A Arneodo

University of Lyon, Lyons, Rhône-Alpes, France

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Publications (259)800.93 Total impact

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    Hanna Julienne, Benjamin Audit, Alain Arneodo
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    ABSTRACT: Epigenetic regulation of the replication program during mammalian cell differentiation remains poorly understood. We performed an integrative analysis of eleven genome-wide epigenetic profiles at 100 kb resolution of Mean Replication Timing (MRT) data in six human cell lines. Compared to the organization in four chromatin states shared by the five somatic cell lines, embryonic stem cell (ESC) line H1 displays (i) a gene-poor but highly dynamic chromatin state (EC4) associated to histone variant H2AZ rather than a HP1-associated heterochromatin state (C4) and (ii) a mid-S accessible chromatin state with bivalent gene marks instead of a polycomb-repressed heterochromatin state. Plastic MRT regions (≲ 20% of the genome) are predominantly localized at the borders of U-shaped timing domains. Whereas somatic-specific U-domain borders are gene-dense GC-rich regions, 31.6% of H1-specific U-domain borders are early EC4 regions enriched in pluripotency transcription factors NANOG and OCT4 despite being GC poor and gene deserts. Silencing of these ESC-specific "master" replication initiation zones during differentiation corresponds to a loss of H2AZ and an enrichment in H3K9me3 mark characteristic of late replicating C4 heterochromatin. These results shed a new light on the epigenetically regulated global chromatin reorganization that underlies the loss of pluripotency and lineage commitment.
    PLoS Computational Biology 02/2015; 11(2):e1003969. DOI:10.1371/journal.pcbi.1003969 · 4.83 Impact Factor
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    ABSTRACT: As the elementary building block of eukaryotic chromatin, the nucleosome is at the heart of the compromise between the necessity of compacting DNA in the cell nucleus and the required accessibility to regulatory proteins. The recent availability of genome-wide experimental maps of nucleosome positions for many different organisms and cell types has provided an unprecedented opportunity to elucidate to what extent the DNA sequence conditions the primary structure of chromatin and in turn participates in the chromatin-mediated regulation of nuclear functions, such as gene expression and DNA replication. In this study, we use in vivo and in vitro genome-wide nucleosome occupancy data together with the set of nucleosome-free regions (NFRs) predicted by a physical model of nucleosome formation based on sequence-dependent bending properties of the DNA double-helix, to investigate the role of intrinsic nucleosome occupancy in the regulation of the replication spatio-temporal programme in human. We focus our analysis on the so-called replication U/N-domains that were shown to cover about half of the human genome in the germline (skew-N domains) as well as in embryonic stem cells, somatic and HeLa cells (mean replication timing U-domains). The 'master' origins of replication (MaOris) that border these megabase-sized U/N-domains were found to be specified by a few hundred kb wide regions that are hyper-sensitive to DNase I cleavage, hypomethylated, and enriched in epigenetic marks involved in transcription regulation, the hallmarks of localized open chromatin structures. Here we show that replication U/N-domain borders that are conserved in all considered cell lines have an environment highly enriched in nucleosome-excluding-energy barriers, suggesting that these ubiquitous MaOris have been selected during evolution. In contrast, MaOris that are cell-type-specific are mainly regulated epigenetically and are no longer favoured by a local abundance of intrinsic NFRs encoded in the DNA sequence. At the smaller few hundred bp scale of gene promoters, CpG-rich promoters of housekeeping genes found nearby ubiquitous MaOris as well as CpG-poor promoters of tissue-specific genes found nearby cell-type-specific MaOris, both correspond to in vivo NFRs that are not coded as nucleosome-excluding-energy barriers. Whereas the former promoters are likely to correspond to high occupancy transcription factor binding regions, the latter are an illustration that gene regulation in human is typically cell-type-specific.
