factors for each family of modes could be determined from the measurement of accumulation rates of metabolites. Moreover, it is shown that individual weights are inversely correlated with the entropy generated by the operation of the used pathways defined in elementary modes. This suggests that evolution developed cellular regulatory patterns that permit diversity of pathways while favoring efficient pathways with low entropy generation. Furthermore, such correlation provides a rational way of estimating metabolic fluxes based on the thermodynamic properties of elementary modes. This is demonstrated with an example in which experimentally determined, intracellular fluxes are shown to be highly correlated with fluxes computed based on elementary modes and reaction entropies. The analysis suggests that the set of elementary modes can be interpreted analogous to a metabolic ensemble of quantum states of a macroscopic system.

Anaerobiosis↗
PubMed2006

Transition state theory can be used in studies of enzyme catalysis: lessons from simulations of tunnelling and dynamical effects in lipoxygenase and other systems.

The idea that enzyme catalysis involves special factors such as coherent fluctuations, quantum mechanical tunnelling and non-equilibrium solvation (NES) effects has gained popularity in recent years. It has also been suggested that transition state theory (TST) cannot be used in studies of enzyme catalysis. The present work uses reliable state of the art simulation approaches to examine the above ideas. We start by demonstrating that we are able to simulate any of the present catalytic proposals using the empirical valence bond (EVB) potential energy surfaces, the dispersed polaron model and the quantized classical path (QCP) approach, as well as the approximate vibronic method. These approaches do not treat the catalytic effects by phenomenological treatments and thus can be considered as first principles approaches (at least their ability to compare enzymatic reaction to the corresponding solution reactions). This work will consider the lipoxygenase reaction, and to lesser extent other enzymes, for specific demonstration. It will be pointed out that our study of the lipoxygenase reaction reproduces the very large observed isotope effect and the observed rate constant while obtaining no catalytic contribution from nuclear quantum mechanical (NQM) effects. Furthermore, it will be clarified that our studies established that the NQM effect decreases rather than increases when the donor-acceptor distance is compressed. The consequences of these findings in terms of the temperature dependence of the kinetic isotope effect and in terms of different catalytic proposals will be discussed. This paper will also consider briefly the dynamical effects and conclude that such effects do not contribute in a significant way to enzyme catalysis. Furthermore, it will be pointed out that, in contrast to recent suggestions, NES effects are not dynamical effects and should therefore be part of the activation free energy rather than the transmission factor. In view of findings of the present work and our earlier works, it seems that TST provides a quantitative tool for studies of enzyme catalysis and that the key open questions are related to the nature of the factors that lead to transition state stabilization.

Catalysis↗
PubMed2005

Strong quantum-confined Stark effect in germanium quantum-well structures on silicon.

Silicon is the dominant semiconductor for electronics, but there is now a growing need to integrate such components with optoelectronics for telecommunications and computer interconnections. Silicon-based optical modulators have recently been successfully demonstrated; but because the light modulation mechanisms in silicon are relatively weak, long (for example, several millimetres) devices or sophisticated high-quality-factor resonators have been necessary. Thin quantum-well structures made from III-V semiconductors such as GaAs, InP and their alloys exhibit the much stronger quantum-confined Stark effect (QCSE) mechanism, which allows modulator structures with only micrometres of optical path length. Such III-V materials are unfortunately difficult to integrate with silicon electronic devices. Germanium is routinely integrated with silicon in electronics, but previous silicon-germanium structures have also not shown strong modulation effects. Here we report the discovery of the QCSE, at room temperature, in thin germanium quantum-well structures grown on silicon. The QCSE here has strengths comparable to that in III-V materials. Its clarity and strength are particularly surprising because germanium is an indirect gap semiconductor; such semiconductors often display much weaker optical effects than direct gap materials (such as the III-V materials typically used for optoelectronics). This discovery is very promising for small, high-speed, low-power optical output devices fully compatible with silicon electronics manufacture.

Journal Article↗
PubMed2006

Comparison of frozen-density embedding and discrete reaction field solvent models for molecular properties.

