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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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Kemeth FP, Alonso S, Echebarria B, Moldenhawer T, Beta C, Kevrekidis IG. Black and gray box learning of amplitude equations: Application to phase field systems. Phys Rev E 2023; 107:025305. [PMID: 36932491 DOI: 10.1103/physreve.107.025305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Accepted: 01/26/2023] [Indexed: 06/18/2023]
Abstract
We present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
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Affiliation(s)
- Felix P Kemeth
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Carrer de Jordi Girona 1-3, 08034 Barcelona, Spain
| | - Blas Echebarria
- Department of Physics, Universitat Politècnica de Catalunya, Carrer de Jordi Girona 1-3, 08034 Barcelona, Spain
| | - Ted Moldenhawer
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Carsten Beta
- Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Ioannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
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Moldenhawer T, Moreno E, Schindler D, Flemming S, Holschneider M, Huisinga W, Alonso S, Beta C. Spontaneous transitions between amoeboid and keratocyte-like modes of migration. Front Cell Dev Biol 2022; 10:898351. [PMID: 36247011 PMCID: PMC9563996 DOI: 10.3389/fcell.2022.898351] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/18/2022] [Indexed: 01/17/2023] Open
Abstract
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
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Affiliation(s)
- Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | - Eduardo Moreno
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sven Flemming
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | | | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- *Correspondence: Carsten Beta,
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Burger GA, van de Water B, Le Dévédec SE, Beltman JB. Density-Dependent Migration Characteristics of Cancer Cells Driven by Pseudopod Interaction. Front Cell Dev Biol 2022; 10:854721. [PMID: 35547818 PMCID: PMC9084912 DOI: 10.3389/fcell.2022.854721] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 03/24/2022] [Indexed: 12/13/2022] Open
Abstract
The ability of cancer cells to invade neighboring tissue from primary tumors is an important determinant of metastatic behavior. Quantification of cell migration characteristics such as migration speed and persistence helps to understand the requirements for such invasiveness. One factor that may influence invasion is how local tumor cell density shapes cell migration characteristics, which we here investigate with a combined experimental and computational modeling approach. First, we generated and analyzed time-lapse imaging data on two aggressive Triple-Negative Breast Cancer (TNBC) cell lines, HCC38 and Hs578T, during 2D migration assays at various cell densities. HCC38 cells exhibited a counter-intuitive increase in speed and persistence with increasing density, whereas Hs578T did not exhibit such an increase. Moreover, HCC38 cells exhibited strong cluster formation with active pseudopod-driven migration, especially at low densities, whereas Hs578T cells maintained a dispersed positioning. In order to obtain a mechanistic understanding of the density-dependent cell migration characteristics and cluster formation, we developed realistic spatial simulations using a Cellular Potts Model (CPM) with an explicit description of pseudopod dynamics. Model analysis demonstrated that pseudopods exerting a pulling force on the cell and interacting via increased adhesion at pseudopod tips could explain the experimentally observed increase in speed and persistence with increasing density in HCC38 cells. Thus, the density-dependent migratory behavior could be an emergent property of single-cell characteristics without the need for additional mechanisms. This implies that pseudopod dynamics and interaction may play a role in the aggressive nature of cancers through mediating dispersal.
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Affiliation(s)
- Gerhard A Burger
- Division of Drug Discovery and Safety, Leiden Academic Centre for Drug Research, Leiden University, Leiden, Netherlands
| | - Bob van de Water
- Division of Drug Discovery and Safety, Leiden Academic Centre for Drug Research, Leiden University, Leiden, Netherlands
| | - Sylvia E Le Dévédec
- Division of Drug Discovery and Safety, Leiden Academic Centre for Drug Research, Leiden University, Leiden, Netherlands
| | - Joost B Beltman
- Division of Drug Discovery and Safety, Leiden Academic Centre for Drug Research, Leiden University, Leiden, Netherlands
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