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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2020, Vol. 15 Issue (1): 13602   https://doi.org/10.1007/s11467-019-0929-9
  本期目录
Motile parameters of cell migration in anisotropic environment derived by speed power spectrum fitting with double exponential decay
Yan-Ping Liu (刘艳平)1, Xiang Li (李翔)1,2, Jing Qu (屈静)1, Xue-Juan Gao (高学娟)1, Qing-Zu He (何情祖)1, Li-Yu Liu (刘雳宇)3, Ru-Chuan Liu (刘如川)3(), Jian-Wei Shuai (帅建伟)1,2,4()
1. Department of Physics, Xiamen University, Xiamen 361005, China
2. State Key Laboratory of Cellular Stress Biology, Innovation Center for Cell Signaling Network, Xiamen University, Xiamen 361102, China
3. College of Physics, Chongqing University, Chongqing 401331, China
4. National Institute for Big Data in Healthcare at Xiamen University, Xiamen 361102, China
 全文: PDF(4094 KB)  
Abstract

Cell migration through anisotropic microenvironment is critical to a wide variety of physiological and pathological processes. However, adequate analytical tools to derive motile parameters to characterize the anisotropic migration are lacking. Here, we proposed a method to obtain the four motile parameters of migration cells based on the anisotropic persistent random walk model which is described by two persistence times and two migration speeds at perpendicular directions. The key process is to calculate the velocity power spectra of cell migration along intrinsically perpendicular directions respectively, then to apply maximum likelihood estimation to derive the motile parameters from the power spectra fitting with double exponential decay. The simulation results show that the averaged persistence times and the corrected migration speeds can be good estimations for motile parameters of cell migration.

Key wordscell migration    heterogeneity    power spectrum    random walk    Langevin equation
收稿日期: 2019-06-23      出版日期: 2019-11-22
Corresponding Author(s): Ru-Chuan Liu (刘如川),Jian-Wei Shuai (帅建伟)   
 引用本文:   
. [J]. Frontiers of Physics, 2020, 15(1): 13602.
Yan-Ping Liu (刘艳平), Xiang Li (李翔), Jing Qu (屈静), Xue-Juan Gao (高学娟), Qing-Zu He (何情祖), Li-Yu Liu (刘雳宇), Ru-Chuan Liu (刘如川), Jian-Wei Shuai (帅建伟). Motile parameters of cell migration in anisotropic environment derived by speed power spectrum fitting with double exponential decay. Front. Phys. , 2020, 15(1): 13602.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-019-0929-9
https://academic.hep.com.cn/fop/CN/Y2020/V15/I1/13602
1 M. Vicente-Manzanares and A. R. Horwitz, Cell migration: An overview, Methods Mol. Biol. 769, 1 (2011)
https://doi.org/10.1007/978-1-61779-207-6_1
2 D. S. Vasilev, N. M. Dubrovskaya, N. L. Tumanova, and I. A. Zhuravin, Prenatal hypoxia in different periods of embryogenesis differentially affects cell migration, neuronal plasticity, and rat behavior in postnatal ontogenesis, Front. Neurosci. 10, 126 (2016)
https://doi.org/10.3389/fnins.2016.00126
3 M. Zalokar and I. Erk, J. Microsc. Biol. Cell. 25, 97 (1976)
4 P. Kulesa, D. L. Ellies, and P. A. Trainor, Comparative analysis of neural crest cell death, migration, and function during vertebrate embryogenesis,Dev. Dyn. 229(1), 14 (2004)
https://doi.org/10.1002/dvdy.10485
5 W. S. Krawczyk, A pattern of epidermal cell migration during wound healing, J. Cell Biol. 49(2), 247 (1971)
https://doi.org/10.1083/jcb.49.2.247
6 G. D. Sharma, J. He, and H. E. P. Bazan, p38 and ERK1/2 coordinate cellular migration and proliferation in epithelial wound healing: Evidence of cross-talk activation between MAP kinase cascades, J. Biol. Chem. 278(24), 21989 (2003)
https://doi.org/10.1074/jbc.M302650200
