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Giverso C, Loy N, Lucci G, Preziosi L. Cell orientation under stretch: A review of experimental findings and mathematical modelling. J Theor Biol 2023; 572:111564. [PMID: 37391125 DOI: 10.1016/j.jtbi.2023.111564] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 06/15/2023] [Indexed: 07/02/2023]
Abstract
The key role of electro-chemical signals in cellular processes had been known for many years, but more recently the interplay with mechanics has been put in evidence and attracted substantial research interests. Indeed, the sensitivity of cells to mechanical stimuli coming from the microenvironment turns out to be relevant in many biological and physiological circumstances. In particular, experimental evidence demonstrated that cells on elastic planar substrates undergoing periodic stretches, mimicking native cyclic strains in the tissue where they reside, actively reorient their cytoskeletal stress fibres. At the end of the realignment process, the cell axis forms a certain angle with the main stretching direction. Due to the importance of a deeper understanding of mechanotransduction, such a phenomenon was studied both from the experimental and the mathematical modelling point of view. The aim of this review is to collect and discuss both the experimental results on cell reorientation and the fundamental features of the mathematical models that have been proposed in the literature.
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Affiliation(s)
- Chiara Giverso
- Department of Mathematical Sciences "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10126, Italy.
| | - Nadia Loy
- Department of Mathematical Sciences "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10126, Italy.
| | - Giulio Lucci
- Department of Mathematical Sciences "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10126, Italy.
| | - Luigi Preziosi
- Department of Mathematical Sciences "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10126, Italy.
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Loy N, Preziosi L. A Statistical Mechanics Approach to Describe Cell Reorientation Under Stretch. Bull Math Biol 2023; 85:60. [PMID: 37249663 PMCID: PMC10229726 DOI: 10.1007/s11538-023-01161-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 04/25/2023] [Indexed: 05/31/2023]
Abstract
Experiments show that when a monolayer of cells cultured on an elastic substratum is subject to a cyclic stretch, cells tend to reorient either perpendicularly or at an oblique angle with respect to the main stretching direction. Due to stochastic effects, however, the distribution of angles achieved by the cells is broader and, experimentally, histograms over the interval [Formula: see text] are usually reported. Here we will determine the evolution and the stationary state of probability density functions describing the statistical distribution of the orientations of the cells using Fokker-Planck equations derived from microscopic rules for describing the reorientation process of the cell. As a first attempt, we shall use a stochastic differential equation related to a very general elastic energy that the cell tries to minimize and, we will show that the results of the time integration and of the stationary state of the related forward Fokker-Planck equation compare very well with experimental results obtained by different researchers. Then, in order to model more accurately the microscopic process of cell reorientation and to shed light on the mechanisms performed by cells that are subject to cyclic stretch, we consider discrete in time random processes that allow to recover Fokker-Planck equations through classical tools of kinetic theory. In particular, we shall introduce a model of reorientation as a function of the rotation angle as a result of an optimal control problem. Also in this latter case the results match very well with experiments.
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Affiliation(s)
- N Loy
- Politecnico di Torino, Torino, Italy.
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3
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Moriel A, Livne A, Bouchbinder E. Cellular orientational fluctuations, rotational diffusion and nematic order under periodic driving. SOFT MATTER 2022; 18:7091-7102. [PMID: 36043855 DOI: 10.1039/d2sm00611a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The ability of living cells to sense the physical properties of their microenvironment and to respond to dynamic forces acting on them plays a central role in regulating their structure, function and fate. Of particular importance is the cellular sensitivity and response to periodic driving forces in noisy environments, encountered in vital physiological conditions such as heart beating, blood vessel pulsation and breathing. Here, we first test and validate two predictions of a mean-field theory of cellular reorientation under periodic driving, which combines the minimization of cellular anisotropic elastic energy with active remodeling forces. We then extend the mean-field theory to include uncorrelated, additive nonequilibrium fluctuations, and show that the theory quantitatively agrees with the experimentally observed stationary probability distributions of the cell body orientation, under a range of biaxial periodic driving forces. The fluctuations theory allows the extraction of the dimensionless active noise amplitude of various cell types, and consequently their rotational diffusion coefficient. We then focus on intra-cellular nematic order, i.e. on orientational fluctuations of actin stress fibers around the cell body orientation, and show experimentally that intra-cellular nematic order increases with both the magnitude of the driving forces and the biaxiality strain ratio. These results are semi-quantitatively explained by applying the same cell body fluctuations theory to orientationally correlated actin stress fiber domains. Finally, an estimate of the energy scale of cellular orientational fluctuations for one cell type is shown to be about six order of magnitude larger than the thermal energy at room temperature. The implications of our findings, which make the quantitative analysis of cell mechanosensitivity more accessible, are discussed.
