The Implementation of the Iterative Diagonalization Scheme and ab initio Molecular Dynamics Simulation with the LAPW Method

Abstract

A new ab initio molecular dynamics method based on the full-potential linearized-augmented-plane-wave (LAPW) basis set has been implemented. The LAPW basis set has been successfully employed for systems containing localized electrons such as first row atoms and transition metals. In our implementation of the LAPW-MD scheme, iterative residual minimization algorithm is used to solve the electronic states problem. The atoms are moved according to forces derived from the Hellman–Feynman theorem and incomplete basis set correction terms. The performance of the program is further enhanced by parallelization. We will discuss technical details of the program implementation and present results obtained from this code to the equilibrium structures and vibrational properties of simple diatomic molecules.     

Visualization of protein-nucleic acid interactions in a virus. Refined structure of intact tobacco mosaic virus at 2.9 A resolution by X-ray fiber diffraction

The structure of tobacco mosaic virus (TMV) has been determined by fiber diffraction methods at 2.9 A resolution, and refined by restrained least-squares to an R-factor of 0.096. Protein-nucleic acid interactions are clearly visible. The final model contains all of the non-hydrogen atoms of the RNA and the protein, 71 water molecules, and two calcium-binding sites. Viral disassembly is driven by electrostatic repulsions between the charges in two carboxyl-carboxylate pairs and a phosphate-carboxylate pair. The phosphate-carboxylate pair and at least one of the carboxyl-carboxylate pairs appear to be calcium-binding sites. Nucleotide specificity, enabling TMV to recognize its own RNA by a repeating pattern of guanine residues, is provided by two guanine-specific hydrogen bonds in one of the three base-binding sites.     

Constraints and missing reactions in the urea cycle.

The stoichiometric relations in a series of biochemical reactions are summarized by a stoichiometric number matrix (with a column for each reaction) and a conservation matrix (with a row for each constraint). These two matrices for a series or cycle of biochemical reactions are related because the columns of the stoichiometric number matrix are in the null space of the conservation matrix, and the rows of the transpose of the conservation matrix are in the null space of the transpose of the stoichiometric number matrix. The conservation matrix for a system of biochemical reactions is of interest because it shows the nature of the constraints in addition to the conservation of atoms and groups. Constraints beyond those for the conservation of atoms and groups indicate "missing reactions" that do not occur because the enzymes involved couple reactions that could occur and still conserve atoms and groups. The interpretation of conservation matrices and stoichiometric matrices for a reaction system is complicated by the fact that they are not unique. However, their row-reduced forms are unique, as are their dimensions, which represent the number of reactants and number of independent reactions. Two matrices that look different contain the same information if they have the same row-reduced form. The urea cycle, which involves five enzyme-catalyzed reactions, and its net reaction are discussed in terms of the linear constraints produced by enzyme catalysis. A procedure to obtain a set of conservation equations that will yield the correct net reaction is described.     

The contribution of phosphate-phosphate repulsions to the free energy of DNA bending

DNA bending is important for the packaging of genetic material, regulation of gene expression and interaction of nucleic acids with proteins. Consequently, it is of considerable interest to quantify the energetic factors that must be overcome to induce bending of DNA, such as base stacking and phosphate–phosphate repulsions. In the present work, the electrostatic contribution of phosphate–phosphate repulsions to the free energy of bending DNA is examined for 71 bp linear and bent-form model structures. The bent DNA model was based on the crystallographic structure of a full turn of DNA in a nucleosome core particle. A Green's function approach based on a linear-scaling smooth conductor-like screening model was applied to ascertain the contribution of individual phosphate–phosphate repulsions and overall electrostatic stabilization in aqueous solution. The effect of charge neutralization by site-bound ions was considered using Monte Carlo simulation to characterize the distribution of ion occupations and contribution of phosphate repulsions to the free energy of bending as a function of counterion load. The calculations predict that the phosphate–phosphate repulsions account for ~30% of the total free energy required to bend DNA from canonical linear B-form into the conformation found in the nucleosome core particle.     

Amide protein exchange and surface conformation of the basic pancreatic trypsin inhibitor in solution. Studies with two-dimensional nuclear magnetic resonance

Dickerson and his colleagues have described the structure of the DNA dodecamer C-G-C-G-A-A-T-T-C-G-C-G in the B form at a level that shows clearly several aspects of some base sequence-dependent departures from the ideal, regular helical structure of B-DNA. I argue that the detailed conformation is a consequence of simple steric repulsive forces between purine bases in consecutive base-pairs but on opposite backbones. These repulsions are a consequence of the “propeller twist” of the base-pairs, together with the larger size of the purine bases, and they may occur in either the major or the minor groove. The argument is conducted in terms of the structural mechanics of a deformable elastic system. These repulsive forces between the base-pairs are resisted by stresses in the helical backbones, which may be studied quantitatively via the variation in torsion angles δ along the backbones, at the points where the sugar rings are connected. There is also a correlation between the cross-chain purine repulsions and the perturbations in helical twist angle between successive base-pairs. The work suggests some comments on the proposed “alternating B” form, the Z form and the A form of DNA.     

