title: A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference.
abstract: Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
authors.affiliation: Department of Medicine, Unit of Computational Medicine, Center for Molecular Medicine, Karolinska Institutet, Solna, Sweden Center for Molecular Medicine, Karolinska Institutet, L8:05, 171 76 Stockholm, Sweden Department of Medicine, Unit of Clinical Epidemiology, Karolinska University Hospital L8, 17176 Stockholm, Sweden Science for Life Laboratory, Stockholm, Sweden jesper.tegner@ki.se.
authors.forename: Jesper
authors.identifier: http://orcid.org/0000-0002-9568-5588
authors.initials: J
authors.lastname: Tegnér
authors.affiliation: Department of Medicine, Unit of Computational Medicine, Center for Molecular Medicine, Karolinska Institutet, Solna, Sweden Center for Molecular Medicine, Karolinska Institutet, L8:05, 171 76 Stockholm, Sweden Department of Medicine, Unit of Clinical Epidemiology, Karolinska University Hospital L8, 17176 Stockholm, Sweden Science for Life Laboratory, Stockholm, Sweden.
authors.forename: Hector
authors.initials: H
authors.lastname: Zenil
authors.affiliation: Department of Medicine, Unit of Computational Medicine, Center for Molecular Medicine, Karolinska Institutet, Solna, Sweden Center for Molecular Medicine, Karolinska Institutet, L8:05, 171 76 Stockholm, Sweden Department of Medicine, Unit of Clinical Epidemiology, Karolinska University Hospital L8, 17176 Stockholm, Sweden Science for Life Laboratory, Stockholm, Sweden.
authors.forename: Narsis A
authors.initials: NA
authors.lastname: Kiani
authors.affiliation: Department of Medicine, Unit of Computational Medicine, Center for Molecular Medicine, Karolinska Institutet, Solna, Sweden Center for Molecular Medicine, Karolinska Institutet, L8:05, 171 76 Stockholm, Sweden Department of Medicine, Unit of Clinical Epidemiology, Karolinska University Hospital L8, 17176 Stockholm, Sweden Science for Life Laboratory, Stockholm, Sweden.
authors.forename: Gordon
authors.initials: G
authors.lastname: Ball
authors.affiliation: Department of Medicine, Unit of Computational Medicine, Center for Molecular Medicine, Karolinska Institutet, Solna, Sweden Center for Molecular Medicine, Karolinska Institutet, L8:05, 171 76 Stockholm, Sweden Department of Medicine, Unit of Clinical Epidemiology, Karolinska University Hospital L8, 17176 Stockholm, Sweden Science for Life Laboratory, Stockholm, Sweden Mucosal and Salivary Biology Division, King's College London Dental Institute, London SE1 9RT, UK.
authors.forename: David
authors.initials: D
authors.lastname: Gomez-Cabrero
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016208:Databases, Factual; D008954:Models, Biological; D008956:Models, Chemical; D008958:Models, Molecular; D011789:Quantum Theory
keywords: big data; computational biology; living systems; model reduction; modelling; systems biology