1
|
Pasquier C, Guerlais V, Pallez D, Rapetti-Mauss R, Soriani O. A network embedding approach to identify active modules in biological interaction networks. Life Sci Alliance 2023; 6:e202201550. [PMID: 37339804 PMCID: PMC10282331 DOI: 10.26508/lsa.202201550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Revised: 06/06/2023] [Accepted: 06/06/2023] [Indexed: 06/22/2023] Open
Abstract
The identification of condition-specific gene sets from transcriptomic experiments is important to reveal regulatory and signaling mechanisms associated with a given cellular response. Statistical methods of differential expression analysis, designed to assess individual gene variations, have trouble highlighting modules of small varying genes whose interaction is essential to characterize phenotypic changes. To identify these highly informative gene modules, several methods have been proposed in recent years, but they have many limitations that make them of little use to biologists. Here, we propose an efficient method for identifying these active modules that operates on a data embedding combining gene expressions and interaction data. Applications carried out on real datasets show that our method can identify new groups of genes of high interest corresponding to functions not revealed by traditional approaches. Software is available at https://github.com/claudepasquier/amine.
Collapse
Affiliation(s)
- Claude Pasquier
- Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis, I3S - UMR7271 - UNS CNRS, Les Algorithmes - bât. Euclide B, Sophia Antipolis, France
| | - Vincent Guerlais
- Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis, I3S - UMR7271 - UNS CNRS, Les Algorithmes - bât. Euclide B, Sophia Antipolis, France
| | - Denis Pallez
- Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis, I3S - UMR7271 - UNS CNRS, Les Algorithmes - bât. Euclide B, Sophia Antipolis, France
| | - Raphaël Rapetti-Mauss
- iBV - Institut de Biologie Valrose, Université Nice Sophia Antipolis, Faculté des Sciences, Parc Valrose, Nice cedex 2, France
| | - Olivier Soriani
- iBV - Institut de Biologie Valrose, Université Nice Sophia Antipolis, Faculté des Sciences, Parc Valrose, Nice cedex 2, France
| |
Collapse
|
2
|
Pasquier C, Robichon A. Temporal and sequential order of nonoverlapping gene networks unraveled in mated female Drosophila. Life Sci Alliance 2021; 5:5/2/e202101119. [PMID: 34844981 PMCID: PMC8645335 DOI: 10.26508/lsa.202101119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 11/11/2021] [Accepted: 11/12/2021] [Indexed: 12/13/2022] Open
Abstract
Mating triggers successive waves of temporal transcriptomic changes within independent gene networks in female Drosophila, suggesting a recruitment of interconnected modules that vanish in late life. In this study, we reanalyzed available datasets of gene expression changes in female Drosophila head induced by mating. Mated females present metabolic phenotypic changes and display behavioral characteristics that are not observed in virgin females, such as repulsion to male sexual aggressiveness, fidelity to food spots selected for oviposition, and restriction to the colonization of new niches. We characterize gene networks that play a role in female brain plasticity after mating using AMINE, a novel algorithm to find dysregulated modules of interacting genes. The uncovered networks of altered genes revealed a strong specificity for each successive period of life span after mating in the female head, with little conservation between them. This finding highlights a temporal order of recruitment of waves of interconnected genes which are apparently transiently modified: the first wave disappears before the emergence of the second wave in a reversible manner and ends with few consolidated gene expression changes at day 20. This analysis might document an extended field of a programmatic control of female phenotypic traits by male seminal fluid.
