1
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Zhou WH, Qiao LR, Xie SJ, Chang Z, Yin X, Xu GK. Mechanical guidance to self-organization and pattern formation of stem cells. SOFT MATTER 2024; 20:3448-3457. [PMID: 38567443 DOI: 10.1039/d4sm00172a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
The self-organization of stem cells (SCs) constitutes the fundamental basis of the development of biological organs and structures. SC-driven patterns are essential for tissue engineering, yet unguided SCs tend to form chaotic patterns, impeding progress in biomedical engineering. Here, we show that simple geometric constraints can be used as an effective mechanical modulation approach that promotes the development of controlled self-organization and pattern formation of SCs. Using the applied SC guidance with geometric constraints, we experimentally uncover a remarkable deviation in cell aggregate orientation from a random direction to a specific orientation. Subsequently, we propose a dynamic mechanical framework, including cells, the extracellular matrix (ECM), and the culture environment, to characterize the specific orientation deflection of guided cell aggregates relative to initial geometric constraints, which agrees well with experimental observation. Based on this framework, we further devise various theoretical strategies to realize complex biological patterns, such as radial and concentric structures. Our study highlights the key role of mechanical factors and geometric constraints in governing SCs' self-organization. These findings yield critical insights into the regulation of SC-driven pattern formation and hold great promise for advancements in tissue engineering and bioactive material design for regenerative application.
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Affiliation(s)
- Wei-Hua Zhou
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
| | - Lin-Ru Qiao
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
| | - She-Juan Xie
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
| | - Zhuo Chang
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
| | - Xu Yin
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
| | - Guang-Kui Xu
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
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2
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Crossley RM, Johnson S, Tsingos E, Bell Z, Berardi M, Botticelli M, Braat QJS, Metzcar J, Ruscone M, Yin Y, Shuttleworth R. Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist. Front Cell Dev Biol 2024; 12:1354132. [PMID: 38495620 PMCID: PMC10940354 DOI: 10.3389/fcell.2024.1354132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 02/12/2024] [Indexed: 03/19/2024] Open
Abstract
The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.
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Affiliation(s)
- Rebecca M. Crossley
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Samuel Johnson
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Erika Tsingos
- Computational Developmental Biology Group, Institute of Biodynamics and Biocomplexity, Utrecht University, Utrecht, Netherlands
| | - Zoe Bell
- Northern Institute for Cancer Research, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Massimiliano Berardi
- LaserLab, Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
- Optics11 life, Amsterdam, Netherlands
| | | | - Quirine J. S. Braat
- Department of Applied Physics and Science Education, Eindhoven University of Technology, Eindhoven, Netherlands
| | - John Metzcar
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, United States
- Department of Informatics, Indiana University, Bloomington, IN, United States
| | | | - Yuan Yin
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
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3
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Marchello R, Colombi A, Preziosi L, Giverso C. A non local model for cell migration in response to mechanical stimuli. Math Biosci 2024; 368:109124. [PMID: 38072125 DOI: 10.1016/j.mbs.2023.109124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 11/17/2023] [Accepted: 12/05/2023] [Indexed: 12/22/2023]
Abstract
Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis. Unlike chemotaxis (i.e. the motion in response to a chemical stimulus), these migratory processes are not yet fully understood from a biological point of view. In this respect, we present a mathematical model of single-cell migration in response to mechanical stimuli, in order to simulate these two processes. Specifically, the cell moves by changing its direction of polarization and its motility according to material properties of the substrate (e.g., stiffness) or in response to proper scalar measures of the substrate strain or stress. The equations of motion of the cell are non-local integro-differential equations, with the addition of a stochastic term to account for random Brownian motion. The mechanical stimulus to be integrated in the equations of motion is defined according to experimental measurements found in literature, in the case of durotaxis. Conversely, in the case of tensotaxis, substrate strain and stress are given by the solution of the mechanical problem, assuming that the extracellular matrix behaves as a hyperelastic Yeoh's solid. In both cases, the proposed model is validated through numerical simulations that qualitatively reproduce different experimental scenarios.
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Affiliation(s)
- Roberto Marchello
- Mathematics Area, SISSA (International School for Advanced Studies), Via Bonomea 265, Trieste, 34136, Italy
| | - Annachiara Colombi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Luigi Preziosi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Chiara Giverso
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy.
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4
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Poonja S, Forero Pinto A, Lloyd MC, Damaghi M, Rejniak KA. Dynamics of Fibril Collagen Remodeling by Tumor Cells: A Model of Tumor-Associated Collagen Signatures. Cells 2023; 12:2688. [PMID: 38067116 PMCID: PMC10705683 DOI: 10.3390/cells12232688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 11/01/2023] [Accepted: 11/17/2023] [Indexed: 12/18/2023] Open
Abstract
Many solid tumors are characterized by a dense extracellular matrix (ECM) composed of various ECM fibril proteins. These proteins provide structural support and a biological context for the residing cells. The reciprocal interactions between growing and migrating tumor cells and the surrounding stroma result in dynamic changes in the ECM architecture and its properties. With the use of advanced imaging techniques, several specific patterns in the collagen surrounding the breast tumor have been identified in both tumor murine models and clinical histology images. These tumor-associated collagen signatures (TACS) include loosely organized fibrils far from the tumor and fibrils aligned either parallel or perpendicular to tumor colonies. They are correlated with tumor behavior, such as benign growth or invasive migration. However, it is not fully understood how one specific fibril pattern can be dynamically remodeled to form another alignment. Here, we present a novel multi-cellular lattice-free (MultiCell-LF) agent-based model of ECM that, in contrast to static histology images, can simulate dynamic changes between TACSs. This model allowed us to identify the rules of cell-ECM physical interplay and feedback that guided the emergence and transition among various TACSs.
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Affiliation(s)
- Sharan Poonja
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center, Research Institute, Tampa, FL 33612, USA
| | - Ana Forero Pinto
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center, Research Institute, Tampa, FL 33612, USA
- Cancer Biology PhD Program, University of South Florida, Tampa, FL 33612, USA
| | - Mark C. Lloyd
- Fujifilm Healthcare US, Inc., Lexington, MA 02421, USA;
| | - Mehdi Damaghi
- Department of Pathology, Renaissance School of Medicine, Stony Brook University, Stony Brook, NY 11794, USA
| | - Katarzyna A. Rejniak
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center, Research Institute, Tampa, FL 33612, USA
- Department of Oncologic Sciences, Morsani School of Medicine, University of South Florida, Tampa, FL 33612, USA
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5
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Régnier L, Bénichou O, Krapivsky PL. Range-Controlled Random Walks. PHYSICAL REVIEW LETTERS 2023; 130:227101. [PMID: 37327439 DOI: 10.1103/physrevlett.130.227101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 04/03/2023] [Accepted: 05/09/2023] [Indexed: 06/18/2023]
Abstract
We introduce range-controlled random walks with hopping rates depending on the range N, that is, the total number of previously distinct visited sites. We analyze a one-parameter class of models with a hopping rate N^{a} and determine the large time behavior of the average range, as well as its complete distribution in two limit cases. We find that the behavior drastically changes depending on whether the exponent a is smaller, equal, or larger than the critical value, a_{d}, depending only on the spatial dimension d. When a>a_{d}, the forager covers the infinite lattice in a finite time. The critical exponent is a_{1}=2 and a_{d}=1 when d≥2. We also consider the case of two foragers who compete for food, with hopping rates depending on the number of sites each visited before the other. Surprising behaviors occur in 1D where a single walker dominates and finds most of the sites when a>1, while for a<1, the walkers evenly explore the line. We compute the gain of efficiency in visiting sites by adding one walker.