We investigate the performance of two discrete solvent models in connection with density functional theory (DFT) for the calculation of molecular properties. In our comparison we include the discrete reaction field (DRF) model, a combined quantum mechanics and molecular mechanics (QM/MM) model using a polarizable force field, and the frozen-density embedding (FDE) scheme. We employ these solvent models for ground state properties (dipole and quadrupole moments) and response properties (electronic excitation energies and frequency-dependent polarizabilities) of a water molecule in the liquid phase. It is found that both solvent models agree for ground state properties, while there are significant differences in the description of response properties. The origin of these differences is analyzed in detail and it is found that they are mainly caused by a different description of the ground state molecular orbitals of the solute. In addition, for the calculation of the polarizabilities, the inclusion of the response of the solvent to the polarization of the solute becomes important. This effect is included in the DRF model, but is missing in the FDE scheme. A way of including it in FDE calculations of the polarizabilities using finite field calculations is demonstrated.

Complex Mixtures↗
PubMed2006

HOCl Ro-vibrational bound-state calculations for nonzero total angular momentum.

The Lanczos homogeneous filter diagonalization method has been employed to compute the HOCl ro-vibrational states for a range of total angular momenta (J = 0, 1, 5, 10, 11, 20, 30) on a newly developed ab initio potential energy surface by Nanbu et al. (J. Theor. Comput. Chem. 2002, 1, 263). For such computationally challenging calculations, a parallel computing strategy has been incorporated into our method to perform the matrix-vector multiplications. For the computed low bound states, a spectroscopic assignment has been made and the widely used approximate adiabatic rotation method has been tested for the broad range of total angular momenta for this deep-well system. Comparison of experimental results with exact quantum mechanical calculations for the selected far-infrared transitions involving the range of total angular momenta has been made possible for the first time.

Computer Simulation↗
PubMed2002

Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions. II. An energy decomposition analysis.

QM/MM methods have been developed as a computationally feasible solution to QM simulation of chemical processes, such as enzyme-catalyzed reactions, within a more approximate MM representation of the condensed-phase environment. However, there has been no independent method for checking the quality of this representation, especially for highly nonisotropic protein environments such as those surrounding enzyme active sites. Hence, the validity of QM/MM methods is largely untested. Here we use the possibility of performing all-QM calculations at the semiempirical PM3 level with a linear-scaling method (MOZYME) to assess the performance of a QM/MM method (PM3/AMBER94 force field). Using two model pathways for the hydride-ion transfer reaction of the enzyme dihydrofolate reductase studied previously (Titmuss et al., Chem Phys Lett 2000, 320, 169-176), we have analyzed the reaction energy contributions (QM, QM/MM, and MM) from the QM/MM results and compared them with analogous-region components calculated via an energy partitioning scheme implemented into MOZYME. This analysis further divided the MOZYME components into Coulomb, resonance and exchange energy terms. For the model in which the MM coordinates are kept fixed during the reaction, we find that the MOZYME and QM/MM total energy profiles agree very well, but that there are significant differences in the energy components. Most significantly there is a large change (approximately 16 kcal/mol) in the MOZYME MM component due to polarization of the MM region surrounding the active site, and which arises mostly from MM atoms close to (<10 A) the active-site QM region, which is not modelled explicitly by our QM/MM method. However, for the model where the MM coordinates are allowed to vary during the reaction, we find large differences in the MOZYME and QM/MM total energy profiles, with a discrepancy of 52 kcal/mol between the relative reaction (product-reactant) energies. This is largely due to a difference in the MM energies of 58 kcal/mol, of which we can attribute approximately 40 kcal/mol to geometry effects in the MM region and the remainder, as before, to MM region polarization. Contrary to the fixed-geometry model, there is no correlation of the MM energy changes with distance from the QM region, nor are they contributed by only a few residues. Overall, the results suggest that merely extending the size of the QM region in the QM/MM calculation is not a universal solution to the MOZYME- and QM/MM-method differences. They also suggest that attaching physical significance to MOZYME Coulomb, resonance and exchange components is problematic. Although we conclude that it would be possible to reparameterize the QM/MM force field to reproduce MOZYME energies, a better way to account for both the effects of the protein environment and known deficiencies in semiempirical methods would be to parameterize the force field based on data from DFT or ab initio QM linear-scaling calculations. Such a force field could be used efficiently in MD simulations to calculate free energies.

Binding Sites↗
PubMed2005

Infrared spectroscopy of the intramolecular hydrogen bond in acethylacetone: a computational approach.