Collapse
|
3
|
Buphamalai P, Kokotovic T, Nagy V, Menche J. Network analysis reveals rare disease signatures across multiple levels of biological organization. Nat Commun 2021; 12:6306. [PMID: 34753928 PMCID: PMC8578255 DOI: 10.1038/s41467-021-26674-1] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 10/19/2021] [Indexed: 01/26/2023] Open
Abstract
Rare genetic diseases are typically caused by a single gene defect. Despite this clear causal relationship between genotype and phenotype, identifying the pathobiological mechanisms at various levels of biological organization remains a practical and conceptual challenge. Here, we introduce a network approach for evaluating the impact of rare gene defects across biological scales. We construct a multiplex network consisting of over 20 million gene relationships that are organized into 46 network layers spanning six major biological scales between genotype and phenotype. A comprehensive analysis of 3,771 rare diseases reveals distinct phenotypic modules within individual layers. These modules can be exploited to mechanistically dissect the impact of gene defects and accurately predict rare disease gene candidates. Our results show that the disease module formalism can be applied to rare diseases and generalized beyond physical interaction networks. These findings open up new venues to apply network-based tools for cross-scale data integration.
Collapse
Affiliation(s)
- Pisanu Buphamalai
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria
- Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Campus Vienna BioCenter 5, 1030, Vienna, Austria
| | - Tomislav Kokotovic
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria
- Ludwig Boltzmann Institute for Rare and Undiagnosed Diseases, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria
- Department of Neurology, Medical University of Vienna, Währinger Gürtel 18-20, 1090, Vienna, Austria
| | - Vanja Nagy
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria
- Ludwig Boltzmann Institute for Rare and Undiagnosed Diseases, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria
- Department of Neurology, Medical University of Vienna, Währinger Gürtel 18-20, 1090, Vienna, Austria
| | - Jörg Menche
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Lazarettgasse 14, AKH BT 25.3, 1090, Vienna, Austria.
- Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Campus Vienna BioCenter 5, 1030, Vienna, Austria.
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria.
| |
Collapse
|
4
|
Pirch S, Müller F, Iofinova E, Pazmandi J, Hütter CVR, Chiettini M, Sin C, Boztug K, Podkosova I, Kaufmann H, Menche J. The VRNetzer platform enables interactive network analysis in Virtual Reality. Nat Commun 2021; 12:2432. [PMID: 33893283 PMCID: PMC8065164 DOI: 10.1038/s41467-021-22570-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 03/09/2021] [Indexed: 12/17/2022] Open
Abstract
Networks provide a powerful representation of interacting components within complex systems, making them ideal for visually and analytically exploring big data. However, the size and complexity of many networks render static visualizations on typically-sized paper or screens impractical, resulting in proverbial ‘hairballs’. Here, we introduce a Virtual Reality (VR) platform that overcomes these limitations by facilitating the thorough visual, and interactive, exploration of large networks. Our platform allows maximal customization and extendibility, through the import of custom code for data analysis, integration of external databases, and design of arbitrary user interface elements, among other features. As a proof of concept, we show how our platform can be used to interactively explore genome-scale molecular networks to identify genes associated with rare diseases and understand how they might contribute to disease development. Our platform represents a general purpose, VR-based data exploration platform for large and diverse data types by providing an interface that facilitates the interaction between human intuition and state-of-the-art analysis methods. Data-rich networks can be difficult to interpret beyond a certain size. Here, the authors introduce a platform that uses virtual reality to allow the visual exploration of large networks, while interfacing with data repositories and other analytical methods to improve the interpretation of big data.
Collapse
Affiliation(s)
- Sebastian Pirch
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria
| | - Felix Müller
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria
| | - Eugenia Iofinova
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria
| | - Julia Pazmandi
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria.,Ludwig Boltzmann Institute for Rare and Undiagnosed Diseases, Vienna, Austria
| | - Christiane V R Hütter
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria
| | - Martin Chiettini
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria
| | - Celine Sin
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria
| | - Kaan Boztug
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria.,Ludwig Boltzmann Institute for Rare and Undiagnosed Diseases, Vienna, Austria.,St. Anna Children's Cancer Research Institute (CCRI), Vienna, Austria.,St. Anna Children's Hospital, Department of Pediatrics and Adolescent Medicine, Medical University of Vienna, Vienna, Austria.,Department of Pediatrics and Adolescent Medicine, Medical University of Vienna, Vienna, Austria
| | - Iana Podkosova
- Institute of Visual Computing and Human-Centered Technology, TU Wien, Vienna, Austria
| | - Hannes Kaufmann
- Institute of Visual Computing and Human-Centered Technology, TU Wien, Vienna, Austria
| | - Jörg Menche
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria. .,Department of Structural and Computational Biology, Max Perutz Labs, University of Vienna, Vienna, Austria. .,Faculty of Mathematics, University of Vienna, Vienna, Austria.
