Efficient implementation of a filtered back-projection algorithm using a voxel-by-voxel approach

The large amount of image data necessary for high-resolution 3D reconstruction of macromolecular assemblies leads to significant increases in the computational time. One of the most time consuming operations is 3D density map reconstruction, and software optimization can greatly reduce the time required for any given structural study. The majority of algorithms proposed for improving the computational effectiveness of a 3D reconstruction are based on a ray-by-ray projection of each image into the reconstructed volume. In this paper, we propose a novel fast implementation of the "filtered back-projection" algorithm based on a voxel-by-voxel principle. Our version of this implementation has been exhaustively tested using both model and real data. We compared 3D reconstructions obtained by the new approach with results obtained by the filtered Back-Projections algorithm and the Fourier-Bessel algorithm commonly used for reconstructing icosahedral viruses. These computational experiments demonstrate the robustness, reliability, and efficiency of this approach.     

Distance-based assessment of the localization of functional annotations in 3D genome reconstructions

Background

Recent studies used the contact data or three-dimensional (3D) genome reconstructions from Hi-C (chromosome conformation capture with next-generation sequencing) to assess the co-localization of functional genomic annotations in the nucleus. These analyses dichotomized data point pairs belonging to a functional annotation as “close” or “far” based on some threshold and then tested for enrichment of “close” pairs. We propose an alternative approach that avoids dichotomization of the data and instead directly estimates the significance of distances within the 3D reconstruction.

Results

We applied this approach to 3D genome reconstructions for Plasmodium falciparum, the causative agent of malaria, and Saccharomyces cerevisiae and compared the results to previous approaches. We found significant 3D co-localization of centromeres, telomeres, virulence genes, and several sets of genes with developmentally regulated expression in P. falciparum; and significant 3D co-localization of centromeres and long terminal repeats in S. cerevisiae. Additionally, we tested the experimental observation that telomeres form three to seven clusters in P. falciparum and S. cerevisiae. Applying affinity propagation clustering to telomere coordinates in the 3D reconstructions yielded six telomere clusters for both organisms.

Conclusions

Distance-based assessment replicated key findings, while avoiding dichotomization of the data (which previously yielded threshold-sensitive results).

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-992) contains supplementary material, which is available to authorized users.     

Subject specific finite element mesh generation of the pelvis from biplanar x-ray images: application to 120 clinical cases

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. The technique was successfully tested on a database of 120 3D reconstructions of pelvises from biplanar X-ray images. For each patient, a full hexahedral subject-specific FE mesh was generated with an accurate surface representation.     

COMMIT: Consideration of metabolite leakage and community composition improves microbial community reconstructions

Composition and functions of microbial communities affect important traits in diverse hosts, from crops to humans. Yet, mechanistic understanding of how metabolism of individual microbes is affected by the community composition and metabolite leakage is lacking. Here, we first show that the consensus of automatically generated metabolic reconstructions improves the quality of the draft reconstructions, measured by comparison to reference models. We then devise an approach for gap filling, termed COMMIT, that considers metabolites for secretion based on their permeability and the composition of the community. By applying COMMIT with two soil communities from the Arabidopsis thaliana culture collection, we could significantly reduce the gap-filling solution in comparison to filling gaps in individual reconstructions without affecting the genomic support. Inspection of the metabolic interactions in the soil communities allows us to identify microbes with community roles of helpers and beneficiaries. Therefore, COMMIT offers a versatile fully automated solution for large-scale modelling of microbial communities for diverse biotechnological applications.     

Assessing the limits of restraint-based 3D modeling of genomes and genomic domains

Restraint-based modeling of genomes has been recently explored with the advent of Chromosome Conformation Capture (3C-based) experiments. We previously developed a reconstruction method to resolve the 3D architecture of both prokaryotic and eukaryotic genomes using 3C-based data. These models were congruent with fluorescent imaging validation. However, the limits of such methods have not systematically been assessed. Here we propose the first evaluation of a mean-field restraint-based reconstruction of genomes by considering diverse chromosome architectures and different levels of data noise and structural variability. The results show that: first, current scoring functions for 3D reconstruction correlate with the accuracy of the models; second, reconstructed models are robust to noise but sensitive to structural variability; third, the local structure organization of genomes, such as Topologically Associating Domains, results in more accurate models; fourth, to a certain extent, the models capture the intrinsic structural variability in the input matrices and fifth, the accuracy of the models can be a priori predicted by analyzing the properties of the interaction matrices. In summary, our work provides a systematic analysis of the limitations of a mean-field restrain-based method, which could be taken into consideration in further development of methods as well as their applications.     

