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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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Schindler D, Moldenhawer T, Beta C, Huisinga W, Holschneider M. Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions. PLoS One 2024; 19:e0297511. [PMID: 38277351 PMCID: PMC10817190 DOI: 10.1371/journal.pone.0297511] [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: 08/27/2023] [Accepted: 01/07/2024] [Indexed: 01/28/2024] Open
Abstract
Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.
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Affiliation(s)
- Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Matthias Holschneider
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
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Qi X, Ma S, Jiang X, Wu H, Zheng J, Wang S, Han K, Zhang T, Gao J, Li X. Single-cell characterization of deformation and dynamics of mesenchymal stem cells in microfluidic systems: A computational study. Phys Rev E 2023; 108:054402. [PMID: 38115453 DOI: 10.1103/physreve.108.054402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 10/13/2023] [Indexed: 12/21/2023]
Abstract
Understanding the homing dynamics of individual mesenchymal stem cells (MSCs) in physiologically relevant microenvironments is crucial for improving the efficacy of MSC-based therapies for therapeutic and targeting purposes. This study investigates the passive homing behavior of individual MSCs in micropores that mimic interendothelial clefts through predictive computational simulations informed by previous microfluidic experiments. Initially, we quantified the size-dependent behavior of MSCs in micropores and elucidated the underlying mechanisms. Subsequently, we analyzed the shape deformation and traversal dynamics of each MSC. In addition, we conducted a systematic investigation to understand how the mechanical properties of MSCs impact their traversal process. We considered geometric and mechanical parameters, such as reduced cell volume, cell-to-nucleus diameter ratio, and cytoskeletal prestress states. Furthermore, we quantified the changes in the MSC traversal process and identified the quantitative limits in their response to variations in micropore length. Taken together, the computational results indicate the complex dynamic behavior of individual MSCs in the confined microflow. This finding offers an objective way to evaluate the homing ability of MSCs in an interendothelial-slit-like microenvironment.
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Affiliation(s)
- Xiaojing Qi
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou 310027, China
| | - Shuhao Ma
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou 310027, China
| | - Xinchi Jiang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310027, China
| | - Honghui Wu
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310027, China
| | - Juanjuan Zheng
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310027, China
| | - Shuo Wang
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou 310027, China
| | - Keqin Han
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou 310027, China
| | - Tianyuan Zhang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310027, China
| | - Jianqing Gao
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310027, China
| | - Xuejin Li
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou 310027, China
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Ioratim-Uba A, Loisy A, Henkes S, Liverpool TB. The nonlinear motion of cells subject to external forces. SOFT MATTER 2022; 18:9008-9016. [PMID: 36399136 PMCID: PMC10141577 DOI: 10.1039/d2sm00934j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Accepted: 11/04/2022] [Indexed: 06/16/2023]
Abstract
To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop.
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Affiliation(s)
| | - Aurore Loisy
- School of Mathematics, University of Bristol, Bristol BS8 1UG, UK.
| | - Silke Henkes
- School of Mathematics, University of Bristol, Bristol BS8 1UG, UK.
- Lorentz Institute for Theoretical Physics, Leiden University, Leiden 2333 CA, The Netherlands
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Wortel IMN, Niculescu I, Kolijn PM, Gov NS, de Boer RJ, Textor J. Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration. Biophys J 2021; 120:2609-2622. [PMID: 34022237 PMCID: PMC8390880 DOI: 10.1016/j.bpj.2021.04.036] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 03/24/2021] [Accepted: 04/14/2021] [Indexed: 12/28/2022] Open
Abstract
Cell migration is astoundingly diverse. Molecular signatures, cell-cell interactions, and environmental structures each play their part in shaping cell motion, yielding numerous morphologies and migration modes. Nevertheless, in recent years, a simple unifying law was found to describe cell migration across many different cell types and contexts: faster cells turn less frequently. This universal coupling between speed and persistence (UCSP) was explained by retrograde actin flow from front to back, but it remains unclear how this mechanism generalizes to cells with complex shapes and cells migrating in structured environments, which may not have a well-defined front-to-back orientation. Here, we present an in-depth characterization of an existing cellular Potts model, in which cells polarize dynamically from a combination of local actin dynamics (stimulating protrusions) and global membrane tension along the perimeter (inhibiting protrusions). We first show that the UCSP emerges spontaneously in this model through a cross talk of intracellular mechanisms, cell shape, and environmental constraints, resembling the dynamic nature of cell migration in vivo. Importantly, we find that local protrusion dynamics suffice to reproduce the UCSP-even in cases in which no clear global, front-to-back polarity exists. We then harness the spatial nature of the cellular Potts model to show how cell shape dynamics limit both the speed and persistence a cell can reach and how a rigid environment such as the skin can restrict cell motility even further. Our results broaden the range of potential mechanisms underlying the speed-persistence coupling that has emerged as a fundamental property of migrating cells.
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Affiliation(s)
- Inge M N Wortel
- Department of Tumor Immunology, Radboud Institute for Molecular Life Sciences, Nijmegen, the Netherlands; Data Science, Institute for Computing and Information Sciences, Radboud University, Nijmegen, the Netherlands.
| | - Ioana Niculescu
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - P Martijn Kolijn
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - Nir S Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Rob J de Boer
- Theoretical Biology and Bioinformatics, Department of Biology, Utrecht University, Utrecht, the Netherlands
| | - Johannes Textor
- Department of Tumor Immunology, Radboud Institute for Molecular Life Sciences, Nijmegen, the Netherlands; Data Science, Institute for Computing and Information Sciences, Radboud University, Nijmegen, the Netherlands.
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