| |
Collapse
|
5
|
Lebraud E, Pinna G, Siberchicot C, Depagne J, Busso D, Fantini D, Irbah L, Robeska E, Kratassiouk G, Ravanat JL, Epe B, Radicella JP, Campalans A. Chromatin recruitment of OGG1 requires cohesin and mediator and is essential for efficient 8-oxoG removal. Nucleic Acids Res 2020; 48:9082-9097. [PMID: 32710616 PMCID: PMC7498353 DOI: 10.1093/nar/gkaa611] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Revised: 07/07/2020] [Accepted: 07/15/2020] [Indexed: 12/29/2022] Open
Abstract
One of the most abundant DNA lesions induced by oxidative stress is the highly mutagenic 8-oxoguanine (8-oxoG), which is specifically recognized by 8-oxoguanine DNA glycosylase 1 (OGG1) to initiate its repair. How DNA glycosylases find small non-helix-distorting DNA lesions amongst millions of bases packaged in the chromatin-based architecture of the genome remains an open question. Here, we used a high-throughput siRNA screening to identify factors involved in the recognition of 8-oxoG by OGG1. We show that cohesin and mediator subunits are required for re-localization of OGG1 and other base excision repair factors to chromatin upon oxidative stress. The association of OGG1 with euchromatin is necessary for the removal of 8-oxoG. Mediator subunits CDK8 and MED12 bind to chromatin and interact with OGG1 in response to oxidative stress, suggesting they participate in the recruitment of the DNA glycosylase. The oxidative stress-induced association between the cohesin and mediator complexes and OGG1 reveals an unsuspected function of those complexes in the maintenance of genomic stability.
Collapse
Affiliation(s)
- Emilie Lebraud
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Guillaume Pinna
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91198 Gif-sur-Yvette, France
| | - Capucine Siberchicot
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Jordane Depagne
- Institute of Cellular and Molecular Radiobiology, U1274 INSERM, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Didier Busso
- Institute of Cellular and Molecular Radiobiology, U1274 INSERM, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Damiano Fantini
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Lamya Irbah
- Institute of Cellular and Molecular Radiobiology, U1274 INSERM, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Elena Robeska
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Gueorgui Kratassiouk
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91198 Gif-sur-Yvette, France
| | - Jean-Luc Ravanat
- Univ. Grenoble Alpes, CEA, CNRS IRIG/SyMMES, F-38054 Grenoble, France
| | - Bernd Epe
- Institute of Pharmaceutical and Biomedical Sciences, University of Mainz, Germany
| | - J Pablo Radicella
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| | - Anna Campalans
- Institut de Biologie François Jacob, Institute of Cellular and Molecular Radiobiology, Université Paris-Saclay, Université de Paris, CEA, 18 route du Panorama, F-92265 Fontenay-aux-Roses, France
| |
Collapse
|
6
|
Rubanova N, Pinna G, Kropp J, Campalans A, Radicella JP, Polesskaya A, Harel-Bellan A, Morozova N. MasterPATH: network analysis of functional genomics screening data. BMC Genomics 2020; 21:632. [PMID: 32928103 PMCID: PMC7491077 DOI: 10.1186/s12864-020-07047-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 09/01/2020] [Indexed: 12/18/2022] Open
Abstract
Background Functional genomics employs several experimental approaches to investigate gene functions. High-throughput techniques, such as loss-of-function screening and transcriptome profiling, allow to identify lists of genes potentially involved in biological processes of interest (so called hit list). Several computational methods exist to analyze and interpret such lists, the most widespread of which aim either at investigating of significantly enriched biological processes, or at extracting significantly represented subnetworks. Results Here we propose a novel network analysis method and corresponding computational software that employs the shortest path approach and centrality measure to discover members of molecular pathways leading to the studied phenotype, based on functional genomics screening data. The method