成纤维细胞在基质刚度梯度作用下趋硬性迁移数值模拟
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摘要
建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20 h以上的长时程问题。
A theoretical model and the ?nite element method(FEM) are used to simulate the durotaxis movement of the cell on an arti?cial substrate with a continuous varying stiffness for the test design. The viscoelastic properties of the cell and the dynamic reactions of the receptors and the ligands between the cell and the substrate, are all considered. The time step equal to that of producing a pair of receptorligand is used for discretizing the functions of the time, turning the dynamic FEM into a static one. And a condition of moving constraint for the cell structure is proposed for eliminating the singularity of the FEM matrix more easily. The simulation results show that there is a rapid ?uctuation of the force in the focal adhesion during the cell durotaxis, the speed of the cell migration, as is consistent with the observation,and the migration process can e?ciently last over 20 hours.
A theoretical model and the ?nite element method(FEM) are used to simulate the durotaxis movement of the cell on an arti?cial substrate with a continuous varying stiffness for the test design. The viscoelastic properties of the cell and the dynamic reactions of the receptors and the ligands between the cell and the substrate, are all considered. The time step equal to that of producing a pair of receptorligand is used for discretizing the functions of the time, turning the dynamic FEM into a static one. And a condition of moving constraint for the cell structure is proposed for eliminating the singularity of the FEM matrix more easily. The simulation results show that there is a rapid ?uctuation of the force in the focal adhesion during the cell durotaxis, the speed of the cell migration, as is consistent with the observation,and the migration process can e?ciently last over 20 hours.
引文
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18 Sackmann E.How actin/myosin crosstalks guide the adhesion,locomotion and polarization of cells.Biochimica et Biophysica Acta(BBA)-Molecular Cell Research,2015,1853(11):3132-3142
19 Harris A K,Wild P,Stopak D.Silicone rubber substrata:a new wrinkle in the study of cell locomotion.Science,1980,208(4440):177-179
20 Oliver T,Lee J,Jacobson K.Forces exerted by locomoting cells.Seminars in Cell Biology,1994,5(3):139-147
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22 Golestaneh AF,Nadler B.Modeling of cell adhesion and deformation mediated by receptor-ligand interactions.Biomechanics&Modeling in Mechanobiology,2016,15(2):371-387
23 Zaman MH,Kamm RD,Matsudaira P,et al.Computational model for cell migration in three-dimensional matrices.Biophysical Journal,2005,89(2):1389-1397
24 Wong HC,Tang WC.Computational study of local and global ECM degradation and the effects on cell speed and cell-matrix tractions.Nano Communication Networks,2011,2(2-3):119-124
25 GI Bell.Models for the specific adhesion of cells to cells.Science,1978,200(4342):618-627
26 Gao H,Qian J,Chen B.Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modelling framework.Journal of the Royal Society Interface,2011,8(62):1217-1232
27 Haga H,Sasaki S,Kawabata K,et al.Elasticity mapping of living fibroblasts by AFM and immunofluorescence observation of the cytoskeleton.Ultramicroscopy,2000,82(1-4):253-258
28 N’Dri NA,Shyy W,Transontay R.Computational modeling of cell adhesion and movement using a continuum-kinetics approach.Biophysical Journal,2003,85(4):2273-2286
