Correlated variations of bond lengths in pseudorotating furanose rings

Correlated variations of bond lengths in pseudorotating furanose rings are investigated by a theoretical method. At first, matrix equations are proposed to determine the spatial coordinates of the ring atoms from the bond lengths, the bond angles, and the pseudorotation parameters. Secondly, a necessary functional form of the variations of the bond lengths of five-membered rings is derived from a consideration of symmetry. Finally, demonstrations are performed on a furanose ring whose bond angle variations have been precisely determined by experimental analyses. The resulting bond length variations are: delta Ri = beta icos(8/5 pi.(i-2)+2P) where delta Ri is the variation of the bond length between atoms i and i+1, P is the pseudorotation phase, and beta i is a negative constant about -0.01 A. These bond length variations are balanced on the apparent strains of the bond lengths and the bond angles.     

Conformation of kainic acid in solution from molecular modelling and NMR spectra

Conformational behaviour of kainic acid in aqueous solution was elucidated by molecular mechanics and dynamics. The pucker of the five-membered ring in kainic acid was examined and compared with that of model compounds. In cyclopentane there is no barrier to pseudorotation, so that all puckered states coexist. In pyrrolidinium, the presence of a hetero-atom in the ring introduces a small barrier (about 0.6 kcal mol(-1)) to pseudorotation, separating two stable regions, A and B, which are equivalent by symmetry. In proline, the presence of the carboxylate group on C2 removes the symmetry but two stable conformational minima, A and B, remain. In kainic acid, the presence of side-chains on C3 and C4 introduces complications resulting in additional sub-minima in both regions, A and B. In solution, kainic acid is a complex mixture of conformers with comparable energies, because of the combination of several stable states of the pyrrolidinium ring with the torsional degrees of freedom arising from the two side-chains. The individual geometries, energies, and estimates of relative populations of these conformers were obtained from molecular dynamics simulations. The calculations were validated by a comparison of predicted inter-proton distances and vicinal proton coupling constants with the experimental quantities derived from NMR spectra.     

Bend of the furanose ring of the double-helical DNA

The interpretation of conformationally dependent double-helical DNA Raman bands, which stipulates their appearance with the furanose ring-puckering vibration is suggested. Quantum-mechanical calculations of the furanose ring-puckering vibration occurring by a pseudorotation pathway are carried out. Vibrational states eigen values and eigen functions are calculated for a double-well pseudorotation potential of the furanose. The obtained value of the pseudorotation barrier 4.2-3.6 kcal/mol proves to be in a good agreement with other theoretical and experimental estimates of the barrier.     

Correlated Variations of Bond Lengths in Pseudorotating Furanose Rings

Abstract

Correlated variations of bond lengths in pseudorotating furanose rings are investigated by a theoretical method. At first, matrix equations are proposed to determine the spatial coordinates of the ring atoms from the bond lengths, the bond angles, and the pseudorotation parameters. Secondly, a necessary functional form of the variations of the bond lengths of five-membered rings is derived from a consideration of symmetry. Finally, demonstrations are performed on a furanose ring whose bond angle variations have been precisely determined by experimental analyses. The resulting bond length variations are:

δR_i = β_iCos(8/5π · (i-2)+2P)

where δR_i is the variation of the bond length between atoms i and i+1, P is the pseudorotation phase, and β_iis a negative constant about ?0.01 Å. These bond length variations are balanced on the apparent strains of the bond lengths and the bond angles.     

Analytic examples of force-free toroidal MHD equilibria

Analytically described toroidal (axisymmetric and three-dimensional) equilibrium magnetic field configurations with a “flat” current density, j=λB (λ = const), are proposed. Such configurations are superpositions of several force-free two-dimensional configurations with plane, axial, or helical coordinate symmetry. Each of them is generated by an exact partial solution to the corresponding Grad-Shafranov equation. A variety of toroidal configurations thus obtained allows one to model topological changes of magnetic surfaces, such as magnetic axis splitting (doublets) in axisymmetric equilibrium configurations and the appearance and interaction of magnetic islands and ergodic lines in three-dimensional configurations.     