works on integrated interactomes that consist of both directed and undirected networks – HIPPIE, SIGNOR, SignaLink, TFactS, KEGG, TransmiR, miRTarBase. The method finds nodes and short simple paths with significant high centrality in subnetworks induced by the hit genes and by so-called final implementers – the genes that are involved in molecular events responsible for final phenotypic realization of the biological processes of interest. We present the application of the method to the data from miRNA loss-of-function screen and transcriptome profiling of terminal human muscle differentiation process and to the gene loss-of-function screen exploring the genes that regulates human oxidative DNA damage recognition. The analysis highlighted the possible role of several known myogenesis regulatory miRNAs (miR-1, miR-125b, miR-216a) and their targets (AR, NR3C1, ARRB1, ITSN1, VAV3, TDGF1), as well as linked two major regulatory molecules of skeletal myogenesis, MYOD and SMAD3, to their previously known muscle-related targets (TGFB1, CDC42, CTCF) and also to a number of proteins such as C-KIT that have not been previously studied in the context of muscle differentiation. The analysis also showed the role of the interaction between H3 and SETDB1 proteins for oxidative DNA damage recognition. Conclusion The current work provides a systematic methodology to discover members of molecular pathways in integrated networks using functional genomics screening data. It also offers a valuable instrument to explain the appearance of a set of genes, previously not associated with the process of interest, in the hit list of each particular functional genomics screening.
Collapse
Affiliation(s)
- Natalia Rubanova
- Institut des Hautes Etudes Scientifiques, Le Bois-Marie 35 rte de Chartres, 91440, Bures-sur-Yvette, France. .,Université Paris Diderot, Paris, France. .,Skolkovo Institute of Science and Technology, Skolkovo, Russia.
| | - Guillaume Pinna
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91198, Gif-sur-Yvette cedex, France
| | - Jeremie Kropp
- Institut des Hautes Etudes Scientifiques, Le Bois-Marie 35 rte de Chartres, 91440, Bures-sur-Yvette, France
| | - Anna Campalans
- Institute of Molecular and Cellular Radiobiology, Institut François Jacob, CEA, F-92265, Fontenay-aux-Roses, France.,INSERM, U967, bâtiment 56 PC 103 18 route du Panorama, BP6 92265, Fontenay-aux-Roses Cedex, France.,Université Paris Sud, U967, bâtiment 56 PC 103 18 route du Panorama, BP6 92265, Fontenay-aux-Roses Cedex, France
| | - Juan Pablo Radicella
- Institute of Molecular and Cellular Radiobiology, Institut François Jacob, CEA, F-92265, Fontenay-aux-Roses, France.,INSERM, U967, bâtiment 56 PC 103 18 route du Panorama, BP6 92265, Fontenay-aux-Roses Cedex, France.,Université Paris Sud, U967, bâtiment 56 PC 103 18 route du Panorama, BP6 92265, Fontenay-aux-Roses Cedex, France
| | - Anna Polesskaya
- Ecole Polytechnique, Université Paris-Saclay, CNRS UMR 7654, Laboratoire de Biochimie, Ecole Polytechnique, 91128, Palaiseau, France
| | - Annick Harel-Bellan
- Institut des Hautes Etudes Scientifiques, Le Bois-Marie 35 rte de Chartres, 91440, Bures-sur-Yvette, France
| | - Nadya Morozova
- Institut des Hautes Etudes Scientifiques, Le Bois-Marie 35 rte de Chartres, 91440, Bures-sur-Yvette, France.,Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91198, Gif-sur-Yvette cedex, France
| |
Collapse
|
7
|
Klein HU, Schäfer M, Bennett DA, Schwender H, De Jager PL. Bayesian integrative analysis of epigenomic and transcriptomic data identifies Alzheimer's disease candidate genes and networks. PLoS Comput Biol 2020; 16:e1007771. [PMID: 32255787 PMCID: PMC7138305 DOI: 10.1371/journal.pcbi.1007771] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Accepted: 03/03/2020] [Indexed: 12/28/2022] Open
Abstract
