Volume 2, Issue 1 (Multidisciplinary Cancer Investigation 2018)                   Multidiscip Cancer Investig 2018, 2(1): 1-12 | Back to browse issues page

XML Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Safaeifard F, Shariatpanahi S P, Goliaei B. A survey on random walk-based stochastic modeling in eukaryotic cell migration with emphasis on its application in cancer. Multidiscip Cancer Investig 2018; 2 (1) :1-12
URL: http://mcijournal.com/article-1-190-en.html
Abstract:   (13548 Views)
Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analysis. In this study, we reviewed the studies conducted on the random walk-based stochastic modeling of the eukaryotic cell migration. This statistical modeling can open some perspectives on more detailed modeling approaches and ultimately lead to more comprehensive knowledge about the biophysical and biochemical foundations of cell migration process.
Type of Study: Review Article | Subject: Other
Received: 2017/07/29 | Accepted: 2017/11/10 | ePublished: 2018/01/1

1. Caballero D, Comelles J, Piel M, Voituriez R, Riveline D. Ratchetaxis: Long-Range Directed Cell Migration by Local Cues. Trends Cell Biol. 2015;25(12):815–27. PMID:26615123 [DOI] [PubMed]
2. Romain B, Hachet-Haas M, Rohr S, Brigand C, Galzi JL, Gaub MP et al. Hypoxia differentially regulated CXCR4 and CXCR7 signaling in colon cancer. Mol Cancer. 2014;13(1):58. [DOI] [PubMed]
3. Cai X, Luo J, Yang X, Deng H, Zhang J, Li S et al. In vivo selection for spine-derived highly metastatic lung cancer cells is associated with increased migration, inflammation and decreased adhesion. Oncotarget. 2015;6(26):22905–17. [DOI] [PubMed]
4. Oelkrug C, Ramage JM. Enhancement of T cell recruitment and infiltration into tumours. Clin Exp Immunol. 2014;178(1):1–8. [DOI] [PubMed]
5. Friedl P, Wolf K. Tumour-cell invasion and migration: diversity and escape mechanisms. Nat Rev Cancer. 2003;3(5):362–74. [DOI] [PubMed]
6. Potdar AA, Jeon J, Weaver AM, Quaranta V, Cummings PT. Human mammary epithelial cells exhibit a bimodal correlated random walk pattern. PLoS One. 2010;5(3):e9636. PMID:20224792 [DOI] [PubMed]
7. Le Dévédec SE, Yan K, de Bont H, Ghotra V, Truong H, Danen EH et al. Systems microscopy approaches to understand cancer cell migration and metastasis. Cell Mol Life Sci. 2010;67(19):3219–40. [DOI] [PubMed]
8. Eddy JA, Funk CC, Price ND. Fostering synergy between cell biology and systems biology. Trends Cell Biol. 2015;25(8):440–5. [DOI] [PubMed]
9. Danuser G, Allard J, Mogilner A. Mathematical modeling of eukaryotic cell migration: insights beyond experiments. Annu Rev Cell Dev Biol. 2013;29(July):501–28. [DOI] [PubMed]
10. Petrie RJ, Yamada KM. Fibroblasts Lead the Way: A Unified View of 3D Cell Motility. Trends Cell Biol. 2015 Nov;25(11):666–74. [DOI] [PubMed]
11. Masuzzo P, Van Troys M, Ampe C, Martens L. Taking Aim at Moving Targets in Computational Cell Migration. Trends Cell Biol. 2016;26(2):88-110. [DOI] [PubMed]
12. Wu Q, Merchant F, Castleman K. Microscope image processing: Academic press; 2010.
13. Sankur B. Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging. 2004 Jan;13(1):146. [DOI]
14. Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. Int J Comput Vis. 1988 Jan;1(4):321–31. [DOI]