The intramolecular hydrogen bond in the enol-acethylacetone (ACAC) is investigated by performing reduced-dimensional quantum calculations. To analyze the shared proton vibrations, two sets of coordinates were employed: normal mode coordinates describing the motion in the vicinity of the most stable configuration, and internal coordinates accounting for the double minimum proton motion. It is proved that the extreme broadness of the OH-stretch band in ACAC is a consequence of the coexistence of two enol-ACAC structures: the global minimum and the transition state for rotation of the distal methyl group. Further, a ground-state tunneling splitting of 116 cm(-1) is found, and it is shown that the inclusion of the kinematic coupling is mandatory when treating large-amplitude proton motion. In the OH-stretch direction a splitting of 853 cm(-1) was predicted.

Journal Article↗
PubMed2005

Impact of the computational method on the geometric and electronic properties of oligo(phenylene vinylene) radical cations.

We report on a quantum-chemical study of the electronic and optical properties of unsubstituted oligo(phenylene vinylene) (OPV) radical cations. Our goal is to distinguish the impact of the choice of molecular geometry from the impact of the choice of quantum-chemical method, on the calculated optical transition energies. The geometry modifications upon ionization of the OPV chains are found to depend critically on the theoretical formalism: Hartree-Fock (HF) geometry optimizations lead to self-localization of the charged defects while pure density functional theory (DFT) results in a complete delocalization of the geometric modifications over the whole conjugated backbone. The electronic structure and vertical transition energy associated with the lowest excited state of the radical cations have been calculated at the post-Hartree-Fock level within a configuration interaction (HF-CI) scheme and using the time-dependent DFT (TD-DFT) formalism for different radical cation geometries. Interestingly, the changes in the calculated optical properties obtained when using different geometric structures are less important within a given method than the differences between methods for a given structure. The optical excitation is localized with HF-CI and delocalized with TD-DFT, almost irrespective of the molecular geometry; as a result, HF-CI excitation energies tend to saturate as the chain length increases, in contrast to the results from TD-DFT.

Journal Article↗
PubMed2003

Ab initio QM/MM study shows there is no general acid in the reaction catalyzed by 4-oxalocrotonate tautomerase.

The mechanism for the reaction catalyzed by the 4-oxalocrotonate tautomerase (4-OT) enzyme has been studied using a quantum mechanical/molecular mechanical (QM/MM) method developed in our laboratory. Total free energy barriers were obtained for the two steps involved in this reaction. In the first step, Pro-1 acts as a general base to abstract a proton from the third carbon of the substrate, 2-oxo-4-hexenedioate, creating a negative charge on the oxygen at C-2 of this substrate. In the second step, the same hydrogen abstracted by the N-terminal Pro-1 is shuttled back to the fifth carbon of the substrate to form the product, 2-oxo-3-hexenedioate. The calculated total free energy barriers are 14.54 and 16.45 kcal/mol for the first and second steps, respectively. Our calculations clearly show that there is no general acid in the reaction. Arg-39' ', which is hydrogen bonded to the carboxylate group of the substrate, and an ordered water, which moves closer to the site of the charge formed in the transition state and intermediate, play the main role in transition state/intermediate stabilization without acting as general acids in the reaction.

Acids↗
PubMed2006

Ultrafast vibrationally-induced dephasing of electronic excitations in PbSe quantum dots.

Vibrationally induced pure-dephasing of electronic states in PbSe quantum dots (QDs) at room temperature is investigated using two independent theoretical approaches based on the optical response function and semiclassical formalisms. Both approaches predict dephasing times of around 10 fs and reproduce the recently measured homogeneous linewidths of optical absorption well. Because dephasing slows down with increasing cluster size, the dephasing times calculated for the small clusters correspond to the lower end of the experimental data. The dephasing is almost independent of the electronic excitation energy and occurs faster for biexcitons than single excitons. The dephasing time is roughly proportional to the square root of the mass of the lighter atom (Se), suggesting that dephasing should be faster in PbS and slower in PbTe relative to PbSe. Core atoms produce stronger dephasing than surface atoms. In the collective description, pure-dephasing occurs via low-frequency acoustic modes, in support of the elastic QD model of dephasing. Because the electron-phonon coupling in PbSe QDs is relatively weak compared to other semiconductor nanocrystals, fast vibrationally induced dephasing can be expected in semiconductor QDs in general.

