A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units

A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π _i=1 ⁿ (2i−3) possible rooted binary phylogenies and the π _i=1 ⁿ⁻¹ (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.     

Density functional theory study of the potassium complexation of an unsymmetrical 1,3-alternate calix[4]-crown-5-N-azacrown-5 bearing two different crown rings

Theoretical studies of an unsymmetrical calix[4]-crown-5-N-azacrown-5 (1) in a fixed 1,3-alternate conformation and the complexes 1·K⁺(a), 1·K⁺(b), 1·K⁺(c) and 1·K⁺K⁺ were performed using density functional theory (DFT) at the B3LYP/6-31G* level. The fully optimized geometric structures of the free macroligand and its 1:1 and 1:2 complexes, as obtained from DFT calculations, were used to perform natural bond orbital (NBO) analysis. The two main types of driving force metal–ligand and cation–π interactions were investigated. NBO analysis indicated that the stabilization interaction energies (E ₂) for O…K⁺ and N…K⁺ are larger than the other intermolecular interactions in each complex. The significant increase in electron density in the RY* or LP* orbitals of K⁺ results in strong host–guest interactions. In addition, the intermolecular interaction thermal energies (ΔE, ΔH, ΔG) were calculated by frequency analysis at the B3LYP/6-31G* level. For all structures, the most pronounced changes in the geometric parameters upon interaction are observed in the calix[4]arene molecule. The results indicate that both the intermolecular electrostatic interactions and the cation–π interactions between the metal ion and π orbitals of the two pairs that face the inverted benzene rings play a significant role.     

Computational (DFT and TD DFT) study of the electron structure of the tautomers/conformers of uridine and deoxyuridine and the processes of intramolecular proton transfers

Six uridine and six deoxyuridine isomers were studied at the B3LYP and TD B3LYP theoretical level and 6–31+G(d) basis function. The stability and the excited states of the isomers were studied in order to clarify some known experimental data. It was established that the rotation of the oxo uracil ring in uridine is energetically more likely to occur in the excited state than in the ground state, driven by the bright ¹ ππ* state and the dark charge transfer ¹nπ* state. Very high energy barriers (on the S_o) were found for thermal intramolecular proton transfer processes.     

Studying Genetic Code by a Matrix Approach

Following Petoukhov and his collaborators, we use two length n zero-one sequences, α and β, to represent a length n genetic sequence ((a) || (b)){\alpha\choose\beta} so that the columns of ((a) || (b)){\alpha\choose\beta} have the following correspondence with the nucleotides: C ~ (0 || 0)C\sim{0\choose0} , U ~ (1 || 0)U\sim{1\choose0} , G ~ (1 || 1)G\sim{1\choose1} , A ~ (0 || 1)A\sim{0\choose1} . Using the Gray code ordering to arrange α and β, we build a 2 ⁿ ×2 ⁿ matrix C _n including all the 4 ⁿ length n genetic sequences. Furthermore, we use the Hamming distance of α and β to construct a 2 ⁿ ×2 ⁿ matrix D _n . We explore structures of these matrices, refine the results in earlier papers, and propose new directions for further research.     

A partial digest approach to restriction site mapping

We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets ofn points are homeometric if the multiset ofn(n−1)/2 distances they determine are the same. Since experimental data contain errors, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyse the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit ofr=Θ(1/n ²) beyond which our technique becomes infeasible. Through simulations, we establish that our technique is robust enough to reconstruct data with relative errors of up to 7.0% in the measured fragment lengths for typical problems, which appears sufficient for certain biological applications.     

Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV)

In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV’s revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ—(Δρ_σ) and π-networks (Δρ_π). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty r_{H - O}^* \rho_{H - O}^* orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρ_π), is based on the transfer of electron density from the π—orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. ETS-NOCV allowed to conclude that the σ(O---HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔE_elstat) is equally as important as orbital interaction term (ΔE_orb). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O---HO bonds, neither qualitative nor quantitative.     

Microsolvation of aminoethanol: a study using DFT combined with QTAIM

The microsolvation of aminoethanol (AE) with one, two, three or four water molecules was investigated using a density functional theory (DFT) approach. Quantum theory of atoms in molecules (QTAIM) analyses were employed to elucidate the hydrogen-bonding characteristics of AE–(H₂O) _n (n = 1–4) complexes. The results showed that AE tends to break its intramolecular OH^AE···N^AE hydrogen bond (H-bond) upon microsolvation and form intermolecular H-bonds with water molecules, while complexes that retain the intramolecular OH^AE···N^AE H-bond show reduced stabilities. The intermolecular H-bond that forms between the nitrogen atom of AE and the hydroxyl of a water molecule is the strongest one for the most stable AE–(H₂O) _n (n = 1–4) complexes, and as n increases from 1 to 4 they grow stronger. The partial covalent character of this H-bond was confirmed by QTAIM analyses. Many-body interaction analysis showed that the relaxation energies and two- and three-body energies make significant contributions to the binding energies of the complexes.     