29 Roy S,Qi HJ.A computational biomimetic study of cell crawling.Biomechanics&Modeling in Mechanobiology,2010,9(5):573-581
30 Gracheva ME,Othmer HG.A continuum model of motility in ameboid cells.Bulletin of Mathematical Biology,2004,66(1):167-193
31 Ghosh K,Pan Z,Guan E,et al.Cell adaptation to a physiologically relevant ECM mimic with different viscoelastic properties.Biomaterials,2007,28(26):671-679
32冯世亮,朱卫平.运动细胞初始极化阶段胞内信号分子双向积聚的分子机制及动态数值模拟.中国科学:物理学·力学·天文学,2012(42):973-986Feng Shiliang,Zhu Weiping.Molecular mechanisms and dynamic simulation of bipolarization of chemotactic cells.Sci Sin-Phys Mech Astron,2012(42):973-986(in Chinese)
33冯世亮,朱卫平.基于信号分子双向输运的运动细胞极性反转模拟.力学学报,2015,47(2):337-345Feng Shiliang,Zhu Weiping.Simulation for reversal of cell polarity based on bidirectional transport of signaling molecules.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):337-345(in Chinese)
34 Plotnikov SV,Waterman CM.Guiding cell migration by tugging.Current Opinion in Cell Biology,2013,25(5):1-13
35 Plotnikov SV,Pasapera AM,Sabass B,et al.Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration.Cell,2012,151(7):1-23
36 Wormer DB,Davis KA,Henderson JH,et al.The Focal adhesion-localized CdGAP regulates matrix rigidity sensing and durotaxis.Plos One,2014,9(3):e91815
2 Thompson SM,Jin W,Chandan VS,et al.MR elastography of hepatocellular carcinoma:correlation of tumor stiffness with histopathology features-preliminary findings.Magnetic Resonance Imaging,2016,37:41-45
3 Berry MF,Engler AJ,Woo YJ,et al.Mesenchymal stem cell injection after myocardial infarction improves myocardial compliance.American Journal of Physiology Heart and Circulatory Physiology,2006,290(6):2196-2203
4张钢,龙勉,吴泽志.肝癌细胞黏弹性的实验研究.解放军医学杂志,2001,26(3):204-206Zhang Gang,Long Mian,Wu Zezhi.Experimental study on viscoelastic properties of hepatocellular carcinoma cells.Med J Chin PLA,2001,26(3):204-206(in Chinese)
5 Vincent LG,Yu SC,Alonso-Latorre B,et al.Mesenchymal stem cell durotaxis depends on substrate stiffness gradient strength.Biotechnology Journal,2013,8(4):472-484
6 Lo CM,Wang HB,Dembo M,et al.Cell movement is guided by the rigidity of the substrate.Biophysical Journal,2000,79(1):144-152
7 Eroshenko N,Ramachandran R,Yadavalli VK,et al.Effect of substrate stiffness on early human embryonic stem cell differentiation.Journal of Biological Engineering,2013,7(1):1-8
8 Whang M,Kim J.Synthetic hydrogels with stiffness gradients for durotaxis study and tissue engineering scaffolds.Tissue Engineering&Regenerative Medicine,2016,13(2):126-139
9 Orsi G,Fagnano M,Maria CD,et al.A new 3D concentration gradient maker and its application in building hydrogels with a 3D stiffness gradient.Journal of Tissue Engineering&Regenerative Medicine,2017,11(1):256-264
10 Mohanty S,Samger K,Heiskanen A,et al.Fabrication of scalable tissue engineering scaffolds with dual-pore microarchitecture by combining 3D printing and particle leaching.Materials Science&Engineering C Materials for Biological Applications,2016,61:180-189
11 Harley BA,Kim HD,Zaman MH,et al.Microarchitecture of three-dimensional scaffolds influences cell migration behavior via junction interactions.Biophysical Journal,2008,95(8):4013-4024
12 Dimilla PA,Barbee K,Lauffenburger DA.Mathematical model for the effects of adhesion and mechanics on cell migration speed.Biophysical Journal,1991,60(1):15-37
13 Dokukina IV,Gracheva ME.A model of fibroblast motility on substrates with different rigidities.Biophysical Journal,2010,98(12):2794-2803
