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Chin. Phys. B, 2021, Vol. 30(9): 090505    DOI: 10.1088/1674-1056/ac11d5
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Nonlinear dynamics of cell migration in anisotropic microenvironment

Yanping Liu(刘艳平)1,†, Da He(何达)2,†, Yang Jiao(焦阳)3,4, Guoqiang Li(李国强)1, Yu Zheng(郑钰)3, Qihui Fan(樊琪慧)5, Gao Wang(王高)1, Jingru Yao(姚静如)1, Guo Chen(陈果)1, Silong Lou(娄四龙)6, and Liyu Liu(刘雳宇)1,‡
1 Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing 401331, China;
2 Spine Surgery, Beijing Jishuitan Hospital, Beijing 100035, China;
3 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA;
4 Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA;
5 Beijing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences(CAS), Beijing 100190, China;
6 Department of Neurosurgery, Chongqing University Cancer Hospital, Chongqing 400030, China
Abstract  Cell migration in anisotropic microenvironment plays an important role in the development of normal tissues and organs as well as neoplasm progression, e.g., osteogenic differentiation of embryonic stem cells was facilitated on stiffer substrates, indicating that the mechanical signals greatly affect both early and terminal differentiation of embryonic stem cells. However, the effect of anisotropy on cell migration dynamics, in particular, in terms of acceleration profiles which is important for recognizing dynamics modes of cell migration and analyzing the regulation mechanisms of microenvironment in mechanical signal transmission, has not been systematically investigated. In this work, we firstly rigorously investigate and quantify the differences between persistent random walk and anisotropic persistent random walk models based on the analysis of cell migration trajectories and velocity auto-covariance function, both qualitatively and quantitatively. Secondly, we introduce the concepts of positive and negative anisotropy based on the motility parameters to study the effect of anisotropy on acceleration profiles, especially the nonlinear decrease and non-monotonic behaviors. We particularly elaborate and discuss the mechanisms, and physical insights of non-monotonic behaviors in the case of positive anisotropy, focusing on the force exerted on migrating cells. Finally, we analyze two types of in vitro cell migration experiments and verify the universality of nonlinear decrease and the consistence of non-monotonic behaviors with numerical results. We conclude that the anisotropy of microenvironment is the cause of the non-monotonic and nonlinear dynamics, and the anisotropic persistent random walk can be as a suitable tool to analyze in vitro cell migration with different combinations of motility parameters. Our analysis provides new insights into the dynamics of cell migration in complex microenvironment, which also has implications in tissue engineering and cancer research.
Keywords:  cell migration      nonlinear behavior      motility parameter      acceleration profile      anisotropic microenvironment  
Received:  01 June 2021      Revised:  27 June 2021      Accepted manuscript online:  07 July 2021
PACS:  05.10.Gg (Stochastic analysis methods)  
  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
  05.40.Fb (Random walks and Levy flights)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974066, 11674043, 11675134, and 11874310), the Natural Science Foundation of Chongqing, China (Grant Nos. cstc2019jcyj-msxmX0477 and cstc2018jcyjA3679), and the Capital Health Development Research Project, China (Grant No. 2020-2-2072).