7 T. Tao, A. Robichaud, S. Nadeau, R. Savoie, B. Gallant, and R. Ouellette, Effect of cumulus cell removal on the fertilization and the day 3 embryo quality in human IVF, International Congress Series 1271, 135 (2004)
https://doi.org/10.1016/j.ics.2004.05.105
8 J. Bowszyc, J. Bowszyc, and T. Machońko, 15-years of studies of the immunological cellular response in syphilis in humans using migration inhibition tests, Przegl. Dermatol. 72(2), 134 (1985)
9 H. Zhang, Y. Han, J. Tao, S. Liu, C. Yan, and S. Li, Cellular repressor of E1A-stimulated genes regulates vascular endothelial cell migration by the ILK/AKT/mTOR/VEGF(165) signaling pathway, Exp. Cell Res. 317(20), 2904 (2011)
https://doi.org/10.1016/j.yexcr.2011.08.012
10 X. L. Fang Wei, M. Cai, Y. Liu, P. Jung, and J. W. Shuai, Regulation of 1, 4, 5-triphosphate receptor channel gating dynamics by mutant presenilin in Alzheimer’s disease cells, Front. Phys. 12(3), 128702 (2017)
https://doi.org/10.1007/s11467-017-0670-1
11 S. X. Liu, Y. Z. Geng, and S. W. Yan, Structural effects and competition mechanisms targeting the interactions between p53 and MDM2 for cancer therapy, Front. Phys. 12(3), 128908 (2017)
https://doi.org/10.1007/s11467-017-0667-9
12 H. C. Berg and F. Dyson, Random walks in biology, Phys. Today 40(3), 73 (1987)
https://doi.org/10.1063/1.2819954
13 L. X. Li, Photon diffusion in a relativistically expanding sphere, Front. Phys. 8(5), 555 (2013)
https://doi.org/10.1007/s11467-013-0390-0
14 X. H. Li, G. Yang, and J. P. Huang, Chaotic-periodic transition in a two-sided minority game, Front. Phys. 11(4), 118901 (2016)
https://doi.org/10.1007/s11467-016-0552-y
15 S. Huang, C. P. Brangwynne, K. K. Parker, and D. E. Ingber, Symmetry-breaking in mammalian cell cohort migration during tissue pattern formation: Role of random-walk persistence, Cell Motil. Cytoskeleton 61(4), 201 (2005)
https://doi.org/10.1002/cm.20077
16 Z. X. Niu, T. Hang, and Y. Chen, Molecular dynamics study of nanodroplet diffusion on smooth solid surfaces, Front. Phys. 13(5), 137804 (2018)
https://doi.org/10.1007/s11467-018-0772-4
17 Y. A. Yan and J. S. Shao, Stochastic description of quantum Brownian dynamics, Front. Phys. 11(4), 110309 (2016)
https://doi.org/10.1007/s11467-016-0570-9
18 M. Boguñá, J. M. Porrà, and J. Masoliver, Generalization of the persistent random walk to dimensions greater than 1, Phys. Rev. E 58(6), 6992 (1998)
https://doi.org/10.1103/PhysRevE.58.6992
19 C. Peggy, A. L. Ny, B. D. Loynes, et al., Persistent random walks (I): Recurrence versus transience, J. Theor. Probab. 31(1), 1 (2016)
https://doi.org/10.1007/s10959-016-0714-4
20 H. I. Wu, B. L. Li, T. A. Springer, and W. H. Neill, Modelling animal movement as a persistent random walk in two dimensions: Expected magnitude of net displacement, Ecol. Modell. 132(1–2), 115 (2000)
https://doi.org/10.1016/S0304-3800(00)00309-4
21 M. Schienbein and H. Gruler, Langevin equation, Fokker-Planck equation and cell migration, Bull. Math. Biol. 55(3), 585 (1993)
https://doi.org/10.1016/S0092-8240(05)80241-1
22 D. S. Lemons and A. Gythiel, Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [Sur la théorie du mouvement brownien, C. R. Acad. Sci. (Paris)146, 530–533 (1908)], Am. J. Phys. 65(11), 1079 (1997)
https://doi.org/10.1119/1.18725
23 J. L. Parada, G. Carrillo-Castañeda, and M. V. Ortega, Profile of the enzymes of the Krebs cycle in Salmonella typhimurium during the utilization of succinate, acetate, and citrate for growth, Rev. Latinoam. Microbiol. 15, 29 (1973)
24 C. S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys. 15(3), 311 (1953)
https://doi.org/10.1007/BF02476407
25 B. Wang, J. Kuo, S. C. Bae, and S. Granick, When Brownian diffusion is not Gaussian, Nat. Mater. 11(6), 481 (2012)
