Building robust age models for speleothems – A case-study using coeval twin stalagmites

We use the uranium-series (U-Th) dating method to investigate the accuracy of a relative chronology based on laminae correlation between a pair of coeval twin stalagmites and compare their stable isotope and trace element records based on the two chronologies. U-Th dating shows that a relative chronology based on laminae correlation can be inaccurate: a hiatus in one of the stalagmites was not recognised, as well as more subtle changes in growth rates. Use of the stratigraphic correlation alone resulted in significant differences in the timing of stable isotopes and trace element peaks, with implications for their interpretation. Our results reveal the importance of a robust and direct chronology with which to interpret proxy data. Poor relative chronologies can lead to a misinterpretation of palaeoclimate data. The study reveals potential implications for speleothem records where proxy data and samples for dating were not taken in close proximity to each other and/or were correlated via laminae over distances of more than a few centimetres

A genome-wide study of Hardy–Weinberg equilibrium with next generation sequence data

Statistical tests for Hardy–Weinberg equilibrium have been an important tool for detecting genotyping errors in the past, and remain important in the quality control of next generation sequence data. In this paper, we analyze complete chromosomes of the 1000 genomes project by using exact test procedures for autosomal and X-chromosomal variants. We find that the rate of disequilibrium largely exceeds what might be expected by chance alone for all chromosomes. Observed disequilibrium is, in about 60% of the cases, due to heterozygote excess. We suggest that most excess disequilibrium can be explained by sequencing problems, and hypothesize mechanisms that can explain exceptional heterozygosities. We report higher rates of disequilibrium for the MHC region on chromosome 6, regions flanking centromeres and p-arms of acrocentric chromosomes. We also detected long-range haplotypes and areas with incidental high disequilibrium. We report disequilibrium to be related to read depth, with variants having extreme read depths being more likely to be out of equilibrium. Disequilibrium rates were found to be 11 times higher in segmental duplications and simple tandem repeat regions. The variants with significant disequilibrium are seen to be concentrated in these areas. For next generation sequence data, Hardy–Weinberg disequilibrium seems to be a major indicator for copy number variation.Peer ReviewedPostprint (published version

Pattern formation in heterogeneous domains

Development of spatial pattern in the early embryo results from the interaction of several processes in a complex hierarchy of mechanisms. Most models for morphogenesis to date have, however, focussed on a particular mechanism. Although such models are capable of capturing some aspects of development they are inconsistent with key experimental observations. Here we consider a two-step hierarchy of patterning mechanisms in which the spatial pattern of a control chemical regulates morphogen diffusivity in an overlaying reaction diffusion system

A model for selection of eyespots on butterfly wings

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

SHV Lactamase Engineering Database: a reconciliation tool for SHV β-lactamases in public databases

<p>Abstract</p> <p>Background</p> <p>SHV β-lactamases confer resistance to a broad range of antibiotics by accumulating mutations. The number of SHV variants is steadily increasing. 117 SHV variants have been assigned in the SHV mutation table (<url>http://www.lahey.org/Studies/</url>). Besides, information about SHV β-lactamases can be found in the rapidly growing NCBI protein database. The SHV β-Lactamase Engineering Database (SHVED) has been developed to collect the SHV β-lactamase sequences from the NCBI protein database and the SHV mutation table. It serves as a tool for the detection and reconciliation of inconsistencies, and for the identification of new SHV variants and amino acid substitutions.</p> <p>Description</p> <p>The SHVED contains 200 protein entries with distinct sequences and 20 crystal structures. 83 protein sequences are included in the both the SHV mutation table and the NCBI protein database, while 35 and 82 protein sequences are only in the SHV mutation table and the NCBI protein database, respectively. Of these 82 sequences, 41 originate from microbial sources, and 22 of them are full-length sequences that harbour a mutation profile which has not been classified yet in the SHV mutation table. 27 protein entries from the NCBI protein database were found to have an inconsistency in SHV name identification. These inconsistencies were reconciled using information from the SHV mutation table and stored in the SHVED.</p> <p>The SHVED is accessible at <url>http://www.LacED.uni-stuttgart.de/classA/SHVED/</url>. It provides sequences, structures, and a multisequence alignment of SHV β-lactamases with the corrected annotation. Amino acid substitutions at each position are also provided. The SHVED is updated monthly and supplies all data for download.</p> <p>Conclusions</p> <p>The SHV β-Lactamase Engineering Database (SHVED) contains information about SHV variants with reconciled annotation. It serves as a tool for detection of inconsistencies in the NCBI protein database, helps to identify new mutations resulting in new SHV variants, and thus supports the investigation of sequence-function relationships of SHV β-lactamases.</p

