Electron and nuclear dynamics in many-electron atoms, molecules and chlorophyll-protein complexes: a review

It has been shown [V.A. Shuvalov, Quantum dynamics of electrons in many-electron atoms of biologically important compounds, Biochemistry (Mosc.) 68 (2003) 1333-1354; V.A. Shuvalov, Quantum dynamics of electrons in atoms of biologically important molecules, Uspekhi biologicheskoi khimii, (Pushchino) 44 (2004) 79-108] that the orbit angular momentum L of each electron in many-electron atoms is L=mVr=nPlanck's and similar to L for one-electron atom suggested by N. Bohr. It has been found that for an atom with N electrons the total electron energy equation E=-(Z(eff))(2)e(4)m/(2n(2)Planck's(2)N) is more appropriate for energy calculation than standard quantum mechanical expressions. It means that the value of L of each electron is independent of the presence of other electrons in an atom and correlates well to the properties of virtual photons emitted by the nucleus and creating a trap for electrons. The energies for elements of the 1st up to the 5th rows and their ions (total amount 240) of Mendeleev' Periodical table were calculated consistent with the experimental data (deviations in average were 5 x 10(-3)). The obtained equations can be used for electron dynamics calculations in molecules. For H(2) and H(2)(+) the interference of electron-photon orbits between the atoms determines the distances between the nuclei which are in agreement with the experimental values. The formation of resonance electron-photon orbit in molecules with the conjugated bonds, including chlorophyll-like molecules, appears to form a resonance trap for an electron with E values close to experimental data. Two mechanisms were suggested for non-barrier primary charge separation in reaction centers (RCs) of photosynthetic bacteria and green plants by using the idea of electron-photon orbit interference between the two molecules. Both mechanisms are connected to formation of the exciplexes of chlorophyll-like molecules. The first one includes some nuclear motion before exciplex formation, the second one is related to the optical transition to a charge transfer state.     

Electron and nuclear dynamics in many-electron atoms, molecules and chlorophyll-protein complexes: A review

It has been shown [V.A. Shuvalov, Quantum dynamics of electrons in many-electron atoms of biologically important compounds, Biochemistry (Mosc.) 68 (2003) 1333-1354; V.A. Shuvalov, Quantum dynamics of electrons in atoms of biologically important molecules, Uspekhi biologicheskoi khimii, (Pushchino) 44 (2004) 79-108] that the orbit angular momentum L of each electron in many-electron atoms is L = mVr = n? and similar to L for one-electron atom suggested by N. Bohr. It has been found that for an atom with N electrons the total electron energy equation E = −(Z^eff)²e⁴m/(2n²?²N) is more appropriate for energy calculation than standard quantum mechanical expressions. It means that the value of L of each electron is independent of the presence of other electrons in an atom and correlates well to the properties of virtual photons emitted by the nucleus and creating a trap for electrons. The energies for elements of the 1st up to the 5th rows and their ions (total amount 240) of Mendeleev' Periodical table were calculated consistent with the experimental data (deviations in average were 5 × 10^− 3). The obtained equations can be used for electron dynamics calculations in molecules. For H₂ and H₂⁺ the interference of electron-photon orbits between the atoms determines the distances between the nuclei which are in agreement with the experimental values. The formation of resonance electron-photon orbit in molecules with the conjugated bonds, including chlorophyll-like molecules, appears to form a resonance trap for an electron with E values close to experimental data. Two mechanisms were suggested for non-barrier primary charge separation in reaction centers (RCs) of photosynthetic bacteria and green plants by using the idea of electron-photon orbit interference between the two molecules. Both mechanisms are connected to formation of the exciplexes of chlorophyll-like molecules. The first one includes some nuclear motion before exciplex formation, the second one is related to the optical transition to a charge transfer state.     