Computer Simulation↗
PubMed2003

Balancing kinetic and thermodynamic control: the mechanism of carbocation cyclization by squalene cyclase.

Molecular dynamics simulations with a combined quantum mechanical and molecular mechanical (QM/MM) potential have been carried out to investigate the squalene-to-hopene carbocation cyclization mechanism in squalene-hopene cyclase (SHC). The present study is based on free energy simulations by constructing the free energy surface for the cyclization steps along the reaction pathway. The picture that emerges for the carbocation cyclization cascade is a delicate balance of thermodynamic and kinetic control that ultimately favors the formation of the final hopanoids carbon skeleton. A key finding is that the five- to six-membered ring expansion process is not a viable reaction pathway for either C- or D-ring formation in the cyclization reaction. The only significant intermediate is the A/B-bicyclic cyclohexyl cation (III), from which two asynchronous concerted reaction pathways lead to, respectively, the 6,6,6,5-tetracyclic carbon skeleton and the 6,6,6,6,5-pentacyclic hopanoids. Experimentally, these two products are observed to have 1% and 99% yields, respectively, in the wild-type enzyme. We conclude that the product distribution in the wild-type enzyme is dictated by kinetic control of these two reaction pathways.

Computer Simulation↗
PubMed1996

Modeling lipophilicity from the distribution of electrostatic potential on a molecular surface.

Molecular lipophilicity L is represented as a function of four surface electrostatic potential descriptors: L = f(B+F, B-F, B+R, B-R). Each B descriptor is computed from the products of elements of molecular surface area, delta(si), and the molecular electrostatic potential (MEP), V(ri), at the center of an area element: B = sigma(i) delta(si) V(r(i)). Octanol-water partition coefficients (P(ow)) are correlated with these four surface-MEP descriptors: log P(ow) = c0 + c1B+F + c2B-F + c3B+R + c4B-R. Good correlations are obtained for homologous series of aliphatic alcohols, amines and acids, as well as for a set of aromatic compounds with various functional groups. Within this approach, we find that the molecular fragment contributions of surface-MEP descriptions to log P are approximately additive. We have computed the values for the following fragments: -CH2-, -CH3, _COOH, -OH and -NH2. These contributions can be used to estimate the molecular lipophilicity and partition coefficients of new compounds, without additional quantum-mechanical calculations. The proposed approach provides a reasonably accurate tool that can be useful in quantitative structure-activity relations for computer-aided rational drug design. More importantly, the correlation model is conceptually simpler than previous work in the literature and can be improved systematically.

Alcohols↗
PubMed2004

Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies.

Free-energy perturbation (FEP) is considered the most accurate computational method for calculating relative solvation and binding free-energy differences. Despite some success in applying FEP methods to both drug design and lead optimization, FEP calculations are rarely used in the pharmaceutical industry. One factor limiting the use of FEP is its low throughput, which is attributed in part to the dependence of conventional methods on the user's ability to develop accurate molecular mechanics (MM) force field parameters for individual drug candidates and the time required to complete the process. In an attempt to find an FEP method that could eventually be automated, we developed a method that uses quantum mechanics (QM) for treating the solute, MM for treating the solute surroundings, and the FEP method for computing free-energy differences. The thread technique was used in all transformations and proved to be essential for the successful completion of the calculations. Relative solvation free energies for 10 structurally diverse molecular pairs were calculated, and the results were in close agreement with both the calculated results generated by conventional FEP methods and the experimentally derived values. While considerably more CPU demanding than conventional FEP methods, this method (QM/MM-based FEP) alleviates the need for development of molecule-specific MM force field parameters and therefore may enable future automation of FEP-based calculations. Moreover, calculation accuracy should be improved over conventional methods, especially for calculations reliant on MM parameters derived in the absence of experimental data.

Journal Article↗
PubMed2006

A combined QM/MM molecular dynamics simulations study of nitrate anion (NO3-) in aqueous solution.