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Affiliation(s)
- L Régnier
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 75005 Paris, France
| | - O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 75005 Paris, France
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
- Santa Fe Institute, Santa Fe, New Mexico 87501, USA
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6
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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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7
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Cell Dissemination in Pancreatic Cancer. Cells 2022; 11:cells11223683. [PMID: 36429111 PMCID: PMC9688670 DOI: 10.3390/cells11223683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 11/11/2022] [Accepted: 11/16/2022] [Indexed: 11/22/2022] Open
Abstract
Pancreatic cancer is a disease notorious for its high frequency of recurrence and low survival rate. Surgery is the most effective treatment for localized pancreatic cancer, but most cancer recurs after surgery, and patients die within ten years of diagnosis. The question persists: what makes pancreatic cancer recur and metastasize with such a high frequency? Herein, we review evidence that subclinical dormant pancreatic cancer cells disseminate before developing metastatic or recurring cancer. We then discuss several routes by which pancreatic cancer migrates and the mechanisms by which pancreatic cancer cells adapt. Lastly, we discuss unanswered questions in pancreatic cancer cell migration and our perspectives.
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8
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Short WD, Olutoye OO, Padon BW, Parikh UM, Colchado D, Vangapandu H, Shams S, Chi T, Jung JP, Balaji S. Advances in non-invasive biosensing measures to monitor wound healing progression. Front Bioeng Biotechnol 2022; 10:952198. [PMID: 36213059 PMCID: PMC9539744 DOI: 10.3389/fbioe.2022.952198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 07/12/2022] [Indexed: 01/09/2023] Open
Abstract
Impaired wound healing is a significant financial and medical burden. The synthesis and deposition of extracellular matrix (ECM) in a new wound is a dynamic process that is constantly changing and adapting to the biochemical and biomechanical signaling from the extracellular microenvironments of the wound. This drives either a regenerative or fibrotic and scar-forming healing outcome. Disruptions in ECM deposition, structure, and composition lead to impaired healing in diseased states, such as in diabetes. Valid measures of the principal determinants of successful ECM deposition and wound healing include lack of bacterial contamination, good tissue perfusion, and reduced mechanical injury and strain. These measures are used by wound-care providers to intervene upon the healing wound to steer healing toward a more functional phenotype with improved structural integrity and healing outcomes and to prevent adverse wound developments. In this review, we discuss bioengineering advances in 1) non-invasive detection of biologic and physiologic factors of the healing wound, 2) visualizing and modeling the ECM, and 3) computational tools that efficiently evaluate the complex data acquired from the wounds based on basic science, preclinical, translational and clinical studies, that would allow us to prognosticate healing outcomes and intervene effectively. We focus on bioelectronics and biologic interfaces of the sensors and actuators for real time biosensing and actuation of the tissues. We also discuss high-resolution, advanced imaging techniques, which go beyond traditional confocal and fluorescence microscopy to visualize microscopic details of the composition of the wound matrix, linearity of collagen, and live tracking of components within the wound microenvironment. Computational modeling of the wound matrix, including partial differential equation datasets as well as machine learning models that can serve as powerful tools for physicians to guide their decision-making process are discussed.
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Affiliation(s)
- Walker D. Short
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Oluyinka O. Olutoye
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Benjamin W. Padon
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Umang M. Parikh
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Daniel Colchado
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Hima Vangapandu
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
| | - Shayan Shams
- Department of Applied Data Science, San Jose State University, San Jose, CA, United States
- School of Biomedical Informatics, University of Texas Health Science Center, Houston, TX, United States
| | - Taiyun Chi
- Department of Electrical and Computer Engineering, Rice University, Houston, TX, United States
| | - Jangwook P. Jung
- Department of Biological Engineering, Louisiana State University, Baton Rouge, LA, United States
| | - Swathi Balaji
- Laboratory for Regenerative Tissue Repair, Division of Pediatric Surgery, Department of Surgery, Texas Children’s Hospital and Baylor College of Medicine, Houston, TX, United States
- *Correspondence: Swathi Balaji,
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9
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Wang ZJ, Thomson M. Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments. Cell Syst 2022; 13:530-546.e12. [PMID: 35679857 DOI: 10.1016/j.cels.2022.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 02/08/2022] [Accepted: 05/12/2022] [Indexed: 01/25/2023]
Abstract
Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.
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Affiliation(s)
- Zitong Jerry Wang
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Matt Thomson
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
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10
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Merino-Casallo F, Gomez-Benito MJ, Martinez-Cantin R, Garcia-Aznar JM. A mechanistic protrusive-based model for 3D cell migration. Eur J Cell Biol 2022; 101:151255. [PMID: 35843121 DOI: 10.1016/j.ejcb.2022.151255] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 06/15/2022] [Accepted: 07/01/2022] [Indexed: 11/17/2022] Open
Abstract
Cell migration is essential for a variety of biological processes, such as embryogenesis, wound healing, and the immune response. After more than a century of research-mainly on flat surfaces-, there are still many unknowns about cell motility. In particular, regarding how cells migrate within 3D matrices, which more accurately replicate in vivo conditions. We present a novel in silico model of 3D mesenchymal cell migration regulated by the chemical and mechanical profile of the surrounding environment. This in silico model considers cell's adhesive and nuclear phenotypes, the effects of the steric hindrance of the matrix, and cells ability to degradate the ECM. These factors are crucial when investigating the increasing difficulty that migrating cells find to squeeze their nuclei through dense matrices, which may act as physical barriers. Our results agree with previous in vitro observations where fibroblasts cultured in collagen-based hydrogels did not durotax toward regions with higher collagen concentrations. Instead, they exhibited an adurotactic behavior, following a more random trajectory. Overall, cell's migratory response in 3D domains depends on its phenotype, and the properties of the surrounding environment, that is, 3D cell motion is strongly dependent on the context.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Maria Jose Gomez-Benito
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Ruben Martinez-Cantin
- Robotics, Perception and Real Time Group (RoPeRT), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Computer Science and System Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain.
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11
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Khan I, Baig MH, Mahfooz S, Imran MA, Khan MI, Dong JJ, Cho JY, Hatiboglu MA. Nanomedicine for Glioblastoma: Progress and Future Prospects. Semin Cancer Biol 2022; 86:172-186. [PMID: 35760272 DOI: 10.1016/j.semcancer.2022.06.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Revised: 06/09/2022] [Accepted: 06/21/2022] [Indexed: 11/29/2022]
Abstract
Glioblastoma is the most aggressive form of brain tumor, accounting for the highest mortality and morbidity rates. Current treatment for patients with glioblastoma includes maximal safe tumor resection followed by radiation therapy with concomitant temozolomide (TMZ) chemotherapy. The addition of TMZ to the conformal radiation therapy has improved the median survival time only from 12 months to 16 months in patients with glioblastoma. Despite these aggressive treatment strategies, patients' prognosis remains poor. This therapeutic failure is primarily attributed to the blood-brain barrier (BBB) that restricts the transport of TMZ from reaching the tumor site. In recent years, nanomedicine has gained considerable attention among researchers and shown promising developments in clinical applications, including the diagnosis, prognosis, and treatment of glioblastoma tumors. This review sheds light on the morphological and physiological complexity of the BBB. It also explains the development of nanomedicine strategies to enhance the permeability of drug molecules across the BBB.