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Affiliation(s)
- Avraham Moriel
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel.
| | - Ariel Livne
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 7610001, Israel
- Diptera.ai, PO Box 39047, Jerusalem 9139002, Israel
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel.
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Pakravan HA, Saidi MS, Firoozabadi B. Endothelial Cells Morphology in Response to Combined WSS and Biaxial CS: Introduction of Effective Strain Ratio. Cell Mol Bioeng 2020; 13:647-657. [PMID: 33281993 DOI: 10.1007/s12195-020-00618-z] [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: 01/12/2020] [Accepted: 05/05/2020] [Indexed: 11/24/2022] Open
Abstract
Introduction Endothelial cells (ECs) morphology strongly depends on the imposed mechanical stimuli. These mechanical stimuli include wall shear stress (WSS) and biaxial cyclic stretches (CS). Under combined loading, the effect of CS is not as simple as pure CS. The present study investigates the morphological response of ECs to the realistic mechanical stimuli. Methods The cell population is theoretically studied using our previous validated model. The mechanical stimuli on ECs are described using four parameters; WSS magnitude (0 to 2.0 Pa), WSS angle (- 50° to 50°), and biaxial CS in two perpendicular directions (0 to 10%). The morphology of ECs is reported using four parameters; average shape index (SI) and orientation angle (OA) of the cell population as well as the standard deviation (SD) of SI and OA as measures for scattering of cells' SI and OA from these average values. Results A new effective strain ratio (ESR) is defined as the ratio of the undesirable CS to the desirable one. The obtained results of the model, illustrated that the SI and OA of cells increase with absolute value of ESR. In addition, the scattering in the SI of cells decreases with the absolute value of ESR, which means that the cell shapes become more regular. It is shown that the angular irregularity of cells increases at higher ESR values. Conclusions The results indicated that, the defined ESR is a stand-alone parameter for describing the realistic mechanical loading on the ECs and their morphological response.
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Affiliation(s)
| | - Mohammad Said Saidi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
| | - Bahar Firoozabadi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
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Stamenović D, Smith ML. Tensional homeostasis at different length scales. SOFT MATTER 2020; 16:6946-6963. [PMID: 32696799 DOI: 10.1039/d0sm00763c] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Tensional homeostasis is a phenomenon of fundamental importance in mechanobiology. It refers to the ability of organs, tissues, and cells to respond to external disturbances by maintaining a homeostatic (set point) level of mechanical stress (tension). It is well documented that breakdown in tensional homeostasis is the hallmark of progression of diseases, including cancer and atherosclerosis. In this review, we surveyed quantitative studies of tensional homeostasis with the goal of providing characterization of this phenomenon across a broad range of length scales, from the organ level to the subcellular level. We considered both static and dynamics approaches that have been used in studies of this phenomenon. Results that we found in the literature and that we obtained from our own investigations suggest that tensional homeostasis is an emergent phenomenon driven by collective rheostatic mechanisms associated with focal adhesions, and by a collective action of cells in multicellular forms, whose impact on tensional homeostasis is cell type-dependent and cell microenvironment-dependent. Additionally, the finding that cadherins, adhesion molecules that are important for formation of cell-cell junctions, promote tensional homeostasis even in single cells, demonstrates their relevance as a signaling moiety.
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Affiliation(s)
- Dimitrije Stamenović
- Department of Biomedical Engineering, Boston University, 44 Cummington Mall, Boston, MA 02215, USA.