The effect of electrostatic interactions on the conformation of the sugar-phosphate backbone in DNA]

The influence of sugar ring flexibility in DNA on the mechanism of the B<-->A conformational transition is studied. The dipole moment of the deoxyribose as a function of its puckered states is calculated by the quantum-mechanical method using the MINDO/3 approximation. The interaction of the sugar dipole with the neighbour molecular groups in polynucleotide chain is estimated. The sugar dipole interaction witch phosphate groups and counterions is shown to be strong and capable to deform the pseudorotation potential of deoxyribose. The effective pseudorotation potential of sugar ring in the B- and A-helices is obtained. The results are used to explain the behaviour of Raman bands in the region of sugar-phosphate vibrations. The mechanism of the effect of electrostatic forces on the sugar-phosphate backbone conformation which is essential for the B<-->A and other structure transitions is offered.     

Influence of electrostatic interactions on the sugar–phosphate backbone conformation in DNA

The influence of sugar ring flexibility in DNA on the mechanism of the B ? A conformational transition is studied. The dipole moment of the deoxyribose as a function of its puckered states is calculated by the quantum-mechanical method using the MINDO/3 approximation. The interaction of the sugar dipole with the neighbor molecular groups in polynucleotide chains is estimated. The sugar dipole interaction with phosphate groups and counterions is shown to be strong and capable to deform the pseudorotation potential of deoxyribose. The effective pseudorotation potential of sugar ring in the B and A helices is obtained. The results are used to explain the behavior of Raman bands in the region of sugar–phosphate vibrations. The mechanism of the effect of electrostatic forces on the sugar–phosphate backbone conformation, which is essential for the B ? A and other structure transitions, is offered. © 1993 John Wiley & Sons, Inc.     

Conformational studies of peptide cyclo-(D-Val-L-Pro-L-Val-D-Pro]3, a cation-binding analogue of valinomycin.

The solution conformation of cyclo-[D-Val-L-Pro-L-Val-D-Pro]3 (PV) and its alkali-metal ion complexes was investigated by proton nuclear magnetic resonance spectroscopy. It is concluded that the cation complexes of PV have S6 symmetry and are essentially isostructural with the K complex of valinomycin. In contrast to valinomycin, the Li- and Na-PV complexes are stable in methanol and have dissociation rate constants that are several orders of magnitude slower than the corresponding valinomycin complexes. Also in contrast to valinomycin, free PV exists in two different conformational states which interconvert at very slow rates (less than 1 s-1). One of these conformers has S6 symmetry and is structurally similar to that of the cation complexes. The other species, which has lower symmetry than S6, is the more stable conformer. Depending upon concentration and solvent polarity, the latter represents between 50 and 75% of the total mixture. It is proposed that PV may have a higher affinity for cations than valinomycin because of its higher potential energy in the uncomplexed state.     

Modeling of nucleic acid complexes with cationic ligands: a specialized molecular mechanics force field and its application.

A potential energy force field designed for modeling nucleic acids and particularly their complexes with cationic ligands is presented. The force field is a modified version of that developed by Weiner, S.J., Kollman, P.A., Nguyen, D.T. and Case, D.A.,J. Comp. Chem. 7,230-252 (1986) and is based upon the use of a distance dependent dielectric constant, epsilon = 4rij, and partially neutralized phosphates to represent solvent and counterion. Changes from the Weiner et al. force field include additional atom types and modifications to van der Waals, electrostatic, hydrogen bonding and torsional parameters. Molecular modeling test cases of the force field are presented for a number of simple small molecules, as well as uracil and benzene dimerization, thymine-adenine and cytosine-guanine base pair formation, and adenosine/deoxyadenosine pseudorotation. Several DNA and RNA oligomers and DNA/RNA intercalation complexes with ethidium are also modeled with the force field. In all cases, the modeling results compare favorably with available experimental results. Additionally, conformational trends observed experimentally for nucleic acids by NMR and X-ray crystallographic techniques are reproduced. The modeling results for ethidium intercalation indicate a complex in which the favorable interactions are primarily van der Waals contacts, and in which electrostatic interactions are a relatively minor component. We feel the force field is particularly useful for molecular mechanics aided drug design, and an analysis of modeling results with respect to design of drugs which bind selectively to RNA is presented.     