Corresponding Authors:  Yanping Liu     E-mail:  lyliu@cqu.edu.cn

Cite this article: 

Yanping Liu(刘艳平), Da He(何达), Yang Jiao(焦阳), Guoqiang Li(李国强), Yu Zheng(郑钰), Qihui Fan(樊琪慧), Gao Wang(王高), Jingru Yao(姚静如), Guo Chen(陈果), Silong Lou(娄四龙), and Liyu Liu(刘雳宇) Nonlinear dynamics of cell migration in anisotropic microenvironment 2021 Chin. Phys. B 30 090505

[1] Berg H C and Dyson F Phys. Today 40 73
[2] Vicente-Manzanares M and Horwitz A R 2011 Methods in molecular biology (Clifton, N.J.) 769 1
[3] Cyster J G 2003 Immunolog. Rev. 195 5
[4] Luster A D, Alon R and von Andrian U H 2005 Nature Immunology 6 1182
[5] Martin P 1997 Science 276 75
[6] Tremel A, Cai A, Tirtaatmadja N, Hughes B D, Stevens G W, Landman K A and O'Connor A J 2009 Chem. Eng. Sci. 64 247
[7] Franz A, Wood W and Martin P 2018 Developmental Cell 44 460
[8] Zalokar M and Erk I 1976 Journal De Microscopie Et De Biologie Cellulaire 25 97
[9] Natarajan D, Marcos-Gutierrez C, Pachnis V and de Graaff E 2002 Development 129 5151
[10] Kulesa P, Ellies D L and Trainor P A 2004 Developmental Dynamics 229 14
[11] Takakura N, Watanabe T, Suenobu S, Yamada Y, Noda T, Ito Y, Satake M and Suda T 2000 Cell 102 199
[12] Ridley A J, Schwartz M A, Burridge K, Firtel R A, Ginsberg M H, Borisy G, Parsons J T and Horwitz A R 2003 Science 302 1704
[13] Sharma G D, He J C and Bazan H E P 2003 J. Bio. Chem. 278 21989
[14] Schaffer A E, Breuss M W, Caglayan A O, Al-Sanaa N, Al-Abdulwahed H Y, Kaymakcalan H, Yilmaz C, Zaki M S, Rosti R O, Copeland B, Baek S T, Musaev D, Scott E C, Ben-Omran T, Kariminejad A, Kayserili H, Mojahedi F, Kara M, Cai N, Silhavy J L, Elsharif S, Fenercioglu E, Barshop B A, Kara B, Wang R G, Stanley V, James K N, Nachnani R, Kalur A, Megahed H, Incecik F, Danda S, Alanay Y, Faqeih E, Melikishvili G, Mansour L, Miller I, Sukhudyan B, Chelly J, Dobyns W B, Bilguvar K, Abou Jamra R, Gunel M and Gleeson J G 2018 Nature Genetics 50 1093
[15] Dang I, Gorelik R, Sousa-Blin C, Derivery E, Guerin C, Linkner J, Nemethova M, Dumortier J G, Giger F A, Chipysheva T A, Ermilova V D, Vacher S, Campanacci V, Herrada I, Planson A G, Fetics S, Henriot V, David V, Oguievetskaia K, Lakisic G, Pierre F, Steffen A, Boyreau A, Peyrieras N, Rottner K, Zinn-Justin S, Cherfils J, Bieche I, Alexandrova A Y, David N B, Small J V, Faix J, Blanchoin L and Gautreau A 2013 Nature 503 281
[16] Lauffenburger D A and Horwitz A F 1996 Cell 84 359
[17] Bergman A J and Zygourakis K 1999 Biomaterials 20 2235
[18] Lo C M, Wang H B, Dembo M and Wang Y L 2000 Biophys. J. 79 144
[19] Raines E W 2000 International Journal of Experimental Pathology 81 173
[20] Polacheck W J, Zervantonakis I K and Kamm R D 2013 Cellular and Molecular Life Sciences 70 1335
[21] Wu P H, Giri A, Sun S X and Wirtz D 2014 Proc. Natl. Acad. Sci. USA 111 3949
[22] Zhu J, Liang L, Jiao Y, Liu L and Allianc U S-C P S-O 2015 Plos One 10 UNSP e0118058
[23] Fink A, Bruckner D B, Schreiber C, Rottgermann P J F, Broedersz C P and Radler J O 2020 Biophys. J. 118 552
[24] Kim J, Zheng Y, Alobaidi A A, Nan H Q, Tian J X, Jiao Y and Sun B 2020 Biophys. J. 118 1177