Estimating Mass Properties of Dinosaurs Using Laser Imaging and 3D Computer Modelling

Body mass reconstructions of extinct vertebrates are most robust when complete to near-complete skeletons allow the reconstruction of either physical or digital models. Digital models are most efficient in terms of time and cost, and provide the facility to infinitely modify model properties non-destructively, such that sensitivity analyses can be conducted to quantify the effect of the many unknown parameters involved in reconstructions of extinct animals. In this study we use laser scanning (LiDAR) and computer modelling methods to create a range of 3D mass models of five specimens of non-avian dinosaur; two near-complete specimens of Tyrannosaurus rex, the most complete specimens of Acrocanthosaurus atokensis and Strutiomimum sedens, and a near-complete skeleton of a sub-adult Edmontosaurus annectens. LiDAR scanning allows a full mounted skeleton to be imaged resulting in a detailed 3D model in which each bone retains its spatial position and articulation. This provides a high resolution skeletal framework around which the body cavity and internal organs such as lungs and air sacs can be reconstructed. This has allowed calculation of body segment masses, centres of mass and moments or inertia for each animal. However, any soft tissue reconstruction of an extinct taxon inevitably represents a best estimate model with an unknown level of accuracy. We have therefore conducted an extensive sensitivity analysis in which the volumes of body segments and respiratory organs were varied in an attempt to constrain the likely maximum plausible range of mass parameters for each animal. Our results provide wide ranges in actual mass and inertial values, emphasizing the high level of uncertainty inevitable in such reconstructions. However, our sensitivity analysis consistently places the centre of mass well below and in front of hip joint in each animal, regardless of the chosen combination of body and respiratory structure volumes. These results emphasize that future biomechanical assessments of extinct taxa should be preceded by a detailed investigation of the plausible range of mass properties, in which sensitivity analyses are used to identify a suite of possible values to be tested as inputs in analytical models.     

Perspectives for the reconstruction of 3D chromatin conformation using single cell Hi-C data

Construction of chromosomes 3D models based on single cell Hi-C data constitute an important challenge. We present a reconstruction approach, DPDchrom, that incorporates basic knowledge whether the reconstructed conformation should be coil-like or globular and spring relaxation at contact sites. In contrast to previously published protocols, DPDchrom can naturally form globular conformation due to the presence of explicit solvent. Benchmarking of this and several other methods on artificial polymer models reveals similar reconstruction accuracy at high contact density and DPDchrom advantage at low contact density. To compare 3D structures insensitively to spatial orientation and scale, we propose the Modified Jaccard Index. We analyzed two sources of the contact dropout: contact radius change and random contact sampling. We found that the reconstruction accuracy exponentially depends on the number of contacts per genomic bin allowing to estimate the reconstruction accuracy in advance. We applied DPDchrom to model chromosome configurations based on single-cell Hi-C data of mouse oocytes and found that these configurations differ significantly from a random one, that is consistent with other studies.     

Manifold Based Optimization for Single-Cell 3D Genome Reconstruction

The three-dimensional (3D) structure of the genome is important for orchestration of gene expression and cell differentiation. While mapping genomes in 3D has for a long time been elusive, recent adaptations of high-throughput sequencing to chromosome conformation capture (3C) techniques, allows for genome-wide structural characterization for the first time. However, reconstruction of "consensus" 3D genomes from 3C-based data is a challenging problem, since the data are aggregated over millions of cells. Recent single-cell adaptations to the 3C-technique, however, allow for non-aggregated structural assessment of genome structure, but data suffer from sparse and noisy interaction sampling. We present a manifold based optimization (MBO) approach for the reconstruction of 3D genome structure from chromosomal contact data. We show that MBO is able to reconstruct 3D structures based on the chromosomal contacts, imposing fewer structural violations than comparable methods. Additionally, MBO is suitable for efficient high-throughput reconstruction of large systems, such as entire genomes, allowing for comparative studies of genomic structure across cell-lines and different species.     

Techniques for and challenges in reconstructing 3D genome structures from 2D chromosome conformation capture data

Chromosome conformation capture technologies that provide frequency information for contacts between genomic regions have been crucial for increasing our understanding of genome folding and regulation. However, such data do not provide direct evidence of the spatial 3D organization of chromatin. In this opinion article, we discuss the development and application of computational methods to reconstruct chromatin 3D structures from experimental 2D contact data, highlighting how such modeling provides biological insights and can suggest mechanisms anchored to experimental data. By applying different reconstruction methods to the same contact data, we illustrate some state-of-the-art of these techniques and discuss our gene resolution approach based on Brownian dynamics and Monte Carlo sampling.     

