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In silico stress fibre content affects peak strain in cytoplasm and nucleus but not in the membrane for uniaxial substrate stretch. Med Biol Eng Comput 2021; 59:1933-1944. [PMID: 34392447 DOI: 10.1007/s11517-021-02393-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: 09/03/2020] [Accepted: 06/13/2021] [Indexed: 10/20/2022]
Abstract
Existing in silico models for single cell mechanics feature limited representations of cytoskeletal structures that contribute substantially to the mechanics of a cell. We propose a micromechanical hierarchical approach to capture the mechanical contribution of actin stress fibres. For a cell-specific fibroblast geometry with membrane, cytoplasm and nucleus, the Mori-Tanaka homogenization method was employed to describe cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in a finite element model of the fibroblast attached to a substrate through focal adhesions. Strain in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch was assessed for different stress fibre volume fractions and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the membrane, whereas the peak strain in cytoplasm, nucleus and membrane increased for increasing elastic modulus of the substrate. Finite element mesh of reconstructed human fibroblast and intracellular strain distribution in cell subjected to substrate stretch.
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Spronck B, Humphrey JD. Arterial Stiffness: Different Metrics, Different Meanings. J Biomech Eng 2019; 141:091004. [PMID: 30985880 PMCID: PMC6808013 DOI: 10.1115/1.4043486] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Revised: 03/25/2019] [Indexed: 12/18/2022]
Abstract
Findings from basic science and clinical studies agree that arterial stiffness is fundamental to both the mechanobiology and the biomechanics that dictate vascular health and disease. There is, therefore, an appropriately growing literature on arterial stiffness. Perusal of the literature reveals, however, that many different methods and metrics are used to quantify arterial stiffness, and reported values often differ by orders of magnitude and have different meanings. Without clear definitions and an understanding of possible inter-relations therein, it is increasingly difficult to integrate results from the literature to glean true understanding. In this paper, we briefly review methods that are used to infer values of arterial stiffness that span studies on isolated cells, excised intact vessels, and clinical assessments. We highlight similarities and differences and identify a single theoretical approach that can be used across scales and applications and thus could help to unify future results. We conclude by emphasizing the need to move toward a synthesis of many disparate reports, for only in this way will we be able to move from our current fragmented understanding to a true appreciation of how vascular cells maintain, remodel, or repair the arteries that are fundamental to cardiovascular properties and function.
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Affiliation(s)
- B. Spronck
- Department of Biomedical Engineering,
Yale University,
New Haven, CT 06520
| | - J. D. Humphrey
- Fellow ASME
Department of Biomedical Engineering,
Yale University,
New Haven, CT 06520;
Vascular Biology and Therapeutics Program,
Yale School of Medicine,
New Haven, CT 06520
e-mail:
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3
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Humphrey JD, Tellides G. Central artery stiffness and thoracic aortopathy. Am J Physiol Heart Circ Physiol 2019; 316:H169-H182. [PMID: 30412443 PMCID: PMC6880196 DOI: 10.1152/ajpheart.00205.2018] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Revised: 10/22/2018] [Accepted: 10/31/2018] [Indexed: 12/20/2022]
Abstract
Thoracic aortopathy, especially aneurysm, dissection, and rupture, is responsible for significant morbidity and mortality. Uncontrolled hypertension and aging are primary risk factors for such conditions, and they contribute to an increase in the mechanical stress on the wall and an increase in its structural vulnerability, respectively. Select genetic mutations also predispose to these lethal conditions, and the collection of known mutations suggests that dysfunctional mechanosensing and mechanoregulation of the extracellular matrix may contribute to pathogenesis and disease progression. In the absence of a well-accepted pharmacotherapy, nonsurgical treatments tend to focus on reducing the mechanical loading on the aorta, particularly via the use of antihypertensive medications and recommendations to avoid strenuous exercises such as weight lifting. In this brief review, we discuss the important effects of central artery stiffening on global hemodynamics and, in particular, on the increase in pulse pressure that acts on the proximal thoracic aorta. We consider Marfan syndrome as an illustrative aortopathy but discuss other conditions leading to thoracic aortic aneurysm and dissection. We highlight the importance of phenotyping the aorta biomechanically, not just clinically, and emphasize the utility of mouse models in elucidating molecular and mechanical mechanisms of disease. Notwithstanding the widely recognized role of central artery stiffening in driving end-organ disease, we suggest that there is similarly a need to consider its key role in thoracic aortopathy.