    Journal of Physics Condensed Matter 01/2015; 27(6):064102. DOI:10.1088/0953-8984/27/6/064102 · 2.22 Impact Factor
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    ABSTRACT: Background Spike-wave discharges (SWD) found in neuroelectrical recordings are pathognomonic to absence epilepsy. The characteristic spike-wave morphology of the spike-wave complex (SWC) constituents of SWDs can be mathematically described by a subset of possible spectral power and phase values. Morlet wavelet transform (MWT) generates time-frequency representations well-suited to identifying this SWC-associated subset. New methodMWT decompositions of SWDs reveal spectral power concentrated at harmonic frequencies. The phase relationships underlying SWC morphology were identified by calculating the differences between phase values at SWD fundamental frequency from the 2nd, 3rd and 4th harmonics, then using the three phase differences as coordinates to generate a density distribution in a {360°x360°x360°} phase difference space. Strain-specific density distributions were generated from SWDs of mice carrying the Gria4, Gabrg2 or Scn8a mutations to determine whether SWC morphological variants reliably mapped to the same regions of the distribution, and if distribution values could be used to detect SWD.Comparison with existing methodsTo the best of our knowledge, this algorithm is the first to employ spectral phase to quantify SWC morphology, making it possible to computationally distinguish SWC morphological subtypes and detect SWDs.Results/conclusionsProof-of-concept testing of the SWDfinder algorithm shows: (1) a major pattern of variation in SWC morphology maps to one axis of the phase difference distribution, (2) variability between the strain-specific distributions reflects differences in the proportions of SWC subtypes generated during SWD, and (3) regularities in the spectral power and phase profiles of SWCs can be used to detect waveforms possessing SWC-like morphology. Copyright © 2014. Published by Elsevier B.V.
    Journal of Neuroscience Methods 12/2014; 242. DOI:10.1016/j.jneumeth.2014.12.016 · 1.96 Impact Factor
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    Pierre Kestener, Alain Arneodo
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    Pierre Kestener, alain arneodo
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    ABSTRACT: The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the "CC-MLO fractal dimension plot", where a "fractal zone" and "Euclidean zones" (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue.
    PLoS ONE 09/2014; 9(9):e107580. DOI:10.1371/journal.pone.0107580 · 3.53 Impact Factor
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    ABSTRACT: Besides their large-scale organization in isochores, mammalian genomes display megabase-sized regions, spanning both genes and intergenes, where the strand nucleotide composition asymmetry decreases linearly, possibly due to replication activity. These so-called skew-N domains cover about a third of the human genome and are bordered by two skew upward jumps that were hypothesized to compose a subset of “master” replication origins active in the germline. Skew-N domains were shown to exhibit a particular gene organization. Genes with CpG-rich promoters likely expressed in the germline are over represented near the master replication origins, with large genes being co-oriented with replication fork progression, which suggests some coordination of replication and transcription. In this study, we describe another skew structure that covers ∼13% of the human genome and that is bordered by putative master replication origins similar to the ones flanking skew-N domains. These skew-split-N domains have a shape reminiscent of a N, but split in half, leaving in the center a region of null skew whose length increases with domain size. These central regions (median size ∼860 kb) have a homogeneous composition, i.e. both a null and constant skew and a constant and low GC content. They correspond to heterochromatin gene deserts found in low-GC isochores with an average gene density of 0.81 promoters/Mb as compared to 7.73 promoters/Mb genome wide. The analysis of epigenetic marks and replication timing data confirms that, in these late replicating heterochomatic regions, the initiation of replication is likely to be random. This contrasts with the transcriptionally active euchromatin state found around the bordering well positioned master replication origins. Altogether skew-N domains and skew-split-N domains cover about 50% of the human genome.
    Computational Biology and Chemistry 08/2014; 53. DOI:10.1016/j.compbiolchem.2014.08.020 · 1.60 Impact Factor
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    ABSTRACT: Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of screening X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. Here we propose a computer-aided multifractal analysis of dynamic infrared (IR) imaging as an efficient method for identifying women with risk of breast cancer. Using a wavelet-based multi-scale method to analyze the temporal fluctuations of breast skin temperature collected from a panel of patients with diagnosed breast cancer and some female volunteers with healthy breasts, we show that the multifractal complexity of temperature fluctuations observed in healthy breasts is lost in mammary glands with malignant tumor. Besides potential clinical impact, these results open new perspectives in the investigation of physiological changes that may precede anatomical alterations in breast cancer development.
