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Chin. Phys. B, 2022, Vol. 31(10): 104602    DOI: 10.1088/1674-1056/ac720a
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Variational approximation methods for long-range force transmission in biopolymer gels

Haiqin Wang(王海钦)1,2, and Xinpeng Xu(徐新鹏)1,2,,†
1. Physics Program, Guangdong Technion-Israel Institute of Technology, 241 Daxue Road, Shantou 515063, China;
2. Technion-Israel Institute of Technology, Haifa 3200003, Israel
Abstract  The variational principle of minimum free energy (MFEVP) has been widely used in research of soft matter statics. The MFEVP can be used not only to derive equilibrium equations (including both bulk equations and boundary conditions), but also to develop direct variational methods (such as Ritz method) to find approximate solutions to these equilibrium equations. We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels. It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in three-dimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.
Keywords:  biopolymer gels      cell-cell communications      force transmission      variational methods  
Received:  28 March 2022      Revised:  07 May 2022      Accepted manuscript online: 
PACS:  46.15.Cc (Variational and optimizational methods)  
  46.25.-y (Static elasticity)  
  87.17.Rt (Cell adhesion and cell mechanics)  
  82.35.Pq (Biopolymers, biopolymerization)  
Fund: X. X. is supported by the National Science Foundation for Young Scientists of China (Grant No. 12004082), Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2019), 2020 Li Ka Shing Foundation Cross-Disciplinary Research (Grant No. 2020LKSFG08A), Provincial Science Foundation of Guangdong (Grant No. 2019A1515110809), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515310005), Featured Innovative Projects (Grant No. 2018KTSCX282), and Youth Talent Innovative Platforms (Grant No. 2018KQNCX318) in Universities in Guangdong Province.
Corresponding Authors:  Xinpeng Xu     E-mail:  xu.xinpeng@gtiit.edu.cn

Cite this article: 

Haiqin Wang(王海钦), and Xinpeng Xu(徐新鹏) Variational approximation methods for long-range force transmission in biopolymer gels 2022 Chin. Phys. B 31 104602

[1] Alberts B, Johnson A, Lewis J, Raff M, Roberts K and Walter P 2007 Molecular Biology of the Cell 5th edn (London: Taylor & Francis)
[2] Wen Q and Janmey P A 2013 Exp. Cell Res. 319 2481
[3] Burla F, Tauber J, Dussi S, van Der Gucht J and Koenderink G H 2019 Nat. Phys. 15 549
[4] Broedersz C P and MacKintosh F C 2014 Rev. Mod. Phys. 86 995
[5] Gardel M L, Shin J H, MacKintosh F C, Mahadevan L, Matsudaira P and Weitz D A 2004 Science 304 1301
[6] Storm C, Pastore J J, MacKintosh F C, Lubensky T C and Janmey P A 2005 Nature 435 191
[7] Van Oosten A S, Vahabi M, Licup A J, Sharma A, Galie P A, MacKintosh F C and Janmey P A 2016 Sci. Rep. 6 19270
[8] Vahabi M, Sharma A, Licup A J, Van Oosten A S, Galie P A, Janmey P A and MacKintosh F C 2016 Soft Matter 12 5050
[9] Xu X and Safran S A 2017 Phys. Rev. E 95 052415
[10] Meng F and Terentjev E M 2016 Soft Matter 12 6749
[11] Meng F and Terentjev E M 2017 Polymers 9 52
[12] Wang H and Xu X 2020 Soft Matter 16 10781
[13] Harris A K, Stopak D and Wild P 1981 Nature 290 249
[14] Winer J P, Oake S and Janmey P A 2009 PloS One 4 e6382
[15] Hall M S, Alisafaei F, Ban E, Feng X, Hui C Y, Shenoy V B and Wu M 2016 Proc. Natl. Acad. Sci. USA 113 14043
[16] Notbohm J, Lesman A, Rosakis P, Tirrell D A and Ravichandran G 2015 J. R. Soc. Interface 12 20150320
[17] Korff T and Augustin H G 1999 J. Cell Sci. 112 3249
[18] Nitsan I, Drori S, Lewis Y E, Cohen S and Tzlil S 2016 Nat. Phys. 12 472
[19] Xu X and Safran S A 2015 Phys. Rev. E 92 032728
[20] Abhilash A S, Baker B M, Trappmann B, Chen C S and Shenoy V B 2014 Biophys. J. 107 1829
[21] Wang H, Abhilash A S, Chen C S, Wells R G and Shenoy V B 2014 Biophys. J. 107 2592
[22] Ronceray P, Broedersz C P and Lenz M 2019 Soft Matter 15 331
[23] Goren S, Koren Y, Xu X and Lesman A 2020 Biophys. J. 118 1152
[24] Safran S A 2018 Statistical thermodynamics of surfaces, interfaces, and membranes (New York: CRC Press)
[25] Wang H, Qian T and Xu X 2021 Soft Matter 17 3634
[26] Jiang Z, Yang X, Wu M and Man X 2020 Chin. Phys. B 29 096803
[27] Yang X, Jiang Z, Lyu P, Ding Z and Man X 2021 Commun. Theor. Phys. 73 047601
[28] Doi M 2021 Prog. Polym. Sci. 112 101339
[29] Wang Y, Liu C, Liu P and Eisenberg B 2020 Phys. Rev. E 102 062147
[30] Wang Q 2020 Generalized onsager principle and it applications frontiers and progress of current soft matter research edtied by Liu X Y (Singapore: Springer) pp. 101—132
[31] Landau L and Lifshitz E M 1986 Theory of Elasticity (Oxford: Pergamon Press)
[32] Treloar L R G 1975 The Physics of Rubber Elasticity (Oxford: Oxford University Press)
[33] Palmer J S and Boyce M C 2008 Acta Biomater. 4 597
[34] Reddy J N 2017 Energy Principles and Variational Methods in Applied Mechanics (New York: John Wiley & Sons)
[35] Doi M 2015 Chin. Phys. B 24 20505
[36] Mao X and Shokef Y 2021 Soft Matter 17 10172
[37] Schwarz U S and Safran S A 2013 Rev. Mod. Phys. 85 1327
[38] Shokef Y and Safran S A 2012 Phys. Rev. Lett. 109 169901
[39] Ben-Yaakov D, Golkov R, Shokef Y and Safran S A 2015 Soft Matter 11 1412
[40] Lekhnitskii S G 1981 Theory of Elasticity of an Anisotropic Body (Moscow: Mir Publishers)
[41] Vader D, Kabla A, Weitz D and Mahadevan L 2009 PloS One 4 e5902
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