Molecular polarization maps as a tool for studies of intermolecular interactions and chemical reactivity

Maps for the interaction energy of acetone, pyrrole, furan, and pyridine with a positive unitary charge were computed using ab initio techniques, together with their molecular electrostatic potentials at the same points. The difference between the interaction and electrostatic potential maps yielded polarization maps for the molecules. Finally, maps for the interaction with a negative charge were obtained as the difference between the polarization and electrostatic potential maps.The calculations were carried out for three planes, 2 Bohr radii, 4 Bohr radii, and 8 Bohr radii from the plane containing the heavy atoms for all the molecules. At larger distances, the interaction and electrostatic maps resemble each other qualitatively; however, at shorter distances, where the polarization effects are more significant, the differences between the maps are notable.Interaction and polarization maps can be routinely evaluated for medium-sized molecules, and are likely to become an important tool in drug design and chemical reactivity.     

Means of optimizing light energy conversion in the primary stages of photosynthesis. II. Optimization of the structure of an uniform photosynthetic unit lattice

The possibility of optimization of the structure of a model photosynthetic unit lattice is analysed. The efficiency of the photosynthetic unit operation is evaluated from the time of excitation energy trapping by reaction centers. The calculations assume a F?rster inductive resonance mechanism for energy transfer within light--harvesting antenna and pairwise dipolar interactions. We use the probability matrix method which is adapted to excitation trapping time (but not to excitation jumps number) calculation. It is shown that the specific anisotropy of the distances between antenna molecules (which is in principle possible due to the diskshaped form of chlorophyll molecules) in combination with the optimal spatial arrangement of reaction centers as "well regulated clusters" allows to decrease the time of excitation energy trapping by over an order of magnitude. The requirements for optimization of the structure of a macroscopic photosynthetic unit lattice and the consequences following from them for the in vivo systems are formulated.     

Photoacoustic spectroscopy of Anacystis nidulans. III. Detection of photosynthetic activities

Photosynthetic activities of Anacystis nidulans can be detected by photoacoustic spectroscopy. Algae treated by a photosynthetic inhibitor are used to provide the signal from the photochemically inactive sample. The results of these measurements correspond well with the activities which can be monitored by conventional biochemical assays. Acoustic data from A. nidulans are used to obtain the action spectrum for photochemical energy storage. It is concluded that phycocyanin harvests light for both photoreactions but that chlorophyll alpha molecules convey most of their excitation energy to photoreaction I. As judged from the relationship between the modulation frequency and the acoustic signal intensity, at least 60% of the photons absorbed at 630 nm perform photochemical work and about half of the useful energy is stored at stable products. Although it cannot be separated from the purely thermal effect, the contribution of modulated oxygen evolution to the acoustic signal of algae is estimated to be relatively small. Due to structural peculiarities, the opposite situation predominates in low frequency measurements performed with leaves from Impatiens petersiana.     

The role of atomic inner shell relaxations for photon-induced DNA damage

The influence of relaxations of atoms making up the DNA and atoms attached to it on radiation-induced cellular DNA damage by photons was studied by very detailed Monte Carlo track structure calculations, as an unusually high importance of inner shell ionizations for biological action was suspected from reports in the literature. For our calculations cross sections for photons and electrons for inner shell orbitals were newly derived and integrated into the biophysical track structure simulation programme PARTRAC. Both the local energy deposition in a small sphere around the interacting relaxed atom, and the number of relaxations per Gy and Gbp were calculated for several target geometries and many monoenergetic photon irradiations. Elements with the highest order number yielded the largest local energy deposition after interaction. The atomic relaxation after ionization of the L1 shell was found to be more biologically efficient than that of the K shell for high Z atoms. Generally, the number of inner shell relaxations produced by photon irradiation was small in comparison to the total number of double strand breaks generated by such radiation. Furthermore, the energy dependence of the total number of photon-induced and electron-induced relaxations at the DNA atoms does not agree with observed RBE values for different biological endpoints. This suggests that the influence of inner shell relaxations of DNA atoms on radiation-induced DNA damage is in general rather small.     

Excluded volume approximation to protein-solvent interaction. The solvent contact model.