    Frontiers in Physiology 05/2014; 5:176. DOI:10.3389/fphys.2014.00176
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    ABSTRACT: The duplication of mammalian genomes is under the control of a spatiotemporal program that orchestrates the positioning and the timing of firing of replication origins. The molecular mechanisms coordinating the activation of about [Formula: see text] predicted origins remain poorly understood, partly due to the intrinsic rarity of replication bubbles, making it difficult to purify short nascent strands (SNS). The precise identification of origins based on the high-throughput sequencing of SNS constitutes a new methodological challenge. We propose a new statistical method with a controlled resolution, adapted to the detection of replication origins from SNS data. We detected an average of 80,000 replication origins in different cell lines. To evaluate the consistency between different protocols, we compared SNS detections with bubble trapping detections. This comparison demonstrated a good agreement between genome-wide methods, with 65% of SNS-detected origins validated by bubble trapping, and 44% of bubble trapping origins validated by SNS origins, when compared at the same resolution. We investigated the interplay between the spatial and the temporal programs of replication at fine scales. We show that most of the origins detected in regions replicated in early S phase are shared by all the cell lines investigated whereas cell-type-specific origins tend to be replicated in late S phase. We shed a new light on the key role of CpG islands, by showing that 80% of the origins associated with CGIs are constitutive. Our results further show that at least 76% of CGIs are origins of replication. The analysis of associations with chromatin marks at different timing of cell division revealed new potential epigenetic regulators driving the spatiotemporal activity of replication origins. We highlight the potential role of H4K20me1 and H3K27me3, the coupling of which is correlated with increased efficiency of replication origins, clearly identifying those marks as potential key regulators of replication origins.
    PLoS Genetics 05/2014; 10(5):e1004282. DOI:10.1371/journal.pgen.1004282 · 8.17 Impact Factor
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    ABSTRACT: We propose a two-dimensional (2-D) space-scale analysis of fringe patterns collected from a diffraction phase microscope based on the 2-D Morlet wavelet transform. We show that the adaptation of a ridge detection method with anisotropic 2-D Morlet mother wavelets is more efficient for analyzing cellular and high refractive index contrast objects than Fourier filtering methods since it can separate phase from intensity modulations. We compare the performance of this ridge detection method on theoretical and experimental images of polymer microbeads and experimental images collected from living myoblasts.
    Journal of Biomedical Optics 03/2014; 19(3):36007. DOI:10.1117/1.JBO.19.3.036007 · 2.75 Impact Factor
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    ABSTRACT: Modelling of the appearance and evolution of tumor diseases is one of the major areas of research in modern biomechanics. The understanding of physiological mechanisms of tumors in the context of biomechanics and mechanobiology can provide a basis for developing new diagnostic techniques and oncological diseases treatment. Biomechnical approaches play an increasing part in designing adequate clinical methods for estimating the state and properties of tissues. The nanobiomechanical methods, measuring the mechanical properties of cells, as well as ultrasonic and different thermal techniques (for example, infrared thermography) are rather effective in differentiating between healthy and abnormal tissues. A quantitative analysis of signals and images is an extremely challenging problem, which is still not completely understood. Its solution will allow researchers to evaluate the norm and pathology criteria. The paper is concerned with the multifractal analysis of the breast skin temperature dynamics measured during examination of mammary glands by the infrared thermography method. The evidential differences between temperature signals of healthy and tumorous mammary glands have been revealed. The health status of normal mammary glands is characterized by the existence of multifractal scaling. By contrast, the temperature signals of mammary glands affected with malignant tumor are characterized by homogeneity and monofractality of temperature fluctuation statistics. The objective, differentiating diagnostic criteria for healthy and tumorous mammary gland found during this study essentially increase the predicting capabilities of dynamic infrared thermography as an effective screening tool for detection of mammary gland oncopathology.
