1
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Klimek A, Mondal D, Block S, Sharma P, Netz RR. Data-driven classification of individual cells by their non-Markovian motion. Biophys J 2024; 123:1173-1183. [PMID: 38515300 PMCID: PMC11140416 DOI: 10.1016/j.bpj.2024.03.023] [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: 01/19/2024] [Revised: 03/11/2024] [Accepted: 03/18/2024] [Indexed: 03/23/2024] Open
Abstract
We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.
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Affiliation(s)
- Anton Klimek
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Debasmita Mondal
- Department of Physics, Indian Institute of Science, Bangalore, India; James Franck Institute, University of Chicago, Chicago, Illinois
| | - Stephan Block
- Institut für Chemie und Biochemie, Freie Universität Berlin, Berlin, Germany
| | - Prerna Sharma
- Department of Physics, Indian Institute of Science, Bangalore, India; Department of Bioengineering, Indian Institute of Science, Bangalore, India
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany.
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2
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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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Liu Y, Jiao Y, Li X, Li G, Wang W, Liu Z, Qin D, Zhong L, Liu L, Shuai J, Li Z. An entropy-based approach for assessing the directional persistence of cell migration. Biophys J 2024; 123:730-744. [PMID: 38366586 PMCID: PMC10995411 DOI: 10.1016/j.bpj.2024.02.010] [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: 10/10/2023] [Revised: 01/23/2024] [Accepted: 02/13/2024] [Indexed: 02/18/2024] Open
Abstract
Cell migration, which is primarily characterized by directional persistence, is essential for the development of normal tissues and organs, as well as for numerous pathological processes. However, there is a lack of simple and efficient tools to analyze the systematic properties of persistence based on cellular trajectory data. Here, we present a novel approach, the entropy of angular distribution , which combines cellular turning dynamics and Shannon entropy to explore the statistical and time-varying properties of persistence that strongly correlate with cellular migration modes. Our results reveal the changes in the persistence of multiple cell lines that are tightly regulated by both intra- and extracellular cues, including Arpin protein, collagen gel/substrate, and physical constraints. Significantly, some previously unreported distinctive details of persistence have also been captured, helping to elucidate how directional persistence is distributed and evolves in different cell populations. The analysis suggests that the entropy of angular distribution-based approach provides a powerful metric for evaluating directional persistence and enables us to better understand the relationships between cellular behaviors and multiscale cues, which also provides some insights into the migration dynamics of cell populations, such as collective cell invasion.
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Affiliation(s)
- Yanping Liu
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona; Department of Physics, Arizona State University, Tempe, Arizona
| | - Xinwei Li
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China
| | - Guoqiang Li
- Chongqing Key Laboratory of Environmental Materials and Remediation Technologies, College of Chemistry and Environmental Engineering, Chongqing University of Arts and Sciences, Chongqing, China
| | - Wei Wang
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China
| | - Zhichao Liu
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China
| | - Dui Qin
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China
| | - Lisha Zhong
- School of Medical Information and Engineering, Southwest Medical University, Luzhou, China
| | - Liyu Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Jianwei Shuai
- Department of Physics, Xiamen University, Xiamen, China; Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen, China; Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, China.
| | - Zhangyong Li
- Chongqing Key Laboratory of Big Data for Bio Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China; Department of Biomedical Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China.
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4
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Pérez-García L, Selin M, Ciarlo A, Magazzù A, Pesce G, Sasso A, Volpe G, Pérez Castillo I, Arzola AV. Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited]. BIOMEDICAL OPTICS EXPRESS 2023; 14:6442-6469. [PMID: 38420310 PMCID: PMC10898575 DOI: 10.1364/boe.495468] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Revised: 08/31/2023] [Accepted: 09/03/2023] [Indexed: 03/02/2024]
Abstract
Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector's finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.
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Affiliation(s)
- Laura Pérez-García
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Martin Selin
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Antonio Ciarlo
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant’Angelo, Via Cintia, I- 80126, Naples, Italy
| | - Alessandro Magazzù
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Giuseppe Pesce
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant’Angelo, Via Cintia, I- 80126, Naples, Italy
| | - Antonio Sasso
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant’Angelo, Via Cintia, I- 80126, Naples, Italy
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Isaac Pérez Castillo
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Alejandro V. Arzola
- Departamento de Física Cuántica y Fotónica, Instituto de Física, Universidad Nacional Autónoma de México, C.P. 04510, Cd. de México, Mexico
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5
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Cerasoli S, Ciliberto S, Marinari E, Oshanin G, Peliti L, Rondoni L. Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator. Phys Rev E 2022; 106:014137. [PMID: 35974646 DOI: 10.1103/physreve.106.014137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.
