Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC.

An approximate Bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure

There is great interest in using amplified fragment length polymorphism (AFLP) markers because they are inexpensive and easy to produce. It is, therefore, possible to generate a large number of markers that have a wide coverage of species genotnes. Several statistical methods have been proposed to study the genetic structure using AFLP's but they assume Hardy-Weinberg equilibrium and do not estimate the inbreeding coefficient, F-IS. A Bayesian method has been proposed by Holsinger and colleagues that relaxes these simplifying assumptions but we have identified two sources of bias that can influence estimates based on these markers: (i) the use of a uniform prior on ancestral allele frequencies and (ii) the ascertainment bias of AFLP markers. We present a new Bayesian method that avoids these biases by using an implementation based on the approximate Bayesian computation (ABC) algorithm. This new method estimates population-specific F-IS and F-ST values and offers users the possibility of taking into account the criteria for selecting the markers that are used in the analyses. The software is available at our web site (http://www-leca.uif-grenoble.fi-/logiciels.htm). Finally, we provide advice on how to avoid the effects of ascertainment bias.

ONeSAMP: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, ONeSAMP that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. ONeSAMP requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. ONeSAMP provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of ONeSAMP with an example data set from a re-introduced population of ibex Capra ibex.

Comparative evaluation of a new effective population size estimator based on approximate Bayesian computation

We describe and evaluate a new estimator of the effective population size (N-e), a critical parameter in evolutionary and conservation biology. This new "SummStat" N-e. estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N-e. Simulations of a Wright-Fisher population with known N-e show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N-e values. We also address the paucity of information about the relative performance of N-e estimators by comparing the SUMMStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated rising initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and Ne less than or equal to 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N-e. The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any, potentially informative summary statistic from Population genetic data.

Metal complexes of a tetraazacyclophane: solution and molecular modelling studies

An alternative synthetic approach to yield the compound 2,3,5,6,8,9,11,14-octahydrobenzo[1][ 1,4,7,10]tetraazacyclotetradecine (bz[14]N-4) is presented. The protonation constants of bz[14]N-4 and the stability constants of its complexes with Ni2+, Cu2+, Zn2+, Cd2+, Pb2+ were determined in H2O at 25degreesC with ionic strength 0.10 mol dm(-3) in KNO3 and they were compared with structurally related macrocycles cyclam (1,4,8,11-tetraazacyclotetradecane) and cyclen (1,4,7,10-tetraazacyclododecane). These studies indicate that only 1 : 1 ( M : L) species are formed in solution, and the ligand exhibits a high affinity for larger ions such as Cd2+ and Pb2+. The X-ray study of [bz[14]N4H3](3+) shows that an inclusion compound with a chloride counter-anion is formed through NH...Cl hydrogen bonds. Spectroscopic data in solution ( electronic and NMR spectra) showed that the macrocycle adopts a planar arrangement upon metal complexation. Molecular mechanics calculations reveal that in spite of the presence of the benzene ring in the macrocyclic framework this ligand can encapsulate metal ions with different stereo-electronic sizes in square planar arrangements. Our results indicate that the presence of the benzene ring in the backbone of the bz[14]N-4 confers a coordination behaviour intermediate between that of cyclam and cyclen.

Self assembly of a model amphiphilic phenylalanine peptide/polyethylene glycol block copolymer in aqueous solution

There has been great interest recently in peptide amphiphiles and block copolymers containing biomimetic peptide sequences due to applications in bionanotechnology. We investigate the self-assembly of the peptide-PEG amphiphile FFFF-PEG5000 containing the hydrophobic sequence of four phenylalanine residues conjugated to PEG of molar mass 5000. This serves as a simple model peptide amphiphile. At very low concentration, association of hydrophobic aromatic phenylalanine residues occurs, as revealed by circular dichroism and UV/vis fluorescence experiments. A critical aggregation concentration associated with the formation of hydrophobic domains is determined through pyrene fluorescence assays. At higher concentration, defined beta-sheets develop as revealed by FTIR spectroscopy and X-ray diffraction. Transmission electron microscopy reveals self-assembled straight fibril structures. These are much shorter than those observed for amyloid peptides, the finite length may be set by the end cap energy due to the hydrophobicity of phenylalanine. The combination of these techniques points to different aggregation processes depending on concentration. Hydrophobic association into irregular aggregates occurs at low concentration, well-developed beta-sheets only developing at higher concentration. Drying of FFFF-PEG5000 solutions leads to crystallization of PEG, as confirmed by polarized optical microscopy (POM), FTIR and X-ray diffraction (XRD). PEG crystallization does not disrupt local beta-sheet structure (as indicated by FTIR and XRD). However on longer lengthscales the beta-sheet fibrillar structure is perturbed because spheruilites from PEG crystallization are observed by POM. (C) 2009 Elsevier B.V. All rights reserved.