[25] Hanahan D and Weinberg R A 2011 Cell 144 646
[26] Jemal A, Siegel R, Xu J and Ward E 2010 Ca-a Cancer Journal for Clinicians 60 277
[27] Codling E A, Plank M J and Benhamou S 2008 Journal of the Royal Society Interface 5 813
[28] Uhlenbeck G E and Ornstein L S 1930 Phys. Rev. 36 0823
[29] Lemons D S and Gythiel A 1997 Am. J. Phys. 65 1079
[30] Darnton N C, Turner L, Rojevsky S and Berg H C 2010 Biophys. J. 98 2082
[31] Li L, Norrelykke S F and Cox E C 2008 Plos One 3 e2093 11
[32] Wu H, Li B L, Springer T A and Neill W H 2000 Ecological Modelling 132 115
[33] Weiss G H 2002 Physica a-Statistical Mechanics and Its Applications 311 Pii s0378-4371(02)00805-1 381
[34] Li L, Cox E C and Flyvbjerg H 2011 Physical Biology 8 046006
[35] Selmeczi D, Mosler S, Hagedorn P H, Larsen N B and Flyvbjerg H 2005 Biophys. J. 89 912
[36] Schienbein M and Gruler H 1993 Bulletin of Mathematical Biology 55 585
[37] Burov S and Barkai E 2008 Phys. Rev. Lett. 100 070601
[38] Singhvi R, Kumar A, Lopez G P, Stephanopoulos G N, Wang D I C, Whitesides G M and Ingber D E 1994 Science 264 696
[39] Chen C S, Mrksich M, Huang S, Whitesides G M and Ingber D E 1997 Science 276 1425
[40] Thery M, Racine V, Piel M, Pepin A, Dimitrov A, Chen Y, Sibarita J B and Bornens M 2006 Proc. Natl. Acad. Sci. USA 103 19771
[41] Maiuri P, Rupprecht J F, Wieser S, Ruprecht V, Benichou O, Carpi N, Coppey M, De Beco S, Gov N, Heisenberg C P, Crespo C L, Lautenschlaeger F, Le Berre M, Lennon-Dumenil A M, Raab M, Thiam H R, Piel M, Sixt M and Voituriez R 2015 Cell 161 374
[42] Prentice-Mott H V, Meroz Y, Carlson A, Levine M A, Davidson M W, Irimia D, Charras G T, Mahadevan L and Shah J V 2016 Proc. Natl. Acad. Sci. USA 113 1267
[43] Caballero D, Voituriez R and Riveline D 2014 Biophys. J. 107 34
[44] Mahmud G, Campbell C J, Bishop K J M, Komarova Y A, Chaga O, Soh S, Huda S, Kandere-Grzybowska K and Grzybowski B A 2009 Nat. Phys. 5 606
[45] Lautscham L A, Kammerer C, Lange J R, Kolb T, Mark C, Schilling A, Strissel P L, Strick R, Gluth C, Rowat A C, Metzner C and Fabry B 2015 Biophys. J. 109 900
[46] Metzner C, Mark C, Steinwachs J, Lautscham L, Stadler F and Fabry B 2015 Nat. Commun. 7516 8
[47] Bruckner D B, Fink A, Schreiber C, Rottgermann P J F, Radler J O and Broedersz C P 2019 Nat. Phys. 15 595
[48] Brückner David B, Fink Alexandra, Radler J O and Broedersz C P 2020 J. R. Soc. Interface 17
[49] Vestergaard C L, Pedersen J N, Mortensen K I and Flyvbjerg H 2015 Eur. Phys. J. Special Topics 224 1151
[50] Liu Y, Jiao Y, Fan Q, Zheng Y, Li G, Yao J, Wang G, Lou S, Chen G, Shuai J and Liu L 2021 Biophys. J. 120 2552
[51] Liu Y, Jiao Y, He D, Fan Q, Zheng Y, Li G, Wang G, Yao J, Chen G, Lou S, Shuai J and Liu L 2021 Phys. Bio. 18 046007
[52] Charras G and Sahai E 2014 Nature Reviews Molecular Cell Biology 15 813
[53] Novikova E A, Raab M, Discher D E and Storm C 2017 Phys. Rev. Lett. 078103 5
[54] Liang L, Jones C, Chen S H, Sun B and Jiao Y 2016 Phys. Bio. 066001 11
[55] Nan H Q, Liang L, Chen G, Liu L Y, Liu R C and Jiao Y 2018 Phys. Rev. E 033311 13
