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Yang H, Meyer F, Huang S, Yang L, Lungu C, Olayioye MA, Buehler MJ, Guo M. Learning Dynamics from Multicellular Graphs with Deep Neural Networks. ARXIV 2024:arXiv:2401.12196v2. [PMID: 38344226 PMCID: PMC10854275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell migratory dynamics from their static configuration is valuable for both understanding and predicting these complex processes. However, the identification of structural features that can indicate multicellular motion has been difficult, and existing metrics largely rely on physical instincts. Here we show that using a graph neural network (GNN), the motion of multicellular collectives can be inferred from a static snapshot of cell positions, in both experimental and synthetic datasets.
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Affiliation(s)
- Haiqian Yang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
| | - Florian Meyer
- Institute of Cell Biology and Immunology, University of Stuttgart, Allmandring 31, 70569 Stuttgart, Germany
| | - Shaoxun Huang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
| | - Liu Yang
- Department of Computer Sciences, University of Wisconsin - Madison, Madison, WI 53706, USA
| | - Cristiana Lungu
- Institute of Cell Biology and Immunology, University of Stuttgart, Allmandring 31, 70569 Stuttgart, Germany
| | - Monilola A. Olayioye
- Institute of Cell Biology and Immunology, University of Stuttgart, Allmandring 31, 70569 Stuttgart, Germany
| | - Markus J. Buehler
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
- Laboratory for Atomistic and Molecular Mechanics (LAMM), Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
- Center for Computational Science and Engineering, Schwarzman College of Computing, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
| | - Ming Guo
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
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Brückner DB, Broedersz CP. Learning dynamical models of single and collective cell migration: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:056601. [PMID: 38518358 DOI: 10.1088/1361-6633/ad36d2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Accepted: 03/22/2024] [Indexed: 03/24/2024]
Abstract
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.
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Affiliation(s)
- David B Brückner
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Chase P Broedersz
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilian-University Munich, Theresienstr. 37, D-80333 Munich, Germany
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3
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Schmitt MS, Colen J, Sala S, Devany J, Seetharaman S, Caillier A, Gardel ML, Oakes PW, Vitelli V. Machine learning interpretable models of cell mechanics from protein images. Cell 2024; 187:481-494.e24. [PMID: 38194965 PMCID: PMC11225795 DOI: 10.1016/j.cell.2023.11.041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 09/20/2023] [Accepted: 11/29/2023] [Indexed: 01/11/2024]
Abstract
Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.
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Affiliation(s)
- Matthew S Schmitt
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Jonathan Colen
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Stefano Sala
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - John Devany
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Shailaja Seetharaman
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Alexia Caillier
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - Margaret L Gardel
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA.
| | - Patrick W Oakes
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA.
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA.
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4
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Mitchell NP, Cislo DJ. TubULAR: tracking in toto deformations of dynamic tissues via constrained maps. Nat Methods 2023; 20:1980-1988. [PMID: 38057529 PMCID: PMC10848277 DOI: 10.1038/s41592-023-02081-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 10/10/2023] [Indexed: 12/08/2023]
Abstract
A common motif in biology is the arrangement of cells into tubes, which further transform into complex shapes. Traditionally, analysis of dynamic tissues has relied on inspecting static snapshots, live imaging of cross-sections or tracking isolated cells in three dimensions. However, capturing the interplay between in-plane and out-of-plane behaviors requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations. Here, we present an analysis framework that builds in toto maps of tissue deformations by following tissue parcels in a static material frame of reference. Our approach then relates in-plane and out-of-plane behaviors and decomposes complex deformation maps into elementary contributions. The tube-like surface Lagrangian analysis resource (TubULAR) provides an open-source implementation accessible either as a standalone toolkit or as an extension of the ImSAnE package used in the developmental biology community. We demonstrate our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. The method naturally generalizes to in vitro and synthetic systems and provides ready access to the mechanical mechanisms relating genetic patterning to organ shape change.
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Affiliation(s)
- Noah P Mitchell
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
| | - Dillon J Cislo
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
- Center for Studies in Physics and Biology, The Rockefeller University, New York, NY, USA.
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Cohen AE, Hastewell AD, Pradhan S, Flavell SW, Dunkel J. Schrödinger Dynamics and Berry Phase of Undulatory Locomotion. PHYSICAL REVIEW LETTERS 2023; 130:258402. [PMID: 37418715 DOI: 10.1103/physrevlett.130.258402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 05/30/2023] [Indexed: 07/09/2023]
Abstract
Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.
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Affiliation(s)
- Alexander E Cohen
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
- Department of Chemical Engineering, Massachusetts Institute of Technology, 25 Ames Street, Cambridge, Massachusetts 02142, USA
| | - Alasdair D Hastewell
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Sreeparna Pradhan
- Picower Institute for Learning and Memory, Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 43 Vassar Street, Cambridge, Massachusetts 02139, USA
| | - Steven W Flavell
- Picower Institute for Learning and Memory, Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 43 Vassar Street, Cambridge, Massachusetts 02139, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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Brandstätter T, Brückner DB, Han YL, Alert R, Guo M, Broedersz CP. Curvature induces active velocity waves in rotating spherical tissues. Nat Commun 2023; 14:1643. [PMID: 36964141 PMCID: PMC10039078 DOI: 10.1038/s41467-023-37054-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 02/26/2023] [Indexed: 03/26/2023] Open
Abstract
The multicellular organization of diverse systems, including embryos, intestines, and tumors relies on coordinated cell migration in curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes have been studied extensively in flat systems, the consequences of geometrical and topological constraints on collective migration in curved systems are largely unknown. Here, we discover a collective mode of cell migration in rotating spherical tissues manifesting as a propagating single-wavelength velocity wave. This wave is accompanied by an apparently incompressible supracellular flow pattern featuring topological defects as dictated by the spherical topology. Using a minimal active particle model, we reveal that this collective mode arises from the effect of curvature on the active flocking behavior of a cell layer confined to a spherical surface. Our results thus identify curvature-induced velocity waves as a mode of collective cell migration, impacting the dynamical organization of 3D curved tissues.
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Affiliation(s)
- Tom Brandstätter
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, The Netherlands
| | - David B Brückner
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria
| | - Yu Long Han
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Ricard Alert
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187, Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstr. 108, 01307, Dresden, Germany
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA
| | - Ming Guo
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany.
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, The Netherlands.
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