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Affiliation(s)
- Sara Cerasoli
- Department of Civil and Environmental Engineering, Princeton University, Princeton New Jersey 08544, USA
| | - Sergio Ciliberto
- Laboratoire de Physique (UMR CNRS 567246), Ecole Normale Supérieure, Allée d'Italie, 69364 Lyon, France
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Luca Peliti
- Santa Marinella Research Institute, Santa Marinella, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
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6
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Ferretti F, Chardès V, Mora T, Walczak AM, Giardina I. Renormalization group approach to connect discrete- and continuous-time descriptions of Gaussian processes. Phys Rev E 2022; 105:044133. [PMID: 35590618 DOI: 10.1103/physreve.105.044133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2021] [Accepted: 02/17/2022] [Indexed: 06/15/2023]
Abstract
Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme may perform very differently for the two tasks, if it is not accurate enough. Exact discretizations, which work equally well at any scale, are characterized by the property of invariance under coarse-graining. Motivated by this observation, we build an explicit renormalization group (RG) approach for Gaussian time series generated by autoregressive models. We show that the RG fixed points correspond to discretizations of linear SDEs, and only come in the form of first order Markov processes or non-Markovian ones. This fact provides an alternative explanation of why standard delay-vector embedding procedures fail in reconstructing partially observed noise-driven systems. We also suggest a possible effective Markovian discretization for the inference of partially observed underdamped equilibrium processes based on the exploitation of the Einstein relation.
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Affiliation(s)
- Federica Ferretti
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
| | - Victor Chardès
- Laboratoire de Physique de l'École Normale supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Thierry Mora
- Laboratoire de Physique de l'École Normale supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Aleksandra M Walczak
- Laboratoire de Physique de l'École Normale supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Irene Giardina
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
- INFN, Unità di Roma 1, 00185 Rome, Italy
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7
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Liu Y, Jiao Y, He D, Fan Q, Zheng Y, Li G, Wang G, Yao J, Chen G, Lou S, Shuai J, Liu L. Deriving time-varying cellular motility parameters via wavelet analysis. Phys Biol 2021; 18. [PMID: 33910180 DOI: 10.1088/1478-3975/abfcad] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 04/28/2021] [Indexed: 11/11/2022]
Abstract
Cell migration, which is regulated by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays an indispensable role in many physiological and pathological process such as normal tissue development and cancer metastasis. However, there is a lack of rigorous and quantitative tools for analyzing the time-varying characteristics of cell migration in heterogeneous microenvironment, resulted from, e.g. the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop a wavelet-analysis approach to derive the time-dependent motility parameters from cell migration trajectories, based on the time-varying persistent random walk model. In particular, the wavelet denoising and wavelet transform are employed to analyze migration velocities and obtain the wavelet power spectrum. Subsequently, the time-dependent motility parameters are derived via Lorentzian power spectrum. Our results based on synthetic data indicate the superiority of the method for estimating the intrinsic transient motility parameters, robust against a variety of stochastic noises. We also carry out a systematic parameter study and elaborate the effects of parameter selection on the performance of the method. Moreover, we demonstrate the utility of our approach via analyzing experimental data ofin vitrocell migration in distinct microenvironments, including the migration of MDA-MB-231 cells in confined micro-channel arrays and correlated migration of MCF-10A cells due to ECM-mediated mechanical coupling. Our analysis shows that our approach can be as a powerful tool to accurately derive the time-dependent motility parameters, and further analyze the time-dependent characteristics of cell migration regulated by complex microenvironment.
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Affiliation(s)
- Yanping Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, United States of America.,Department of Physics, Arizona State University, Tempe, Arizona 85287, United States of America
| | - Da He
- Spine Surgery, Beijing Jishuitan Hospital, Beijing, 100035, People's Republic of China
| | - Qihui Fan
- Beijing National Laboratory for Condensed Matte Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Yu Zheng
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States of America
| | - Guoqiang Li
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
| | - Gao Wang
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
| | - Jingru Yao
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
| | - Guo Chen
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
| | - Silong Lou
- Department of Neurosurgery, Chongqing University Cancer Hospital, Chongqing, 400030, People's Republic of China
| | - Jianwei Shuai
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen 361005, People's Republic of China.,Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325000, People's Republic of China
| | - Liyu Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, 401331, People's Republic of China
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8
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Liu Y, Jiao Y, Fan Q, Zheng Y, Li G, Yao J, Wang G, Lou S, Chen G, Shuai J, Liu L. Shannon entropy for time-varying persistence of cell migration. Biophys J 2021; 120:2552-2565. [PMID: 33940024 DOI: 10.1016/j.bpj.2021.04.026] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 03/10/2021] [Accepted: 04/26/2021] [Indexed: 12/13/2022] Open
Abstract
Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and pathological processes. Cell migration is typically modeled as a persistent random walk, which depends on two critical motility parameters, i.e., migration speed and persistence time. It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data. Here, we introduce the normalized Shannon entropy (SE) based on the FPS of cellular velocity autocovariance function to quantify migration dynamics. The SE introduced here possesses a similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration, attaining the maximal value of unity for purely diffusive migration (i.e., SE = 1 for the most "random" dynamics) and the minimal value of 0 for purely ballistic dynamics (i.e., SE = 0 for the most "ordered" dynamics). We also find that SE is strongly correlated with the migration persistence but is less sensitive to the migration speed. Moreover, we introduce the time-varying SE based on the WPS of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which typically results from complex and time-varying intra- or extracellular mechanisms. We employ our approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the SE and wavelet transform (i.e., SE-based approach) offers a simple and efficient tool to quantify cell migration dynamics in complex microenvironment.