Het-PDB Navi.: a database for protein-small molecule interactions

The genomes of more than 100 species have been sequenced, and the biological functions of encoded proteins are now actively being researched. Protein function is based on interactions between proteins and other molecules. One approach to assuming protein function based on genomic sequence is to predict interactions between an encoded protein and other molecules. As a data source for such predictions, knowledge regarding known protein-small molecule interactions needs to be compiled. We have, therefore, surveyed interactions between proteins and other molecules in Protein Data Bank (PDB), the protein three-dimensional (3D) structure database. Among 20,685 entries in PDB (April, 2003), 4,189 types of small molecules were found to interact with proteins. Biologically relevant small molecules most often found in PDB were metal ions, such as calcium, zinc, and magnesium. Sugars and nucleotides were the next most common. These molecules are known to act as cofactors for enzymes and/or stabilizers of proteins. In each case of interactions between a protein and small molecule, we found preferred amino acid residues at the interaction sites. These preferences can be the basis for predicting protein function from genomic sequence and protein 3D structures. The data pertaining to these small molecules were collected in a database named Het-PDB Navi., which is freely available at http://daisy.nagahama-i-bio.ac.jp/golab/hetpdbnavi.html and linked to the official PDB home page.     

A phylogeny of anisopterous dragonflies (Insecta,Odonata) using mtRNA genes and mixed nucleotide/doublet models

The application of mixed nucleotide/doublet substitution models has recently received attention in RNA‐based phylogenetics. Within a Bayesian approach, it was shown that mixed models outperformed analyses relying on simple nucleotide models. We analysed an mt RNA data set of dragonflies representing all major lineages of Anisoptera plus outgroups, using a mixed model in a Bayesian and parsimony (MP) approach. We used a published mt 16S rRNA secondary consensus structure model and inferred consensus models for the mt 12S rRNA and tRNA valine. Secondary structure information was used to set data partitions for paired and unpaired sites on which doublet or nucleotide models were applied, respectively. Several different doublet models are currently available of which we chose the most appropriate one by a Bayes factor test. The MP reconstructions relied on recoded data for paired sites in order to account for character covariance and an application of the ratchet strategy to find most parsimonious trees. Bayesian and parsimony reconstructions are partly differently resolved, indicating sensitivity of the reconstructions to model specification. Our analyses depict a tree in which the damselfly family Lestidae is sister group to a monophyletic clade Epiophlebia + Anisoptera, contradicting recent morphological and molecular work. In Bayesian analyses, we found a deep split between Libelluloidea and a clade ‘Aeshnoidea’ within Anisoptera largely congruent with Tillyard’s early ideas of anisopteran evolution, which had been based on evidently plesiomorphic character states. However, parsimony analysis did not support a clade ‘Aeshnoidea’, but instead, placed Gomphidae as sister taxon to Libelluloidea. Monophyly of Libelluloidea is only modestly supported, and many inter‐family relationships within Libelluloidea do not receive substantial support in Bayesian and parsimony analyses. We checked whether high Bayesian node support was inflated owing to either: (i) wrong secondary consensus structures; (ii) under‐sampling of the MCMC process, thereby missing other local maxima; or (iii) unrealistic prior assumptions on topologies or branch lengths. We found that different consensus structure models exert strong influence on the reconstruction, which demonstrates the importance of taxon‐specific realistic secondary structure models in RNA phylogenetics.     

Functional Metabolic Map of Faecalibacterium prausnitzii,a Beneficial Human Gut Microbe

The human gut microbiota plays a central role in human well-being and disease. In this study, we present an integrated, iterative approach of computational modeling, in vitro experiments, metabolomics, and genomic analysis to accelerate the identification of metabolic capabilities for poorly characterized (anaerobic) microorganisms. We demonstrate this approach for the beneficial human gut microbe Faecalibacterium prausnitzii strain A2-165. We generated an automated draft reconstruction, which we curated against the limited biochemical data. This reconstruction modeling was used to develop in silico and in vitro a chemically defined medium (CDM), which was validated experimentally. Subsequent metabolomic analysis of the spent medium for growth on CDM was performed. We refined our metabolic reconstruction according to in vitro observed metabolite consumption and secretion and propose improvements to the current genome annotation of F. prausnitzii A2-165. We then used the reconstruction to systematically characterize its metabolic properties. Novel carbon source utilization capabilities and inabilities were predicted based on metabolic modeling and validated experimentally. This study resulted in a functional metabolic map of F. prausnitzii, which is available for further applications. The presented workflow can be readily extended to other poorly characterized and uncharacterized organisms to yield novel biochemical insights about the target organism.     