The finite number of global motion patterns available to symmetric protein complexes

In PDB, more than half of the entries are structure complexes and of these complexes, most are symmetric, composed of identical subunits. Complex formation is the way through which larger structures and even molecular machines are assembled and built in nature. In this work, we apply group theory and carry out a comprehensive study of the global motion patterns of protein complexes of various symmetries. The work presents for the first time a comprehensive list of all the symmetric, aesthetically pleasing, global motion patterns available to complexes of cyclic, dihedral, tetrahedral, or octahedral symmetry. Our results clearly demonstrate that complexes with the same symmetry will have the same global motion patterns and thus may function in a similar way, and that there are only a finite number of global motion patterns available to symmetric complexes as the number of protein symmetry groups is effectively finite. The work complements our current understanding of the principle of complex formation that has been mostly structure‐based by providing novel dynamics‐based insights. Furthermore, as dynamics is closely tied to function, these motion patterns can provide global insights into the general functional mechanisms of protein complexes.     

Crystallization and initial X-ray diffraction characterization of complexes of FxFG nucleoporin repeats with nuclear transport factors

NTF2 and importin-beta are transport factors that mediate nuclear protein import and which interact with nuclear pore proteins (nucleoporins) during translocation from the cytoplasm to the nucleus through nuclear pore complexes. We employed a native gel electrophoresis method to assess the interaction of nucleoporin constructs that contain FxFG sequence repeats with NTF2 and truncation mutants of importin-beta to determine suitable fragments for crystallization. Based on these data, we obtained crystals of complexes between yeast NTF2 and a construct containing five FxFG nucleoporin repeats from the yeast nucleoporin Nsp1p and between a construct containing residues 1-442 of human importin-beta and the same nucleoporin construct. The yeast NTF2-nucleoporin crystals have trigonal symmetry and diffract past 2.8 A resolution using synchrotron radiation, whereas the importin-beta-nucleoporin complex crystals have P2(1)2(1)2 orthorhombic symmetry and diffract past 3.2 A resolution.     

On the mechanism of ATP synthesis in oxidative phosphorylation: A review

It is shown that the presently available evidence supports the existence of two entry points for water oxygen in the mitochondrial oxygen exchanges. This in turn provides support for the pseudorotation reaction mechanism of ATP synthesis which is the only mechanism of ATP synthesis proposed to date allowing for two entry points of water oxygen. It is also shown that the pseudorotation mechanism can resolve the apparent paradox of a P₁ ? H₂O exchange·separate from the reversal of phosphorylation yet dependent on the mechanism of P₁ activation. In addition an interpretation consistent with the experimental observations concerning As_i-induced stimulation of respiration and effects associated with oligomycin and aurovertin is shown to follow from the analysis of the oxygen exchanges. Implications of the pseudorotation mechanism for the mechanism of energy coupling in oxidative phosphorylation are discussed.     

Atomic-resolution STM structure of DNA and localization of the retinoic acid binding site

Single-molecule imaging by scanning tunnelling microscopy (STM) yields the atomic-resolution (0.6A) structure of individual B-type DNA molecules. The strong correlation between these STM structures and those predicted from the known base sequence indicates that sequencing of single DNA molecules using STM may be feasible. There is excellent agreement between the STM and X-ray structures, but subtle differences exist due to radial distortions. We show that the interactions of other molecules with DNA, their binding configurations, and the structure of these complexes can be studied at the single-molecule level. The anti-cancer drug retinoic acid (RA) binds selectively to the minor groove of DNA with up to 6 RA molecules per DNA turn and with the plane of the RA molecule approximately parallel to the DNA symmetry axis. Similar studies for other drug molecules will be valuable in the a priori evaluation of the effectiveness of anti-cancer drugs.     

On periodicities in metabolizing systems

Following a previous study by A. Weinberg, the author investigates periodical diffusion phenomena produced in a spherical cell by a simple coupled set of chemical reactions. The general solution even for a spherical cell does not possess spherical symmetry. It is found that periodic oscillations are possible with a frequency spectrum determined by a set of “eigenvalues”. However, these oscillations are all damped even if the system of coupled reactions which is responsible for them has non-damped solutions. Therefore, although very complex and highly asymmetrical configurations of concentrations may be thus produced in the cell, none of those configurations, except some possible centrally symmetric ones, is lasting.     