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Affiliation(s)
- J. D. Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut
- Vascular Biology and Therapeutics Program, Yale University, New Haven, Connecticut
| | - G. Tellides
- Department of Surgery, Yale University, New Haven, Connecticut
- Vascular Biology and Therapeutics Program, Yale University, New Haven, Connecticut
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Klinge S, Aygün S, Gilbert RP, Holzapfel GA. Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2993. [PMID: 29633544 DOI: 10.1002/cnm.2993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Revised: 03/22/2018] [Accepted: 03/22/2018] [Indexed: 06/08/2023]
Abstract
The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.
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Affiliation(s)
- S Klinge
- Institute of Mechanics, TU Dortmund University, Dortmund, 44227, Germany
| | - S Aygün
- Institute of Mechanics, TU Dortmund University, Dortmund, 44227, Germany
| | - R P Gilbert
- Department of Mathematical Sciences, University of Delaware, Newark, Delaware, 19716, USA
| | - G A Holzapfel
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16-II, Graz, 8010, Austria
- Faculty of Engineering Science and Technology, Norwegian University of Science and Technology, Trondheim, 7491, Norway
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Cheng B, Lin M, Huang G, Li Y, Ji B, Genin GM, Deshpande VS, Lu TJ, Xu F. Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses. Phys Life Rev 2017; 22-23:88-119. [PMID: 28688729 PMCID: PMC5712490 DOI: 10.1016/j.plrev.2017.06.016] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Accepted: 06/14/2017] [Indexed: 12/11/2022]
Abstract
Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.
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Affiliation(s)
- Bo Cheng
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China
| | - Min Lin
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China
| | - Guoyou Huang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China
| | - Yuhui Li
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China
| | - Baohua Ji
- Biomechanics and Biomaterials Laboratory, Department of Applied Mechanics, Beijing Institute of Technology, Beijing, China
| | - Guy M Genin
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China; Department of Mechanical Engineering & Materials Science, and NSF Science and Technology Center for Engineering Mechanobiology, Washington University in St. Louis, St. Louis 63130, MO, USA
| | - Vikram S Deshpande
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
| | - Tian Jian Lu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China
| | - Feng Xu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China; Bioinspired Engineering and Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an 710049, PR China.
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Sakamoto Y, Buchanan RM, Sacks MS. On intrinsic stress fiber contractile forces in semilunar heart valve interstitial cells using a continuum mixture model. J Mech Behav Biomed Mater 2016; 54:244-58. [PMID: 26476967 PMCID: PMC4698364 DOI: 10.1016/j.jmbbm.2015.09.027] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2015] [Revised: 09/21/2015] [Accepted: 09/22/2015] [Indexed: 01/12/2023]
Abstract
Heart valve interstitial cells (VICs) play a critical role in the maintenance and pathophysiology of heart valve tissues. Normally quiescent in the adult, VICs can become activated in periods of growth and disease. When activated, VICs exhibit increased levels of cytokines and extracellular matrix (ECM) synthesis, and upregulated expression and strong contraction of α-smooth muscle actin (α-SMA) fibers. However, it remains unknown how expression and contraction of the α-SMA fibers, which vary among different VIC types, contribute to the overall VIC mechanical responses, including the nucleus and cytoskeleton contributions. In the present study, we developed a novel solid-mixture model for VIC biomechanical behavior that incorporated 1) the underlying cytoskeletal network, 2) the oriented α-SMA stress fibers with passive elastic and active contractile responses, 3) a finite deformable elastic nucleus. We implemented the model in a full 3D finite element simulation of a VIC based on known geometry. Moreover, we examined the respective mechanical responses of aortic and pulmonary VICs (AVICs and PVICs, respectively), which are known to have different levels of α-SMA expression levels and contractile behaviors. To calibrate the model, we simulated the combined mechanical responses of VICs in both micropipette aspiration (MA) and atomic force microscopy (AFM) experiments. These two states were chosen as the VICs were under significantly different mechanical loading conditions and activation states, with the α-SMA fibers inactivated in the MA studies while fully activated in the AFM studies. We also used the AFM to study the mechanical property of the nucleus. Our model predicted that the substantial differences found in stiffening of the AVIC compared to the PVICs was due to a 9 to 16 times stronger intrinsic AVIC α-SMA stress fiber contractile force. Model validation was done by simulating a traction force microscopy experiment to estimate the forces the VICs exert on the underlying substrate, and found good agreement with reported traction force microscopy results. Further, estimated nuclear stiffness for both AVICs and PVICs were similar and comparable to the literature, and were both unaffected by VIC activation level. These results suggest substantial functional differences between AVICs and PVICs at the subcellular level. Moreover, this first VIC computational biomechanical model is but a first step in developing a comprehensive, integrated view of the VIC pathophysiology and interactions with the valve ECM micro-environment based on simulation technologies.