Important properties of globular proteins, such as the stability of its folded state, depend sensitively on interactions with solvent molecules. Existing methods for estimating these interactions, such as the geometrical surface model, are either physically misleading or too time consuming to be applied routinely in energy calculations. As an alternative, we derive here a simple model for the interactions between protein atoms and solvent atoms in the first hydration layer, the solvent contact model, based on the conservation of the total number of atomic contacts, a consequence of the excluded-volume effect. The model has the conceptual advantage that protein-protein contacts and protein-solvent contacts are treated in the same language and the technical advantage that the solvent term becomes a particularly simple function of interatomic distances. The model allows rapid calculation of any physical property that depends only on the number and type of protein-solvent nearest-neighbor contacts. We propose use of the method in the calculation of protein solvation energies, conformational energy calculations, and molecular dynamics simulations.     

Voxel model of individual cells and its implementation in microdosimetric calculations using GEANT4

Accurate dosimetric calculations at cellular and sub-cellular levels are crucial to obtain an increased understanding of the interactions of ionizing radiation with a cell and its nucleus and cytoplasm. Ion microbeams provide a superior opportunity to irradiate small biological samples, e.g., DNA, cells, and to compare their response to computer simulations. However, the phantoms used to simulate small biological samples at cellular levels are often simplified as simple volumes filled with water. As a first step to improve the situation in comparing measurements of cell response to ionizing radiation with model calculations, a realistic voxel model of a KB cell was constructed and used together with an already constructed geometry and tracking 4 (GEANT4) model of the horizontal microbeam line of the Centre d’Etudes Nucléaires de Bordeaux-Gradignan (CENBG) 3.5 MV Van de Graaf accelerator at the CENBG, France. The microbeam model was then implemented into GEANT4 for simulations of the average number of particles hitting an irradiated cell when a specified number of particles are produced in the beam line. The result shows that when irradiating the developed voxel model of a KB cell with 200 α particles, with a nominal energy of 3 MeV in the beam line and 2.34 MeV at the cell entrance, 100 particles hit the cell on average. The mean specific energy is 0.209 ± 0.019 Gy in the nucleus and 0.044 ± 0.001 Gy in the cytoplasm. These results are in agreement with previously published data, which indicates that this model could act as a reference model for dosimetric calculations of radiobiological experiments, and that the proposed method could be applied to build a cell model database.     

Role of the electrostatic interactions in pre-orientation of subunits in the formation of protein-protein complexes

Theoretical estimation of contribution of the electrostatic interactions to pre-orientation of ribonuclease subunits in process of complex formation was carried out. The subunit was considered as a multipole consisting of partial charges of all atoms of the molecule. The object of investigation was a system of two subunits with their centers of gravity fixed at some distance in vacuum. It was proposed that each subunit independently could rotate freely around its fixed center of gravity. The relative orientation states of the subunits in such system were searched at which the system has electrostatic energy minima (equilibrium states). In first approximation the equilibrium states were found using especially designed approximate method for electrostatic interaction energy calculation, which permitted to calculate and compare the energies of the system in 24(5) (approximately 8 10(6)) states with different mutual orientation of subunits. The angular coordinates of the found equilibrium states were further specified by calculation with gradient sliding method. Angular coordinates of the equilibrium states and the shapes of energy surface cuts along each coordinate angle were calculated also for the intersubunits distances diminished down to 50 angstroms. The dispersions of the angular coordinates of equilibrium states caused by heat movement (at T=300 degrees) and their changes with shortening the distance between centers of gravity of subunits were estimated. Mutual orientation of subunits in the equilibrium states of the system under consideration was found to be similar to their mutual orientations in complex. Also it was found that relaxation time of the system, caused by electrostatic interaction of subunits, after removing the system from an equilibrium state, is much less in vacuum than the mean time between their Brownian collisions at room temperature. It follows from these results that in the case of ribonuclease in vacuum the electrostatic interactions of its subunits must be strong enough to realize the effective pre-orientation of subunits during their Brownian approach from distances of the order 100 angstroms. Preliminary consideration taking into account the effect of surrounding water molecules on the electrostatic interactions of ribonuclease subunits showed that weakening of the interaction must be much less than in the case when one uses in its calculation the macroscopic dielectric permeability value equal to 80. So the results obtained for vacuum seem to be true for water solution also. More strict theoretical analysis of this problem will be carried out in the following publication.     