https://doi.org/10.1038/nmat3308
26 T. H. Harris, E. J. Banigan, D. A. Christian, C. Konradt, E. D. Tait Wojno, K. Norose, E. H. Wilson, B. John, W. Weninger, A. D. Luster, A. J. Liu, and C. A. Hunter, Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells, Nature 486(7404), 545 (2012)
https://doi.org/10.1038/nature11098
27 D. W. Sims, E. J. Southall, N. E. Humphries, G. C. Hays, C. J. A. Bradshaw, J. W. Pitchford, A. James, M. Z. Ahmed, A. S. Brierley, M. A. Hindell, D. Morritt, M. K. Musyl, D. Righton, E. L. C. Shepard, V. J. Wearmouth, R. P. Wilson, M. J. Witt, and J. D. Metcalfe, Scaling laws of marine predator search behaviour, Nature 451(7182), 1098 (2008)
https://doi.org/10.1038/nature06518
28 A. Czirók, K. Schlett, E. Madarasz, and T. Vicsek, Exponential distribution of locomotion activity in cell cultures, Phys. Rev. Lett. 81(14), 3038 (1998)
https://doi.org/10.1103/PhysRevLett.81.3038
29 A. Upadhyaya, J. P. Rieu, J. A. Glazier, and Y. Sawada, Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates, Physica A 293(3–4), 549 (2001)
https://doi.org/10.1016/S0378-4371(01)00009-7
30 D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg, Cell motility as persistent random motion: Theories from experiments, Biophys. J. 89(2), 912 (2005)
https://doi.org/10.1529/biophysj.105.061150
31 L. Liu, G. Duclos, B. Sun, J. Lee, A. Wu, Y. Kam, E. D. Sontag, H. A. Stone, J. C. Sturm, R. A. Gatenby, and R. H. Austin, Minimization of thermodynamic costs in cancer cell invasion, Proc. Natl. Acad. Sci. USA 110(5), 1686 (2013)
https://doi.org/10.1073/pnas.1221147110
32 J. Zhu, L. Liang, Y. Jiao, and L. Liu, Enhanced invasion of metastatic cancer cells via extracellular matrix interface, PLOS One 10(2), e0118058 (2015)
https://doi.org/10.1371/journal.pone.0118058
33 P. H. Wu, A. Giri, S. X. Sun, and D. Wirtz, Threedimensional cell migration does not follow a random walk, Proc. Natl. Acad. Sci. USA 111(11), 3949 (2014)
https://doi.org/10.1073/pnas.1318967111
34 P. H. Wu, A. Giri, and D. Wirtz, Statistical analysis of cell migration in 3D using the anisotropic persistent random walk model, Nat. Protoc. 10(3), 517 (2015)
https://doi.org/10.1038/nprot.2015.030
35 B. B. Mandelbrot and J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10(4), 422 (1968)
https://doi.org/10.1137/1010093
36 R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep. 339(1), 1 (2000)
https://doi.org/10.1016/S0370-1573(00)00070-3
37 B. Liu and J. Goree, Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma, Phys. Rev. Lett. 100(5), 055003 (2008)
https://doi.org/10.1103/PhysRevLett.100.055003
38 M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells, Biophys. J. 87(5), 3518 (2004)
https://doi.org/10.1529/biophysj.104.044263
39 C. L. Stokes, D. A. Lauffenburger, and S. K. Williams, Migration of individual microvessel endothelial cells: Stochastic model and parameter measurement, J. Cell. Sci. 99(Pt 2), 419 (1991)
40 L. Li, E. C. Cox, and H. Flyvbjerg, “Dicty dynamics”: Dictyostelium motility as persistent random motion, Phys. Biol. 8(4), 046006 (2011)
https://doi.org/10.1088/1478-3975/8/4/046006
41 F. Höfling and T. Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76(4), 046602 (2013)
https://doi.org/10.1088/0034-4885/76/4/046602
42 V. Zaburdaev, S. Denisov, and J. Klafter, Lévy walks, Rev. Mod. Phys. 87(2), 483 (2015)
https://doi.org/10.1103/RevModPhys.87.483
43 R. T. Tranquillo, D. A. Lauffenburger, and S. H. Zigmond, A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations, J. Cell Biol. 106(2), 303 (1988)
https://doi.org/10.1083/jcb.106.2.303
