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Germano DPJ, Zanca A, Johnston ST, Flegg JA, Osborne JM. Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems. Bull Math Biol 2023; 85:111. [PMID: 37805982 PMCID: PMC10560655 DOI: 10.1007/s11538-023-01214-8] [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: 06/05/2023] [Accepted: 09/11/2023] [Indexed: 10/10/2023]
Abstract
Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.
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Affiliation(s)
- Domenic P. J. Germano
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Adriana Zanca
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Stuart T. Johnston
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Jennifer A. Flegg
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - James M. Osborne
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
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2
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Fischer SC, Bassel GW, Kollmannsberger P. Tissues as networks of cells: towards generative rules of complex organ development. J R Soc Interface 2023; 20:20230115. [PMID: 37491909 PMCID: PMC10369035 DOI: 10.1098/rsif.2023.0115] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 07/05/2023] [Indexed: 07/27/2023] Open
Abstract
Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.
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Affiliation(s)
- Sabine C. Fischer
- Center for Computational and Theoretical Biology, Faculty of Biology, University of Würzburg, Würzburg, Germany
| | - George W. Bassel
- School of Life Sciences, The University of Warwick, Coventry, UK
| | - Philip Kollmannsberger
- Biomedical Physics, Department of Physics, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
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3
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Gonçalves IG, García-Aznar JM. Hybrid computational models of multicellular tumour growth considering glucose metabolism. Comput Struct Biotechnol J 2023; 21:1262-1271. [PMID: 36814723 PMCID: PMC9939553 DOI: 10.1016/j.csbj.2023.01.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Revised: 01/30/2023] [Accepted: 01/30/2023] [Indexed: 02/04/2023] Open
Abstract
Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.
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Key Words
- ABM, agent-based model
- ATP, adenosine triphosphate
- CA, cellular automata
- CPM, cellular Potts model
- ECM, extracellular matrix
- FBA, Flux Balance Analysis
- FDG-PET, [18F]-fluorodeoxyglucose-positron emission tomography
- MCTS, multicellular tumour spheroids
- ODEs, ordinary differential equations
- PDEs, partial differential equations
- SBML, Systems Biology Markup Language
- Warburg effect
- agent-based models
- glucose metabolism
- hybrid modelling
- multicellular simulations
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Affiliation(s)
- Inês G Gonçalves
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
| | - José Manuel García-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
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Movilla N, Gonçalves IG, Borau C, García-Aznar JM. A novel integrated experimental and computational approach to unravel fibroblast motility in response to chemical gradients in 3D collagen matrices. Integr Biol (Camb) 2022; 14:212-227. [PMID: 36756930 DOI: 10.1093/intbio/zyad002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 01/06/2023] [Accepted: 01/07/2023] [Indexed: 02/10/2023]
Abstract
Fibroblasts play an essential role in tissue repair and regeneration as they migrate to wounded areas to secrete and remodel the extracellular matrix. Fibroblasts recognize chemical substances such as growth factors, which enhance their motility towards the wounded tissues through chemotaxis. Although several studies have characterized single-cell fibroblast motility before, the migration patterns of fibroblasts in response to external factors have not been fully explored in 3D environments. We present a study that combines experimental and computational efforts to characterize the effect of chemical stimuli on the invasion of 3D collagen matrices by fibroblasts. Experimentally, we used microfluidic devices to create chemical gradients using collagen matrices of distinct densities. We evaluated how cell migration patterns were affected by the presence of growth factors and the mechanical properties of the matrix. Based on these results, we present a discrete-based computational model to simulate cell motility, which we calibrated through the quantitative comparison of experimental and computational data via Bayesian optimization. By combining these approaches, we predict that fibroblasts respond to both the presence of chemical factors and their spatial location. Furthermore, our results show that the presence of these chemical gradients could be reproduced by our computational model through increases in the magnitude of cell-generated forces and enhanced cell directionality. Although these model predictions require further experimental validation, we propose that our framework can be applied as a tool that takes advantage of experimental data to guide the calibration of models and predict which mechanisms at the cellular level may justify the experimental findings. Consequently, these new insights may also guide the design of new experiments, tailored to validate the variables of interest identified by the model.
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Affiliation(s)
- Nieves Movilla
- Department of Mechanical Engineering, Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Spain
| | - Inês G Gonçalves
- Department of Mechanical Engineering, Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Spain
| | - Carlos Borau
- Department of Mechanical Engineering, Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Spain
| | - Jose Manuel García-Aznar
- Department of Mechanical Engineering, Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Spain
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Senthilkumar I, Howley E, McEvoy E. Thermodynamically-motivated chemo-mechanical models and multicellular simulation to provide new insight into active cell and tumour remodelling. Exp Cell Res 2022; 419:113317. [PMID: 36028058 DOI: 10.1016/j.yexcr.2022.113317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 07/19/2022] [Accepted: 08/08/2022] [Indexed: 11/25/2022]
Abstract
Computational models can shape our understanding of cell and tissue remodelling, from cell spreading, to active force generation, adhesion, and growth. In this mini-review, we discuss recent progress in modelling of chemo-mechanical cell behaviour and the evolution of multicellular systems. In particular, we highlight recent advances in (i) free-energy based single cell models that can provide new fundamental insight into cell spreading, cancer cell invasion, stem cell differentiation, and remodelling in disease, and (ii) mechanical agent-based models to simulate large numbers of discrete interacting cells in proliferative tumours. We describe how new biological understanding has emerged from such theoretical models, and the trade-offs and constraints associated with current approaches. Ultimately, we aim to make a case for why theory should be integrated with an experimental workflow to optimise new in-vitro studies, to predict feedback between cells and their microenvironment, and to deepen understanding of active cell behaviour.