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    ABSTRACT: The wavelet transform modulus maxima (WTMM) method was used in a multifractal analysis of skin breast temperature time-series recorded using dynamic infrared (IR) thermography. Multifractal scaling was found for healthy breasts as the signature of a continuous change in the shape of the probability density function (pdf) of temperature fluctuations across time scales from similar to 0.3 to 3 s. In contrast, temperature time-series from breasts with malignant tumors showed homogeneous monofractal temperature fluctuations statistics. These results highlight dynamic IR imaging as a very valuable non-invasive technique for preliminary screening in asymptomatic women to identify those with risk of breast cancer. Copyright (C) EPLA, 2013
    EPL (Europhysics Letters) 12/2013; 104(6):68001. DOI:10.1209/0295-5075/104/68001 · 2.27 Impact Factor
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    ABSTRACT: Surface plasmon microscopy is widely recognized for its high sensitivity to nanoscale dielectric or metallic structures confined in a close neighborhood of a gold surface. Recently, its coupling to high-numerical-aperture objective lenses pushed its resolution down to the diffraction limit. Here, we show that the same microscope configuration can be used to excite standing guided waves in asymmetric slabs, which definitely extends the range of applications of this type of microscopy from nano-to microscale structure imaging. We demonstrate experimen-tally on PPMA films that the V …Z† response of a scanning surface plasmon microscope can be Fourier inverted in order to obtain the reflectivity curve R…ν†. When the guided waves are excited, R…ν† shows a finite number of sharp peaks corresponding to quantified guiding modes from which one can extract both the refractive index (RI) and the thickness of the layer at the point focused by the microscope. This device can thus be used to reconstruct RI and thickness contours of dielectric samples with a high spatial resolution. © 2013 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (110.3175) Interferometric imaging; (100.6950) Tomographic image processing; (100.3190) Inverse problems; (230.7400) Waveguides, slab. http://dx.doi.org/10.1364/OL.38.004269
    Optics Letters 10/2013; 38(21):4269. DOI:10.1364/OL.38.004269 · 3.39 Impact Factor
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    ABSTRACT: The Replicon Theory proposed 50years ago has proven to apply for replicons of the three domains of life. Here we review our knowledge of genome organization into single and multiple replicons in bacteria, archae and eukarya. Bacterial and archaeal replicator/initiator systems are quite specific and efficient whereas eukaryotic replicons show degenerate specificity and efficiency, allowing for complex regulation of origin firing time. We expand on recent evidence that ~50% of the human genome is organized as∼1,500 megabase-sized replication domains with a characteristic parabolic (U-shaped) replication timing profile and linear (N-shaped) gradient of replication fork polarity. These N/U domains correspond to self-interacting segments of the chromatin fiber bordered by open chromatin zones and replicate by cascades of origin firing initiating at their borders and propagating to their center, possibly by fork-stimulated initiation. The conserved occurrence of this replication pattern in the germline of mammals has resulted over evolutionary times in the formation of megabase-sized domains with an N-shaped nucleotide compositional skew profile due to replication-associated mutational asymmetries. Overall, these results reveal an evolutionarily conserved but developmentally plastic organisation of replication that is driving mammalian genome evolution.
    Journal of Molecular Biology 10/2013; DOI:10.1016/j.jmb.2013.09.021 · 3.91 Impact Factor
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    ABSTRACT: Advances in genomic studies have led to significant progress in understanding the epigenetically controlled interplay between chromatin structure and nuclear functions. Epigenetic modifications were shown to play a key role in transcription regulation and genome activity during development and differentiation or in response to the environment. Paradoxically, the molecular mechanisms that regulate the initiation and the maintenance of the spatio-temporal replication program in higher eukaryotes, and in particular their links to epigenetic modifications, still remain elusive. By integrative analysis of the genome-wide distributions of thirteen epigenetic marks in the human cell line K562, at the 100 kb resolution of corresponding mean replication timing (MRT) data, we identify four major groups of chromatin marks with shared features. These states have different MRT, namely from early to late replicating, replication proceeds though a transcriptionally active euchromatin state (C1), a repressive type of chromatin (C2) associated with polycomb complexes, a silent state (C3) not enriched in any available marks, and a gene poor HP1-associated heterochromatin state (C4). When mapping these chromatin states inside the megabase-sized U-domains (U-shaped MRT profile) covering about 50% of the human genome, we reveal that the associated replication fork polarity gradient corresponds to a directional path across the four chromatin states, from C1 at U-domains borders followed by C2, C3 and C4 at centers. Analysis of the other genome half is consistent with early and late replication loci occurring in separate compartments, the former correspond to gene-rich, high-GC domains of intermingled chromatin states C1 and C2, whereas the latter correspond to gene-poor, low-GC domains of alternating chromatin states C3 and C4 or long C4 domains. This new segmentation sheds a new light on the epigenetic regulation of the spatio-temporal replication program in human and provides a framework for further studies in different cell types, in both health and disease.