44 G. A. Dunn, Characterising a kinesis response: Time averaged measures of cell speed and directional persistence, Agents Actions Suppl. 12, 14 (1983)
https://doi.org/10.1007/978-3-0348-9352-7_1
45 C. L. Stokes and D. A. Lauffenburger, Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis, J. Theor. Biol. 152(3), 377 (1991)
https://doi.org/10.1016/S0022-5193(05)80201-2
46 M. R. Parkhurst and W. M. Saltzman, Quantification of human neutrophil motility in three-dimensional collagen gels: Effect of collagen concentration, Biophys. J. 61(2), 306 (1992)
https://doi.org/10.1016/S0006-3495(92)81838-6
47 R. Gorelik and A. Gautreau, Quantitative and unbiased analysis of directional persistence in cell migration, Nat. Protoc. 9(8), 1931 (2014)
https://doi.org/10.1038/nprot.2014.131
48 J. N. Pedersen, L. Li, C. Grǎdinaru, R. H. Austin, E. C. Cox, and H. Flyvbjerg, How to connect time-lapse recorded trajectories of motile microorganisms with dynamical models in continuous time, Phys. Rev. E 94(6–1), 062401 (2016)
https://doi.org/10.1103/PhysRevE.94.062401
49 A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. B 39(1), 1 (1977)
https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
50 C. L. Vestergaard, J. N. Pedersen, K. I. Mortensen, and H. Flyvbjerg, Estimation of motility parameters from trajectory data, Eur. Phys. J. Spec. Top. 224(7), 1151 (2015)
https://doi.org/10.1140/epjst/e2015-02452-5
51 C. L. Vestergaard, P. C. Blainey, and H. Flyvbjerg, Optimal estimation of diffusion coefficients from singleparticle trajectories, Phys. Rev. E 89(2), 022726 (2014)
https://doi.org/10.1103/PhysRevE.89.022726
52 J. H. Chen and H. Y. Fan, On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations, Front. Phys. 10(1), 100301 (2015)
https://doi.org/10.1007/s11467-014-0445-x
53 Z. K. Wu, P. Li, and Y. Z. Gu, Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media, Front. Phys. 12(5), 124203 (2017)
https://doi.org/10.1007/s11467-016-0613-2
54 K. Katoh, K. Misawa, K. Kuma, and T. Miyata, MAFFT: A novel method for rapid multiple sequence alignment based on fast Fourier transform, Nucleic Acids Res. 30(14), 3059 (2002)
https://doi.org/10.1093/nar/gkf436
55 S. B. Weinstein and P. M. Ebert, Data transmission by frequency division multiplexing using the discrete Fourier transform, IEEE Trans. Commun. Tech. 19, 628 (1971)
https://doi.org/10.1109/TCOM.1971.1090705
56 S. F. Nørrelykke and H. Flyvbjerg, Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers, Rev. Sci. Instrum. 81(7), 075103 (2010)
https://doi.org/10.1063/1.3455217
57 Y. Liu, X. Zhang, Y. Wu, W. Liu, X. Li, R. Liu, L. Liu, and J. Shuai, Derivation of persistent time for anisotropic migration of cells, Chin. Phys. B 26(12), 128707 (2017)
https://doi.org/10.1088/1674-1056/26/12/128707
58 N. Le Bihan and J. Mars, Singular value decomposition of quaternion matrices: A new tool for vector-sensor signal processing, Signal Processing 84(7), 1177 (2004)
https://doi.org/10.1016/j.sigpro.2004.04.001
59 M. E. Wall, A. Rechtsteiner, and L. M. Rocha, Singular value decomposition and principal component analysis, arXiv: physics/0208101v4 (2002)
60 K. Berg-Sørensen and H. Flyvbjerg, Power spectrum analysis for optical tweezers, Rev. Sci. Instrum. 75(3), 594 (2004)
https://doi.org/10.1063/1.1645654
61 J. R. Xie and B. H. Wang, Modularity-like objective function in annotated networks, Front. Phys. 12(6), 128903 (2017)
https://doi.org/10.1007/s11467-017-0657-y
62 R. Gorelik and A. Gautreau, The Arp2/3 inhibitory protein arpin induces cell turning by pausing cell migration, Cytoskeleton (Hoboken) 72(7), 362 (2015)
https://doi.org/10.1002/cm.21233
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