15. Liu JS. Monte Carlo strategies in scientific computing: Springer Science & Business Media; 2008.
16. Codling EA, Plank MJ, Benhamou S. Random walk models in biology. 2008;(April):813–34. [DOI]
17. da Silva PC, Rosembach TV, Santos AA, Rocha MS, Martins ML. Normal and tumoral melanocytes exhibit q-Gaussian random search patterns. PLoS One. 2014;9(9):e104253. [DOI] [PubMed]
18. Nelson P. Biological Physics : Energy, Information, Life. 2002;
19. Despósito MA, Viñales AD. Sub diffusive behavior in a trapping potential: mean square displacement and velocity autocorrelation function. 2009 Feb 16; [DOI]
20. Ibe OC. Elements of Random Walk and Diffusion Processes. 2013. 253 pp. [DOI]
21. Schilling R, Song R, Vondracek Z. Bernstein functions: theory and applications. 2012. [DOI]
22. Einstein A. On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat. Ann Phys. 1905;322:549–60. [DOI]
23. Höfling F, Franosch T. Anomalous transport in the crowded world of biological cells. Rep Prog Phys. 2013;76(4):046602. [DOI] [PubMed]
24. Gallach Pérez D, Punzón Quijorna E, Sanz R, Torres-Costa V, García Ruiz JP, Manso Silván M. Nanotopography enhanced mobility determines mesenchymal stem cell distribution on micropatterned semiconductors bearing nanorough areas. Colloids Surf B Biointerfaces. 2015 ;126:146–53. [DOI] [PubMed]
25. Vainstein MH, Lapas LC, Oliveira FA. Anomalous diffusion. arXiv preprint arXiv:08050270. 2008.
26. Despósito MA, Viñales AD. Subdiffusive behavior in a trapping potential: mean square displacement and velocity autocorrelation function. Phys Rev E Stat Nonlin Soft Matter Phys. 2009;80(2 Pt 1):021111. [DOI] [PubMed]
27. Benhamou S. How many animals really do the Lévy walk? Ecology. 2007;88(8):1962–9. [DOI] [PubMed]
28. Kedzia A, Rybaczuk M, Andrzejak R. Fractal dimensions of human brain cortex vessels during the fetal period. Med Sci Monit. 2002;8(3):MT46–51. [PubMed]
29. Harris TH, Banigan EJ, Christian DA, Konradt C, Tait Wojno ED, Norose K et al. Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells. Nature. 2012;486(7404):545–8. [DOI] [PubMed]
30. Tsallis C, Bukman DJ. Anomalous diffusion in the presence of external forces: exact time-dependent solutions and their thermostatistical basis. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996;54(3):R2197–200. [DOI] [PubMed]
31. Upadhyaya A, Rieu J-P, Glazier JA, Sawada Y. Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates. Phys A Stat Mech its Appl. 2001 15;293(3–4):549–58. [DOI]
32. Souza Vilela Podestá T, Venzel Rosembach T, Aparecida Dos Santos A, Lobato Martins M. Anomalous diffusion and q-Weibull velocity distributions in epithelial cell migration. PLoS One. 2017 Jul;12(7):e0180777. [DOI] [PubMed]
33. Tang X, Wadsworth WG. SAX-3 (Robo) and UNC-40 (DCC) Regulate a Directional Bias for Axon Guidance in Response to Multiple Extracellular Cues. Labrador J-P, editor. PLoS One. 2014;15;9(10):e110031.
34. Nishikawa M, Hörning M, Ueda M, Shibata T. Excitable signal transduction induces both spontaneous and directional cell asymmetries in the phosphatidylinositol lipid signaling system for eukaryotic chemotaxis. Biophys J. 2014;106(3):723–34. [DOI] [PubMed]
35. Li S, Huang NF, Hsu S. Mechanotransduction in endothelial cell migration. J Cell Biochem. 2005;96(6):1110–26. [DOI] [PubMed]
36. Vermolen FJ, Mul MM, Gefen A. Semi-stochastic cell-level computational modeling of the immune system response to bacterial infections and the effects of antibiotics. Biomech Model Mechanobiol. 2014;13(4):713–34. [DOI] [PubMed]
37. Coelho FM, Natale D, Soriano SF, Hons M, Swoger J, Mayer J et al. Naive B-cell trafficking is shaped by local chemokine availability and LFA-1-independent stromal interactions. Blood. 2013;121(20):4101–9. [DOI] [PubMed]
38. Vroomans RM, Marée AF, de Boer RJ, Beltman JB. Chemotactic migration of T cells towards dendritic cells promotes the detection of rare antigens. PLOS Comput Biol. 2012;8(11):e1002763. [DOI] [PubMed]
39. Yang K, Wu J, Xu G, Xie D, Peretz-Soroka H, Santos S, et al. A dual-docking microfluidic cell migration assay (D2-Chip) for testing neutrophil chemotaxis and the memory effect. Integrative Biology. 2017;9(4):303-12. [DOI]
40. Liu X, Asokan SB, Bear JE, Haugh JM. Quantitative analysis of B-lymphocyte migration directed by CXCL13. Integr Biol (United Kingdom). 2016;8(8).