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Affiliation(s)
- Imran Khan
- Department of Molecular Biology, Beykoz Institute of Life Sciences and Biotechnology, Bezmialem Vakif University, Yalıköy St., Beykoz, Istanbul, Turkey
| | - Mohammad Hassan Baig
- Department of Family Medicine, Gangnam Severance Hospital, Yonsei University College of Medicine, Gangnam-gu, Seoul, 120-752, Republic of Korea
| | - Sadaf Mahfooz
- Department of Molecular Biology, Beykoz Institute of Life Sciences and Biotechnology, Bezmialem Vakif University, Yalıköy St., Beykoz, Istanbul, Turkey
| | - Mohammad Azhar Imran
- Department of Internal Medicine, Gangnam Severance Hospital, Yonsei University College of Medicine, Gangnam-gu, Seoul, 120-752, Republic of Korea
| | - Mohd Imran Khan
- Department of Internal Medicine, Gangnam Severance Hospital, Yonsei University College of Medicine, Gangnam-gu, Seoul, 120-752, Republic of Korea
| | - Jae-June Dong
- Department of Family Medicine, Gangnam Severance Hospital, Yonsei University College of Medicine, Gangnam-gu, Seoul, 120-752, Republic of Korea
| | - Jae Yong Cho
- Department of Internal Medicine, Gangnam Severance Hospital, Yonsei University College of Medicine, Gangnam-gu, Seoul, 120-752, Republic of Korea.
| | - Mustafa Aziz Hatiboglu
- Department of Molecular Biology, Beykoz Institute of Life Sciences and Biotechnology, Bezmialem Vakif University, Yalıköy St., Beykoz, Istanbul, Turkey; Department of Neurosurgery, Bezmialem Vakif University Medical School, Vatan Street, Fatih, Istanbul, Turkey.
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12
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Rayat Pisheh H, Ansari M, Eslami H. How is mechanobiology involved in bone regenerative medicine? Tissue Cell 2022; 76:101821. [DOI: 10.1016/j.tice.2022.101821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Revised: 04/27/2022] [Accepted: 05/10/2022] [Indexed: 10/18/2022]
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13
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Bersie-Larson LM, Lai VK, Dhume RY, Provenzano PP, Barocas VH, Tranquillo RT. Elucidating the signal for contact guidance contained in aligned fibrils with a microstructural-mechanical model. J R Soc Interface 2022; 19:20210951. [PMID: 35582810 DOI: 10.1098/rsif.2021.0951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Despite its importance in physiological processes and tissue engineering, the mechanism underlying cell contact guidance in an aligned fibrillar network has defied elucidation due to multiple interdependent signals that such a network presents to cells, namely, anisotropy of adhesion, porosity and mechanical behaviour. A microstructural-mechanical model of fibril networks was used to assess the relative magnitudes of these competing signals in networks of varied alignment strength based on idealized cylindrical pseudopods projected into the aligned and orthogonal directions and computing the anisotropy of metrics chosen for adhesion, porosity and mechanical behaviour: cylinder-fibre contact area for adhesion, persistence length of pores for porosity and total force to displace fibres from the cylindrical volume as well as network stiffness experienced upon cylinder retraction for mechanical behaviour. The signals related to mechanical anisotropy are substantially higher than adhesion and porosity anisotropy, especially at stronger network alignments, although their signal to noise (S/N) values are substantially lower. The former finding is consistent with a recent report that fibroblasts can sense fibril alignment via anisotropy of network mechanical resistance, and the model reveals this can be due to either mechanical resistance to pseudopod protrusion or retraction given their signal and S/N values are similar.
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Affiliation(s)
- Lauren M Bersie-Larson
- Department of Biomedical Engineering, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA
| | - Victor K Lai
- Department of Chemical Engineering, University of Minnesota - Duluth, Duluth, MN, USA
| | - Rohit Y Dhume
- Department of Mechanical Engineering, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA
| | - Paolo P Provenzano
- Department of Biomedical Engineering, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA
| | - Victor H Barocas
- Department of Biomedical Engineering, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA
| | - Robert T Tranquillo
- Department of Biomedical Engineering, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA.,Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, Minneapolis, MN 55455, USA
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14
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Conte M, Loy N. Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis. Bull Math Biol 2022; 84:42. [PMID: 35150333 PMCID: PMC8840942 DOI: 10.1007/s11538-021-00978-1] [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: 04/23/2021] [Accepted: 11/23/2021] [Indexed: 11/29/2022]
Abstract
Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. Precisely, several biochemical and biophysical cues give rise to tactic migration in the direction of their specific targets. Thus, this defines a multi-cue environment in which cells have to sort and combine different, and potentially competitive, stimuli. We propose a non-local kinetic model for cell migration in which cell polarization is influenced simultaneously by two external factors: contact guidance and chemotaxis. We propose two different sensing strategies, and we analyze the two resulting transport kinetic models by recovering the appropriate macroscopic limit in different regimes, in order to observe how the cell size, with respect to the variation of both external fields, influences the overall behavior. This analysis shows the importance of dealing with hyperbolic models, rather than drift-diffusion ones. Moreover, we numerically integrate the kinetic transport equations in a two-dimensional setting in order to investigate qualitatively various scenarios. Finally, we show how our setting is able to reproduce some experimental results concerning the influence of topographical and chemical cues in directing cell motility.
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Affiliation(s)
- Martina Conte
- Department of Mathematical Sciences, "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
| | - Nadia Loy
- Department of Mathematical Sciences, "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
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15
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Vernerey FJ, Lalitha Sridhar S, Muralidharan A, Bryant SJ. Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms. Chem Rev 2021; 121:11085-11148. [PMID: 34473466 DOI: 10.1021/acs.chemrev.1c00046] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.
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Affiliation(s)
- Franck J Vernerey
- Department of Mechanical Engineering, University of Colorado at Boulder, 1111 Engineering Drive, Boulder, Colorado 80309-0428, United States.,Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States
| | - Shankar Lalitha Sridhar
- Department of Mechanical Engineering, University of Colorado at Boulder, 1111 Engineering Drive, Boulder, Colorado 80309-0428, United States
| | - Archish Muralidharan
- Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States
| | - Stephanie J Bryant
- Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States.,Department of Chemical and Biological Engineering, University of Colorado at Boulder, 3415 Colorado Avenue, Boulder, Colorado 80309-0596, United States.,BioFrontiers Institute, University of Colorado at Boulder, 3415 Colorado Avenue, Boulder, Colorado 80309-0596, United States
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16
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Scott M, Żychaluk K, Bearon RN. A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2021; 38:333-354. [PMID: 34189581 DOI: 10.1093/imammb/dqab009] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 06/09/2021] [Accepted: 06/10/2021] [Indexed: 11/14/2022]
Abstract
The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.
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Affiliation(s)
- M Scott
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
| | - K Żychaluk
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
| | - R N Bearon
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
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17
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Macnamara CK. Biomechanical modelling of cancer: Agent‐based force‐based models of solid tumours within the context of the tumour microenvironment. COMPUTATIONAL AND SYSTEMS ONCOLOGY 2021. [DOI: 10.1002/cso2.1018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Affiliation(s)
- Cicely K. Macnamara
- School of Mathematics and Statistics Mathematical Institute University of St Andrews St Andrews Fife UK
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18
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Yeoman B, Shatkin G, Beri P, Banisadr A, Katira P, Engler AJ. Adhesion strength and contractility enable metastatic cells to become adurotactic. Cell Rep 2021; 34:108816. [PMID: 33691109 PMCID: PMC7997775 DOI: 10.1016/j.celrep.2021.108816] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 01/10/2021] [Accepted: 02/10/2021] [Indexed: 11/05/2022] Open
Abstract
Significant changes in cell stiffness, contractility, and adhesion, i.e., mechanotype, are observed during a variety of biological processes. Whether cell mechanics merely change as a side effect of or driver for biological processes is still unclear. Here, we sort genotypically similar metastatic cancer cells into strongly adherent (SA) versus weakly adherent (WA) phenotypes to study how contractility and adhesion differences alter the ability of cells to sense and respond to gradients in material stiffness. We observe that SA cells migrate up a stiffness gradient, or durotax, while WA cells largely ignore the gradient, i.e., adurotax. Biophysical modeling and experimental validation suggest that differences in cell migration and durotaxis between weakly and strongly adherent cells are driven by differences in intra-cellular actomyosin activity. These results provide a direct relationship between cell phenotype and durotaxis and suggest how, unlike other senescent cells, metastatic cancer cells navigate against stiffness gradients.