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Affiliation(s)
- Yusuke Sakamoto
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, 201 East 24th Street, POB 5.236, 1 University Station C0200, Austin, TX 78712, USA
| | - Rachel M Buchanan
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, 201 East 24th Street, POB 5.236, 1 University Station C0200, Austin, TX 78712, USA
| | - Michael S Sacks
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, 201 East 24th Street, POB 5.236, 1 University Station C0200, Austin, TX 78712, USA.
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Determination of local and global elastic moduli of valve interstitial cells cultured on soft substrates. J Biomech 2013; 46:1967-71. [PMID: 23746597 DOI: 10.1016/j.jbiomech.2013.05.001] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Revised: 04/04/2013] [Accepted: 05/02/2013] [Indexed: 01/01/2023]
Abstract
The elasticity of the extracellular matrix profoundly affects biological responses of cells, but also their mechanical properties. Single cell mechanical properties are often measured by atomic force microscopy (AFM), but technical guidelines for AFM measurement of cells grown on soft substrates are not well established. In this study, the local and global elastic moduli of aortic valve interstitial cells (VICs) cultured on soft polyacrylamide substrates (3-144kPa) were characterized via AFM force mapping using pyramidal and spherical tips, respectively. Local and global VIC modulus values both increased with substrate stiffness (p<0.05), with the average local cell modulus being consistently two to three times greater than the global modulus (p<0.05). For local measurements, a minimum of four measurements was required to observe the trend of increasing cell modulus with substrate stiffness, but there was no advantage to testing additional spots. The Hertz model was relatively accurate in estimating the global cell elastic modulus (<12% error, based on validated finite element analyses), despite the cells being of finite thickness and grown on deformable substrates, neither of which are accounted for in the Hertz model. The results of this study provide practical guidelines for efficient AFM-based measurement of the mechanical properties of cells on gels. They also provide new physiologically-relevant data on VIC mechanical properties and their correlation with substrate stiffness-dependent cytoskeletal changes, with relevance to heart valve mechanobiology and disease.
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Unterberger MJ, Schmoller KM, Bausch AR, Holzapfel GA. A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis. J Mech Behav Biomed Mater 2012; 22:95-114. [PMID: 23601624 DOI: 10.1016/j.jmbbm.2012.11.019] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2012] [Revised: 11/26/2012] [Accepted: 11/28/2012] [Indexed: 01/07/2023]
Abstract
The mechanical properties of a cell are defined mainly by the cytoskeleton. One contributor within this three-dimensional structure is the actin cortex which is located underneath the lipid bilayer. It forms a nearly isotropic and densely cross-linked protein network. We present a continuum mechanical formulation for describing the mechanical properties of in vitro model systems based on their micro-structure, i.e. the behavior of a single filament and its spatial arrangement. The network is considered elastic, viscous effects being neglected. Filamentous actin is a biopolymer with a highly nonlinear force-stretch relationship. This can be well described by a worm-like chain model that includes extensibility of the filament, which we call the β-model. A comparison with experimental data shows good agreement with values for the physically interpretable parameters. To make these properties applicable to three dimensions we used a non-affine micro-sphere network, which accounts for filaments, equally distributed in space. The assembled model results in a strain-energy density which is a function of the deformation gradient, and it is validated with experimental data from rheological experiments of in vitro reconstituted actin networks. The Cauchy stress and elasticity tensors are obtained within the continuum mechanics framework and implemented into a finite element program to solve boundary-value problems.