    PLoS Computational Biology 10/2013; 9(10):e1003233. DOI:10.1371/journal.pcbi.1003233 · 4.83 Impact Factor
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    ABSTRACT: We review the existence of a new type of megabase-sized replication domains along the human genome. These domains are revealed in 7 somatic cell types by U-shaped patterns in the replication timing profiles. In the germline, these domains appear as N-shaped patterns in the DNA compositional asymmetry profiles resulting from replication-associated mutational asymmetries. We demonstrated that the average replication fork polarity is directly proportional to both the DNA compositional asymmetry and the derivative of the replication timing profile. Hence, the average fork polarity changes in a linear manner across U/N-replication domains enlightening a robust mode of replication across cell types and during evolution. Using genome-wide chromatin conformation data, we found that the replication domains remarkably coincide with self-interacting folding units of the chromatin fiber and that their borders are long-range interconnected hubs in the chromatin interaction graph. Altogether our results suggest that the spatio-temporal replication program is intimately coupled to a high-order 3D organization of the human genome.
  • R E Boulos, A Arneodo, P Jensen, B Audit
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    ABSTRACT: We use graph theory to analyze chromatin interaction (Hi-C) data in the human genome. We show that a key functional feature of the genome-"master" replication origins-corresponds to DNA loci of maximal network centrality. These loci form a set of interconnected hubs both within chromosomes and between different chromosomes. Our results open the way to a fruitful use of graph theory concepts to decipher DNA structural organization in relation to genome functions such as replication and transcription. This quantitative information should prove useful to discriminate between possible polymer models of nuclear organization.
    Physical Review Letters 09/2013; 111(11):118102. DOI:10.1103/PhysRevLett.111.118102 · 7.73 Impact Factor
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    ABSTRACT: Increasing knowledge of chromatin structure in various cell types raises the challenge of deciphering the contribution of epigenetic modifications to the regulation of nuclear functions in mammals. In a recent study, we have analysed the genome-wide distributions of thirteen epigenetic marks in the human cell line K562 at 100 kb resolution of Mean Replication Timing (MRT) data. Using classical clustering techniques, we have shown that the combinatorial complexity of these epigenetic data can be reduced to four predominant chromatin states that replicate at different periods of the S-phase. C1 is an early replicating transcriptionally active euchromatin state, C2 a mid-S repressive type of chromatin associated with Polycomb complexes, C3 a silent chromatin with lack of chromatin marks that replicates later than C2 but before C4, a HP1-associated heterochromatin state that replicates at the end of S-phase. These four chromatin states display remarkable similarities with those recently reported in fly, worm and plants at higher ∼ 1 kb resolution of gene expression data. Here, we extend our integrative analysis of epigenetic data in the K562 human cell line to this smaller scale by focusing on gene promoters (±3 kb around transcription start sites). We show that these promoters can similarly be classified into four main chromatin states: P1 regroups all the marks of transcriptionally active chromatin and corresponds to CpG rich promoters of highly expressed genes; P2 is notably associated with the histone modification H3K27me3 that is the mark of a polycomb repressed chromatin state; P3 corresponds to promoters that are not enriched for any available marks as the signature of a ‘null’ or ‘black’ silent heterochromatin state and P4 characterizes the few gene promoters that contain only the constitutive heterochromatin histone modification H3K9me3. When investigating the coherence between promoter activity (P1, P2, P3 or P4) and the large-scale chromatin environment (C1, C2, C3 or C4), we find that the higher the gene density in a considered 100 kb-window, the higher (resp. the lower) the probability of a P1 active promoter (resp. silent P2, P3 and P4 promoters) to be surrounded by an open euchromatin C1 (resp. facultative C2, black C3 or HP1-associated C4 heterochromatin) environment. From large to small scales, it is mainly C4 and to a lesser extent C3 heterochromatin environments both corresponding to gene poor regions, that strongly conditions promoters to belong to the inactive P3 and P4 classes. If C1 (resp. C2) environment surrounds a majority of corresponding active P1 (resp. P2) promoters, it also contains a non-negligible proportion of inactive P2 and P3 (resp. active P1 and inactive P3) promoters. When further investigating the large-scale organization of human genes with respect to ‘master’ replication origins that were shown to border megabase-sized U-shaped MRT domains, we reveal some significant enrichment of highly expressed P1 genes in a closed neighbourhood of these early initiation zones consistently with the gradient of chromatin states observed from C1 at U-domain borders followed by C2, C3 and C4 at U-domain centers. On the contrary to P2 promoters that are mainly found in the C2 environment at finite distance (∼200–300 kb) from U-domain borders, the inactive P3 and P4 promoters are distributed rather homogeneously inside U-domains. The generalization of our study to different cell types including ES, somatic and cancer cells is likely to provide new insight on the global reorganization of replication domains during differentiation (or disease) in relation to coordinated changes in chromatin environment and gene expression.