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Affiliation(s)
- Benjamin Yeoman
- Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093, USA; Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182, USA
| | - Gabriel Shatkin
- Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093, USA
| | - Pranjali Beri
- Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093, USA
| | - Afsheen Banisadr
- Biomedical Sciences Program, University of California, San Diego, La Jolla, CA 92093, USA
| | - Parag Katira
- Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182, USA; Computational Sciences Research Center, San Diego State University, San Diego, CA 92182, USA.
| | - Adam J Engler
- Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093, USA; Biomedical Sciences Program, University of California, San Diego, La Jolla, CA 92093, USA.
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19
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Buttenschön A, Edelstein-Keshet L. Bridging from single to collective cell migration: A review of models and links to experiments. PLoS Comput Biol 2020; 16:e1008411. [PMID: 33301528 PMCID: PMC7728230 DOI: 10.1371/journal.pcbi.1008411] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.
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Affiliation(s)
- Andreas Buttenschön
- Department of Mathematics, University of British Columbia, Vancouver, Canada
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20
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Shatkin G, Yeoman B, Birmingham K, Katira P, Engler AJ. Computational models of migration modes improve our understanding of metastasis. APL Bioeng 2020; 4:041505. [PMID: 33195959 PMCID: PMC7647620 DOI: 10.1063/5.0023748] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 10/23/2020] [Indexed: 01/07/2023] Open
Abstract
Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell–extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.
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Affiliation(s)
- Gabriel Shatkin
- Department of Bioengineering, University of California, San Diego, La Jolla, California 92093, USA
| | | | - Katherine Birmingham
- Department of Bioengineering, University of California, San Diego, La Jolla, California 92093, USA
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21
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Campbell EJ, Bagchi P. A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion. Biomech Model Mechanobiol 2020; 20:167-191. [PMID: 32772275 DOI: 10.1007/s10237-020-01376-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 08/01/2020] [Indexed: 12/24/2022]
Abstract
Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.
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Affiliation(s)
- Eric J Campbell
- Mechanical and Aerospace Engineering Department, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA
| | - Prosenjit Bagchi
- Mechanical and Aerospace Engineering Department, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA.
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22
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Zhang J, Li S, Cai Q, Wang Z, Cao J, Yu T, Xie T. Exogenous diethyl aminoethyl hexanoate ameliorates low temperature stress by improving nitrogen metabolism in maize seedlings. PLoS One 2020; 15:e0232294. [PMID: 32353025 PMCID: PMC7192554 DOI: 10.1371/journal.pone.0232294] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2019] [Accepted: 04/11/2020] [Indexed: 01/24/2023] Open
Abstract
Spring maize sowing occurs during a period of low temperature (LT) in Northeast
China, and the LT suppresses nitrogen (N) metabolism and photosynthesis, further
reducing dry matter accumulation. Diethyl aminoethyl hexanoate (DA-6) improves N
metabolism; hence, we studied the effects of DA-6 on maize seedlings under LT
conditions. The shoot and root fresh weight and dry weight decreased by
17.70%~20.82% in the LT treatment, and decreased by 5.81%~13.57% in the LT +
DA-6 treatment on the 7th day, respectively. Exogenous DA-6
suppressed the increases in ammonium (NH4+) content and
glutamate dehydrogenase (GDH) activity, and suppressed the decreases in nitrate
(NO3–) and nitrite (NO2–)
contents, and activities of nitrate reductase (NR), nitrite reductase (NiR),
glutamine synthetase (GS), glutamate synthase (GOGAT) and transaminase
activities. NiR activity was most affected by DA-6 under LT conditions.
Additionally, exogenous DA-6 suppressed the net photosynthetic rate (Pn)
decrease, and the suppressed the increases of superoxide anion radical
(O2·−) generation rate and hydrogen peroxide
(H2O2) content. Taken together, our results suggest
that exogenous DA-6 mitigated the repressive effects of LT on N metabolism by
improving photosynthesis and modulating oxygen metabolism, and subsequently
enhanced the LT tolerance of maize seedlings.
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Affiliation(s)
- Jianguo Zhang
- College of Agriculture, Northeast Agricultural University, Harbin, P.R.
China
- Maize Research Institute, Heilongjiang Academy of Agricultural Sciences,
Harbin, P.R. China
| | - Shujun Li
- Maize Research Institute, Heilongjiang Academy of Agricultural Sciences,
Harbin, P.R. China
| | - Quan Cai
- Maize Research Institute, Heilongjiang Academy of Agricultural Sciences,
Harbin, P.R. China
| | - Zhenhua Wang
- College of Agriculture, Northeast Agricultural University, Harbin, P.R.
China
- * E-mail:
| | - Jingsheng Cao
- Maize Research Institute, Heilongjiang Academy of Agricultural Sciences,
Harbin, P.R. China
| | - Tao Yu
- Maize Research Institute, Heilongjiang Academy of Agricultural Sciences,
Harbin, P.R. China
| | - Tenglong Xie
- College of Agriculture, Northeast Agricultural University, Harbin, P.R.
China
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23
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Malik AA, Wennberg B, Gerlee P. The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration. Bull Math Biol 2020; 82:49. [PMID: 32248312 PMCID: PMC7128007 DOI: 10.1007/s11538-020-00721-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Accepted: 03/15/2020] [Indexed: 01/06/2023]
Abstract
The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.
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Affiliation(s)
- A A Malik
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden.
| | - B Wennberg
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden
| | - P Gerlee
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96, Gothenburg, Sweden
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24
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Iwasa M. A mechanical toy model linking cell-substrate adhesion to multiple cellular migratory responses. J Biol Phys 2019; 45:401-421. [PMID: 31834551 DOI: 10.1007/s10867-019-09536-2] [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: 06/07/2019] [Accepted: 11/27/2019] [Indexed: 10/25/2022] Open
Abstract
During cell migration, forces applied to a cell from its environment influence the motion. When the cell is placed on a substrate, such a force is provided by the cell-substrate adhesion. Modulation of adhesivity, often performed by the modulation of the substrate stiffness, tends to cause common responses for cell spreading, cell speed, persistence, and random motility coefficient. Although the reasons for the response of cell spreading and cell speed have been suggested, other responses are not well understood. In this study, we develop a simple toy model for cell migration driven by the relation of two forces: the adhesive force and the plasma membrane tension. The simplicity of the model allows us to perform the calculation not only numerically but also analytically, and the analysis provides formulas directly relating the adhesivity to cell spreading, persistence, and the random motility coefficient. Accordingly, the results offer a unified picture on the causal relations between those multiple cellular responses. In addition, cellular properties that would influence the migratory behavior are suggested.
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Affiliation(s)
- Masatomo Iwasa
- Center for General Education, Aichi Institute of Technology, Toyota, 470-0392, Japan.