Species abundance distributions in neutral models with immigration or mutation and general lifetimes

We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate λ. Thus, the population size is a homogeneous, binary Crump–Mode–Jagers process (which is not necessarily a Markov process). We assume that types are clonally inherited. We consider two classes of speciation models in this setting. In the immigration model, new individuals of an entirely new species singly enter the population at constant rate μ (e.g., from the mainland into the island). In the mutation model, each individual independently experiences point mutations in its germ line, at constant rate θ. We are interested in the species abundance distribution, i.e., in the numbers, denoted I _n (k) in the immigration model and A _n (k) in the mutation model, of species represented by k individuals, k = 1, 2, . . . , n, when there are n individuals in the total population. In the immigration model, we prove that the numbers (I _t (k); k ≥ 1) of species represented by k individuals at time t, are independent Poisson variables with parameters as in Fisher’s log-series. When conditioning on the total size of the population to equal n, this results in species abundance distributions given by Ewens’ sampling formula. In particular, I _n (k) converges as n → ∞ to a Poisson r.v. with mean γ/k, where γ : = μ/λ. In the mutation model, as n → ∞, we obtain the almost sure convergence of n ⁻¹ A _n (k) to a nonrandom explicit constant. In the case of a critical, linear birth–death process, this constant is given by Fisher’s log-series, namely n ⁻¹ A _n (k) converges to α ^k /k, where α : = λ/(λ + θ). In both models, the abundances of the most abundant species are briefly discussed.     

Frequency of Antibiotic Resistance in a Swine Facility 2.5 Years After a Ban on Antibiotics

The addition of antibiotics to livestock feed has contributed to the selection of antibiotic-resistant bacteria in concentrated animal feeding operations and agricultural ecosystems. The objective of this study was to assess the occurrence of resistance to chlortetracycline and tylosin among bacterial populations at the Swine Complex of McGill University (Province of Quebec, Canada) in the absence of antibiotic administration to pigs for 2.5 years prior to the beginning of this study. Feces from ten pigs born from the same sow and provided feed without antibiotic were sampled during suckling (n = 6 for enumerations, n = 10 for PCR), weanling (n = 10 both for PCR and enumerations), growing (n = 10 both for PCR and enumerations), and finishing (n = 10 both for PCR and enumerations). The percentage of chlortetracycline-resistant anaerobic bacterial populations (Tet^R) was higher than that of tylosin-resistant anaerobic bacterial populations (Tyl^R) at weanling, growing, and finishing. Prior to the transportation of animals to the slaughterhouse, resistant populations varied between 6.5 and 9.4 Log colony-forming units g humid feces⁻¹. In all pigs, tet(L), tet(O), and erm(B) were detected at suckling and weanling, whereas only tet(O) was detected at growing and finishing. The abundance of tet(O) was similar between males and females at weanling and growing and reached 5.1 × 10⁵ and 5.6 × 10⁵ copies of tet(O)/ng of total DNA in males and females, respectively, at finishing. Results showed high abundances and proportions of Tet^R and Tyl^R anaerobic bacterial populations, as well as the occurrence of tet and erm resistance genes within these populations despite the absence of antibiotic administration to pigs at this swine production facility since January 2007, i.e., 2.5 years prior to the beginning of this study. This work showed that the occurrence of bacterial resistance to chlortetracycline and tylosin is high at the Swine Complex of McGill University.     

Recrafting the neighbor-joining method

Background  

The neighbor-joining method by Saitou and Nei is a widely used method for constructing phylogenetic trees. The formulation of the method gives rise to a canonical Θ(n ³) algorithm upon which all existing implementations are based.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

Antitumor activity of bent metallocenes: electronic structure analysis using DFT computations