Dental homologies in lamniform sharks (Chondrichthyes: Elasmobranchii).

The dentitions of lamniform sharks are said to exhibit a unique heterodonty called the "lamnoid tooth pattern." The presence of an inflated hollow "dental bulla" on each jaw cartilage allows the recognition of homologous teeth across most modern macrophagous lamniforms based on topographic correspondence through the "similarity test." In most macrophagous lamniforms, three tooth rows are supported by the upper dental bulla: two rows of large anterior teeth followed by a row of small intermediate teeth. The lower tooth row occluding between the two rows of upper anterior teeth is the first lower anterior tooth row. Like the first and second lower anterior tooth rows, the third lower tooth row is supported by the dental bulla and may be called the first lower intermediate tooth row. The lower intermediate tooth row occludes between the first and second upper lateral tooth rows situated distal to the upper dental bulla, and the rest of the upper and lower tooth rows, all called lateral tooth rows, occlude alternately. Tooth symmetry cannot be used to identify their dental homology. The presence of dental bullae can be regarded as a synapomorphy of Lamniformes and this character is more definable than the "lamnoid tooth pattern." The formation of the tooth pattern appears to be related to the evolution of dental bullae. This study constitutes the first demonstration of supraspecific tooth-to-tooth dental homologies in nonmammalian vertebrates.     

Computer modeling and folding of four-helix bundles

In the context of simplified models of globular proteins, the requirements for the unique folding to a four-helix bundle have been addressed through a new Monte Carlo procedure. In particular, the relative importance of secondary versus tertiary interactions in determining the nature of the folded structure is examined. Various cases spanning the extremes where tertiary interactions completely dominate to that where tertiary interactions are negligible have been explored. Not surprisingly, the folding to unique four-helix bundles is found to depend on an adequate balance of the secondary and tertiary interactions. Moreover, because the simplified model is composed of spheres representing α-carbons and side chains, the geometry of the latter being based on small real amino acids, the role played by the side chains, and the problems associated with packing and hard-core repulsions, are considered. Also, possible folding intermediates and their relationship with the experimentally observed molten globule state are explored. From these studies, a general set of rules is extracted which should aid in the further design of more detailed protein models adequate to more fully investigate the protein folding problem. Finally, the relationship between our conclusions and experimental work with specifically designed sequences is briefly discussed. © 1993 Wiley-Liss, Inc.     

The rearranged genetic code and its implications in evolution and biochemistry

We rearrange the genetic code and present a table of codons. The chemical properties of the amino acids coded by codons, and the evolutionary trend of codons are well reflected in the order of this table, from which two rules can be drawn: (1) the polarity/non-polarity and hydrophilicity/hydrophobicity of amino acids coded for by codons alternate row by row in the table; (2) in general, the lower down in the table, the earlier the codons are in terms of evolution.     

Component communities of parasites in the grayling Thymallus thymallus (L.) (Salmoniformes, Thymallidae) and the minnow Phoxinus phoxinus (L.) (Cypriniformes, Cyprinidae) from the Pechora River

Component communities of parasites of Thymallus thymallus and Phoxinus phoxinus are described. The communities differ in the number of species and in the number of dominate species, which is one in P. phoxinus and usually two in T. thymallus. In the first case the dominate species is allogenic, while in the second case dominate species are autogenic. Values of the species diversity indexes are also different for these communities. The differences between parasite communities of T. thymallus and P. phoxinus underline positions of these hosts in hydrobiocenose. Species specialists take first place in the parasite communities both of the hosts, that is characteristic for the parasite communities of the fishes from the boreal submountain faunistic complex. Parasite communities in both of the hosts consist of three groups of species discriminated by the ratio of their biomasses, that suggests forming of the groups by a coordination of the species biomasses.     

Bending Rigidities and Interdomain Forces in Membranes with Coexisting Lipid Domains

To precisely quantify the fundamental interactions between heterogeneous lipid membranes with coexisting liquid-ordered (Lo) and liquid-disordered (Ld) domains, we performed detailed osmotic stress small-angle x-ray scattering experiments by exploiting the domain alignment in raft-mimicking lipid multibilayers. Performing a Monte Carlo-based analysis allowed us to determine with high reliability the magnitude and functional dependence of interdomain forces concurrently with the bending elasticity moduli. In contrast to previous methodologies, this approach enabled us to consider the entropic undulation repulsions on a fundamental level, without having to take recourse to crudely justified mean-field-like additivity assumptions. Our detailed Hamaker-coefficient calculations indicated only small differences in the van der Waals attractions of coexisting Lo and Ld phases. In contrast, the repulsive hydration and undulation interactions differed significantly, with the latter dominating the overall repulsions in the Ld phase. Thus, alignment of like domains in multibilayers appears to originate from both, hydration and undulation repulsions.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

Accuracy of bristle placement on a leg segment in Drosophila melanogaster

Bristle positions in two rows of bristles on the basitarsus of the second leg of the fruitfly Drosophila melanogaster were analyzed in order to determine the accuracy of bristle placement within these rows. Within each row the positions of the two terminal bristles were found to be approximately equally variable, and positional variability was found to increase toward the middle of each row. Rows having fewer bristles manifested more positional variability in their midsection. These results are interpreted in terms of a possible bristle spacing mechanism involving repulsive forces between mobile bristle cells.     