The photochemical origins of life and photoreaction of ferrous ion in the archaean oceans

A general argument is made for the photochemical origins of life. A constant flux of free energy is required to maintain the organized state of matter called life. Solar photons are the unique source of the large amounts of energy probably require to initiate this organization and certainly required for the evolution of life to occur. The completion of this argument will require the experimental determination of suitable photochemical reactions. Our work shows that biogenetic porphyrins readily photooxidize substrates and emit hydrogen in the presence of a catalyst. These results are consistent with the Granick hypothesis, which relates a biosynthetic pathway to its evolutionary origin. We have shown that photoexcitation of ferrous ion at neutral pH with near ultraviolet light produces hydrogen with high quantum yield. This same simple system may reduce carbon dioxide to formaldehyde and further products. These reactions offer a solution to the dilemma confronting the Oparin-Urey-Miller model of the chemical origin of life. If carbon dioxide is the main form of carbon on the primitive earth, the ferrous photoreaction may provide the reduced carbon necessary for the formation of amino acids and other biogenic molecules. These results suggest that this progenitor of modern photosynthesis may have contributed to the chemical origins of life.     

Hydration of nucleic acid bases studied using novel atom-atom potential functions

New simple atom-atom potential functions for simulating behavior of nucleic acids and their fragments in aqueous solutions are suggested. These functions contains terms which are inversely proportional to the first (electrostatics), sixth (or tenth for the atoms, forming hydrogen bonds) and twelfth (repulsion of all the atoms) powers of interatomic distance. For the refinement of the potential function parameters calculations of ice lattice energy, potential energy and configuration of small clusters consisting of water and nucleic acid base molecules as well as Monte Carlo simulation of liquid water were performed. Calculations using new potential functions give rise to more linear hydrogen bonds between water and base molecules than using other potentials. Sites of preferential hydration of five nucleic bases - uracil, thymine, cytosine, guanine and adenine as well as of 6,6,9-trimethyladenine were found. In the most energetically favourable sites water molecular interacts with two adjacent hydrophilic centres of the base. Studies of interaction of the bases with several water molecules showed that water-water interactions play an important role in the arrangement of the nearest to the base water molecules. Hydrophilic centres are connected by "bridges" formed by hydrogen bonded water molecules. The results obtained are consistent with crystallographic and mass-spectrometric data.     

Study of Ca2+-binding centers of parvalbumin by the distant fine structure of x-ray absorption spectra

An investigation of Ca2+-binding centers of parvalbumin II and III by analysing distant fine structure of X-ray absorption spectra of metal was performed. Protein preparations of parvalbumin II and III in which Ca2+ was isomorphically replaced by Tb3+ were studied. For spectra analyses a standard method of Fourier transformation was used. The middle of the first absorption maximum was taken as origin for energy calculations. Comparison of spectra and modules of Fourier transformations for normalized oscillations of the X-ray spectra of absorption of the II and III components, revealed that the spectra and Fourier-transformants coincide in the 2--6 A interval. This allows to infer the coincidence of the coordinate numbers, average interatomic distances and their dispersions in Ca2+-binding centers of the two protein components.     