The antitumor activities of bent metallocenes [Cp–M–Cp]²⁺ (M = Ti, V, Nb, Mo) and complexes of them with guanine, adenine, thymine and cytosine nucleotides have been probed using electronic structure calculations. DFT/BP86 calculations have revealed that the bent metallocene–nucleotide interaction strongly depends on the stability of the hydrolyzed form of the bent metallocene dichloride [Cp₂M]²⁺ species, and in turn the stability of the [Cp₂M]²⁺ species strongly depends on the electronic structure of [Cp₂M]²⁺. Detailed electronic structure and Walsh energy analyses have been carried out for the hydrolyzed forms of four [Cp–M–Cp]²⁺ (M = Ti, V, Nb, Mo) species to find out why the bent structure is unusually stable. Energy changes that occur during the bending process in frontier molecular orbitals as well as the p(π)–d(π) overlap have been invoked to account for the anticipated antitumor activities of these species. The bonding situation and the interactions in bent metallocene–nucleotide adducts were elucidated by fragment analysis. Of the four nucleotides complexed with the four bent metallocenes, adenine and guanine show better binding abilities than the other two nucleotides. Metallocenes of second-row transition metals exhibit better binding with pyrimidine-base nucleotides. In particular, the Lewis acidic bent metallocenes interact strongly with nucleotides. The antitumor activity is directly related to the binding strength of the bent metallocene with nucleotide adducts, and the computed interaction energy values correlate very well with the experimentally observed antitumor activities.     

Structural characterization of a carbon monoxide adduct of a heme–DNA complex

Abstract  

The structure of a carbon monoxide (CO) adduct of a complex between heme and a parallel G-quadruplex DNA formed from a single repeat sequence of the human telomere, d(TTAGGG), has been characterized using ¹H and ¹³C NMR spectroscopy and density function theory calculations. The study revealed that the heme binds to the 3′-terminal G-quartet of the DNA though a π–π stacking interaction between the porphyrin moiety of the heme and the G-quartet. The π–π stacking interaction between the pseudo-C ₂-symmetric heme and the C ₄-symmetric G-quartet in the complex resulted in the formation of two isomers possessing heme orientations differing by 180° rotation about the pseudo-C ₂ axis with respect to the DNA. These two slowly interconverting heme orientational isomers were formed in a ratio of approximately 1:1, reflecting that their thermodynamic stabilities are identical. Exogenous CO is coordinated to heme Fe on the side of the heme opposite the G-quartet in the complex, and the nature of the Fe–CO bond in the complex is similar to that of the Fe–CO bonds in hemoproteins. These findings provide novel insights for the design of novel DNA enzymes possessing metalloporphyrins as prosthetic groups.     

Computational experience with a parallel algorithm for tetrangle inequality bound smoothing

Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( ₄ ⁿ ) quadruples requires O(n ⁴) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n ³ log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.     

On the existence of MHn species with M=Al, Ga and n=4, 5, 6. Computational study of structures, stabilities and bonding

Based on second-order perturbation theory (MP2) predictions with large 6-311++G(3df, 3pd) basis set we have reviewed the possible structures and stabilities of a series of neutral MH_n(M=Al, Ga; n=4, 5, 6) species. For AlH₄ and AlH₅, our results confirm the previous theoretical findings, which indicate the dihydrogen C_s complexes (²A′) AlH₂(H₂) and (¹A′) AlH₃(H₂), respectively, as the lowest energy isomers. We found, similarly, C_s (²A′) GaH₂(H₂) and (¹A′) GaH₃(H₂) van der Waals complexes as the most stable species of the gallium analogues GaH₄ and GaH₅. The calculated H₂ dissociation energies (D_e) for AlH₂(H₂) and AlH₃(H₂) are of the order 1.8–2.5 kcalmol¹, whereas this range of values for GaH₂(H₂) and GaH₃(H₂) is 1.4–1.8 kcalmol¹ . Symmetry-adapted perturbation theory (SAPT) was used to analyze the interaction energies of these dihydrogen complexes (for n=5) to determine why the Ga species show a smaller binding energy than the Al species. The SAPT partitioning of the interaction energy showed significant differences between AlH₃(H₂) and GaH₃(H₂), resulting from the much stronger “hydride” character of the aluminum species. The experimental observation of AlH₂(H₂) and AlH₃(H₂), and likely GaH₃(H₂), via low-temperature matrix isolation has been reported recently by Pullumbi et al. and Andrews et al., supporting the theoretical predictions. For n=6, we found the degenerate C₂(²A) and C_s(²A′) MH₂(H₂)₂ “double H₂” type van der Waals complexes as the lowest energy species for both M=Al and Ga.Electronic Supplementary Material Supplementary material is available for this article at     

Minimum sample sizes for identifying chromosomal fragile sites from individuals: Monte Carlo estimation

