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Ban E, Wang H, Franklin JM, Liphardt JT, Janmey PA, Shenoy VB. Strong triaxial coupling and anomalous Poisson effect in collagen networks. Proc Natl Acad Sci U S A 2019; 116:6790-6799. [PMID: 30894480 PMCID: PMC6452734 DOI: 10.1073/pnas.1815659116] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
While cells within tissues generate and sense 3D states of strain, the current understanding of the mechanics of fibrous extracellular matrices (ECMs) stems mainly from uniaxial, biaxial, and shear tests. Here, we demonstrate that the multiaxial deformations of fiber networks in 3D cannot be inferred solely based on these tests. The interdependence of the three principal strains gives rise to anomalous ratios of biaxial to uniaxial stiffness between 8 and 9 and apparent Poisson's ratios larger than 1. These observations are explained using a microstructural network model and a coarse-grained constitutive framework that predicts the network Poisson effect and stress-strain responses in uniaxial, biaxial, and triaxial modes of deformation as a function of the microstructural properties of the network, including fiber mechanics and pore size of the network. Using this theoretical approach, we found that accounting for the Poisson effect leads to a 100-fold increase in the perceived elastic stiffness of thin collagen samples in extension tests, reconciling the seemingly disparate measurements of the stiffness of collagen networks using different methods. We applied our framework to study the formation of fiber tracts induced by cellular forces. In vitro experiments with low-density networks showed that the anomalous Poisson effect facilitates higher densification of fibrous tracts, associated with the invasion of cancerous acinar cells. The approach developed here can be used to model the evolving mechanics of ECM during cancer invasion and fibrosis.
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Affiliation(s)
- Ehsan Ban
- Center for Engineering Mechanobiology, University of Pennsylvania, Philadelphia, PA 19104
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
| | - Hailong Wang
- Center for Engineering Mechanobiology, University of Pennsylvania, Philadelphia, PA 19104
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
- Department of Modern Mechanics, Chinese Academy of Sciences Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, Anhui 230027, China
| | - J Matthew Franklin
- Department of Bioengineering, Stanford University, Stanford, CA 94305
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305
| | - Jan T Liphardt
- Department of Bioengineering, Stanford University, Stanford, CA 94305
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305
| | - Paul A Janmey
- Center for Engineering Mechanobiology, University of Pennsylvania, Philadelphia, PA 19104
- Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia, PA 19104
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
| | - Vivek B Shenoy
- Center for Engineering Mechanobiology, University of Pennsylvania, Philadelphia, PA 19104;
- 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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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] [What about the content of this article? (0)] [Affiliation(s)] [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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