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Affiliation(s)
- Yanping Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona; Department of Physics, Arizona State University, Tempe, Arizona
| | - Qihui Fan
- Beijing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
| | - Yu Zheng
- Department of Physics, Arizona State University, Tempe, Arizona
| | - Guoqiang Li
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Jingru Yao
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Gao Wang
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Silong Lou
- Department of Neurosurgery, Chongqing University Cancer Hospital, Chongqing, China
| | - Guo Chen
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China
| | - Jianwei Shuai
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen 361005, China; Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325000, China.
| | - Liyu Liu
- Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China.
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9
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Brückner DB, Arlt N, Fink A, Ronceray P, Rädler JO, Broedersz CP. Learning the dynamics of cell-cell interactions in confined cell migration. Proc Natl Acad Sci U S A 2021; 118:e2016602118. [PMID: 33579821 PMCID: PMC7896326 DOI: 10.1073/pnas.2016602118] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following, and sliding past each other upon collision. Capitalizing on this large experimental dataset of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting noncancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and antifriction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types.
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Affiliation(s)
- David B Brückner
- Arnold Sommerfeld Center for Theoretical Physics, Department of Physics, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
- Center for NanoScience, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
| | - Nicolas Arlt
- Arnold Sommerfeld Center for Theoretical Physics, Department of Physics, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
- Center for NanoScience, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
| | - Alexandra Fink
- Center for NanoScience, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
- Faculty of Physics, Ludwig-Maximilian-University, D-80539 Munich, Germany
| | - Pierre Ronceray
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ 08544
| | - Joachim O Rädler
- Center for NanoScience, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany;
- Faculty of Physics, Ludwig-Maximilian-University, D-80539 Munich, Germany
| | - Chase P Broedersz
- Arnold Sommerfeld Center for Theoretical Physics, Department of Physics, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany;
- Center for NanoScience, Ludwig-Maximilian-University Munich, D-80333 Munich, Germany
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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10
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Mitterwallner BG, Schreiber C, Daldrop JO, Rädler JO, Netz RR. Non-Markovian data-driven modeling of single-cell motility. Phys Rev E 2021; 101:032408. [PMID: 32289977 DOI: 10.1103/physreve.101.032408] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 01/07/2020] [Indexed: 01/23/2023]
Abstract
Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extracted memory function we formulate a generalized exactly solvable cell migration model which indicates that negative friction generates cell persistence over long timescales. The nonequilibrium character of cell motion is investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model that involves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process.
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Affiliation(s)
- Bernhard G Mitterwallner
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Christoph Schreiber
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Jan O Daldrop
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Joachim O Rädler
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
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11
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Brückner DB, Ronceray P, Broedersz CP. Inferring the Dynamics of Underdamped Stochastic Systems. PHYSICAL REVIEW LETTERS 2020; 125:058103. [PMID: 32794851 DOI: 10.1103/physrevlett.125.058103] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Revised: 04/26/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.
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Affiliation(s)
- David B Brückner
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilian-University Munich, Theresienstr. 37, D-80333 Munich, Germany
| | - Pierre Ronceray
- Center for the Physics of Biological Function, Princeton University, Princeton, New Jersey 08544, USA
| | - Chase P Broedersz
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilian-University Munich, Theresienstr. 37, D-80333 Munich, Germany
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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12
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Fortuna I, Perrone GC, Krug MS, Susin E, Belmonte JM, Thomas GL, Glazier JA, de Almeida RMC. CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates. Biophys J 2020; 118:2801-2815. [PMID: 32407685 PMCID: PMC7264849 DOI: 10.1016/j.bpj.2020.04.024] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Revised: 04/20/2020] [Accepted: 04/20/2020] [Indexed: 11/16/2022] Open
Abstract
Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.