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Affiliation(s)
- Michael J Unterberger
- Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria
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McKee CT, Last JA, Russell P, Murphy CJ. Indentation versus tensile measurements of Young's modulus for soft biological tissues. TISSUE ENGINEERING. PART B, REVIEWS 2011; 17:155-64. [PMID: 21303220 PMCID: PMC3099446 DOI: 10.1089/ten.teb.2010.0520] [Citation(s) in RCA: 407] [Impact Index Per Article: 29.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2010] [Accepted: 02/07/2011] [Indexed: 12/21/2022]
Abstract
In this review, we compare the reported values of Young's modulus (YM) obtained from indentation and tensile deformations of soft biological tissues. When the method of deformation is ignored, YM values for any given tissue typically span several orders of magnitude. If the method of deformation is considered, then a consistent and less ambiguous result emerges. On average, YM values for soft tissues are consistently lower when obtained by indentation deformations. We discuss the implications and potential impact of this finding.
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Affiliation(s)
- Clayton T. McKee
- Department of Surgical and Radiological Science, School of Veterinary Medicine, University of California Davis, Davis, California
| | - Julie A. Last
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin
| | - Paul Russell
- Department of Surgical and Radiological Science, School of Veterinary Medicine, University of California Davis, Davis, California
| | - Christopher J. Murphy
- Department of Surgical and Radiological Science, School of Veterinary Medicine, University of California Davis, Davis, California
- Department of Ophthalmology and Vision Science, School of Medicine, University of California Davis, Davis, California
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10
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Azeloglu EU, Costa KD. Atomic force microscopy in mechanobiology: measuring microelastic heterogeneity of living cells. Methods Mol Biol 2011; 736:303-29. [PMID: 21660735 DOI: 10.1007/978-1-61779-105-5_19] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Recent findings clearly demonstrate that cells feel mechanical forces, and respond by altering their -phenotype and modulating their mechanical environment. Atomic force microscope (AFM) indentation can be used to mechanically stimulate cells and quantitatively characterize their elastic properties, providing critical information for understanding their mechanobiological behavior. This review focuses on the experimental and computational aspects of AFM indentation in relation to cell biomechanics and pathophysiology. Key aspects of the indentation protocol (including preparation of substrates, selection of indentation parameters, methods for contact point detection, and further post-processing of data) are covered. Historical perspectives on AFM as a mechanical testing tool as well as studies of cell mechanics and physiology are also highlighted.
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Affiliation(s)
- Evren U Azeloglu
- Cardiovascular Research Center, Mount Sinai School of Medicine, New York, NY, USA
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12
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Hsu HJ, Lee CF, Kaunas R. A dynamic stochastic model of frequency-dependent stress fiber alignment induced by cyclic stretch. PLoS One 2009; 4:e4853. [PMID: 19319193 PMCID: PMC2656616 DOI: 10.1371/journal.pone.0004853] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Accepted: 02/16/2009] [Indexed: 11/19/2022] Open
Abstract
BACKGROUND Actin stress fibers (SFs) are mechanosensitive structural elements that respond to forces to affect cell morphology, migration, signal transduction and cell function. Cells are internally stressed so that SFs are extended beyond their unloaded lengths, and SFs tend to self-adjust to an equilibrium level of extension. While there is much evidence that cells reorganize their SFs in response to matrix deformations, it is unclear how cells and their SFs determine their specific response to particular spatiotemporal changes in the matrix. METHODOLOGY/PRINCIPAL FINDINGS Bovine aortic endothelial cells were subjected to cyclic uniaxial stretch over a range of frequencies to quantify the rate and extent of stress fiber alignment. At a frequency of 1 Hz, SFs predominantly oriented perpendicular to stretch, while at 0.1 Hz the extent of SF alignment was markedly reduced and at 0.01 Hz there was no alignment at all. The results were interpreted using a simple kinematic model of SF networks in which the dynamic response depended on the rates of matrix stretching, SF turnover, and SF self-adjustment of extension. For these cells, the model predicted a threshold frequency of 0.01 Hz below which SFs no longer respond to matrix stretch, and a saturation frequency of 1 Hz above which no additional SF alignment would occur. The model also accurately described the dependence of SF alignment on matrix stretch magnitude. CONCLUSIONS The dynamic stochastic model was capable of describing SF reorganization in response to diverse temporal and spatial patterns of stretch. The model predicted that at high frequencies, SFs preferentially disassembled in the direction of stretch and achieved a new equilibrium by accumulating in the direction of lowest stretch. At low stretch frequencies, SFs self-adjusted to dissipate the effects of matrix stretch. Thus, SF turnover and self-adjustment are each important mechanisms that cells use to maintain mechanical homeostasis.