Specific damage induced by X-ray radiation and structural changes in the primary photoreaction of bacteriorhodopsin

Bacteriorhodopsin, the sole membrane protein of the purple membrane of Halobacterium salinarum, functions as a light-driven proton pump. A 3-D crystal of bacteriorhodopsin, which was prepared by the membrane fusion method, was used to investigate structural changes in the primary photoreaction. It was observed that when a frozen crystal was exposed to a low flux of X-ray radiation (5 x 10(14)photons mm(-2)), nearly half of the protein was converted into an orange species, exhibiting absorption peaks at 450 nm, 478 nm and 510 nm. The remainder retained the normal photochemical activity until Asp85 in the active site was decarboxlyated by a higher flux of X-ray radiation (10(16)photons mm(-2)). The procedure of diffraction measurement was improved so as to minimize the effects of the radiation damage and determine the true structural change associated with the primary photoreaction. Our structural model of the K intermediate indicates that the Schiff base linkage and the adjacent bonds in the polyene chain of retinal are largely twisted so that the Schiff base nitrogen atom still interacts with a water molecule located near Asp85. With respect to the other part of the protein, no appreciable displacement is induced in the primary photoreaction.     

Incorporation of lone pairs into the electrostatic term in the empirical intra- and intermolecular energy calculations

The method hitherto used for estimating the electrostatic term in empirical intramolecular calculations of stable conformations of biologically important molecules and macromolecules and intermolecular calculations of molecular associations or packing energy in molecular crystals had been analyzed. It has been shown that the contribution of atomic hybridization moments is omitted in the calculation of electrostatic interactions from net atomic charges localized on nuclei which have been determined by standard quantum-chemical methods. This contribution plays an important part in determining electrostatic interactions, mainly in molecules containing atoms with lone pairs. Simultaneously, a modified method for calculating the electrostatic term comprising the interaction of the lone pairs, which are represented by atomic hybridization moments, has been proposed. The relationship between the atomic hybridization moment and the bond angle has been expressed for some typical configurations occurring in biologically important molecules. Finally, this new approach is illustrated by results of the conformational analysis of some model compounds for biomolecules and compared with the approach used so far for the estimation of the electrostatic interaction in empirical methods of calculation of the intra- and intermolecular energy.     

Sequence-dependent motions of DNA: a normal mode analysis at the base-pair level

Computer simulation of the dynamic structure of DNA can be carried out at various levels of resolution. Detailed high resolution information about the motions of DNA is typically collected for the atoms in a few turns of double helix. At low resolution, by contrast, the sequence-dependence features of DNA are usually neglected and molecules with thousands of base pairs are treated as ideal elastic rods. The present normal mode analysis of DNA in terms of six base-pair "step" parameters per chain residue addresses the dynamic structure of the double helix at intermediate resolution, i.e., the mesoscopic level of a few hundred base pairs. Sequence-dependent effects are incorporated into the calculations by taking advantage of "knowledge-based" harmonic energy functions deduced from the mean values and dispersion of the base-pair "step" parameters in high-resolution DNA crystal structures. Spatial arrangements sampled along the dominant low frequency modes have end-to-end distances comparable to those of exact polymer models which incorporate all possible chain configurations. The normal mode analysis accounts for the overall bending, i.e., persistence length, of the double helix and shows how known discrepancies in the measured twisting constants of long DNA molecules could originate in the deformability of neighboring base-pair steps. The calculations also reveal how the natural coupling of local conformational variables affects the global motions of DNA. Successful correspondence of the computed stretching modulus with experimental data requires that the DNA base pairs be inclined with respect to the direction of stretching, with chain extension effected by low energy transverse motions that preserve the strong van der Waals' attractions of neighboring base-pair planes. The calculations further show how one can "engineer" the macroscopic properties of DNA in terms of dimer deformability so that polymers which are intrinsically straight in the equilibrium state exhibit the mesoscopic bending anisotropy essential to DNA curvature and loop formation.     