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Affiliation(s)
- Ismael Fortuna
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
| | - Gabriel C Perrone
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
| | - Monique S Krug
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
| | - Eduarda Susin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
| | - Julio M Belmonte
- Biocomplexity Institute and Department of Intelligent Systems Engineering, Indiana University, Bloomington, Indiana; Department of Physics, North Carolina State University, Raleigh, North Carolina
| | - Gilberto L Thomas
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil.
| | - James A Glazier
- Biocomplexity Institute and Department of Intelligent Systems Engineering, Indiana University, Bloomington, Indiana
| | - Rita M C de Almeida
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil; Instituto Nacional de Ciência e Tecnologia, Sistemas Complexos, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil; Program de Pós Graduação em Bioinformática, Universidade Federal do Rio Grande do Norte, Natal, Rio Grande do Norte, Brazil.
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13
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Jerison ER, Quake SR. Heterogeneous T cell motility behaviors emerge from a coupling between speed and turning in vivo. eLife 2020; 9:53933. [PMID: 32427565 PMCID: PMC7237209 DOI: 10.7554/elife.53933] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Accepted: 04/30/2020] [Indexed: 12/20/2022] Open
Abstract
T cells in vivo migrate primarily via undirected random walks, but it remains unresolved how these random walks generate an efficient search. Here, we use light sheet microscopy of T cells in the larval zebrafish as a model system to study motility across large populations of cells over hours in their native context. We show that cells do not perform Levy flight; rather, there is substantial cell-to-cell variability in speed, which persists over timespans of a few hours. This variability is amplified by a correlation between speed and directional persistence, generating a characteristic cell behavioral manifold that is preserved under a perturbation to cell speeds, and seen in Mouse T cells and Dictyostelium. Together, these effects generate a broad range of length scales over which cells explore in vivo.
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Affiliation(s)
| | - Stephen R Quake
- Department of Applied Physics, Stanford University, Stanford, United States.,Department of Bioengineering, Stanford University, Stanford, United States.,Chan Zuckerberg Biohub, San Francisco, United States
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14
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Kwon T, Kwon OS, Cha HJ, Sung BJ. Stochastic and Heterogeneous Cancer Cell Migration: Experiment and Theory. Sci Rep 2019; 9:16297. [PMID: 31704971 PMCID: PMC6841739 DOI: 10.1038/s41598-019-52480-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Accepted: 10/16/2019] [Indexed: 12/14/2022] Open
Abstract
Cell migration, an essential process for normal cell development and cancer metastasis, differs from a simple random walk: the mean-square displacement (〈(Δr)2(t)〉) of cells sometimes shows non-Fickian behavior, and the spatiotemporal correlation function (G(r, t)) of cells is often non-Gaussian. We find that this intriguing cell migration should be attributed to heterogeneity in a cell population, even one with a homogeneous genetic background. There are two limiting types of heterogeneity in a cell population: cellular heterogeneity and temporal heterogeneity. Cellular heterogeneity accounts for the cell-to-cell variation in migration capacity, while temporal heterogeneity arises from the temporal noise in the migration capacity of single cells. We illustrate that both cellular and temporal heterogeneity need to be taken into account simultaneously to elucidate cell migration. We investigate the two-dimensional migration of A549 lung cancer cells using time-lapse microscopy and find that the migration of A549 cells is Fickian but has a non-Gaussian spatiotemporal correlation. We find that when a theoretical model considers both cellular and temporal heterogeneity, the model reproduces all of the anomalous behaviors of cancer cell migration.
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Affiliation(s)
- Taejin Kwon
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul, 04107, Republic of Korea
| | - Ok-Seon Kwon
- Department of Life Sciences, Sogang University, Seoul, 04107, Republic of Korea
| | - Hyuk-Jin Cha
- College of Pharmacy, Seoul National University, Seoul, 08826, Republic of Korea.
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul, 04107, Republic of Korea.
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15
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Alonso S, Stange M, Beta C. Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells. PLoS One 2018; 13:e0201977. [PMID: 30138392 PMCID: PMC6107139 DOI: 10.1371/journal.pone.0201977] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2018] [Accepted: 07/25/2018] [Indexed: 11/18/2022] Open
Abstract
Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.
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Affiliation(s)
- Sergio Alonso
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
- * E-mail:
| | - Maike Stange
- Institute of Physics and Astronomy, Universität Potsdam, Potsdam, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, Universität Potsdam, Potsdam, Germany
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16
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Cherstvy AG, Nagel O, Beta C, Metzler R. Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells. Phys Chem Chem Phys 2018; 20:23034-23054. [DOI: 10.1039/c8cp04254c] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Oliver Nagel
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Carsten Beta
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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