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Jahromi R, Pakravan HA, Saidi MS, Firoozabadi B. Primary stenosis progression versus secondary stenosis formation in the left coronary bifurcation: A mechanical point of view. Biocybern Biomed Eng 2019. [DOI: 10.1016/j.bbe.2018.11.006] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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Chagnon-Lessard S, Jean-Ruel H, Godin M, Pelling AE. Cellular orientation is guided by strain gradients. Integr Biol (Camb) 2018; 9:607-618. [PMID: 28534911 DOI: 10.1039/c7ib00019g] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The strain-induced reorientation response of cyclically stretched cells has been well characterized in uniform strain fields. In the present study, we comprehensively analyse the behaviour of human fibroblasts subjected to a highly non-uniform strain field within a polymethylsiloxane microdevice. Our results indicate that the strain gradient amplitude and direction regulate cell reorientation through a coordinated gradient avoidance response. We provide critical evidence that strain gradient is a key physical cue that can guide cell organization. Specifically, our work suggests that cells are able to pinpoint the location under the cell of multiple physical cues and integrate this information (strain and strain gradient amplitudes and directions), resulting in a coordinated response. To gain insight into the underlying mechanosensing processes, we studied focal adhesion reorganization and the effect of modulating myosin-II contractility. The extracted focal adhesion orientation distributions are similar to those obtained for the cell bodies, and their density is increased by the presence of stretching forces. Moreover, it was found that the myosin-II activity promoter calyculin-A has little effect on the cellular response, while the inhibitor blebbistatin suppresses cell and focal adhesion alignment and reduces focal adhesion density. These results confirm that similar internal structures involved in sensing and responding to strain direction and amplitude are also key players in strain gradient mechanosensing and avoidance.
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Affiliation(s)
- Sophie Chagnon-Lessard
- Department of Physics, Center for Interdisciplinary Nanophysics, University of Ottawa, 598 King Edward, Ottawa, ON K1N 6N5, Canada.
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Pakravan HA, Saidi MS, Firoozabadi B. A multiscale approach for determining the morphology of endothelial cells at a coronary artery. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33. [PMID: 28445003 DOI: 10.1002/cnm.2891] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2016] [Revised: 04/11/2017] [Accepted: 04/23/2017] [Indexed: 06/07/2023]
Abstract
The morphology of endothelial cells (ECs) may be an indication for determining atheroprone sites. Until now, there has been no clinical imaging technique to visualize the morphology of ECs in the arteries. The present study introduces a computational technique for determining the morphology of ECs. This technique is a multiscale simulation consisting of the artery scale and the cell scale. The artery scale is a fluid-structure interaction simulation. The input for the artery scale is the geometry of the coronary artery, that is, the dynamic curvature of the artery due to the cardiac motion, blood flow, blood pressure, heart rate, and the mechanical properties of the blood and the arterial wall, the measurements of which can be obtained for a specific patient. The results of the artery scale are wall shear stress (WSS) and cyclic strains as the mechanical stimuli of ECs. The cell scale is an inventive mass-and-spring model that is able to determine the morphological response of ECs to any combination of mechanical stimuli. The results of the multiscale simulation show the morphology of ECs at different locations of the coronary artery. The results indicate that the atheroprone sites have at least 1 of 3 factors: low time-averaged WSS, high angle of WSS, and high longitudinal strain. The most probable sites for atherosclerosis are located at the bifurcation region and lie on the myocardial side of the artery. The results also indicated that a higher dynamic curvature is a negative factor and a higher pulse pressure is a positive factor for protection against atherosclerosis.
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Affiliation(s)
- Hossein Ali Pakravan
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
- Department of Mechanical Engineering, Shiraz University, Shiraz, Iran
| | - Mohammad Said Saidi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
| | - Bahar Firoozabadi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
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Yang L, Carrington LJ, Erdogan B, Ao M, Brewer BM, Webb DJ, Li D. Biomechanics of cell reorientation in a three-dimensional matrix under compression. Exp Cell Res 2016; 350:253-266. [PMID: 27919745 DOI: 10.1016/j.yexcr.2016.12.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Revised: 11/30/2016] [Accepted: 12/01/2016] [Indexed: 01/02/2023]
Abstract
Although a number of studies have reported that cells cultured on a stretchable substrate align away from or perpendicular to the stretch direction, how cells sense and respond to compression in a three-dimensional (3D) matrix remains an open question. We analyzed the reorientation of human prostatic normal tissue fibroblasts (NAFs) and cancer-associated fibroblasts (CAFs) in response to 3D compression using a Fast Fourier Transform (FFT) method. Results show that NAFs align to specific angles upon compression while CAFs exhibit a random distribution. In addition, NAFs with enhanced contractile force induced by transforming growth factor β (TGF-β) behave in a similar way as CAFs. Furthermore, a theoretical model based on the minimum energy principle has been developed to provide insights into these observations. The model prediction is in agreement with the observed cell orientation patterns in several different experimental conditions, disclosing the important role of stress fibers and inherent cell contractility in cell reorientation.