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Affiliation(s)
- Hui-Ju Hsu
- Department of Biomedical Engineering, Texas A&M University, College Station, Texas, United States of America
| | - Chin-Fu Lee
- Department of Biomedical Engineering, Texas A&M University, College Station, Texas, United States of America
| | - Roland Kaunas
- Department of Biomedical Engineering, Texas A&M University, College Station, Texas, United States of America
- * E-mail:
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Need for a Continuum Biochemomechanical Theory of Soft Tissue and Cellular Growth and Remodeling. BIOMECHANICAL MODELLING AT THE MOLECULAR, CELLULAR AND TISSUE LEVELS 2009. [DOI: 10.1007/978-3-211-95875-9_1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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14
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Azeloglu EU, Bhattacharya J, Costa KD. Atomic force microscope elastography reveals phenotypic differences in alveolar cell stiffness. J Appl Physiol (1985) 2008; 105:652-61. [PMID: 18535125 DOI: 10.1152/japplphysiol.00958.2007] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
To understand the connection between alveolar mechanics and key biochemical events such as surfactant secretion, one first needs to characterize the underlying mechanical properties of the lung parenchyma and its cellular constituents. In this study, the mechanics of three major cell types from the neonatal rat lung were studied; primary alveolar type I (AT1) and type II (AT2) epithelial cells and lung fibroblasts were isolated using enzymatic digestion. Atomic force microscopy indentation was used to map the three-dimensional distribution of apparent depth-dependent pointwise elastic modulus. Histograms of apparent modulus data from all three cell types indicated non-Gaussian distributions that were highly skewed and appeared multimodal for AT2 cells and fibroblasts. Nuclear stiffness in all three cell types was similar (2.5+/-1.0 kPa in AT1 vs. 3.1+/-1.5 kPa in AT2 vs. 3.3+/-0.8 kPa in fibroblasts; n=10 each), whereas cytoplasmic moduli were significantly higher in fibroblasts and AT2 cells (6.0+/-2.3 and 4.7+/-2.9 kPa vs. 2.5+/-1.2 kPa). In both epithelial cell types, actin was arranged in sparse clusters, whereas prominent actin stress fibers were observed in lung fibroblasts. No systematic difference in actin or microtubule organization was noted between AT1 and AT2 cells. Atomic force microscope elastography, combined with live-cell fluorescence imaging, revealed that the stiffer measurements in AT2 cells often colocalized with lamellar bodies. These findings partially explain reported heterogeneity of alveolar cell deformation during in situ lung inflation and provide needed data for better understanding of how mechanical stretch influences surfactant release.
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Affiliation(s)
- Evren U Azeloglu
- Department of Biomedical Engineering, Columbia University, and Department of Medicine and Physiology, St. Luke's-Roosevelt Hospital Center, 1210 Amsterdam Ave., 351-H Engineering Terrace, MC8904, New York, NY 10027, USA
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Kang I, Panneerselvam D, Panoskaltsis VP, Eppell SJ, Marchant RE, Doerschuk CM. Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-alpha. Biophys J 2008; 94:3273-85. [PMID: 18199670 PMCID: PMC2275697 DOI: 10.1529/biophysj.106.099333] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2006] [Accepted: 09/17/2007] [Indexed: 11/18/2022] Open
Abstract
Mechanical properties of living cells can be determined using atomic force microscopy (AFM). In this study, a novel analysis was developed to determine the mechanical properties of adherent monolayers of pulmonary microvascular endothelial cells (ECs) using AFM and finite element modeling, which considers both the finite thickness of ECs and their nonlinear elastic properties, as well as the large strain induced by AFM. Comparison of this model with the more traditional Hertzian model, which assumes linear elastic behavior, small strains, and infinite cell thickness, suggests that the new analysis can predict the mechanical response of ECs during AFM indentation better than Hertz's model, especially when using force-displacement data obtained from large indentations (>100 nm). The shear moduli and distensibility of ECs were greater when using small indentations (<100 nm) compared to large indentations (>100 nm). Tumor necrosis factor-alpha induced changes in the mechanical properties of ECs, which included a decrease in the average shear moduli that occurred in all regions of the ECs and an increase in distensibility in the central regions when measured using small indentations. These changes can be modeled as changes in a chain network structure within the ECs.