A Monte Carlo simulation procedure was used to estimate the exact level of the standardized X ² test statistic (X _s ²) for randomness in the FSM methodology for the identification of fragile sites from chromosomal breakage data for single individuals. A random-number generator was used to simulate 10 000 chromosomal breakage data sets, each corresponding to the null hypothesis of no fragile sites for numbers of chromosomal breaks (n) from 1 to 2000 and at three levels of chromosomal band resolution (k). The reliability of the test was assessed by comparisons of the empirical and nominal α levels for each of the corresponding values of n and k. These analyses indicate that the sparse and discrete nature of chromosomal breakage data results in large and unpredictable discrepancies between the empirical and nominal α levels when fragile site identifications are based on small numbers of breaks (n < 0.5 k). With n≥ 0.5 k, the distribution of X _s ² appears to be stable and non-significant differences in the empirical and nominal α levels are generally obtained. These results are inherent to the nature of the data and are, therefore, relevant to any statistical model for the identification of fragile sites from chromosomal breakage data. For FSM identification of fragile sites at α = 0.05, we suggest that n≥ 0.5 k is the minimum reliable number of mapped chromosomal breaks per individual. Received: 28 April 1997 / Accepted: 1 July 1997     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Sex-related differences in thermoregulatory responses while wearing protective clothing

This study examined the thermoregulatory responses of men (group M) and women (group F) to uncompensable heat stress. In total, 13 M [mean (SD) age 31.8 (4.7) years, mass 82.7 (12.5) kg, height␣1.79␣(0.06) m, surface area to mass ratio 2.46␣(0.18) m² · kg⁻¹ · 10⁻², Dubois surface area 2.01 (0.16) m², %body fatness 14.6 (3.9)%, V˙O_2peak 49.0 (4.8) ml · kg⁻¹ · min⁻¹] and 17 F [23.2 (4.2) years, 62.4 (7.7) kg, 1.65 (0.07) m, 2.71 (0.14) m² · kg⁻¹ · 10⁻², 1.68 (0.13) m², 20.2 (4.8)%, 43.2 (6.6) ml · kg⁻¹ · min⁻¹, respectively] performed light intermittent exercise (repeated intervals of 15 min of walking at 4.0 km · h⁻¹ followed by 15 min of seated rest) in the heat (40°C, 30% relative humidity) while wearing nuclear, biological, and chemical protective clothing (0.29 m² ·°C · W⁻¹ or 1.88 clo, Woodcock vapour permeability coefficient 0.33 i _m). Group F consisted of eight non-users and nine users of oral contraceptives tested during the early follicular phase of their menstrual cycle. Heart rates were higher for F throughout the session reaching 166.7 (15.9) beats · min⁻¹ at 105 min (n = 13) compared with 145.1 (14.4) beats · min⁻¹ for M. Sweat rates and evaporation rates from the clothing were lower and average skin temperature () was higher for F. The increase in rectal temperature (T _re) was significantly faster for the F, increasing 1.52 (0.29)°C after 105 min compared with an increase of 1.37 (0.29)°C for M. Tolerance times were significantly longer for M [142.9 (24.5) min] than for F [119.3 (17.3) min]. Partitional calorimetric estimates of heat storage (S) revealed that although the rate of S was similar between genders [42.1 (6.6) and 46.1 (9.7) W · m⁻² for F and M, respectively], S expressed per unit of total mass was significantly lower for F [7.76 (1.44) kJ · kg⁻¹] compared with M [9.45 (1.26) kJ · kg⁻¹]. When subjects were matched for body fatness (n = 8 F and 8 M), tolerance times [124.5 (14.7) and 140.3 (27.4) min for F and M, respectively] and S [8.67 (1.44) and 9.39 (1.05) kJ · kg⁻¹ for F and M, respectively] were not different between the genders. It was concluded that females are at a thermoregulatory disadvantage compared with males when wearing protective clothing and exercising in a hot environment. This disadvantage can be attributed to the lower specific heat of adipose versus non-adipose tissue and a higher percentage body fatness. Accepted: 31 October 1997     

Theoretical study on the structural,vibrational, and thermodynamic properties of the (Br<Subscript>2</Subscript>GaN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–4) clusters

The molecular geometries, vibrational properties, and thermodynamic properties of the clusters (Br₂GaN₃) _n (n = 1–4) were studied at the B3LYP/6-311+G* level. The optimized clusters (Br₂GaN₃) _n (n = 2–4) were all found to possess a cyclic structure consisting of Ga atoms bridged by the α-nitrogen of the azide groups. A discussion of the relationships between the geometrical parameters and the degree of oligomerization n is provided. Features in the IR spectra were assigned by vibrational analysis. Trends in thermodynamic properties with temperature and degree of oligomerization n are discussed. Thermodynamic analysis of the gas-phase reaction showed that the formation of the clusters (Br₂GaN₃) _n (n = 2–4) is thermodynamically favorable considering the enthalpies at 298.2 K. The calculated results for the Gibbs free energies were negative, which indicates that the oligomerizations can occur spontaneously at 298.2 K.