Self-assembly in aqueous solution of a modified amyloid beta peptide fragment

The self-assembly in films dried from aqueous solutions of a modified amyloid beta peptide fragment is studied. We focus on sequence A beta(16-20), KLVFF, extended by two alanines at the N-terminus to give AAKLVFF. Self-assembly into twisted ribbon fibrils is observed, as confirmed by transmission electron microscopy (TEM). Dynamic light scattering reveals the semi-flexible nature of the AAKLVFF fibrils, while polarized optical microscopy shows that the peptide fibrils crystallize after an aqueous solution of AAKLVFF is matured over 5 days. The secondary structure of the fibrils is studied by FT-IR, circular dichroism and X-ray diffraction (XRD), which provide evidence for beta-sheet structure in the fibril. From high resolution TEM it is concluded that the average width of an AAKLVFF fibril is (63 +/- 18) nm, indicating that these fibrils comprise beta-sheets with multiple repeats of the unit cell, determined by XRD to have b and c dimensions 1.9 and 4.4 nm with an a axis 0.96 nm, corresponding to twice the peptide backbone spacing in the antiparallel beta-sheet. (C) 2008 Elsevier B.V. All rights reserved.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

A novel copper(I) complex that is a monomeric single helix in solid state but a dimeric double helix in solution

Single helical [(CuL)-L-I]ClO4.12CH(2)Cl(2) (L=1:2 condensate of benzil dihydrazone and 2-acetylpyridine) unfolds and coils up in CH2Cl2 solution to generate double helical [(Cu2L2)-L-I](2+).

Mono- and binuclear bipyridyl derivatives of the Mo(eta(3)-C3H5)(CO)(2) fragment: structural studies and fluxionality in solution

New mono- and binuclear complexes of the Mo(eta(3)-C3H5)(CO)(2) fragment, containing bipyridyl ligands (2,2'-bpy, 4,4'-Me-2-2,2'-bpy) as chelates, and mono- (4-CNpy, 4-Mepy, NCMe, Br) or bidentate nitrogen ligands (4,4'-bpy, bipyridylethylene, pyrazine) as terminal or bridging ligands, respectively, were prepared. The binuclear complex [{Mo(eta(3)-C3H5)(CO)(2)(2,2'-bpy)}(2)(mu-4,4'-bpy)][PF6](2) (2) was shown by X-ray diffraction to assemble in the crystal forming large channels with a rectangular section. A longer bridge, such as bipyridylethylene, led to a different structure (3). 4-CNpy behaved as monodentate ligand (4), coordinating through the pyridine nitrogen as a terminal ligand. NMR spectroscopy studies showed that the complexes exhibited a fluxional behavior in solution, the endo and exo forms of the more symmetrical equatorial isomers being usually present and interconverting in solution. The solid state structures of the complexes revealed a preference for the more symmetrical equatorial isomer, with the two chelate ligands in trans positions in the binuclear species. The rings tended to become parallel in the organized crystal. (C) 2003 Elsevier B.V. All rights reserved.

Selectivity of bis(calix[4]diquinone) ionophores towards metal ions in solvent dimethylsulfoxide: a molecular mechanics and molecular dynamics study

Molecular modelling studies have been carried out on two bis(calix[4]diqu(inone) ionophores, each created from two (calix[4]diquinone)arenes bridged at their bottom rims via alkyl chains (CH2)(n), 1: n = 3, 2; n = 4, in order to understand the reported selectivity of these ligands towards different sized metal ions such as Na+, K+, Rb+, and Cs+ in dmso solution. Conformational. analyses have been carried out which show that in the lowest energy conformations of the two macrocycles, the individual calix[4]diquinones exhibit a combination of partial cone, 1,3-alternate and cone conformations. The interactions of these alkali metals with the macrocycles have been studied in the gas phase and in a periodic box of solvent dmso by molecular mechanics and molecular dynamics calculations. Molecular mechanics calculations have been carried out on the mode of entry of the ions into the macrocycles and suggest that this is likely to occur from the side of the central cavity, rather than through the main axis of the calix[4]diquinones. There are energy barriers of ca. 19 kcal mol(-1) for this entry path in the gas phase, but in solution no energy barrier is found. Molecular dynamics simulations show that in both 1 and 2, though particularly in the latter macrocycle, one or two solvent molecules are bonded to the metal throughout the course of the simulation, often to the exclusion, of one or more of the ether oxygen atoms. By contrast the carbonyl oxygen atoms remain bonded to the metal atoms throughout with bond lengths that remain significantly less than those to the ether oxygen atoms. Free energy perturbation studies have been carried out in dmso and indicate that for 1, the selectivity follows the order Rb+ approximate to K+ > Cs+ >> Na+, which is partially in agreement with the experimental results. The energy differences are small and indeed the ratio between stability constants found for Cs+ and K+ complexes is only 0.60, showing that 1 has only a slight preference for K+. For the larger receptor 2, which is better suited to metal complexation, the binding affinity follows the pattern Cs+ >> Rb+ >> K+ >> Na+, with energy differences of 5.75, 2.61, 2.78 kcal mol(-1) which is perfectly consistent with experimental results.