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Affiliation(s)
- Inkyung Kang
- Division of Integrative Biology, Department of Pediatrics, Rainbow Babies and Children's Hospital and Case Western Reserve University, Cleveland, Ohio, USA
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Bacabac RG, Mizuno D, Schmidt CF, MacKintosh FC, Van Loon JJWA, Klein-Nulend J, Smit TH. Round versus flat: bone cell morphology, elasticity, and mechanosensing. J Biomech 2008; 41:1590-8. [PMID: 18402963 DOI: 10.1016/j.jbiomech.2008.01.031] [Citation(s) in RCA: 105] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2006] [Revised: 11/11/2007] [Accepted: 01/24/2008] [Indexed: 01/16/2023]
Abstract
There is increasing evidence that cell function and mechanical properties are closely related to morphology. However, most in vitro studies investigate flat adherent cells, which might not reflect physiological geometries in vivo. Osteocytes, the mechanosensors in bone, reside within ellipsoid containment, while osteoblasts adhere to flatter bone surfaces. It is unknown whether morphology difference, dictated by the geometry of attachment is important for cell rheology and mechanosensing. We developed a novel methodology for investigating the rheology and mechanosensitivity of bone cells under different morphologies using atomic force microscopy and our two-particle assay for optical tweezers. We found that the elastic constant of MLO-Y4 osteocytes when flat and adherent (>1 kPa) largely differed when round but partially adherent (<1 kPa). The elastic constant of round suspended MLO-Y4 osteocytes, MC3T3-E1 osteoblasts, and primary osteoblasts were similarly <1 kPa. The mechanosensitivity of round suspended MLO-Y4 osteocytes was investigated by monitoring nitric oxide (NO) release, an essential signaling molecule in bone. A preliminary observation of high NO release from round suspended MLO-Y4 osteocytes in response to approximately 5 pN force is reported here, in contrast with previous studies where flat cells routinely release lesser NO while being stimulated with higher force. Our results suggest that a round cellular morphology supports a less stiff cytoskeleton configuration compared with flat cellular morphology. This implies that osteocytes take advantage of their ellipsoid morphology in vivo to sense small strains benefiting bone health. Our assay provides novel opportunities for in vitro studies under a controlled suspended morphology versus commonly studied adherent morphologies.
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Affiliation(s)
- Rommel G Bacabac
- Department of Oral Cell Biology, Academic Centre for Dentistry Amsterdam-UvA and Vrije Universiteit, Amsterdam, The Netherlands.
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Rocha GM, Miranda K, Weissmüller G, Bisch PM, de Souza W. Ultrastructure of Trypanosoma cruzi revisited by atomic force microscopy. Microsc Res Tech 2008; 71:133-9. [PMID: 17992694 DOI: 10.1002/jemt.20535] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Most advances in atomic force microscopy (AFM) have been accomplished in recent years. Previous attempts to use AFM to analyze the organization of pathogenic protozoa did not significantly contribute with new structural information. In this work, we introduce a new perspective to the study of the ultrastructure of the epimastigote form of Trypanosoma cruzi by AFM. Images were compared with those obtained using field emission scanning electron microscopy of critical point dried cells and transmission electron microscopy of negative stained detergent-extracted and air-dried cells. AFM images of epimastigote forms showed a flagellum furrow separating the axoneme from the paraflagellar rod (PFR) present from the emergence of the flagellar pocket to the tip of the flagellum. At high magnification, a row of periodically organized structures, which probably correspond to the link between the axoneme, the PFR and the flagellar membrane were seen along the furrow. In the origin of the flagellum, two basal bodies were identified. Beyond the basal bodies, small periodically arranged protrusions, positioned at 400 nm from the flagellar basis were seen. This structure was formed by nine substructures distributed around the flagellar circumference and may correspond to the flagellar necklace. Altogether, our results demonstrate the importance of the application of AFM in the structural characterization of the surface components and cytoskeleton on protozoan parasites.
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Affiliation(s)
- Gustavo Miranda Rocha
- Laboratório de Ultraestrutura Celular Hertha Meyer, Instituto de Biofísica Carlos Chagas Filho, Universidade Federal do Rio de Janeiro, Av. Carlos Chagas Filho s/n, 21941-902, Ilha do Fundão, Rio de Janeiro, RJ, Brazil
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18
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Lin DC, Horkay F. Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond. SOFT MATTER 2008; 4:669-682. [PMID: 32907170 DOI: 10.1039/b714637j] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We survey recent progress in the application of nanoindentation to characterize the local mechanical properties of polymer gels and biological tissues. We review the theories, analytical models based thereon, and data processing techniques commonly used to determine elastic properties of these classes of materials by instrumented nanoindentation. Examples from the testing of synthetic and biological gels are used to illustrate the limitations of existing theories and approaches. Emphasis is placed on the need for contact mechanics models that more accurately represent the large-strain behaviour of soft matter.