41. Abeddoust M, Shamloo A. A model for cell density effect on stress fiber alignment and collective directional migration. Phys Biol. 2015;12(6):066023. [DOI] [PubMed]
42. Vedula SR, Leong MC, Lai TL, Hersen P, Kabla AJ, Lim CT et al. Emerging modes of collective cell migration induced by geometrical constraints. Proc Natl Acad Sci USA. 2012;109(32):12974–9. [DOI] [PubMed]
43. Niculescu I, Textor J, de Boer RJ. Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration. PLOS Comput Biol. 2015;11(10):e1004280. [DOI] [PubMed]
44. Muzzio NE, Pasquale MA, González PH, Arvia AJ. Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies. J Biol Phys. 2014;40(3):285–308. [DOI] [PubMed]
45. Missirlis D, Spatz JP. Combined effects of PEG hydrogel elasticity and cell-adhesive coating on fibroblast adhesion and persistent migration. Biomacromolecules. 2014;15(1):195–205. [DOI] [PubMed]
46. Raab M, Swift J, Dingal PC, Shah P, Shin JW, Discher DE. Crawling from soft to stiff matrix polarizes the cytoskeleton and phosphoregulates myosin-II heavy chain. J Cell Biol. 2012;199(4):669–83. [DOI] [PubMed]
47. Novikova EA, Raab M, Discher DE, Storm C. Persistence-Driven Durotaxis: Generic, Directed Motility in Rigidity Gradients. Phys Rev Lett. 2017;118(7):078103. [DOI] [PubMed]
48. Reymann AC, Boujemaa-Paterski R, Martiel JL, Guérin C, Cao W, Chin HF et al. Actin network architecture can determine myosin motor activity. Science. 2012;336(6086):1310–4. [DOI] [PubMed]
49. Chia PH, Chen B, Li P, Rosen MK, Shen K. Local F-actin network links synapse formation and axon branching. Cell. 2014;156(1-2):208–20. [DOI] [PubMed]
50. Colin A, Bonnemay L, Gayrard C, Gautier J, Gueroui Z. Triggering signaling pathways using F-actin self-organization. Sci Rep. 2016;6(1):34657. [DOI] [PubMed]
51. Rangarajan R, Zaman MH. Modeling cell migration in 3D: status and challenges. Vol. 2. Cell Adhes Migr. 2008;2(2):106–9. [DOI]
52. Li L, Nørrelykke SF, Cox EC. Persistent cell motion in the absence of external signals: a search strategy for eukaryotic cells. PLoS One. 2008;3(5):e2093. [DOI] [PubMed]
53. Metzler R, Jeon JH, Cherstvy AG, Barkai E. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys Chem Chem Phys. 2014;16(44):24128–64. [DOI] [PubMed]
54. Rosser G, Fletcher AG, Maini PK, Baker RE. The effect of sampling rate on observed statistics in a correlated random walk. J R Soc Interface. 2013;10(85):20130273. [DOI] [PubMed]
55. Caballero D, Voituriez R, Riveline D. Protrusion fluctuations direct cell motion. Biophys J. 2014 Jul;107(1):34–42. [DOI] [PubMed]
56. Cooper RM, Wingreen NS, Cox EC. An excitable cortex and memory model successfully predicts new pseudopod dynamics. PLoS One. 2012;7(3):e33528. [DOI] [PubMed]
57. Nishimura SI, Ueda M, Sasai M. Non-Brownian dynamics and strategy of amoeboid cell locomotion. Phys Rev E - Stat Nonlinear. Soft Matter Phys. 2012;85(4):41909.