14 Zeng X,Li S.A three dimensional soft matter cell model for Mechanotransduction.Soft Matter,2012,8(21):5765-5776
15 Zaari N,Rajagopalan P,Kim S,et al.Photopolymerization in microfluidic gradient generators:microscale control of substrate compliance to manipulate cell response.Advanced Materials,2004,16(16):2133-2137
16 Zhao XK,Cheng Y,Cheng ML,et al.Focal adhesion kinase regulates fibroblast migration via integrin beta-1 and plays a central role in fibrosis.Scientific Reports,2016,6:19276
17 Ascione F,Vasaturo A,Caserta S,et al.Comparison between fibroblast wound healing and cell random migration assays in vitro.Experimental Cell Research,2016,347(1):123-132
18 Sackmann E.How actin/myosin crosstalks guide the adhesion,locomotion and polarization of cells.Biochimica et Biophysica Acta(BBA)-Molecular Cell Research,2015,1853(11):3132-3142
19 Harris A K,Wild P,Stopak D.Silicone rubber substrata:a new wrinkle in the study of cell locomotion.Science,1980,208(4440):177-179
20 Oliver T,Lee J,Jacobson K.Forces exerted by locomoting cells.Seminars in Cell Biology,1994,5(3):139-147
21 Wells A,Gupta K,Chang P,et al.Epidermal growth factor receptor-mediated motility in fibroblasts.Microscopy Research&Technique,2015,43(5):395-411
22 Golestaneh AF,Nadler B.Modeling of cell adhesion and deformation mediated by receptor-ligand interactions.Biomechanics&Modeling in Mechanobiology,2016,15(2):371-387
23 Zaman MH,Kamm RD,Matsudaira P,et al.Computational model for cell migration in three-dimensional matrices.Biophysical Journal,2005,89(2):1389-1397
24 Wong HC,Tang WC.Computational study of local and global ECM degradation and the effects on cell speed and cell-matrix tractions.Nano Communication Networks,2011,2(2-3):119-124
25 GI Bell.Models for the specific adhesion of cells to cells.Science,1978,200(4342):618-627
26 Gao H,Qian J,Chen B.Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modelling framework.Journal of the Royal Society Interface,2011,8(62):1217-1232
27 Haga H,Sasaki S,Kawabata K,et al.Elasticity mapping of living fibroblasts by AFM and immunofluorescence observation of the cytoskeleton.Ultramicroscopy,2000,82(1-4):253-258
28 N’Dri NA,Shyy W,Transontay R.Computational modeling of cell adhesion and movement using a continuum-kinetics approach.Biophysical Journal,2003,85(4):2273-2286
29 Roy S,Qi HJ.A computational biomimetic study of cell crawling.Biomechanics&Modeling in Mechanobiology,2010,9(5):573-581
30 Gracheva ME,Othmer HG.A continuum model of motility in ameboid cells.Bulletin of Mathematical Biology,2004,66(1):167-193
31 Ghosh K,Pan Z,Guan E,et al.Cell adaptation to a physiologically relevant ECM mimic with different viscoelastic properties.Biomaterials,2007,28(26):671-679
32冯世亮,朱卫平.运动细胞初始极化阶段胞内信号分子双向积聚的分子机制及动态数值模拟.中国科学:物理学·力学·天文学,2012(42):973-986Feng Shiliang,Zhu Weiping.Molecular mechanisms and dynamic simulation of bipolarization of chemotactic cells.Sci Sin-Phys Mech Astron,2012(42):973-986(in Chinese)
33冯世亮,朱卫平.基于信号分子双向输运的运动细胞极性反转模拟.力学学报,2015,47(2):337-345Feng Shiliang,Zhu Weiping.Simulation for reversal of cell polarity based on bidirectional transport of signaling molecules.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):337-345(in Chinese)
34 Plotnikov SV,Waterman CM.Guiding cell migration by tugging.Current Opinion in Cell Biology,2013,25(5):1-13
35 Plotnikov SV,Pasapera AM,Sabass B,et al.Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration.Cell,2012,151(7):1-23
36 Wormer DB,Davis KA,Henderson JH,et al.The Focal adhesion-localized CdGAP regulates matrix rigidity sensing and durotaxis.Plos One,2014,9(3):e91815