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Affiliation(s)
- Lijie Yang
- Department of Mechanical Engineering, Vanderbilt University, Nashville 37235, TN, USA
| | - Léolène Jean Carrington
- Department of Biological Sciences and Vanderbilt Kennedy Center for Research on Human Development, Vanderbilt University, Nashville 37235, TN, USA
| | - Begum Erdogan
- Department of Biological Sciences and Vanderbilt Kennedy Center for Research on Human Development, Vanderbilt University, Nashville 37235, TN, USA
| | - Mingfang Ao
- Department of Biological Sciences and Vanderbilt Kennedy Center for Research on Human Development, Vanderbilt University, Nashville 37235, TN, USA
| | - Bryson M Brewer
- Department of Mechanical Engineering, Vanderbilt University, Nashville 37235, TN, USA
| | - Donna J Webb
- Department of Biological Sciences and Vanderbilt Kennedy Center for Research on Human Development, Vanderbilt University, Nashville 37235, TN, USA.
| | - Deyu Li
- Department of Mechanical Engineering, Vanderbilt University, Nashville 37235, TN, USA.
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10
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Pakravan HA, Saidi MS, Firoozabadi B. A mechanical model for morphological response of endothelial cells under combined wall shear stress and cyclic stretch loadings. Biomech Model Mechanobiol 2016; 15:1229-43. [PMID: 26769119 DOI: 10.1007/s10237-015-0756-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2015] [Accepted: 12/22/2015] [Indexed: 12/17/2022]
Abstract
The shape and morphology of endothelial cells (ECs) lining the blood vessels are a good indicator for atheroprone and atheroprotected sites. ECs of blood vessels experience both wall shear stress (WSS) and cyclic stretch (CS). These mechanical stimuli influence the shape and morphology of ECs. A few models have been proposed for predicting the morphology of ECs under WSS or CS. In the present study, a mathematical cell population model is developed to simulate the morphology of ECs under combined WSS and CS conditions. The model considers the cytoskeletal filaments, cell-cell interactions, and cell-extracellular matrix interactions. In addition, the reorientation and polymerization of microfilaments are implemented in the model. The simulations are performed for different conditions: without mechanical stimuli, under pure WSS, under pure CS, and under combined WSS and CS. The results are represented as shape and morphology of ECs, shape index, and angle of orientation. The model is validated qualitatively and quantitatively with several experimental studies, and good agreement with experimental studies is achieved. To the best of our knowledge, it is the first model for predicting the morphology of ECs under combined WSS and CS condition. The model can be used to indicate the atheroprone regions of a patient's artery.
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Affiliation(s)
- H A Pakravan
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
| | - M S Saidi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
| | - B Firoozabadi
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
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PAKRAVAN HOSSEINALI, SAIDI MOHAMMADSAID, FIROOZABADI BAHAR. FSI SIMULATION OF A HEALTHY CORONARY BIFURCATION FOR STUDYING THE MECHANICAL STIMULI OF ENDOTHELIAL CELLS UNDER DIFFERENT PHYSIOLOGICAL CONDITIONS. J MECH MED BIOL 2015. [DOI: 10.1142/s021951941550089x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Atherosclerosis is a world-spread and well-known disease. This disease strongly relates to the endothelial cells (ECs) function. Normally, the endothelial cells align in the flow direction in the atheroprotected sites; however, in the case of atheroprone sites these cells orient randomly. The mechanical stimuli such as wall shear stress and strains could determine the morphology and function of the endothelial cells. In the present study, we numerically simulated the left main coronary artery (LCA) and its branches to left anterior descending (LAD) and left circumflex coronary (LCX) artery using fluid–structure interaction (FSI) modeling. The results were presented as longitudinal and circumferential strains of ECs as well as wall shear stress. Wide ranges of heart rate, cardiac motion, systolic and diastolic pressures were considered and their effects on mechanical stimuli were described in detail. The results showed that these factors could greatly influence the risk of atherosclerosis and the location of atherosclerotic lesions.