58. Ridley AJ, Schwartz MA, Burridge K, Firtel RA, Ginsberg MH, Borisy G, et al. Cell Migration: Integrating Signals from Front to Back. Science (80). 2003 Dec 5;302(5651):1704–9.
59. Van Haastert PJ. A model for a correlated random walk based on the ordered extension of pseudopodia. PLOS Comput Biol. 2010;6(8):e1000874. [DOI] [PubMed]
60. Bourne HR, Weiner O. Cell polarity: A chemical compass. Nat. 2002;2002:4196902.
61. Maiuri P, Rupprecht JF, Wieser S, Ruprecht V, Bénichou O, Carpi N et al. Actin flows mediate a universal coupling between cell speed and cell persistence. Cell. 2015;161(2):374–86. [DOI] [PubMed]
62. Read MN, Bailey J, Timmis J, Chtanova T. Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection. PLOS Comput Biol. 2016;12(9):e1005082. [DOI] [PubMed]
63. Miller MJ, Wei SH, Parker I, Cahalan MD. Two-Photon Imaging of Lymphocyte Motility and Antigen Response in Intact Lymph Node. Science (80-).2002 Jun 7;296(5574):1869–73. [DOI]
64. Banigan EJ, Harris TH, Christian DA, Hunter CA, Liu AJ. Heterogeneous CD8 + T Cell Migration in the Lymph Node in the Absence of Inflammation Revealed by Quantitative Migration Analysis. 2015;1–20.
65. O’Connor MJ, Hauser AE, Haberman AM, Kleinstein SH. Activated germinal centre B cells undergo directed migration. Int J Data Min Bioinform. 2011;5(3):321–31. [DOI] [PubMed]
66. Fooksman DR, Schwickert TA, Victora GD, Dustin ML, Nussenzweig MC, Skokos D. Development and migration of plasma cells in the mouse lymph node. Immunity. 2010 Jul;33(1):118–27. [DOI] [PubMed]
67. Garcia R, Moss F, Nihongi A, Strickler JR, Göller S, Erdmann U et al. Optimal foraging by zooplankton within patches: the case of Daphnia. Math Biosci. 2007 Jun;207(2):165–88. [DOI] [PubMed]
68. Asano S, Ito S, Takahashi K, Furuya K, Kondo M, Sokabe M et al. Matrix stiffness regulates migration of human lung fibroblasts. Physiol Rep. 2017 May;5(9):e13281. [DOI] [PubMed]
69. Rieu JP, Upadhyaya A, Glazier JA, Ouchi NB, Sawada Y. Diffusion and deformations of single hydra cells in cellular aggregates. Biophys J. 2000 Oct;79(4):1903–14 [DOI] [PubMed]
70. Huang YL, Tung CK, Zheng A, Kim BJ, Wu M. Interstitial flows promote amoeboid over mesenchymal motility of breast cancer cells revealed by a three dimensional microfluidic model. Integr Biol. 2015 Nov;7(11):1402–11. [DOI] [PubMed]
71. Niculescu I, Textor J, de Boer RJ. Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration. PLOS Comput Biol. 2015 Oct;11(10):e1004280. [DOI] [PubMed]
72. Fricke GM, Letendre KA, Moses ME, Cannon JL. Persistence and Adaptation in Immunity: T Cells Balance the Extent and Thoroughness of Search. PLOS Comput Biol. 2016 Mar;12(3):e1004818. [DOI] [PubMed]
73. Zhou P, Li B, Liu F, Zhang M, Wang Q, Liu Y et al. The epithelial to mesenchymal transition (EMT) and cancer stem cells: implication for treatment resistance in pancreatic cancer. Mol Cancer. 2017 Feb;16(1):52. [DOI] [PubMed]
74. Brabletz T. EMT and MET in metastasis: where are the cancer stem cells? Cancer Cell. 2012 Dec;22(6):699–701. [DOI] [PubMed]
75. Box GE, Tiao GC. Bayesian inference in statistical analysis. Wiley; 1992. 588 pp. [DOI]
76. Metzner C, Mark C, Steinwachs J, Lautscham L, Stadler F, Fabry B. Superstatistical analysis and modelling of heterogeneous random walks. Nat Commun. 2015 Jun;6(1):7516. [DOI] [PubMed]
77. Jones PJ, Sim A, Taylor HB, Bugeon L, Dallman MJ, Pereira B et al. Inference of random walk models to describe leukocyte migration. Phys Biol. 2015 Sep;12(6):066001. [DOI] [PubMed]
78. Wu PH, Giri A, Sun SX, Wirtz D. Three-dimensional cell migration does not follow a random walk. Proc Natl Acad Sci USA. 2014 Mar;111(11):3949–54. [DOI] [PubMed]