Morphology,Ontogeny, and Molecular Phylogeny of Two Freshwater Species of Deviata (Ciliophora,Hypotrichia) from Southern China

The morphology and partial morphogenesis of two freshwater hypotrichous ciliates, Deviata brasiliensis Siqueira‐Castro et al., 2009 and Deviata rositae Küppers et al., 2007, isolated from southern China, were investigated using live observation and protargol staining. Our populations resemble the original ones in terms of their live characters and ciliary patterns. The main determinable morphogenetic features of D. brasiliensis basically correspond with those of the type population. However, the origin of anlage V for either proter or opisthe is ambiguous: whether anlage V for the proter originates from parental frontoventral row 2 (the same as in the original population) or parental frontoventral row 3 (the same as in Deviata abbrevescens) or even de novo is not clear; the anlage V for the opisthe is possibly derived from frontoventral row 3 and further migrates to frontoventral row 2, like that in D. abbrevescens. In addition, the SSU rRNA gene was first sequenced for both species. Molecular phylogenetic analyses suggest that the genus Deviata is non‐monophyletic and has a close relationship with Perisincirra paucicirrata.     

Combination of extended X-ray absorption fine structure spectroscopy with lipidic cubic phases for the study of cation binding in bacteriorhodopsin

We have performed a quantitative X-ray absorption fine structure analysis of bacteriorhodopsin in purple membrane patches and in lipidic cubic phases regenerated with Mn²⁺. Lipidic cubic phases and purple membrane results have been compared, demonstrating that the lipidic cubic phase process does not introduce relevant distortions in the local geometry of the cation binding sites. For both samples, we have observed similarities for Mn²⁺ coordination in terms of type, number, and average distances of surrounding atoms, indicating a first coordination shell composed by 6 O atoms, and 3/4 C atoms located in the second coordination shell.     

The structure and development of a somatotopic map in crickets: The cercal afferent projection

A group of club-shaped sensilla called clavate hairs, located on the cercus of crickets (Acheta domesticus), are part of a specialized sensory system which monitors the orientation of a cricket with respect to the earth's gravitational field. The clavate hairs occur in rows which run proximodistally on the medial aspect of the cercus and each hair can be identified by specifying which row a hair is in and what position it is in within the row. The array of hairs is constant from individual to individual, and thus each hair can be identified in each specimen. The soma of a single bipolar sensory neuron is located in the integument below each hair; its dendrite projects into the hair and its axon projects to a well-defined area of the abdominal ganglion called the cercal glomerulus. All of the neurons within a row project to a particular area of the cercal glomerulus and different rows project to different areas within the glomerulus. Within a row neurons project to slightly different parts of the target area for that row. Thus a highly ordered projection pattern is produced which is tentatively called somatotopic. The development of the first clavate neuron to appear was examined from the first instar to the adult instar. The terminal arborization of this first hair was in no way unusual and its growth paralleled ganglion growth, maintaining a relatively constant position with respect to ganglion coordinates. A second clavate neuron behaved similarly, its arborization was fully formed when the receptor first appeared in the third instar and merely enlarged as the ganglion grew.     

More Parsimonious Linar-By-Linear Associatin Model in the Analysis of Cross-Classifications Having Ordered Categories

For the analysis of cross-classifications having ordered categories, this paper proposes a model which is more parsimonious than the linear-by-linear association (LL) model (that is, which can be described in terms of fewer parameters than the LL model). In a special case, this model is more parsimonious than the uniform association (U) model. Under this model, the expected frequency on a log scale is a linear function of row and column variables for fixed column and row variables, respectively. For the well-known operation and dumping severity data, the parsimonious U model proposed here fits well, and new interpretations are added.     

Sauropod tracks of the Cameros Basin (Spain): Identification, trackway patterns and changes over the Jurassic-Cretaceous

Sauropod tracks make up only about 2% of the Cameros Basin ichnocenosis, but they are present over the entire time span represented by the Cameros sediments. The makers of these tracks are identified in terms of their associated trackway pattern as either wide or narrow-gauge morphotypes. Narrow-gauge trackways dominate the Tithonian-Berriasian interval. Wide-gauge trackways become notably more common after the Berriasian, although narrow-gauge trackways are still present and dominate the Cameros ecosystems even during the Aptian. At this time, an interesting equilibrium between titanosauriform and non-titanosauriform sauropod trackways is evident, although the latter are somewhat more common. A review of the Iberian sauropod bone record suggests that Turiasauria + Euhelopidae, Rebbachisauridae and Titanosauriformes are the three groups mainly responsible for the Cameros Basin sauropod ichnocenosis.