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Affiliation(s)
- David C Lin
- Laboratory of Integrative and Medical Biophysics, National Institutes of Health, Bethesda, MD 20892, USA.
| | - Ferenc Horkay
- Laboratory of Integrative and Medical Biophysics, National Institutes of Health, Bethesda, MD 20892, USA.
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19
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Merryman WD, Liao J, Parekh A, Candiello JE, Lin H, Sacks MS. Differences in tissue-remodeling potential of aortic and pulmonary heart valve interstitial cells. ACTA ACUST UNITED AC 2007; 13:2281-9. [PMID: 17596117 DOI: 10.1089/ten.2006.0324] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Heart valve interstitial cells (VICs) appear to have a dynamic and reversible phenotype, an attribute speculated to be necessary for valve tissue remodeling during times of development and repair. Therefore, we hypothesized that the cytoskeletal (CSK) remodeling capability of the aortic and pulmonary VICs (AVICs and PVICs, respectively), which are dominated by smooth muscle alpha-actin, would exhibit unique contractile behaviors when seeded on collagen gels. Using a porcine cell source, we observed that VIC populations did not contract the gels at early time points (2 and 4 hours) as dermal fibroblasts did, but formed a central cluster of cells prior to contraction. After clustering, VICs appeared to radiate out from the center of the gels, whereas fibroblasts did not migrate but contracted the gels locally. VIC gels treated with transforming growth factor beta1 contracted the gels rapidly, revealing similar sensitivity to the cytokine. Moreover, we evaluated the initial mechanical state of the underlying CSK by comparing AVIC and PVIC stiffness with atomic force microscopy. Not only were AVICs significantly stiffer (p < 0.001) than the PVICs, but they also contracted the gels significantly more at 24 and 48 hours (p < 0.001). Taken together, these findings suggest that the AVICs are capable of inducing greater extra cellular matrix contraction, possibly manifesting in a more pronounced ability to remodel valvular tissues. Moreover, significant mechanobiological differences between AVICs and PVICs exist, and may have implications for understanding native valvular tissue remodeling. Elucidating these differences will also define important functional endpoints in the development of tissue engineering approaches for heart valve repair and replacement.
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Affiliation(s)
- W David Merryman
- Engineered Tissue Mechanics and Mechanobiology Laboratory, Department of Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15219, USA
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20
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Unnikrishnan GU, Unnikrishnan VU, Reddy JN. Constitutive material modeling of cell: a micromechanics approach. J Biomech Eng 2007; 129:315-23. [PMID: 17536898 DOI: 10.1115/1.2720908] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.
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Affiliation(s)
- G U Unnikrishnan
- Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
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21
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Na S, Meininger G, Humphrey J. A theoretical model for F-actin remodeling in vascular smooth muscle cells subjected to cyclic stretch. J Theor Biol 2006; 246:87-99. [PMID: 17240401 PMCID: PMC1993548 DOI: 10.1016/j.jtbi.2006.11.015] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2006] [Revised: 10/27/2006] [Accepted: 11/27/2006] [Indexed: 01/09/2023]
Abstract
A constrained mixture theory model was developed and used to estimate remodeling of F-actin in vascular smooth muscle cells that were subjected to 10% equibiaxial stretching for up to 30min. The model was based on a synthesis of data on time-dependent changes in atomic force microscopy measured cell stiffness and immunofluorescence measured focal adhesion associated vinculin as well as data on stress fiber stiffness and pre-stretch. Results suggest that an observed acute (after 2min of stretching) increase in cell stiffness is consistent with an increased stretch of the originally present F-actin plus an assembly of new F-actin having nearly homeostatic values of stretch. Moreover, the subsequent (after 30min of stretching) decrease in cell stiffness back towards the baseline value is consistent with a replacement of the overstretched original filaments with the new (reassembled), less stretched filaments. That is, overall cell response is consistent with a recently proposed concept of "tensional homeostasis" whereby cells seek to maintain constant certain mechanical factors via a remodeling of intracellular and transmembrane proteins. Although there is a need to refine the model based on more comprehensive data sets, using multiple experimental approaches, the present results suggest that a constrained mixture theory can capture salient features of the dynamics of F-actin remodeling and that it offers some advantages over many past methods of modeling, particularly those based on classical linearized viscoelasticity.