79. Davis B. Reinforced random walk. Probability Theory and Related Fields. 1990;84(2):203-29.
80. Zhang M, Zhu C. Global existence of solutions to a hyperbolic-parabolic system. Proceedings of the American Mathematical Society. 2007;135(4):1017-27.
81. Levine HA, Sleeman BD, Nilsen-Hamilton M. Mathematical modeling of the onset of capillary formation initiating angiogenesis. J Math Biol. 2001 Mar;42(3):195–238. [DOI] [PubMed]
82. Plank MJ, Sleeman BD, Jones PF. A Mathematical Model of an In Vitro Experiment to Investigate Endothelial Cell Migration. J Theor Med. 2002;4(4):251–70. [DOI]
83. Jain HV, Jackson TL. A hybrid model of the role of VEGF binding in endothelial cell migration and capillary formation. Front Oncol. 2013 May;3(May):102. [PubMed]
84. Bibbona E, Panfilo G, Tavella P. The Ornstein–Uhlenbeck process as a model of a low pass filtered white noise. Metrologia. 2008 Dec;45(6):S117–26. [DOI]
85. Uhlenbeck GE, Ornstein LS. On the Theory of the Brownian Motion. Phys Rev. 1930 Sep;36(5):823–41. [DOI]
86. Dieterich P, Klages R, Preuss R, Schwab A. Anomalous dynamics of cell migration. Proc Natl Acad Sci U S A. 2008;105(2):459-63. [DOI] [PubMed]
87. Stokes CL, Lauffenburger DA, Williams SK. Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J Cell Sci. 1991;99(Pt 2):419–30. [PubMed]
88. Snyder S, DeJulius C, Willits RK. Electrical Stimulation Increases Random Migration of Human Dermal Fibroblasts. Ann Biomed Eng. 2017;45(9):2049–60. [DOI] [PubMed]
89. Dunn GA, Brown AF. A unified approach to analysing cell motility. J Cell Sci Suppl. 1987;8 Supplement 8:81–102. https://doi.org/10.1242/jcs.1987.Supplement_8.5 [PubMed]
90. Li L, Cox EC, Flyvbjerg H. ‘Dicty dynamics’: Dictyostelium motility as persistent random motion. Phys Biol. 2011;8(4):046006. [DOI] [PubMed]
91. Fürth R. Reinhold. Die Brownsche Bewegung bei Berücksichtigung einer Persistenz der Bewegungsrichtung. Mit Anwendungen auf die Bewegung lebender Infusorien. Z Phys. 1920 ;2(3):244–56. [DOI]
92. Selmeczi D, Mosler S, Hagedorn PH, Larsen NB, Flyvbjerg H. Cell motility as persistent random motion: theories from experiments. Biophys J. 2005;89(2):912–31. [DOI] [PubMed]

Add your comments about this article : Your username or Email:

Send email to the article author

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2023 CC BY-NC 4.0 | Multidisciplinary Cancer Investigation

Designed & Developed by : Yektaweb