Biomedical research studies have generated large multi-omic datasets to study complex diseases like Alzheimer’s disease (AD). An important aim of these studies is the identification of candidate genes that demonstrate congruent disease-related alterations across the different data types measured by the study. We developed a new method to detect such candidate genes in large multi-omic case-control studies that measure multiple data types in the same set of samples. The method is based on a gene-centric integrative coefficient quantifying to what degree consistent differences are observed in the different data types. For statistical inference, a Bayesian hierarchical model is used to study the distribution of the integrative coefficient. The model employs a conditional autoregressive prior to integrate a functional gene network and to share information between genes known to be functionally related. We applied the method to an AD dataset consisting of histone acetylation, DNA methylation, and RNA transcription data from human cortical tissue samples of 233 subjects, and we detected 816 genes with consistent differences between persons with AD and controls. The findings were validated in protein data and in RNA transcription data from two independent AD studies. Finally, we found three subnetworks of jointly dysregulated genes within the functional gene network which capture three distinct biological processes: myeloid cell differentiation, protein phosphorylation and synaptic signaling. Further investigation of the myeloid network indicated an upregulation of this network in early stages of AD prior to accumulation of hyperphosphorylated tau and suggested that increased CSF1 transcription in astrocytes may contribute to microglial activation in AD. Thus, we developed a method that integrates multiple data types and external knowledge of gene function to detect candidate genes, applied the method to an AD dataset, and identified several disease-related genes and processes demonstrating the usefulness of the integrative approach. Recent technological advances have led to a new generation of studies that interrogate multiple molecular levels in the same target tissue of a set of subjects, generating complex multi-omic datasets with which to study disease mechanism. These datasets of genetic, epigenomic, transcriptomic, and other data have the potential to reveal novel biological insights; however, integrative analyses remain challenging and require new computational methods. We developed an integrative Bayesian approach to detect genes with consistent differences between case and control samples across multiple data types. The method further integrates prior knowledge about gene function in the form of a gene functional similarity network to improve statistical inference by sharing information between related genes. We applied our method to an Alzheimer’s disease dataset of epigenomic and transcriptomic data and detected and then validated several novel and known candidate genes as well as three major disease-related biological processes. One of these processes reflected microglial activation and included the cytokine CSF1. Single-nucleus data revealed that CSF1 was primarily upregulated in astrocytes, implicating the involvement of this cell type in microglial activation. Hence, we demonstrated that integrative analysis approaches to multi-omic datasets can improve candidate gene detection and thereby generate new insights into complex diseases.
Collapse
Affiliation(s)
- Hans-Ulrich Klein
- Center for Translational & Computational Neuroimmunology, Department of Neurology, Columbia University Irving Medical Center, New York, New York, United States of America
- Taub Institute for Research on Alzheimer's Disease and the Aging Brain, Columbia University Irving Medical Center, New York, New York, United States of America
- * E-mail:
| | - Martin Schäfer
- Mathematical Institute, Heinrich Heine University, Düsseldorf, Germany
| | - David A. Bennett
- Rush Alzheimer’s Disease Center, Rush University Medical Center, Chicago, Illinois, United States of America
| | - Holger Schwender
- Mathematical Institute, Heinrich Heine University, Düsseldorf, Germany
| | - Philip L. De Jager
- Center for Translational & Computational Neuroimmunology, Department of Neurology, Columbia University Irving Medical Center, New York, New York, United States of America
- Taub Institute for Research on Alzheimer's Disease and the Aging Brain, Columbia University Irving Medical Center, New York, New York, United States of America
| |
Collapse
|