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25
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Bubba F, Pouchol C, Ferrand N, Vidal G, Almeida L, Perthame B, Sabbah M. A chemotaxis-based explanation of spheroid formation in 3D cultures of breast cancer cells. J Theor Biol 2019; 479:73-80. [PMID: 31283914 DOI: 10.1016/j.jtbi.2019.07.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Revised: 05/24/2019] [Accepted: 07/03/2019] [Indexed: 10/26/2022]
Abstract
Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro cultures of breast cancer cells exhibiting patterns. Understanding their formation is of particular interest in the context of cancer since metastases have been shown to be created by cells moving in clusters. In this paper, we propose that the main mechanism which leads to the emergence of patterns is chemotaxis, i.e., oriented movement of cells towards high concentration zones of a signal emitted by the cells themselves. Studying a Keller-Segel PDE system to model chemotactical auto-organization of cells, we prove that it admits Turing unstable solutions under a time-dependent condition. This result is illustrated by two-dimensional simulations of the model showing spheroidal patterns. They are qualitatively compared to the biological results and their variability is discussed both theoretically and numerically.
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Affiliation(s)
- Federica Bubba
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, 4 pl. Jussieu, Paris 75005, France
| | - Camille Pouchol
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, 4 pl. Jussieu, Paris 75005, France
| | - Nathalie Ferrand
- Sorbonne Université, INSERM, Laboratoire de Biologie du Cancer et Thérapeutique, Centre de Recherche Saint-Antoine, Paris 75012, France
| | - Guillaume Vidal
- CELENYS, Biopolis 2, 75 route de Lyons-la-forêt, Rouen 76000, France
| | - Luis Almeida
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, 4 pl. Jussieu, Paris 75005, France.
| | - Benoît Perthame
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, 4 pl. Jussieu, Paris 75005, France
| | - Michèle Sabbah
- Sorbonne Université, INSERM, Laboratoire de Biologie du Cancer et Thérapeutique, Centre de Recherche Saint-Antoine, Paris 75012, France
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26
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Shuttleworth R, Trucu D. Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix. J Theor Biol 2019; 486:110040. [PMID: 31604075 DOI: 10.1016/j.jtbi.2019.110040] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Revised: 08/27/2019] [Accepted: 10/07/2019] [Indexed: 11/28/2022]
Abstract
Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. This new cell subpopulation often carries higher invasive abilities and permits a quicker spread of the tumour. Building upon the recent multiscale modelling framework for cancer invasion within a fibrous ECM introduced in Shuttleworth and Trucu, (2019), in this paper we consider the process of local invasion by a heterotypic tumour consisting of two cancer cell populations mixed with a two-phase ECM. To that end, we address the double feedback link between the tissue-scale cancer dynamics and the cell-scale molecular processes through the development of a two-part modelling framework that crucially incorporates the multiscale dynamic redistribution of oriented fibres occurring within a two-phase extra-cellular matrix and combines this with the multiscale leading edge dynamics exploring key matrix-degrading enzymes molecular processes along the tumour interface that drive the movement of the cancer boundary. The modelling framework will be accompanied by computational results that explore the effects of the underlying fibre network on the overall pattern of cancer invasion.
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Affiliation(s)
| | - Dumitru Trucu
- University of Dundee, Dundee, Scotland DD1 4HN, United Kingdom.
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27
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Li A, Sun M, Spill F, Sun R, Zaman MH. Are the Effects of Independent Biophysical Factors Linearly Additive? A 3D Tumor Migration Model. Biophys J 2019; 117:1702-1713. [PMID: 31630809 DOI: 10.1016/j.bpj.2019.09.037] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 08/16/2019] [Accepted: 09/10/2019] [Indexed: 01/19/2023] Open
Abstract
Interstitial fluid flow plays a critical role in tumor cell invasion, yet this role has not been explored extensively in combination with other microenvironmental factors. Here, we establish a novel computational model of three-dimensional breast cancer cell migration to unveil the effect of interstitial fluid flow in the dependence of various extracellular matrix (ECM) physical properties. Our model integrates several principal factors: fluid dynamics, autologous chemotaxis, collagen fiber network structure, ECM stiffness, and cell-fiber and cell-flow interaction. First, independently with an aligned collagen fiber network and interstitial fluid flow, this model is validated by successfully reproducing the cell migration patterns. In the model, the interstitial fluid flow leads to directional symmetry breaking of chemotactic migration and synergizes with the ECM orientation to regulate cell migration. This synergy is universal in both the mesenchymal and the amoeboid migration modes, despite the fact that the cell-ECM interaction are different. Consequently, we construct a cell displacement function depending on these factors. Our cell migration model enables three-dimensional cancer migration prediction, mechanism exploration, and inhibition treatment design in a complex tumor microenvironment.
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Affiliation(s)
- Ang Li
- MOE Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
| | - Meng Sun
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts
| | - Fabian Spill
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts; School of Mathematics, University of Birmingham, Birmingham, United Kingdom
| | - Ren Sun
- MOE Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China.
| | - Muhammad H Zaman
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts; Howard Hughes Medical Institute, Boston University, Boston, Massachusetts.
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28
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Reinhardt JW, Gooch KJ. An Agent-Based Discrete Collagen Fiber Network Model of Dynamic Traction Force-Induced Remodeling. J Biomech Eng 2019; 140:2654976. [PMID: 28975252 DOI: 10.1115/1.4037947] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2017] [Indexed: 01/17/2023]
Abstract
Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress-strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress-strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 μm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 μm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.
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Affiliation(s)
- James W Reinhardt
- Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210 e-mail:
| | - Keith J Gooch
- Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210.,Dorothy M. Davis Heart & Lung Research Institute, The Ohio State University, 473 W. 12th Avenue, Columbus, OH 43210 e-mail:
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Scott KE, Rychel K, Ranamukhaarachchi S, Rangamani P, Fraley SI. Emerging themes and unifying concepts underlying cell behavior regulation by the pericellular space. Acta Biomater 2019; 96:81-98. [PMID: 31176842 DOI: 10.1016/j.actbio.2019.06.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Revised: 05/28/2019] [Accepted: 06/04/2019] [Indexed: 12/29/2022]
Abstract
Cells reside in a complex three-dimensional (3D) microenvironment where physical, chemical, and architectural features of the pericellular space regulate important cellular functions like migration, differentiation, and morphogenesis. A major goal of tissue engineering is to identify which properties of the pericellular space orchestrate these emergent cell behaviors and how. In this review, we highlight recent studies at the interface of biomaterials and single cell biophysics that are lending deeper insight towards this goal. Advanced methods have enabled the decoupling of architectural and mechanical features of the microenvironment, revealing multiple mechanisms of adhesion and mechanosensing modulation by biomaterials. Such studies are revealing important roles for pericellular space degradability, hydration, and adhesion competition in cell shape, volume, and differentiation regulation. STATEMENT OF SIGNIFICANCE: Cell fate and function are closely regulated by the local extracellular microenvironment. Advanced methods at the interface of single cell biophysics and biomaterials have shed new light on regulators of cell-pericellular space interactions by decoupling more features of the complex pericellular milieu than ever before. These findings lend deeper mechanistic insight into how biomaterials can be designed to fine-tune outcomes like differentiation, migration, and collective morphogenesis.
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Affiliation(s)
- Kiersten E Scott
- Bioengineering, University of California San Diego Jacobs School of Engineering, 9500 Gilman Drive #0435, La Jolla, CA 92093, USA.
| | - Kevin Rychel
- Bioengineering, University of California San Diego Jacobs School of Engineering, 9500 Gilman Drive #0435, La Jolla, CA 92093, USA.
| | - Sural Ranamukhaarachchi
- Bioengineering, University of California San Diego Jacobs School of Engineering, 9500 Gilman Drive #0435, La Jolla, CA 92093, USA.
| | - Padmini Rangamani
- Mechanical and Aerospace Engineering, University of California San Diego Jacobs School of Engineering, 9500 Gilman Drive #0411, La Jolla, CA 92093, USA.
| | - Stephanie I Fraley
- Bioengineering, University of California San Diego Jacobs School of Engineering, 9500 Gilman Drive #0435, La Jolla, CA 92093, USA.
