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Tran PN, Ray S, Lemma L, Li Y, Sweeney R, Baskaran A, Dogic Z, Hong P, Hagan MF. Deep-learning optical flow for measuring velocity fields from experimental data. SOFT MATTER 2024. [PMID: 39225732 DOI: 10.1039/d4sm00483c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/04/2024]
Abstract
Deep learning-based optical flow (DLOF) extracts features in adjacent video frames with deep convolutional neural networks. It uses those features to estimate the inter-frame motions of objects. We evaluate the ability of optical flow to quantify the spontaneous flows of microtubule (MT)-based active nematics under different labeling conditions, and compare its performance to particle image velocimetry (PIV). We obtain flow velocity ground truths either by performing semi-automated particle tracking on samples with sparsely labeled filaments, or from passive tracer beads. DLOF produces more accurate velocity fields than PIV for densely labeled samples. PIV cannot reliably distinguish contrast variations at high densities, particularly along the nematic director. DLOF overcomes this limitation. For sparsely labeled samples, DLOF and PIV produce comparable results, but DLOF gives higher-resolution fields. Our work establishes DLOF as a versatile tool for measuring fluid flows in a broad class of active, soft, and biophysical systems.
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Affiliation(s)
- Phu N Tran
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Sattvic Ray
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Linnea Lemma
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Yunrui Li
- Department of Computer Science, Brandeis University, Waltham, MA 02453, USA.
| | - Reef Sweeney
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
- Biomolecular and Engineering Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Pengyu Hong
- Department of Computer Science, Brandeis University, Waltham, MA 02453, USA.
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
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2
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Ghosh S, Joshi C, Baskaran A, Hagan MF. Spatiotemporal control of structure and dynamics in a polar active fluid. SOFT MATTER 2024. [PMID: 39188251 DOI: 10.1039/d4sm00547c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/28/2024]
Abstract
We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.
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Affiliation(s)
- Saptorshi Ghosh
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Chaitanya Joshi
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
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3
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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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Vélez-Cerón I, Guillamat P, Sagués F, Ignés-Mullol J. Probing active nematics with in situ microfabricated elastic inclusions. Proc Natl Acad Sci U S A 2024; 121:e2312494121. [PMID: 38451942 PMCID: PMC10945829 DOI: 10.1073/pnas.2312494121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 01/27/2024] [Indexed: 03/09/2024] Open
Abstract
In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.
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Affiliation(s)
- Ignasi Vélez-Cerón
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona08028, Spain
- Institute of Nanoscience and Nanotechnology, IN2UB, Universitat de Barcelona, Barcelona08028, Spain
| | - Pau Guillamat
- Institute for Bioengineering of Catalonia, The Barcelona Institute for Science and Technology, Barcelona08028, Spain
| | - Francesc Sagués
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona08028, Spain
- Institute of Nanoscience and Nanotechnology, IN2UB, Universitat de Barcelona, Barcelona08028, Spain
| | - Jordi Ignés-Mullol
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona08028, Spain
- Institute of Nanoscience and Nanotechnology, IN2UB, Universitat de Barcelona, Barcelona08028, Spain
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Li Y, Zarei Z, Tran PN, Wang Y, Baskaran A, Fraden S, Hagan MF, Hong P. A machine learning approach to robustly determine director fields and analyze defects in active nematics. SOFT MATTER 2024; 20:1869-1883. [PMID: 38318759 DOI: 10.1039/d3sm01253k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.
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Affiliation(s)
- Yunrui Li
- Computer Science Department, Brandeis University, USA.
| | - Zahra Zarei
- Physics Department, Brandeis University, USA
| | - Phu N Tran
- Physics Department, Brandeis University, USA
| | - Yifei Wang
- Computer Science Department, Brandeis University, USA.
| | | | - Seth Fraden
- Physics Department, Brandeis University, USA
| | | | - Pengyu Hong
- Computer Science Department, Brandeis University, USA.
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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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Mitchell KA, Sabbir MMH, Geumhan K, Smith SA, Klein B, Beller DA. Maximally mixing active nematics. Phys Rev E 2024; 109:014606. [PMID: 38366395 DOI: 10.1103/physreve.109.014606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Accepted: 11/30/2023] [Indexed: 02/18/2024]
Abstract
Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.
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Affiliation(s)
- Kevin A Mitchell
- Physics Department, University of California, Merced, California 95344, USA
| | | | - Kevin Geumhan
- Physics Department, University of California, Merced, California 95344, USA
| | - Spencer A Smith
- Physics Department, Mount Holyoke College, South Hadley, Massachusetts 01075, USA
| | - Brandon Klein
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Daniel A Beller
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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