[56] Nan H Q, Zheng Y, Lin Y H H, Chen S H, Eddy C Z, Tian J X, Xu W X, Sun B and Jiao Y 2019 Soft Matter 15 6938
[57] Zheng Y, Nan H, Liu Y P, Fan Q H, Wang X C, Liu R C, Liu L Y, Ye F F, Sun B and Jiao Y 2019 Phys. Rev. E 043303 13
[58] Zheng Y, Fan Q H, Eddy C Z, Wang X C, Sun B, Ye F F and Jiao Y 2020 Phys. Rev. E 102 052409
[59] Fan Q, Zheng Y, Wang X, Xie R, Ding Y, Wang B, Yu X, Lu Y, Liu L, Li Y, Li M, Zhao Y, Jiao Y and Ye F 2021 Angewandte Chemie (International ed. in English) 60 11858
[60] Han W, Chen S, Yuan W, Fan Q, Tian J, Wang X, Chen L, Zhang X, Wei W, Liu R, Qu J, Jiao Y, Austin R H and Liu L 2016 Proc. Natl. Acad. Sci. USA 113 11208
[61] Liu Y P, Li X, Qu J, Gao X J, He Q Z, Liu L Y, Liu R C and Shuai J W 2020 Frontiers of Physics 15 13602
[62] Liu Y P, Zhang X C, Wu Y L, Liu W, Li X, Liu R C, Liu L Y and Shuai J W 2017 Chin. Phys. B 26 128707
[63] Wu P H, Giri A and Wirtz D 2015 Nature Protocols 10 517
[64] Jeon J H, Leijnse N, Oddershede L B and Metzler R 2013 New J. Phys. 15 045011
[65] Pedersen J N, Li L, Gradinaru C, Austin R H, Cox E C and Flyvbjerg H 2016 Phys. Rev. E 94 062401
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[1] PAN ZHONG, WU RONG-HAN, WANG QI-MING. EFFECTIVE CAVITY LENGTH IN VERTICAL CAVITY SURFACE EMITTING LASER[J]. Acta Phys. Sin. (Overseas Edition), 1995, 4(11): 810 -815 .
[2] Hou Bang-Pin, Liu Jie, Hu Ping. Sum and two-atom dipole squeezing in a system of a two-mode vacuum field interacting with two coupled atoms[J]. Chin. Phys., 2002, 11(1): 30 -34 .
[3] Sun Li-Qun, Wang Jia, Hong Tao, Tian Qian. A virtual optical probe based on evanescent wave interference[J]. Chin. Phys., 2002, 11(10): 1022 -1027 .
[4] Fang Jian-Hui, Zhao Song-Qing. Noether's theorem of a rotational relativistic variable mass system[J]. Chin. Phys., 2002, 11(5): 445 -449 .
[5] Chen Chao, Wang Zhi-Wen. Inequalities of the electron density at the nucleus and radial expectation values of the ground state for the lithium isoelectronic sequence[J]. Chin. Phys., 2003, 12(6): 604 -609 .
[6] Wang Peng-Ye, Xie Ping, Yin Hua-Wei. Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations[J]. Chin. Phys., 2003, 12(6): 674 -679 .
[7] Zhang Bai-Gang, Yao Jian-Quan, Ding Xin, Wang Peng, Xu De-Gang, Zhang Fan, Zhang Hao, Yu Guo-Jun. Low-threshold, high-efficiency, high-repetition-rate optical parametric generator based on periodically poled LiNbO3[J]. Chin. Phys., 2004, 13(3): 364 -368 .
[8] Fang Da-Wei, Zhang Zai-Xuan, Zhao Shi-Long, Zhang Li-Yan, Wang Bao-Ling, Xu Shi-Qing, Jiang Zhong-Hong. Host dependent thermal stability and frequency upconversion of Er3+-doped heavy metal xyfluoride germanate glasses[J]. Chin. Phys., 2005, 14(11): 2246 -2250 .
[9] Luo Shao-Kai, Cai Jian-Le, Jia Li-Qun. A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations[J]. Chin. Phys., 2005, 14(4): 656 -659 .
[10] Cheng Qing-Hua, Cao Li, Xu Da-Hai, Wu Da-Jin. Time evolution of the intensity correlation function in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts[J]. Chin. Phys., 2005, 14(6): 1159 -1167 .