    Frontiers in Life Science 06/2013; 7(1-2). DOI:10.1080/21553769.2013.832706 · 0.17 Impact Factor
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    ABSTRACT: During the first embryonic division in Caenorhabditis elegans, the mitotic spindle is pulled toward the posterior pole of the cell and undergoes vigorous transverse oscillations. We identified variations in spindle trajectories by analyzing the outwardly similar one-cell stage embryo of its close relative Caenorhabditis briggsae. Compared with C. elegans, C. briggsae embryos exhibit an anterior shifting of nuclei in prophase and reduced anaphase spindle oscillations. By combining physical perturbations and mutant analysis in both species, we show that differences can be explained by interspecies changes in the regulation of the cortical Gα-GPR-LIN-5 complex. However, we found that in both species (1) a conserved positional switch controls the onset of spindle oscillations, (2) GPR posterior localization may set this positional switch, and (3) the maximum amplitude of spindle oscillations is determined by the time spent in the oscillating phase. By investigating microevolution of a subcellular process, we identify new mechanisms that are instrumental to decipher spindle positioning.
    The Journal of Cell Biology 05/2013; DOI:10.1083/jcb.201210110 · 9.69 Impact Factor

Publication Stats

8k Citations
800.93 Total Impact Points


  • 2009–2015
    • University of Lyon
      Lyons, Rhône-Alpes, France
    • Claude Bernard University Lyon 1
      Villeurbanne, Rhône-Alpes, France
  • 2003–2014
    • Ecole normale supérieure de Lyon
      • UMR 5672 - Laboratoire de Physique
      Lyons, Rhône-Alpes, France
  • 2001–2014
    • French National Centre for Scientific Research
      • Centre de génétique moléculaire
      Lutetia Parisorum, Île-de-France, France
  • 2012
    • Université Paris-Sud 11
      • Centre de Génétique Moléculaire (CGM)
      Orsay, Île-de-France, France
  • 1970–2012
    • Centre de Recherche Paul Pascal
      Pessac, Aquitaine, France
  • 2010
    • University of Liège
      Luik, Walloon, Belgium
  • 2007–2010
    • University of Maine
      • Department Mathematics & Statistics
      Orono, Minnesota, United States
    • Center for Molecular Genetics
      Gif, Île-de-France, France
  • 2006
    • Johns Hopkins University
      • Department of Mechanical Engineering
      Baltimore, Maryland, United States
  • 2005
    • Ecole polytechnique fédérale de Lausanne
      Lausanne, Vaud, Switzerland
  • 1993–2005
    • Ecole Normale Supérieure de Paris
      • Laboratoire de Physique Théorique
      Paris, Ile-de-France, France
    • Cornell University
      Итак, New York, United States
  • 1998–2000
    • Université Bordeaux Montaigne
      Pessac, Aquitaine, France
  • 1990–1991
    • University of Bordeaux
      Burdeos, Aquitaine, France
  • 1987–1991
    • University of Texas at Austin
      • Center for Nonlinear Dynamics
      Austin, Texas, United States
  • 1988
    • University of Nice-Sophia Antipolis
      Nice, Provence-Alpes-Côte d'Azur, France