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30
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Bui J, Conway DE, Heise RL, Weinberg SH. Mechanochemical Coupling and Junctional Forces during Collective Cell Migration. Biophys J 2019; 117:170-183. [PMID: 31200935 DOI: 10.1016/j.bpj.2019.05.020] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Revised: 05/09/2019] [Accepted: 05/22/2019] [Indexed: 12/31/2022] Open
Abstract
Cell migration, a fundamental physiological process in which cells sense and move through their surrounding physical environment, plays a critical role in development and tissue formation, as well as pathological processes, such as cancer metastasis and wound healing. During cell migration, dynamics are governed by the bidirectional interplay between cell-generated mechanical forces and the activity of Rho GTPases, a family of small GTP-binding proteins that regulate actin cytoskeleton assembly and cellular contractility. These interactions are inherently more complex during the collective migration of mechanically coupled cells because of the additional regulation of cell-cell junctional forces. In this study, we adapted a recent minimal modeling framework to simulate the interactions between mechanochemical signaling in individual cells and interactions with cell-cell junctional forces during collective cell migration. We find that migration of individual cells depends on the feedback between mechanical tension and Rho GTPase activity in a biphasic manner. During collective cell migration, waves of Rho GTPase activity mediate mechanical contraction/extension and thus synchronization throughout the tissue. Further, cell-cell junctional forces exhibit distinct spatial patterns during collective cell migration, with larger forces near the leading edge. Larger junctional force magnitudes are associated with faster collective cell migration and larger tissue size. Simulations of heterogeneous tissue migration exhibit a complex dependence on the properties of both leading and trailing cells. Computational predictions demonstrate that collective cell migration depends on both the emergent dynamics and interactions between cellular-level Rho GTPase activity and contractility and multicellular-level junctional forces.
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Affiliation(s)
- Justin Bui
- Department of Chemical Engineering, University of California Berkeley, Berkeley, California
| | - Daniel E Conway
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia
| | - Rebecca L Heise
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia
| | - Seth H Weinberg
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, Virginia.
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31
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Malik AA, Gerlee P. Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis. J Math Biol 2019; 78:2289-2315. [PMID: 30972438 PMCID: PMC6534528 DOI: 10.1007/s00285-019-01344-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Revised: 01/25/2019] [Indexed: 12/17/2022]
Abstract
Durotaxis, the phenomena where cells migrate up a gradient in substrate stiffness, remains poorly understood. It has been proposed that durotaxis results from the reinforcement of focal adhesions on stiff substrates. In this paper we formulate a mathematical model of single cell migration on elastic substrates with spatially varying stiffness. We develop a stochastic model where the cell moves by updating the position of its adhesion sites at random times, and the rate of updates is determined by the local stiffness of the substrate. We investigate two physiologically motivated mechanisms of stiffness sensing. From the stochastic model of single cell migration we derive a population level description in the form of a partial differential equation for the time evolution of the density of cells. The equation is an advection–diffusion equation, where the advective velocity is proportional to the stiffness gradient. The model shows quantitative agreement with experimental results in which cells tend to cluster when seeded on a matrix with periodically varying stiffness.
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Affiliation(s)
- Adam A Malik
- Mathematical Sciences, Chalmers University of Technology, 41296, Göteborg, Sweden. .,Mathematical Sciences, University of Gothenburg, 41296, Göteborg, Sweden.
| | - Philip Gerlee
- Mathematical Sciences, Chalmers University of Technology, 41296, Göteborg, Sweden.,Mathematical Sciences, University of Gothenburg, 41296, Göteborg, Sweden
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32
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Conlon GA, Murray GI. Recent advances in understanding the roles of matrix metalloproteinases in tumour invasion and metastasis. J Pathol 2019; 247:629-640. [DOI: 10.1002/path.5225] [Citation(s) in RCA: 88] [Impact Index Per Article: 17.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Revised: 12/11/2018] [Accepted: 12/19/2018] [Indexed: 12/18/2022]
Affiliation(s)
- Guy A Conlon
- Department of PathologyNHS Grampian, Aberdeen Royal Infirmary Aberdeen UK
| | - Graeme I Murray
- Department of Pathology, School of MedicineMedical Sciences and Nutrition, University of Aberdeen Aberdeen UK
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Merino-Casallo F, Gomez-Benito MJ, Juste-Lanas Y, Martinez-Cantin R, Garcia-Aznar JM. Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration. Front Physiol 2018; 9:1246. [PMID: 30271351 PMCID: PMC6142046 DOI: 10.3389/fphys.2018.01246] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Accepted: 08/17/2018] [Indexed: 11/13/2022] Open
Abstract
Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Maria J Gomez-Benito
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Yago Juste-Lanas
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Ruben Martinez-Cantin
- Centro Universitario de la Defensa, Zaragoza, Spain.,SigOpt, Inc., San Francisco, CA, United States
| | - Jose M Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
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34
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Sfakianakis N, Brunk A. Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM. Bull Math Biol 2018; 80:2789-2827. [PMID: 30159856 DOI: 10.1007/s11538-018-0460-0] [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: 09/12/2017] [Accepted: 06/29/2018] [Indexed: 10/28/2022]
Abstract
We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.
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Affiliation(s)
- N Sfakianakis
- Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany.
| | - A Brunk
- Institute of Mathematics, Johannes Gutenberg-University, Staudingerweg 9, 55128, Mainz, Germany
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35
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Campbell EJ, Bagchi P. A computational model of amoeboid cell motility in the presence of obstacles. SOFT MATTER 2018; 14:5741-5763. [PMID: 29873659 DOI: 10.1039/c8sm00457a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Locomotion of amoeboid cells is mediated by finger-like protrusions of the cell body, known as pseudopods, which grow, bifurcate, and retract in a dynamic fashion. Pseudopods are the primary mode of locomotion for many cells within the human body, such as leukocytes, embryonic cells, and metastatic cancer cells. Amoeboid motility is a complex and multiscale process, which involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Additionally, cells within the human body are subject to a confined 3D environment known as the extra-cellular matrix (ECM), which resembles a fluid-filled porous medium. In this article, we present a 3D, multiphysics computational approach coupling fluid mechanics, solid mechanics, and a pattern formation model to simulate locomotion of amoeboid cells through a porous matrix composed of a viscous fluid and an array of finite-sized spherical obstacles. The model combines reaction-diffusion of activator/inhibitors, extreme deformation of the cell, pseudopod dynamics, cytoplasmic and extracellular fluid motion, and fully resolved extracellular matrix. A surface finite-element method is used to obtain the cell deformation and activator/inhibitor concentrations, while the fluid motion is solved using a combined finite-volume and spectral method. The immersed-boundary methods are used to couple the cell deformation, obstacles, and fluid. The model is able to recreate squeezing and weaving motion of cells through the matrix. We study the influence of matrix porosity, obstacle size, and cell deformability on the motility behavior. It is found that below certain values of these parameters, cell motion is completely inhibited. Phase diagrams are presented depicting such motility limits. Interesting dynamics seen in the presence of obstacles but absent in unconfined medium, such as freezing or cell arrest, probing, doubling-back, and tug-of-war are predicted. Furthermore, persistent unidirectional motion of cells that is often observed in an unconfined medium is shown to be lost in presence of obstacles, and is attributed to an alteration of the pseudopod dynamics. The same mechanism, however, allows the cell to find a new direction to penetrate further into the matrix without being stuck in one place. The results and analysis presented here show a strong coupling between cell deformability and ECM properties, and provide new fluid mechanical insights on amoeboid motility in confined medium.