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Affiliation(s)
- HOSSEIN ALI PAKRAVAN
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
| | - MOHAMMAD SAID SAIDI
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
| | - BAHAR FIROOZABADI
- Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
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12
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Nie W, Wei MT, Ou-Yang HD, Jedlicka SS, Vavylonis D. Formation of contractile networks and fibers in the medial cell cortex through myosin-II turnover, contraction, and stress-stabilization. Cytoskeleton (Hoboken) 2015; 72:29-46. [PMID: 25641802 DOI: 10.1002/cm.21207] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2014] [Accepted: 12/31/2014] [Indexed: 12/24/2022]
Abstract
The morphology of adhered cells depends crucially on the formation of a contractile meshwork of parallel and cross-linked fibers along the contacting surface. The motor activity and minifilament assembly of non-muscle myosin-II is an important component of cortical cytoskeletal remodeling during mechanosensing. We used experiments and computational modeling to study cortical myosin-II dynamics in adhered cells. Confocal microscopy was used to image the medial cell cortex of HeLa cells stably expressing myosin regulatory light chain tagged with GFP (MRLC-GFP). The distribution of MRLC-GFP fibers and focal adhesions was classified into three types of network morphologies. Time-lapse movies show: myosin foci appearance and disappearance; aligning and contraction; stabilization upon alignment. Addition of blebbistatin, which perturbs myosin motor activity, leads to a reorganization of the cortical networks and to a reduction of contractile motions. We quantified the kinetics of contraction, disassembly and reassembly of myosin networks using spatio-temporal image correlation spectroscopy (STICS). Coarse-grained numerical simulations include bipolar minifilaments that contract and align through specified interactions as basic elements. After assuming that minifilament turnover decreases with increasing contractile stress, the simulations reproduce stress-dependent fiber formation in between focal adhesions above a threshold myosin concentration. The STICS correlation function in simulations matches the function measured in experiments. This study provides a framework to help interpret how different cortical myosin remodeling kinetics may contribute to different cell shape and rigidity depending on substrate stiffness.
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Affiliation(s)
- Wei Nie
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania
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Jiang L, Yang C, Zhao L, Zheng Q. Stress fiber response to mechanics: a free energy dependent statistical model. SOFT MATTER 2014; 10:4603-4608. [PMID: 24763746 DOI: 10.1039/c3sm52914b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
An experimental observation has been puzzling scientists for years: cells tend to align perpendicular to cyclic uniaxial strain, but parallel to external static strain. Recent experimental results demonstrate that both the magnitude of the external strain and the cell contractility manipulate the cells' orientation under cyclic uniaxial strain. In light of these reports, we introduce a minimum free energy model to explain the different orientation tendencies of cells subjected to external strain, and elucidate the significant role of cell contractility in this issue. With the present model, we successfully explain a series of well-documented phenomena: (1) cells orient nearly parallel to static uniaxial strain; (2) cell alignment depends on the magnitude of the cyclic uniaxial strain; (3) under cyclic uniaxial stretch, a tensioned contractility results in a strengthened perpendicular alignment of the cells, whereas a contractility relaxation results in a nearly parallel alignment. In addition, this model also successfully describes the functional relationship between cell contractility and substrate stiffness.
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Affiliation(s)
- Li Jiang
- Institute of Biomechanics and Medical Engineering, Engineering Mechanics Department, School of Aerospace, Tsinghua University, Beijing 100084, China.
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Abstract
Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations – cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell’s passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells, measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.
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Vernerey FJ, Farsad M. A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading. J Math Biol 2014; 68:989-1022. [PMID: 23463540 PMCID: PMC3855150 DOI: 10.1007/s00285-013-0656-8] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2011] [Revised: 01/23/2013] [Indexed: 01/11/2023]
Abstract
Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell's cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell's boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.
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Affiliation(s)
- Franck J Vernerey
- Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, USA,
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Wood ST, Dean BC, Dean D. A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models. Med Image Anal 2013; 17:337-47. [PMID: 23395283 PMCID: PMC3626120 DOI: 10.1016/j.media.2012.12.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2011] [Revised: 10/20/2012] [Accepted: 12/11/2012] [Indexed: 10/27/2022]
Abstract
This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery.
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Affiliation(s)
- Scott T Wood
- Department of Bioengineering, Clemson University, Clemson, SC 29634-0905, USA.