Configurations of metallocyclams and relevance to anti-HIV activity

Antiviral cyclam macrocycles block viral entry into cells by binding to the CXCR4 co-receptor. Cyclams bind transition metal ions strongly and can potentially form a range of trans (I-V) and cis configurations which may be recognised differently by co-receptor proteins. A survey of the CSD (crystallographic structural database) shows that the trans-III configuration is the most common in the solid state for complexes of cyclam itself. Other configurations can be induced by N-substitution or ternary complexation and by interaction with solvents in solution. We report X-ray structures for the square-planar trans-III complexes [Pd(cyclam)]Cl(2).2MeOH and the C-C linked dimer [Pd(2)(2,2'-bi-(1,4,8,11-tetraazacyclotetradecane))](ClO4)(4), in which the planes of the two cyclam rings are close to perpendicular (100.1 degrees ), and for tetra-N-benzyl-cyclam and its 5-coordinate Ni(II) complex [Ni(Bz(4)-cyclam)Cl]Cl which has the unusual trans-I configuration.     

A novel mirror-symmetry analysis approach for the study of macromolecular assemblies imaged by electron microscopy

Multivariate statistical symmetry analysis is widely employed in single-particle electron-microscopy studies for the detection of symmetry components within a set of noisy two-dimensional images. So far, this technique has been used to retrieve information from the analysis of end-on view oriented particles only. Here, we propose a method to detect symmetry components from side- and tilted-view oriented particles. This method is validated using a number of in silico generated as well as real datasets, can be used to analyze stoichiometrically heterogeneous datasets, and is useful for separating particle datasets with respect to their symmetry components. Additionally, translational components in lock-washer ring configurations can be detected. Most relevantly, this method represents a powerful tool for the characterisation of distinct symmetry components within multi-layered protein assemblies, and any putative symmetry mismatch between layers. Such configurations have often been postulated, though rarely observed directly, and are thought to have a crucial role in conferring dynamicity to molecular machineries like nucleic acid packaging motors, ClpAP/ClpXP proteases, flagellar motors and the F1/F0 ATPase.     

ATTRACT-EM: A New Method for the Computational Assembly of Large Molecular Machines Using Cryo-EM Maps

Many of the most important functions in the cell are carried out by proteins organized in large molecular machines. Cryo-electron microscopy (cryo-EM) is increasingly being used to obtain low resolution density maps of these large assemblies. A new method, ATTRACT-EM, for the computational assembly of molecular assemblies from their components has been developed. Based on concepts from the protein-protein docking field, it utilizes cryo-EM density maps to assemble molecular subunits at near atomic detail, starting from millions of initial subunit configurations. The search efficiency was further enhanced by recombining partial solutions, the inclusion of symmetry information, and refinement using a molecular force field. The approach was tested on the GroES-GroEL system, using an experimental cryo-EM map at 23.5 Å resolution, and on several smaller complexes. Inclusion of experimental information on the symmetry of the systems and the application of a new gradient vector matching algorithm allowed the efficient identification of docked assemblies in close agreement with experiment. Application to the GroES-GroEL complex resulted in a top ranked model with a deviation of 4.6 Å (and a 2.8 Å model within the top 10) from the GroES-GroEL crystal structure, a significant improvement over existing methods.     

Combinatorics of giant hexagonal bilayer hemoglobins

The paper discusses combinatorial and probabilistic models allowing to characterize various aspects of spacial symmetry and structural heterogeneity of the giant hexagonal bilayer hemoglobins (HBL Hb). Linker-dodecamer configurations of HBL are described for two and four linker types (occurring in the two most studied HBL Hb of Arenicola and Lumbricus, respectively), and the most probable configurations are found. It is shown that, for HBL with marked dodecamers, the number of 'normal-marked' pairs of dodecamers in homological position follows a binomial distribution. The group of symmetries of the dodecamer substructure of HBL is identified with the dihedral group D6. Under natural symmetry assumptions, the total dipole moment of the dodecamer substructure of HBL is shown to be zero. Biological implications of the mathematical findings are discussed.