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Affiliation(s)
- Eric J Campbell
- Mechanical and Aerospace Engineering Department, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA.
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36
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Ozdemir-Kaynak E, Qutub AA, Yesil-Celiktas O. Advances in Glioblastoma Multiforme Treatment: New Models for Nanoparticle Therapy. Front Physiol 2018; 9:170. [PMID: 29615917 PMCID: PMC5868458 DOI: 10.3389/fphys.2018.00170] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 02/20/2018] [Indexed: 11/30/2022] Open
Abstract
The most lethal form of brain cancer, glioblastoma multiforme, is characterized by rapid growth and invasion facilitated by cell migration and degradation of the extracellular matrix. Despite technological advances in surgery and radio-chemotherapy, glioblastoma remains largely resistant to treatment. New approaches to study glioblastoma and to design optimized therapies are greatly needed. One such approach harnesses computational modeling to support the design and delivery of glioblastoma treatment. In this paper, we critically summarize current glioblastoma therapy, with a focus on emerging nanomedicine and therapies that capitalize on cell-specific signaling in glioblastoma. We follow this summary by discussing computational modeling approaches focused on optimizing these emerging nanotherapeutics for brain cancer. We conclude by illustrating how mathematical analysis can be used to compare the delivery of a high potential anticancer molecule, delphinidin, in both free and nanoparticle loaded forms across the blood-brain barrier for glioblastoma.
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Affiliation(s)
- Elif Ozdemir-Kaynak
- Department of Bioengineering, Faculty of Engineering, Ege University, Bornova-Izmir, Turkey
| | - Amina A Qutub
- Department of Bioengineering, Rice University, Houston, TX, United States
| | - Ozlem Yesil-Celiktas
- Department of Bioengineering, Faculty of Engineering, Ege University, Bornova-Izmir, Turkey.,Biomaterials Innovation Research Center, Division of Biomedical Engineering, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States.,Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, United States
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37
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Rajagopal V, Holmes WR, Lee PVS. Computational modeling of single-cell mechanics and cytoskeletal mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2018; 10:e1407. [PMID: 29195023 PMCID: PMC5836888 DOI: 10.1002/wsbm.1407] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 08/19/2017] [Accepted: 09/07/2017] [Indexed: 01/10/2023]
Abstract
Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
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Affiliation(s)
- Vijay Rajagopal
- Cell Structure and Mechanobiology Group, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
| | - William R. Holmes
- Department of Physics and AstronomyVanderbilt UniversityNashvilleTNUSA
| | - Peter Vee Sin Lee
- Cell and Tissue Biomechanics Laboratory, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
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38
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Creation of Three-Dimensional Liver Tissue Models from Experimental Images for Systems Medicine. Methods Mol Biol 2018; 1506:319-362. [PMID: 27830563 DOI: 10.1007/978-1-4939-6506-9_22] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
In this chapter, we illustrate how three-dimensional liver tissue models can be created from experimental image modalities by utilizing a well-established processing chain of experiments, microscopic imaging, image processing, image analysis and model construction. We describe how key features of liver tissue architecture are quantified and translated into model parameterizations, and show how a systematic iteration of experiments and model simulations often leads to a better understanding of biological phenomena in systems biology and systems medicine.
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39
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Poleszczuk J, Macklin P, Enderling H. Agent-Based Modeling of Cancer Stem Cell Driven Solid Tumor Growth. Methods Mol Biol 2018; 1516:335-346. [PMID: 27044046 DOI: 10.1007/7651_2016_346] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Computational modeling of tumor growth has become an invaluable tool to simulate complex cell-cell interactions and emerging population-level dynamics. Agent-based models are commonly used to describe the behavior and interaction of individual cells in different environments. Behavioral rules can be informed and calibrated by in vitro assays, and emerging population-level dynamics may be validated with both in vitro and in vivo experiments. Here, we describe the design and implementation of a lattice-based agent-based model of cancer stem cell driven tumor growth.
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Affiliation(s)
- Jan Poleszczuk
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, 33647, USA
| | - Paul Macklin
- Center for Applied Molecular Medicine, University of Southern California, Los Angeles, CA, 90033, USA
| | - Heiko Enderling
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, 33647, USA.
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40
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Abstract
Cell migration is an adaptive process that depends on and responds to physical and molecular triggers. Moving cells sense and respond to tissue mechanics and induce transient or permanent tissue modifications, including extracellular matrix stiffening, compression and deformation, protein unfolding, proteolytic remodelling and jamming transitions. Here we discuss how the bi-directional relationship of cell-tissue interactions (mechanoreciprocity) allows cells to change position and contributes to single-cell and collective movement, structural and molecular tissue organization, and cell fate decisions.
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41
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Schumacher LJ, Kulesa PM, McLennan R, Baker RE, Maini PK. Multidisciplinary approaches to understanding collective cell migration in developmental biology. Open Biol 2017; 6:rsob.160056. [PMID: 27278647 PMCID: PMC4929938 DOI: 10.1098/rsob.160056] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Accepted: 05/05/2016] [Indexed: 12/18/2022] Open
Abstract
Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell–cell interactions, cell–environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions.
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Affiliation(s)
- Linus J Schumacher
- Mathematics, University of Oxford, Oxford, UK Department of Life Sciences and Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, UK
| | - Paul M Kulesa
- Stowers Institute for Medical Research, 1000 E 50th Street, Kansas City, MO 60114, USA
| | - Rebecca McLennan
- Stowers Institute for Medical Research, 1000 E 50th Street, Kansas City, MO 60114, USA
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42
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Rens EG, Merks RMH. Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch. Biophys J 2017; 112:755-766. [PMID: 28256235 DOI: 10.1016/j.bpj.2016.12.012] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Revised: 10/21/2016] [Accepted: 12/02/2016] [Indexed: 12/28/2022] Open
Abstract
During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.
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Affiliation(s)
- Elisabeth G Rens
- Life Sciences, Centrum Wiskunde & Informatica, Amsterdam, the Netherlands; Mathematical Institute, Leiden University, Leiden, the Netherlands
| | - Roeland M H Merks
- Life Sciences, Centrum Wiskunde & Informatica, Amsterdam, the Netherlands; Mathematical Institute, Leiden University, Leiden, the Netherlands.
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43
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Szymańska Z, Cytowski M, Mitchell E, Macnamara CK, Chaplain MAJ. Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling. Bull Math Biol 2017. [PMID: 28634857 DOI: 10.1007/s11538-017-0292-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.
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Affiliation(s)
- Zuzanna Szymańska
- ICM, University of Warsaw, ul. Pawińskiego 5a, 02-106, Warsaw, Poland
| | - Maciej Cytowski
- ICM, University of Warsaw, ul. Pawińskiego 5a, 02-106, Warsaw, Poland
| | - Elaine Mitchell
- Division of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, UK
| | - Cicely K Macnamara
- School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK
| | - Mark A J Chaplain
- School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK.
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Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process. NPJ Syst Biol Appl 2017. [PMID: 28649436 PMCID: PMC5445583 DOI: 10.1038/s41540-017-0010-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell–cell interactions. This is important as cell–cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell–cell adhesion or repulsion are known to play a significant role. Cell motility is a central process in wound healing and relies on complex cell-cell interactions. A team of mathematicians led by Ruth Baker and Kit Yates at the University of Oxford utilised computer simulations to re-design wound-healing assays that efficiently identify cell motility parameters. New experimental designs through computer simulation can more accurately identify cell motility parameters by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results describe time and cost-saving alterations for an experimental method for evaluate complex cell-cell interactions.