Synthesis, structure and solution chemistry of mixed-ligand oxovanadium(IV) and oxovanadium(V) complexes incorporating tridentate ONO donor hydrazone ligands

In the title family, the ONO donor ligands are the acetylhydrazones of salicylaidehyde (H2L1) and 2-hydroxyacetophenone (H2L2) (general abbreviation, H2L). The reaction of bis(acetylacetonato)oxovanadium(IV) with a mixture of tridentate H2L and a bidentate NN donor [e.g., 2,2'-bipyridine(bpy) or 1,10-phenanthroline(phen), hereafter B] ligands in equimolar ratio afforded the tetravalent complexes of the type [(VO)-O-IV(L)(B)]; complexes (1)-(4) whereas, if B is replaced by 8-hydroxyquinoline(Hhq) (which is a bidentate ON donor ligand), the above reaction mixture yielded the pentavalent complexes of the type [(VO)-O-V(L)(hq)]; complexes (5) and (6). Aerial oxygen is most likely the oxidant (for the oxidation of V-IV -> V-V) in the synthesis of pentavalent complexes (5) and (6). [(VO)-O-IV(L)(B)] complexes are one electron paramagnetic and display axial EPR spectra, while the [(VO)-O-V(L)(hq)] complexes are diamagnetic. The X-ray structure of [(VO)-O-V(L-2)(hq)] (6) indicates that H2L2 ligand is bonded with the vanadium meridionally in a tridentate dinegative fashion through its phenolic-O, enolic-O and imine-N atoms. The general bond length order is: oxo < phenolato < enolato. The V-O (enolato) bond is longer than V-O (phenolato) bond by similar to 0.07 angstrom and is identical with V-O (carboxylate) bond. H-1 NMR spectrum of (6) in CDCl3 solution indicates that the binding nature in the solid state is also retained in solution. Complexes (1)(4) display two ligand-field transitions in the visible region near 820 and 480 nm in DMF solution and exhibit irreversible oxidation peak near +0.60 V versus SCE in DMSO solution, while complexes (5) and (6) exhibit only LMCT band near 535 nm and display quasi-reversible one electron reduction peak near -0.10 V versus SCE in CH2Cl2 solution. The VO3+-VO2+ E-1/2 values shift considerably to more negative values when neutral NN donor is replaced by anionic ON donor species and it also provides better VO3+ binding via phenolato oxygen. For a given bidentate ligand, E-1/2 increases in the order: (L-2)(2-) < (L-1)(2-). (c) 2004 Elsevier B.V. All rights reserved.

Synthesis, structure, solution chemistry and the electronic effect of para substituents on the vanadium center in a family of mixed-ligand [(VO)-O-V(ONO)(ON)] compexes

Four tridentate dibasic ONO donor hydrazone ligands derived from the condensation of benzoylhydrazine with either 2-hydroxyacetophenone or its para substituted derivatives (H2L1-4, general abbreviation H2L) have been used as primary ligands and 8-hydroxyquinoline (Hhq, a bidentate monobasic ON donor species) has been used as auxiliary ligand. The reaction of [(VO)-O-IV(acac)21 with H2L in methanol followed by the addition of Hhq in equimolar ratio under aerobic condition afforded the mixed-ligand oxovanadium(V) complexes of the type [(VO)-O-V(L)(hq)] (1-4) in excellent yield. The X-ray structure of the compound [(VO)-O-V(L-4)(hq)] (4) indicates that the H2L4 ligand is bonded with vanadium meridionally in a tridentate dinegative fashion through its deprotonated phenolic-O, deprotonated enolic-O and imine-N atoms. The V-O bond length order is: oxo < phenolato < enolato. H-1 NMR spectra of 4 in CDCl3 solution indicates that it's solid-state structure is retained in solution. Complexes are diamagnetic and exhibit only ligand to metal charge transfer (LMCT) transition band near 530 nm in CH2Cl2 solution in addition to intra-ligand pi-pi* transition band near 335 rim and they display quasi-reversible one electron reduction peak near -0.10 V versus SCE in CH2Cl2 solution. lambda(max) (for LMCT transition) and the reduction peak potential (E-p(c)) values of the complexes are found to be linearly related with the Hammett (sigma) constants of the substituents in the aryloxy ring of the hydrazone ligands. lambda(max) and E-p(c) values show large dependence d lambda(max)/d sigma = 32.54 nm and dE(p)(c)/d sigma = 0.19 V, respectively, on the Hammett constant. (c) 2006 Elsevier B.V. All rights reserved.

Solution self-assembly of hybrid block copolymers containing poly(ethylene glycol) and amphiphilic beta-strand peptide sequences

The self-assembly in aqueous solution of hybrid block copolymers consisting of amphiphilic β-strand peptide sequences flanked by one or two PEG chains was investigated by means of circular dichroism spectroscopy, small-angle X-ray scattering, and transmission electron microscopy. In comparison with the native peptide sequence, it was found that the peptide secondary structure was stabilized against pH variation in the di-and tri-block copolymers with PEG. Small-angle X-ray scattering indicated the presence of fibrillar structures, the dimensions of which are comparable to the estimated width of a β-strand (with terminal PEG chains in the case of the copolymers). Transmission electron microscopy on selectively stained and dried specimens shows directly the presence of fibrils. It is proposed that these fibrils result from the hierarchical self-assembly of peptide β-strands into helical tapes, which then stack into fibrils.