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Affiliation(s)
- Irish Senthilkumar
- School of Computer Science, College of Science and Engineering, National University of Ireland Galway, Ireland; Biomedical Engineering, College of Science and Engineering, National University of Ireland Galway, Ireland
| | - Enda Howley
- School of Computer Science, College of Science and Engineering, National University of Ireland Galway, Ireland
| | - Eoin McEvoy
- Biomedical Engineering, College of Science and Engineering, National University of Ireland Galway, Ireland.
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Scott LE, Griggs LA, Narayanan V, Conway DE, Lemmon CA, Weinberg SH. A hybrid model of intercellular tension and cell-matrix mechanical interactions in a multicellular geometry. Biomech Model Mechanobiol 2020; 19:1997-2013. [PMID: 32193709 PMCID: PMC7502553 DOI: 10.1007/s10237-020-01321-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2019] [Accepted: 03/13/2020] [Indexed: 12/18/2022]
Abstract
Epithelial cells form continuous sheets of cells that exist in tensional homeostasis. Homeostasis is maintained through cell-to-cell junctions that distribute tension and balance forces between cells and their underlying matrix. Disruption of tensional homeostasis can lead to epithelial-mesenchymal transition (EMT), a transdifferentiation process in which epithelial cells adopt a mesenchymal phenotype, losing cell-cell adhesion and enhancing cellular motility. This process is critical during embryogenesis and wound healing, but is also dysregulated in many disease states. To further understand the role of intercellular tension in spatial patterning of epithelial cell monolayers, we developed a multicellular computational model of cell-cell and cell-substrate forces. This work builds on a hybrid cellular Potts model (CPM)-finite element model to evaluate cell-matrix mechanical feedback of an adherent multicellular cluster. Cellular movement is governed by thermodynamic constraints from cell volume, cell-cell and cell-matrix contacts, and durotaxis, which arises from cell-generated traction forces on a finite element substrate. Junction forces at cell-cell contacts balance these traction forces, thereby producing a mechanically stable epithelial monolayer. Simulations were compared to in vitro experiments using fluorescence-based junction force sensors in clusters of cells undergoing EMT. Results indicate that the multicellular CPM model can reproduce many aspects of EMT, including epithelial monolayer formation dynamics, changes in cell geometry, and spatial patterning of cell-cell forces in an epithelial tissue.
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Affiliation(s)
- Lewis E Scott
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
| | - Lauren A Griggs
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
| | - Vani Narayanan
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
| | - Daniel E Conway
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
| | - Christopher A Lemmon
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
| | - Seth H Weinberg
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA.
- Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA.
- Davis Heart and Lung Research Institute, The Ohio State University Wexner Medical Center, Columbus, OH, USA.
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Xin Y, Karunarathna Mudiyanselage CM, Just W. Development of epithelial tissues: How are cleavage planes chosen? PLoS One 2018; 13:e0205834. [PMID: 30403682 PMCID: PMC6221281 DOI: 10.1371/journal.pone.0205834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Accepted: 10/02/2018] [Indexed: 11/21/2022] Open
Abstract
The cross-section of a cell in a monolayer epithelial tissue can be modeled mathematically as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed for explaining this phenomenon. The highly parsimonious simulation model of (Patel et al., PLoS Comput. Biol., 2009) that takes into account only the number of sides of a given cell and cell division already achieves a remarkably good fit with empirical distributions from Drosophila, Hydra, Xenopus, Cucumber, and Anagallis. Within the same modeling framework as in that paper, we introduce additional options for the choice of the endpoints of the cleavage plane that appear to be biologically more realistic. By taking the same data sets as our benchmarks, we found that combinations of some of our new options consistently gave better fits with each of these data sets than previously studied ones. Both our algorithm and simulation data are made available as research tools for future investigations.
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Affiliation(s)
- Ying Xin
- Department of Mathematics, Ohio University, Athens, Ohio, 45701, United States of America
- Department of Mathematical Sciences, Montana State University, Bozeman, Montana, 59717, United States of America
- * E-mail:
| | | | - Winfried Just
- Department of Mathematics, Ohio University, Athens, Ohio, 45701, United States of America
- Quantitative Biology Institute, Ohio University, Athens, Ohio, 45701, United States of America
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8
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A hybrid computational model for collective cell durotaxis. Biomech Model Mechanobiol 2018; 17:1037-1052. [DOI: 10.1007/s10237-018-1010-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Accepted: 02/17/2018] [Indexed: 12/17/2022]
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