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Ahmadzadeh H, Webster MR, Behera R, Jimenez Valencia AM, Wirtz D, Weeraratna AT, Shenoy VB. Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion. Proc Natl Acad Sci U S A 2017; 114:E1617-E1626. [PMID: 28196892 PMCID: PMC5338523 DOI: 10.1073/pnas.1617037114] [Citation(s) in RCA: 109] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy-based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion.
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Affiliation(s)
- Hossein Ahmadzadeh
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
| | - Marie R Webster
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Reeti Behera
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Angela M Jimenez Valencia
- Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218
- Physical Sciences-Oncology Center, The Johns Hopkins University, Baltimore, MD 21218
- Institute for NanoBioTechnology, The Johns Hopkins University, Baltimore, MD 21218
| | - Denis Wirtz
- Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218
- Physical Sciences-Oncology Center, The Johns Hopkins University, Baltimore, MD 21218
- Institute for NanoBioTechnology, The Johns Hopkins University, Baltimore, MD 21218
- Department of Oncology, The Johns Hopkins School of Medicine, Baltimore, MD 21218
- Department of Pathology, The Johns Hopkins School of Medicine, Baltimore, MD 21218
| | - Ashani T Weeraratna
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Vivek B Shenoy
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104;
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
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3D hybrid modelling of vascular network formation. J Theor Biol 2016; 414:254-268. [PMID: 27890575 DOI: 10.1016/j.jtbi.2016.11.013] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Revised: 09/06/2016] [Accepted: 11/16/2016] [Indexed: 12/13/2022]
Abstract
We develop an off-lattice, agent-based model to describe vasculogenesis, the de novo formation of blood vessels from endothelial progenitor cells during development. The endothelial cells that comprise our vessel network are viewed as linearly elastic spheres that move in response to the forces they experience. We distinguish two types of endothelial cells: vessel elements are contained within the network and tip cells are located at the ends of vessels. Tip cells move in response to mechanical forces caused by interactions with neighbouring vessel elements and the local tissue environment, chemotactic forces and a persistence force which accounts for their tendency to continue moving in the same direction. Vessel elements are subject to similar mechanical forces but are insensitive to chemotaxis. An angular persistence force representing interactions with the local tissue is introduced to stabilise buckling instabilities caused by cell proliferation. Only vessel elements proliferate, at rates which depend on their degree of stretch: elongated elements have increased rates of proliferation, and compressed elements have reduced rates. Following division, the fate of the new cell depends on the local mechanical environment: the probability of forming a new sprout is increased if the parent vessel is highly compressed and the probability of being incorporated into the parent vessel increased if the parent is stretched. Simulation results reveal that our hybrid model can reproduce the key qualitative features of vasculogenesis. Extensive parameter sensitivity analyses show that significant changes in network size and morphology are induced by varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and the sprouting probability to mechanical stretch. Varying the chemotactic sensitivity directly influences the directionality of the networks. The degree of branching, and thereby the density of the networks, is influenced by the sprouting probability. Glyphs that simultaneously depict several network properties are introduced to show how these and other network quantities change over time and also as model parameters vary. We also show how equivalent glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, in the longer term, for model validation. We conclude that our biomechanical hybrid model can generate vascular networks that are qualitatively similar to those generated from in vitro and in vivo experiments.
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Kassab GS, An G, Sander EA, Miga MI, Guccione JM, Ji S, Vodovotz Y. Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective. Ann Biomed Eng 2016; 44:2611-25. [PMID: 27015816 DOI: 10.1007/s10439-016-1596-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2015] [Accepted: 03/18/2016] [Indexed: 12/18/2022]
Abstract
In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.
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Affiliation(s)
- Ghassan S Kassab
- California Medical Innovations Institute, San Diego, CA, 92121, USA
| | - Gary An
- Department of Surgery, University of Chicago, Chicago, IL, 60637, USA
| | - Edward A Sander
- Department of Biomedical Engineering, University of Iowa, Iowa City, IA, 52242, USA
| | - Michael I Miga
- Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, 37235, USA
| | - Julius M Guccione
- Department of Surgery, University of California, San Francisco, CA, 94143, USA
| | - Songbai Ji
- Thayer School of Engineering, Dartmouth College, Hanover, NH, 03755, USA.,Department of Surgery and of Orthopaedic Surgery, Geisel School of Medicine, Dartmouth College, Hanover, NH, 03755, USA
| | - Yoram Vodovotz
- Department of Surgery, University of Pittsburgh, W944 Starzl Biomedical Sciences Tower, 200 Lothrop St., Pittsburgh, PA, 15213, USA. .,Center for Inflammation and Regenerative Modeling, McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA, 15219, USA.
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Dallon JC, Evans EJ, Ehrlich HP. A mathematical model of collagen lattice contraction. J R Soc Interface 2015; 11:rsif.2014.0598. [PMID: 25142520 DOI: 10.1098/rsif.2014.0598] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Two mathematical models for fibroblast-collagen interaction are proposed which reproduce qualitative features of fibroblast-populated collagen lattice contraction. Both models are force based and model the cells as individual entities with discrete attachment sites; however, the collagen lattice is modelled differently in each model. In the collagen lattice model, the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fibre model, the nodes are not triangulated, are less interconnected, and the collagen fibres are modelled as a string of nodes. Both models suggest that the overall increase in stress of the lattice as it contracts is not the cause of the reduced rate of contraction, but that the reduced rate of contraction is due to inactivation of the fibroblasts.
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Affiliation(s)
- J C Dallon
- Department of Mathematics, Brigham Young University, Provo, UT 84602-6539, USA
| | - E J Evans
- Department of Mathematics, Brigham Young University, Provo, UT 84602-6539, USA
| | - H Paul Ehrlich
- Division of Plastic Surgery, Hershey Medical Center, Hershey, PA 17033, USA
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Cell Invasion Dynamics into a Three Dimensional Extracellular Matrix Fibre Network. PLoS Comput Biol 2015; 11:e1004535. [PMID: 26436883 PMCID: PMC4593642 DOI: 10.1371/journal.pcbi.1004535] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2015] [Accepted: 09/05/2015] [Indexed: 01/02/2023] Open
Abstract
The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intracellular mechanics of cellular and nuclear membranes, contractile actin stress fibers, and focal adhesion dynamics; 3) structural mechanics of ECM fiber networks; and 4) reaction-diffusion mass transfers of seven biochemical concentrations in related with chemotaxis, proteolysis, haptotaxis, and degradation in ECM to predict dynamic behaviors of filopodia that penetrate into a 3D ECM fiber network. The tip of each filopodium crawls along ECM fibers, tugs the surrounding fibers, and contracts or retracts depending on the strength of the binding and the ECM stiffness and pore size. This filopodium-ECM interaction is modeled as a stochastic process based on binding kinetics between integrins along the filopodial shaft and the ligands on the surrounding ECM fibers. This filopodia stochastic model is integrated into migratory dynamics of a whole cell in order to predict the cell invasion into 3D ECM in response to chemotaxis, haptotaxis, and durotaxis cues. Predicted average filopodia speed and that of the cell membrane advance agreed with experiments of 3D HUVEC migration at r(2) > 0.95 for diverse ECMs with different pore sizes and stiffness.
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Cytowski M, Szymanska Z. Large-Scale Parallel Simulations of 3D Cell Colony Dynamics: The Cellular Environment. Comput Sci Eng 2015. [DOI: 10.1109/mcse.2015.66] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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