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17
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Foucard L, Vernerey FJ. Dynamics of Stress Fibers Turnover in Contractile Cells. JOURNAL OF ENGINEERING MECHANICS 2012; 138:10.1061/(ASCE)EM.1943-7889.0000430. [PMID: 29147066 PMCID: PMC5685556 DOI: 10.1061/(asce)em.1943-7889.0000430] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Accepted: 02/27/2012] [Indexed: 06/07/2023]
Abstract
Numerous experiments have shown that contractile cells like fibroblasts adapt their internal structure to their microenvironment by generating and orienting a network of stress fibers (SFs). This phenomenon has been modeled in previous studies with stability analysis through calculation of the fiber's potential or strain energy, where SFs are assigned a constant elasticity. Recent experiments have shown that the elasticity in SFs is rate dependent, resulting in a different stress fiber organization under constant or cyclic stretching. Here, a thermodynamical model that describes the anisotropic polymerization of the contractile units into SFs via the calculation of the mechanochemical potential of the two constituents is proposed. The stretch-dependent part of the SF potential is made of two terms that describe the passive and active behavior of the SF. In this paper, it is shown that the contributions of these two terms vary widely under constant or cyclic stretching as the SFs exhibit a rate-dependent elasticity and lead to two very different anisotropic SF organizations. It is further demonstrated that the substrate stiffness as well as its Poisson's ratio and anisotropy play a crucial role in the formation and organization of the SFs, consistent with what has been observed in various experiments.
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Affiliation(s)
- Louis Foucard
- Ph.D. Student, Dept. of Civil, Environmental, and Architectural Engineering, Univ. of Colorado at Boulder, 1111 Engineering Dr., P.O. Box 428 UCB, Boulder, CO 80309-0428
| | - Franck J. Vernerey
- Assistant Professor, Dept. of Civil, Environmental, Architectural Engineering, Univ. of Colorado at Boulder, 1111 Engineering Dr., P.O. Box 428 UCB, Boulder, CO 80309-0428
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18
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Abbott RD, Howe AK, Langevin HM, Iatridis JC. Live free or die: stretch-induced apoptosis occurs when adaptive reorientation of annulus fibrosus cells is restricted. Biochem Biophys Res Commun 2012; 421:361-6. [PMID: 22516752 DOI: 10.1016/j.bbrc.2012.04.018] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2012] [Accepted: 04/03/2012] [Indexed: 01/07/2023]
Abstract
High matrix strains in the intervertebral disc occur during physiological motions and are amplified around structural defects in the annulus fibrosus (AF). It remains unknown if large matrix strains in the human AF result in localized cell death. This study investigated strain amplitudes and substrate conditions where AF cells were vulnerable to stretch-induced apoptosis. Human degenerated AF cells were subjected to 1 Hz-cyclic tensile strains for 24h on uniformly collagen coated substrates and on substrates with 40 μm stripes of collagen that restricted cellular reorientation. AF cells were capable of responding to stretch (stress fibers and focal adhesions aligned perpendicular to the direction of stretch), but were vulnerable to stretch-induced apoptosis when cytoskeletal reorientation was restricted, as could occur in degenerated states due to fibrosis and crosslink accumulation and at areas where high strains occur (around structural defects, delaminations, and herniations).
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Affiliation(s)
- Rosalyn D Abbott
- School of Engineering, University of Vermont, Burlington, VT 05405, USA.
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19
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Foucard L, Vernerey FJ. A thermodynamical model for stress-fiber organization in contractile cells. APPLIED PHYSICS LETTERS 2012; 100:13702-137024. [PMID: 22271931 PMCID: PMC3262846 DOI: 10.1063/1.3673551] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2011] [Accepted: 12/05/2011] [Indexed: 05/31/2023]
Abstract
Cell mechanical adaptivity to external stimuli is vital to many of its biological functions. A critical question is therefore to understand the formation and organization of the stress fibers from which emerge the cell's mechanical properties. By accounting for the mechanical aspects and the viscoelastic behavior of stress fibers, we here propose a thermodynamic model to predict the formation and orientation of stress fibers in contractile cells subjected to constant or cyclic stretch and different substrate stiffness. Our results demonstrate that the stress fibers viscoelastic behavior plays a crucial role in their formation and organization and shows good consistency with various experiments.