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Steady-state patterns in a reaction diffusion system with mixed boundary conditions

A number of models for pattern formation and regulation are based on the hypothesis that a diffusible morphogen supplies positional information that can interpreted by cells. Such models fall into two main classes:- those in which pattern arises from distributed sources and/or sinks of the morphogens, and those which can spontaneously produce pattern via the interaction of reaction and transport. In source-sink models, specialized cells maintain the concentration of the morphogen at fixed levels, and given a suitable distribution of sources and sinks, a tissue can be proportioned into any number of cell types with a threshold interpretation mechanism. However, the spatial pattern established is strongly dependent on the distances between the sources and sinks, and additional hyoptheses must be invoked to ensure that the pattern is invariant under changes in the scale of the system

Structure of the hDmc1-ssDNA filament reveals the principles of its architecture

In eukaryotes, meiotic recombination is a major source of genetic diversity, but its defects in humans lead to abnormalities such as Down's, Klinefelter's and other syndromes. Human Dmc1 (hDmc1), a RecA/Rad51 homologue, is a recombinase that plays a crucial role in faithful chromosome segregation during meiosis. The initial step of homologous recombination occurs when hDmc1 forms a filament on single-stranded (ss) DNA. However the structure of this presynaptic complex filament for hDmc1 remains unknown. To compare hDmc1-ssDNA complexes to those known for the RecA/Rad51 family we have obtained electron microscopy (EM) structures of hDmc1-ssDNA nucleoprotein filaments using single particle approach. The EM maps were analysed by docking crystal structures of Dmc1, Rad51, RadA, RecA and DNA. To fully characterise hDmc1-DNA complexes we have analysed their organisation in the presence of Ca2+, Mg2+, ATP, AMP-PNP, ssDNA and dsDNA. The 3D EM structures of the hDmc1-ssDNA filaments allowed us to elucidate the principles of their internal architecture. Similar to the RecA/Rad51 family, hDmc1 forms helical filaments on ssDNA in two states: extended (active) and compressed (inactive). However, in contrast to the RecA/Rad51 family, and the recently reported structure of hDmc1-double stranded (ds) DNA nucleoprotein filaments, the extended (active) state of the hDmc1 filament formed on ssDNA has nine protomers per helical turn, instead of the conventional six, resulting in one protomer covering two nucleotides instead of three. The control reconstruction of the hDmc1-dsDNA filament revealed 6.4 protein subunits per helical turn indicating that the filament organisation varies depending on the DNA templates. Our structural analysis has also revealed that the N-terminal domain of hDmc1 accomplishes its important role in complex formation through domain swapping between adjacent protomers, thus providing a mechanistic basis for coordinated action of hDmc1 protomers during meiotic recombination

Indexing Strategies for Rapid Searches of Short Words in Genome Sequences

Searching for matches between large collections of short (14–30 nucleotides) words and sequence databases comprising full genomes or transcriptomes is a common task in biological sequence analysis. We investigated the performance of simple indexing strategies for handling such tasks and developed two programs, fetchGWI and tagger, that index either the database or the query set. Either strategy outperforms megablast for searches with more than 10,000 probes. FetchGWI is shown to be a versatile tool for rapidly searching multiple genomes, whose performance is limited in most cases by the speed of access to the filesystem. We have made publicly available a Web interface for searching the human, mouse, and several other genomes and transcriptomes with oligonucleotide queries