The structural and dynamical properties of NO3- in dilute aqueous solution have been investigated by means of two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, namely HF/MM and B3LYP/MM, in which the ion and its surrounding water molecules were treated at HF and B3LYP levels of accuracy, respectively, using the DZV+ basis set. On the basis of both HF and B3LYP methods, a well-defined first hydration shell of NO3- is obtainable, but the shell is quite flexible and the hydrogen-bond interactions between NO3- and water are rather weak. With respect to the detailed analysis of the geometrical arrangement and vibrations of NO3-, the experimentally observed solvent-induced symmetry breaking of the ion is well reflected. In addition, the dynamical information, i.e., the bond distortions and shifts in the corresponding bending and stretching frequencies as well as the mean residence time of water molecules surrounding the NO3- ion, clearly indicates the "structure-breaking" ability of this ion in aqueous solution. From a methodical point of view it seems that both the HF and B3LYP methods are not too different in describing this hydrated ion by means of a QM/MM simulation. However, the detailed analysis of the dynamics properties indicates a better suitability of the HF method compared to the B3LYP-DFT approach.

Anions↗
PubMed2005

Impact of nuclear quantum effects on the molecular structure of bihalides and the hydrogen fluoride dimer.

The structural impact of nuclear quantum effects is investigated for a set of bihalides, [XHX](-), X = F, Cl, and Br, and the hydrogen fluoride dimer. Structures are calculated with the vibrational self-consistent-field (VSCF) method, the second-order vibrational perturbation theory method (VPT2), and the nuclear-electronic orbital (NEO) approach. In the VSCF and VPT2 methods, the vibrationally averaged geometries are calculated for the Born-Oppenheimer electronic potential energy surface. In the NEO approach, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wave functions are calculated variationally with molecular orbital methods. Electron-electron and electron-proton dynamical correlation effects are included in the NEO approach using second-order perturbation theory (NEO-MP2). The nuclear quantum effects are found to alter the distances between the heavy atoms by 0.02-0.05 A for the systems studied. These effects are of similar magnitude as the electron correlation effects. For the bihalides, inclusion of the nuclear quantum effects with the NEO-MP2 or the VSCF method increases the X-X distance. The bihalide X-X distances are similar for both methods and are consistent with two-dimensional grid calculations and experimental values, thereby validating the use of the computationally efficient NEO-MP2 method for these types of systems. For the hydrogen fluoride dimer, inclusion of nuclear quantum effects decreases the F-F distance with the NEO-MP2 method and increases the F-F distance with the VSCF and VPT2 methods. The VPT2 F-F distances for the hydrogen fluoride dimer and the deuterated form are consistent with the experimentally determined values. The NEO-MP2 F-F distance is in excellent agreement with the distance obtained experimentally for a model that removes the large amplitude bending motions. The analysis of these calculations provides insight into the significance of electron-electron and electron-proton correlation, anharmonicity of the vibrational modes, and nonadiabatic effects for hydrogen-bonded systems.

Dimerization↗
PubMed2004

Spectral difference Lanczos method for efficient time propagation in quantum control theory.

Spectral difference methods represent the real-space Hamiltonian of a quantum system as a banded matrix which possesses the accuracy of the discrete variable representation (DVR) and the efficiency of finite differences. When applied to time-dependent quantum mechanics, spectral differences enhance the efficiency of propagation methods for evolving the Schrodinger equation. We develop a spectral difference Lanczos method which is computationally more economical than the sinc-DVR Lanczos method, the split-operator technique, and even the fast-Fourier-Transform Lanczos method. Application of fast propagation is made to quantum control theory where chirped laser pulses are designed to dissociate both diatomic and polyatomic molecules. The specificity of the chirped laser fields is also tested as a possible method for molecular identification and discrimination.

Journal Article↗
PubMed2007

Computational study on the relative acidity of acetic acid by the QM/MM method combined with the theory of energy representation.

We have applied the quantum mechanical/molecular mechanical (QM/MM) method combined with the theory of energy representation (ER) to study the acidity of acetic acid in aqueous solution. We have focused our attention on the relative acidity DeltapK(a) of the molecule with respect to water solvent to circumvent the ambiguity of the solvation free energies of the molecular species referred to as proton. The value of DeltapK(a) for the acetic acid has been computed as -11.5 when we adopt the free energy change in the gas phase obtained by the B3LYP functional, which is in excellent agreement with the experimental value of -11.0. It has been demonstrated that the QM/MM-ER approach recently developed gives an adequate description for the solvation free energies related to the acidity/basicity calculations of organic molecules.

Acetic Acid↗