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Affiliation(s)
- Louis Foucard
- Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428, USA
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20
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Deguchi S, Matsui TS, Iio K. The position and size of individual focal adhesions are determined by intracellular stress-dependent positive regulation. Cytoskeleton (Hoboken) 2011; 68:639-51. [DOI: 10.1002/cm.20541] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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21
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Morioka M, Parameswaran H, Naruse K, Kondo M, Sokabe M, Hasegawa Y, Suki B, Ito S. Microtubule dynamics regulate cyclic stretch-induced cell alignment in human airway smooth muscle cells. PLoS One 2011; 6:e26384. [PMID: 22022610 PMCID: PMC3195692 DOI: 10.1371/journal.pone.0026384] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2010] [Accepted: 09/26/2011] [Indexed: 01/06/2023] Open
Abstract
Microtubules are structural components of the cytoskeleton that determine cell shape, polarity, and motility in cooperation with the actin filaments. In order to determine the role of microtubules in cell alignment, human airway smooth muscle cells were exposed to cyclic uniaxial stretch. Human airway smooth muscle cells, cultured on type I collagen-coated elastic silicone membranes, were stretched uniaxially (20% in strain, 30 cycles/min) for 2 h. The population of airway smooth muscle cells which were originally oriented randomly aligned near perpendicular to the stretch axis in a time-dependent manner. However, when the cells treated with microtubule disruptors, nocodazole and colchicine, were subjected to the same cyclic uniaxial stretch, the cells failed to align. Lack of alignment was also observed for airway smooth muscle cells treated with a microtubule stabilizer, paclitaxel. To understand the intracellular mechanisms involved, we developed a computational model in which microtubule polymerization and attachment to focal adhesions were regulated by the preexisting tensile stress, pre-stress, on actin stress fibers. We demonstrate that microtubules play a central role in cell re-orientation when cells experience cyclic uniaxial stretching. Our findings further suggest that cell alignment and cytoskeletal reorganization in response to cyclic stretch results from the ability of the microtubule-stress fiber assembly to maintain a homeostatic strain on the stress fiber at focal adhesions. The mechanism of stretch-induced alignment we uncovered is likely involved in various airway functions as well as in the pathophysiology of airway remodeling in asthma.
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Affiliation(s)
- Masataka Morioka
- Department of Respiratory Medicine, Nagoya University Graduate School of Medicine, Nagoya, Japan
| | - Harikrishnan Parameswaran
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts, United States of America
| | - Keiji Naruse
- Department of Cardiovascular Physiology, Okayama University Graduate School of Medicine, Okayama, Japan
| | - Masashi Kondo
- Department of Respiratory Medicine, Nagoya University Graduate School of Medicine, Nagoya, Japan
| | - Masahiro Sokabe
- Department of Physiology, Nagoya University Graduate School of Medicine, Nagoya, Japan
| | - Yoshinori Hasegawa
- Department of Respiratory Medicine, Nagoya University Graduate School of Medicine, Nagoya, Japan
| | - Béla Suki
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts, United States of America
| | - Satoru Ito
- Department of Respiratory Medicine, Nagoya University Graduate School of Medicine, Nagoya, Japan
- * E-mail:
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22
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Rahimzadeh J, Meng F, Sachs F, Wang J, Verma D, Hua SZ. Real-time observation of flow-induced cytoskeletal stress in living cells. Am J Physiol Cell Physiol 2011; 301:C646-52. [PMID: 21653900 PMCID: PMC3174563 DOI: 10.1152/ajpcell.00099.2011] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2011] [Accepted: 06/06/2011] [Indexed: 01/23/2023]
Abstract
The mechanical stress due to shear flow has profound effects on cell proliferation, transport, gene expression, and apoptosis. The mechanisms for flow sensing and transduction are unclear, but it is postulated that fluid flow pulls upon the apical surface, and the resulting stress is eventually transmitted through the cytoskeleton to adhesion plaques on the basal surface. Here we report a direct observation of this flow-induced stress in the cytoskeleton in living cells using a parallel plate microfluidic chip with a fluorescence resonance energy transfer (FRET)-based mechanical stress sensor in actinin. The sensing cassette was genetically inserted into the cytoskeletal host protein and transfected into Madin-Darby canine kidney cells. A shear stress of 10 dyn/cm(2) resulted in a rapid increase in the FRET ratio indicating a decrease in stress across actinin with flow. The effect was reversible, and cells were able to respond to repeated stimulation and showed adaptive changes in the cytoskeleton. Flow-induced Ca(2+) elevation did not affect the response, suggesting that flow-induced changes in actinin stress are insensitive to intracellular Ca(2+) level. The reduction in FRET ratio suggests actin filaments are under normal compression in the presence of flow shear stress due to changes in cell shape, and/or actinin is not in series with actin. Treatment with cytochalasin-D that disrupts F-actin reduced prestress and the response to flow. The FRET/flow method is capable of resolving changes of stress in multiple proteins with optical spatial resolution and time resolution >1 Hz. This promises to provide insight into the force distribution and transduction in all cells.