Three-dimensional FRET reconstruction microscopy for analysis of dynamic molecular interactions in live cells

Analysis of cellular pathways requires concentration measurements of dynamically interacting molecules within the three-dimensional (3D) space of single living cells. Förster resonance energy transfer (FRET) microscopy from widefield, from confocal, and potentially from superresolution microscopes can access this information; however, these measurements are distorted by the inherent 3D blurring of optical imaging, spectral overlap of fluorophores, and detection noise. We propose a mathematical model of these processes and demonstrate, through simulation, how these distortions limit the dynamic range and sensitivity of conventional FRET microscopy. Using this model, we devise and validate a new approach (called 3D-FRET stoichiometry reconstruction, 3DFSR) for reconstructing 3D distributions of bound and free fluorescent molecules. Previous attempts to reconstruct 3D-FRET data relied on sequential spectral unmixing and deconvolution, a process that corrupts the detection statistics. We demonstrate that 3DFSR is superior to these approaches since it simultaneously models spectral mixing, optical blurring, and detection noise. To achieve the full potential of this technique, we developed an instrument capable of acquiring 3D-FRET data rapidly and sensitively from single living cells. Compared with conventional FRET microscopy, our 3D-FRET reconstruction technique and new instrumentation provides orders of magnitude gains in both sensitivity and accuracy wherein sustained high-resolution four-dimensional (x,y,z,t) imaging of molecular interactions inside living cells was achieved. These results verify previous observations that Cdc42 signaling is localized to the advancing margins of forming phagosomes in macrophages.     

A statistical model of ChIA-PET data for accurate detection of chromatin 3D interactions

Identification of three-dimensional (3D) interactions between regulatory elements across the genome is crucial to unravel the complex regulatory machinery that orchestrates proliferation and differentiation of cells. ChIA-PET is a novel method to identify such interactions, where physical contacts between regions bound by a specific protein are quantified using next-generation sequencing. However, determining the significance of the observed interaction frequencies in such datasets is challenging, and few methods have been proposed. Despite the fact that regions that are close in linear genomic distance have a much higher tendency to interact by chance, no methods to date are capable of taking such dependency into account. Here, we propose a statistical model taking into account the genomic distance relationship, as well as the general propensity of anchors to be involved in contacts overall. Using both real and simulated data, we show that the previously proposed statistical test, based on Fisher''s exact test, leads to invalid results when data are dependent on genomic distance. We also evaluate our method on previously validated cell-line specific and constitutive 3D interactions, and show that relevant interactions are significant, while avoiding over-estimating the significance of short nearby interactions.     

Robustness of metabolic map reconstruction

With the ever increasing amount of genomic data available, the interest for generating biochemical pathways has grown tremendously. So far, mainly complete genomes have been used to reconstruct the biochemical pathways and their associated interactions. However, a large number of low coverage genomes, as well as other sources of partial genomic data, are currently available for many organisms. In order to be able to use incomplete data for metabolic reconstruction, the inherent properties of this procedure need to be investigated. In this short note, we describe the robustness and predictive power of metabolic reconstructions using partial information from Schizosaccharomyces pombe. We also discuss the implications of the results on reference genome projects as well as other large-scale sequencing data.     

Optimisation of a Stirred Bioreactor through the Use of a Novel Holographic Correlation Velocimetry Flow Measurement Technique

We describe a method for measuring three dimensional (3D) velocity fields of a fluid at high speed, by combining a correlation-based approach with in-line holography. While this method utilizes tracer particles contained within the flow, our method does not require the holographic reconstruction of 3D images. The direct flow reconstruction approach developed here allows for measurements at seeding densities in excess of the allowable levels for techniques based on image or particle reconstruction, thus making it suited for biological flow measurement, such as the flow in bioreactor. We outline the theory behind our method, which we term Holographic Correlation Velocimetry (HCV), and subsequently apply it to both synthetic and laboratory data. Moreover, because the system is based on in-line holography, it is very efficient with regard to the use of light, as it does not rely on side scattering. This efficiency could be utilized to create a very high quality system at a modest cost. Alternatively, this efficiency makes the system appropriate for high-speed flows and low exposure times, which is essential for imaging dynamic systems.