Singular manifolds of proteomic drivers to model the evolution of inflammatory bowel disease status

The conditions who denotes the presence of an immune disease are often represented by interaction graphs. These informative, but complex structures are susceptible to being perturbed at different levels. The mode in which that perturbation occurs is still of utmost importance in areas such as reprogramming therapeutics. In this sense, the overall graph architecture is well characterise by module identification. Topological overlap-related measures make possible the localisation of highly specific module regulators that can perturb other nodes, potentially causing the entire system to change behaviour or collapse. We provide a geometric framework explaining such situations in the context of inflammatory bowel diseases (IBD). IBD are important chronic disorders of the gastrointestinal tract which incidence is dramatically increasing worldwide. Our approach models different IBD status as Riemannian manifolds defined by the graph Laplacian of two high throughput proteome screenings. Identifies module regulators as singularities within the manifolds (the so-called singular manifolds). And reinterprets the characteristic IBD nonlinear dynamics as compensatory responses to perturbations on those singularities. Thus, we could control the evolution of the disease status by reconfiguring particular setups of immune system to an innocuous target state.

[1]  S. P. Cornelius,et al.  Realistic control of network dynamics , 2013, Nature Communications.

[2]  G. Wainrib,et al.  Topological Modelling of Deep Ulcerations in Patients with Ulcerative Colitis , 2017 .

[3]  E. Stein Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. , 1970 .

[4]  Jie Sun,et al.  Controllability transition and nonlocality in network control. , 2013, Physical review letters.

[5]  M. Ashburner,et al.  Gene Ontology: tool for the unification of biology , 2000, Nature Genetics.

[6]  Huaiyu Zhu On Information and Sufficiency , 1997 .

[7]  S. Horvath,et al.  A General Framework for Weighted Gene Co-Expression Network Analysis , 2005, Statistical applications in genetics and molecular biology.

[8]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[9]  Gary D. Bader,et al.  The GeneMANIA prediction server: biological network integration for gene prioritization and predicting gene function , 2010, Nucleic Acids Res..

[10]  P. Lakatos,et al.  The burden of inflammatory bowel disease in Europe. , 2013, Journal of Crohn's & colitis.

[11]  Bin Zhang,et al.  Defining clusters from a hierarchical cluster tree: the Dynamic Tree Cut package for R , 2008, Bioinform..

[12]  Jens Timmer,et al.  Fast integration-based prediction bands for ordinary differential equation models , 2016, Bioinform..

[13]  Adilson E. Motter,et al.  Controlling Complex Networks with Compensatory Perturbations , 2011, ArXiv.

[14]  J. Hugot,et al.  Increased Proliferation of the Ileal Epithelium as a Remote Effect of Ulcerative Colitis , 2016, Inflammatory bowel diseases.

[15]  Mikhail Belkin,et al.  Toward Understanding Complex Spaces: Graph Laplacians on Manifolds with Singularities and Boundaries , 2012, COLT.

[16]  S. P. Cornelius,et al.  Comment on "Controllability of Complex Networks with Nonlinear Dynamics" , 2011, 1108.5739.

[17]  Jonathan G. Lees,et al.  Systematic computational prediction of protein interaction networks , 2011, Physical biology.

[18]  Peter Langfelder,et al.  Eigengene networks for studying the relationships between co-expression modules , 2007, BMC Systems Biology.

[19]  D. Figeys,et al.  Proteomic analysis of ascending colon biopsies from a paediatric inflammatory bowel disease inception cohort identifies protein biomarkers that differentiate Crohn's disease from UC , 2016, Gut.

[20]  Rui Luo,et al.  Is My Network Module Preserved and Reproducible? , 2011, PLoS Comput. Biol..

[21]  S. Danese,et al.  Actors and Factors in the Resolution of Intestinal Inflammation: Lipid Mediators As a New Approach to Therapy in Inflammatory Bowel Diseases , 2017, Front. Immunol..

[22]  Christine A. Orengo,et al.  Finding the “Dark Matter” in Human and Yeast Protein Network Prediction and Modelling , 2010, PLoS Comput. Biol..

[23]  A. Gasbarrini,et al.  The Innate and Adaptive Immune System as Targets for Biologic Therapies in Inflammatory Bowel Disease , 2017, International journal of molecular sciences.

[24]  B. Hammock,et al.  Soluble epoxide hydrolase: gene structure, expression and deletion. , 2013, Gene.

[25]  Robert D. Nowak,et al.  Multi-Manifold Semi-Supervised Learning , 2009, AISTATS.

[26]  Jun Dong,et al.  Geometric Interpretation of Gene Coexpression Network Analysis , 2008, PLoS Comput. Biol..

[27]  Dong Chen,et al.  Nonlinear manifold representations for functional data , 2012, 1205.6040.

[28]  Steve Horvath,et al.  WGCNA: an R package for weighted correlation network analysis , 2008, BMC Bioinformatics.

[29]  S. Horvath Weighted Network Analysis: Applications in Genomics and Systems Biology , 2011 .