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Affiliation(s)
- Jason Rahimzadeh
- Department of Physiology and Biophysics, State University of New York-Buffalo, USA
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23
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Zhao L, Sang C, Yang C, Zhuang F. Effects of stress fiber contractility on uniaxial stretch guiding mitosis orientation and stress fiber alignment. J Biomech 2011; 44:2388-94. [PMID: 21767844 DOI: 10.1016/j.jbiomech.2011.06.033] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2010] [Revised: 06/29/2011] [Accepted: 06/29/2011] [Indexed: 11/28/2022]
Abstract
It has been documented that mitosis orientation (MO) is guided by stress fibers (SFs), which are perpendicular to exogenous cyclic uniaxial stretch. However, the effect of mechanical forces on MO and the mechanism of stretch-induced SFs reorientation are not well elucidated to date. In the present study, we used murine 3T3 fibroblasts as a model, to investigate the effects of uniaxial stretch on SFO and MO utilizing custom-made stretch device. We found that cyclic uniaxial stretch induced both SFs and mitosis directions orienting perpendicularly to the stretch direction. The F-actin and myosin II blockages, which resulted in disoriented SFs and mitosis directions under uniaxial stretch, suggested a high correlation between SFO and MO. Y27632 (10 μM), ML7 (50 μM, or 75 μM), and blebbistatin (50 μM, or 75 μM) treatments resulted in SFO parallel to the principle stretch direction. Upon stimulating and inhibiting the phosphorylation of myosin light chain (p-MLC), we observed a monotonic proportion of SFO to the level of p-MLC. These results suggested that the level of cell contraction is crucial to the response of SFs, either perpendicular or parallel, to the external stretch. Showing the possible role of cell contractility in tuning SFO under external stretch, our experimental data are valuable to understand the predominant factor controlling SFO response to exogenous uniaxial stretch, and thus helpful for improving mechanical models.
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Affiliation(s)
- Lei Zhao
- School of Biological Science and Medical Engineering, Beihang University, Beijing 100191, China
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24
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Kaunas R, Deguchi S. Multiple Roles for Myosin II in Tensional Homeostasis Under Mechanical Loading. Cell Mol Bioeng 2011. [DOI: 10.1007/s12195-011-0175-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022] Open
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25
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A Model for Stress Fiber Realignment Caused by Cytoskeletal Fluidization During Cyclic Stretching. Cell Mol Bioeng 2010; 4:67-80. [PMID: 21666861 DOI: 10.1007/s12195-010-0152-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022] Open
Abstract
Uniaxial cyclic substrate stretching results in a concerted change of cytoskeletal organization such that stress fibers (SFs) realign away from the direction of stretching. Recent experiments revealed that brief transient stretch promptly ablates cellular contractile stress by means of cytoskeletal fluidization, followed by a slow stress recovery by means of resolidification. This, in turn, suggests that fluidization, resolidification and SF realignment may be linked together during stretching. We propose a mathematical model that simulates the effects of fluidization and resolidification on cytoskeletal contractile stress in order to investigate how these phenomena affect cytoskeletal realignment in response to pure uniaxial stretching of the substrate. The model comprises of individual elastic SFs anchored at the endpoints to an elastic substrate. Employing the global stability convention, the model predicts that in response to repeated stretch-unstretch cycles, SFs tend to realign in the direction perpendicular to stretching, consistent with data from the literature. The model is used to develop a computational scheme for predicting changes in cell orientation and polarity during stretching and how they relate to the underlying alterations in the cytoskeletal organization. We conclude that depletion of cytoskeletal contractile stress by means of fluidization and subsequent stress recovery by means of resolidification may play a key role in reorganization of cytoskeletal SFs in response to uniaxial stretching of the substrate.
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