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Affiliation(s)
- S. Na
- Department of Biomedical Engineering and M.E. DeBakey Institute Texas A&M University, College Station, TX 77843
| | - G.A. Meininger
- Dalton Cardiovascular Research Center and Department of Pharmacology and Physiology University of Missouri-Columbia, Columbia, MO 65211
| | - J.D. Humphrey
- Department of Biomedical Engineering and M.E. DeBakey Institute Texas A&M University, College Station, TX 77843
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Lin DC, Dimitriadis EK, Horkay F. Robust Strategies for Automated AFM Force Curve Analysis—I. Non-adhesive Indentation of Soft, Inhomogeneous Materials. J Biomech Eng 2006; 129:430-40. [PMID: 17536911 DOI: 10.1115/1.2720924] [Citation(s) in RCA: 225] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young’s modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young’s modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young’s modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.
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Affiliation(s)
- David C Lin
- Laboratory of Integrative and Medical Biophysics, National Institutes of Health, 9 Memorial Drive, Bldg. 9 Rm. 1E118, Bethesda, MD 20892, USA.
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Méndez-Vilas A, Gallardo-Moreno AM, González-Martín ML. Nano-mechanical exploration of the surface and sub-surface of hydrated cells of Staphylococcus epidermidis. Antonie van Leeuwenhoek 2006; 89:373-86. [PMID: 16779634 DOI: 10.1007/s10482-005-9041-y] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/21/2005] [Indexed: 10/24/2022]
Abstract
The surface of hydrated cells of Staphylococcus epidermidis has been probed using an atomic force microscope. While local force measurements over the surface of bacteria reveal a heterogeneous chemical surface, with heterogeneous mechanical properties, different kinds of force curves appear with high frequency, and are thought to provide information on features contributing strongly to the overall mechanical and surface behaviour of the cell. Force curves often present two different mechanical regimes, being the first one (outer) of about 48 nm thick, and presenting a local relative elasticity of about 0.08 N/m, which is about a third of the relative elasticity of the inner part of the cell wall, harder, with a relative elasticity of about 0.24 N/m, in water. Both regimes appears as straight lines in the force versus distance curves (the 'corresponding' stress-strain curves in contact mechanics), but hysteresis is observed between the approach and the retraction line in the inner regime, indicating a degree of viscoelasticity. No viscoelasticity is observed in the outer regime, however, which presents quite linear and juxtaposed approach-retraction lines. These kinds of force curves do not present measurable pull-off forces nor snap-in forces, which indicates an almost null interaction between tip and bacterial surface, which could be in agreement with the measured very high hydrophobicity of this strain. Another kind of force curve has been observed recurrently, showing peaks in the retraction curves. Adhesive pull-off forces were measured giving an average of about 2 nN. Interestingly, however, these force curves appear only when quite irregular and wavy retraction curves are present, from the very beginning of its trace (maximum indentation). This leads us to think that these pull-off forces measured by our AFM do not give information on surface forces-unbinding events at the surface of the bacteria, but could be related to events at the sub-surface of the cell surface. Oscillations seen in the retraction curve in the portion corresponding to the contact with the bacteria surface could be due to rupture phenomena within the multilayered cell wall architecture expected in Gram-positive bacteria as Staphylococcus epidermidis, which could result in local irreversible deformations of the cell surface. Imaging with a sharp tip in contact mode sometimes leads to surface damage. Force curves recorded over damaged parts of the cell surface showed a completely different behaviour, in many cases with two well-defined high-adhesion peaks, and also interestingly, with snap-in forces of about 0-2 nN, which seems to indicate a completely different electrical/hydrophobicity state only a few nanometers down from the surface. Similar indentation effects can occur in the contact of a bacterial cell with a solid surface, even when showing only atomic-molecular-scale roughness, thus interacting not only with the very surface of the cell, especially when soft layers are present in the outer. Our results highlight the importance of the cell surface mechanical properties and their interplay with purely surface properties when analyzing cell-material interaction, and show the AFM as a useful method for investigating this.
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Affiliation(s)
- Antonio Méndez-Vilas
- Departamento de Física, Universidad de Extremadura, Avda de Elvas s/n, 06071, Badajoz, Spain.
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