Hydration of Nucleic Acid Bases Studied Using Novel Atom-Atom Potential Functions

Abstract

New simple atom-atom potential functions for simulating behavior of nucleic acids and their fragments in aqueous solutions are suggested. These functions contain terms which are inversely proportional to the first (electrostatics), sixth (or tenth for the atoms, forming hydrogen bonds) and twelfth (repulsion of all the atoms) powers of interatomic distance. For the refinement of the potential function parameters calculations of ice lattice energy, potential energy and configuration of small clusters consisting of water and nucleic acid base molecules as well as Monte Carlo simulation of liquid water were performed. Calculations using new potential functions give rise to more linear hydrogen bonds between water and base molecules than using other potentials. Sites of preferential hydration of five nucleic bases—uracil, thymine, cytosine, guanine and adenine as well as of 6,6,9-trimethyladenine were found. In the most energetically favourable sites water molecule interacts with two adjacent hydrophilic centres of the base. Studies of interaction of the bases with several water molecules showed that water-water interaction play an important role in the arrangement of the nearest to the base water molecules. Hydrophilic centres are connected by “bridges” formed by hydrogen bonded water molecules. The results obtained are consistent with crystallographic and mass-spectrometric data.     

Beta decay and the origin of biological chirality: New experimental results

The proposed connection between the parity-violating handedness of beta particles in radioactive decay and the sign (L) of biological chirality (the Vester-Ulbricht [V-U] hypothesis) is being investigated by measuring the theoretically predicted asymmetry in the formation of triplet positronium in amino acid enantiomers by low energy positrons under reversal of the helicity of the positrons. We find the asymmetry in leucine to be (0.8±1.0)×10^–4, i.e. consistent with the theoretical, prediction of 10^–6 to 10^–7. The apparatus is now sensitive enough to test the predicted asymmetry in optically active molecules which have heavy atoms at their chiral centers. The connection between these results and asymmetry in radiolysis by beta-decay electrons is made, and the implications of our limits for the V-U hypothesis discussed. Although the above limits are 10⁶ times lower than direct measurements of radiolysis, they are still not small enough to allow us to rule out the V-U hypothesis.     

(13)C MAS NMR and photo-CIDNP reveal a pronounced asymmetry in the electronic ground state of the special pair of Rhodobacter sphaeroides reaction centers

Reaction centers of wild-type Rhodobacter sphaeroides were selectively (13)C-isotope labeled in bacteriochlorophyll and bacteriopheophytin. (13)C solid-state CP/MAS NMR and photo-CIDNP were used to provide insight into the electronic structure of the primary electron donor and acceptor on the atomic scale. The first 2-dimensional photochemically induced dynamic nuclear polarization (photo-CIDNP) (13)C-(13)C solid-state MAS NMR spectra reveal that negative charging of the two BChl rings of the primary donor is involved in ground-state tuning of the oxidation potential of these cofactors in the protein via local electrostatic interactions. In particular, the (13)C shifts show moderate differences in the electronic structure between the two BChl molecules of the special pair in the electronic ground state, which can be attributed to hydrogen bonding of one of the BChl molecules. The major fraction of the electron spin density is strongly delocalized over the two BChl molecules of the special pair and the photochemically active BPhe. A small fraction of the pi-spin density is distributed over a fourth component, which is assigned to the accessory BChl. Comparison of the photo-CIDNP data with "dark" NMR spectra obtained in ultra high field indicates a rigid special pair environment upon photoreaction and suggests that structural changes of the aromatic macrocycles of the two BChl molecules of the special pair do not significantly contribute to the reorganization energy associated with the charge-transfer process.     

Crystal packing of pyrimidine nucleosides--a study in terms of empirical van der Waals' potential energy

Molecular interactions in 32 crystal structures of pyrimidine nucleosides and nucleoside derivatives have been studied in terms of empirical van der Waals' energy. The stacking patterns have been classified into three types according to the symmetry operations involved within the pattern. Halogen and sulphur atoms were included in the calculations where necessary. Model columns of stacked molecules were set up in a computer calculation giving the energy for different amounts of base overlap. There was a tendency for the crystal positions of the molecules to agree with the minima of the energy maps, which showed the predominance of the van der Waals' forces in determining the base-stacking arrangement. The position of the energy minimum was correlated with the molecular conformation defined by the C-N glycosidic torsion angle.