為了理解細胞在基板上爬行的力學機制，本論文提出了一個一維理論模型。此模
型包含了肌凝蛋白的收縮力、細胞骨架的黏滯力、鍵結和基板的阻力以及細胞前
後端肌動蛋白絲聚合之間的交互作用。數值模擬本模型的結果顯示（1）肌凝蛋
白的收縮力（2）肌動蛋白絲的聚合速率在細胞前後端的不對稱性（3）鍵結分布
的不對稱性可以幫助細胞爬行。當細胞利用收縮力爬行時，其靜止狀態時流場分
布為零，肌凝蛋白與鍵結在細胞中均勻分布。當肌動蛋白絲的聚合加入模型中時，
其靜止狀態的流場為逆流分布，肌凝蛋白向中間聚集，鍵結分布靠近細胞兩端。
當細胞開始移動時，流場與肌凝蛋白的分布失去前後對稱性，細胞前端的鍵結密
度會因為突出(protrusion)而降低。當細胞移動的速度越快，鍵結分布的極值會
越來越靠近細胞中段，這是因為成熟的鍵結需要時間形成。

To understand how the intracellular mechanics affect the motion of a cell, we develop a one-dimensional model for cell migration on a solid substrate. This model includes contractile force from actomyosin network, viscous stress in the cytoskeleton, actin polymerization at the ends of the cell, drag force due to substrate and cell-substrate bonds. Our numerical solutions show that cell motility is facilitated by (i) active contractility of the actyomyosin gel, (ii) asymmetric actin polymerization at cell ends, and (iii) symmetry-breaking in the distribution of cell-substrate bonds. The flow field is zero everywhere in the rest state when the cell motility is facilitated only by active contractility. The corresponding bond density is uniform. The flow field becomes retrograde in the rest state when actin polymerization is included. The corresponding bond density has peaks close to the cell ends for catch bonds. When the cell starts to move, the flow drives the asymmetric distribution of myosin motors. The bond density at the leading end becomes lower due to protrusion. As the speed of the cell increases, bonds in the leading half of the cell move closer to the center because the slow growth of mature focal adhesion complexes.

[1] P Recho, T Putelat, and L Truskinovsky. Contraction-driven cell motility. Physical
Review Letters, 111(10):108102, 2013.
[2] Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Ra
, Keith Roberts, and Peter
Walter. Molecular biology of the cell 4th edn (new york: Garland science).
[3] Xiaorong Fu, Ge Liu, Alexander Halim, Yang Ju, Qing Luo, and Guanbin Song. Mesenchymal
stem cell migration and tissue repair. Cells, 8(8):784, 2019.
[4] Laurence Zitvogel, Maha Ayyoub, Bertrand Routy, and Guido Kroemer. Microbiome
and anticancer immunosurveillance. Cell, 165(2):276, 2016.
[5] Geo
rey M Cooper and Robert E Hausman. The development and causes of cancer.
The cell: A molecular approach, 2, 2000.
[6] Abbas A. K. Fausto N. Aster J. C. Kumar, V. Robbins and Cotran pathologic basis of
disease. Elsevier Saunders, 2015.
[7] Howard C Berg. E. coli in Motion. Springer, New York, 2008.
[8] Peter Devreotes and Alan Rick Horwitz. Signaling networks that regulate cell migration.
Cold Spring Harbor Perspectives in Biology, 7(8):a005959, 2015.
[9] Gregory H Altman, Rebecca L Horan, Ivan Martin, Jian Farhadi, Peter RH Stark,
Vladimir Volloch, John C Richmond, Gordana Vunjak-Novakovic, and David L Kaplan.
Cell di
erentiation by mechanical stress. The FASEB Journal, 16(2):1, 2002.
[10] Felix Rico, Calvin Chu, Midhat H Abdulreda, Yujing Qin, and Vincent T Moy. Temperature
modulation of integrin-mediated cell adhesion. Biophysical Journal, 99(5):1387,
2010.
[11] Kota Miura and Florian Siegert. Light a
ects camp signaling and cell movement activity
in dictyostelium discoideum. Proceedings of the National Academy of Sciences, USA,
97(5):2111, 2000.
[12] Frank Juelicher, Karsten Kruse, Jacques Prost, and J-F Joanny. Active behavior of the
cytoskeleton. Physics Reports, 449(1-3):3, 2007.
[13] D Bray. Cell Movements: from Molecules to Motility 2nd. Garland Science, New York,
2001.
[14] Rob Phillips, Jane Kondev, Julie Theriot, and Hernan Garcia. Physical biology of the
cell. Garland Science, New York, 2012.
[15] Thomas D Pollard. Regulation of actin filament assembly by arp2/3 complex and
formins. Annu. Rev. Biophys. Biomol. Struct., 36:451, 2007.
[16] Christopher S Chen, Jose L Alonso, Emanuele Ostuni, George M Whitesides, and Donald
E Ingber. Cell shape provides global control of focal adhesion assembly. Biochemical
and Biophysical Research Communications, 307(2):355, 2003.
[17] Benjamin Geiger, Alexander Bershadsky, Roumen Pankov, and Kenneth M Yamada.
Transmembrane crosstalk between the extracellular matrix and the cytoskeleton. Nature
Reviews Molecular Cell Biology, 2(11):793, 2001.
[18] Joanne E Murphy-Ullrich. The de-adhesive activity of matricellular proteins: is intermediate
cell adhesion an adaptive state? The Journal of Clinical Investigation, 107(7):785,
2001.
[19] Alex Mogilner and Leah Edelstein-Keshet. Regulation of actin dynamics in rapidly
moving cells: a quantitative analysis. Biophysical journal, 83(3):1237, 2002.
[20] Ricard Alert and Xavier Trepat. Physical models of collective cell migration. Annual
Review of Condensed Matter Physics, 11:77, 2020.
[21] Pierre Recho and Lev Truskinovsky. Cell locomotion in one dimension. In Physical
Models of Cell Motility, page 135. Springer, New York, 2016.
[22] Thibaut Putelat, Pierre Recho, and Lev Truskinovsky. Mechanical stress as a regulator
of cell motility. Physical Review E, 97(1):012410, 2018.
[23] Katsuhisa Tawada and Ken Sekimoto. Protein friction exerted by motor enzymes
through a weak-binding interaction. Journal of Theoretical Biology, 150(2):193, 1991.
[24] Ke Hu, Lin Ji, Kathryn T Applegate, Gaudenz Danuser, and Clare M Waterman-Storer.
Differential transmission of actin motion within focal adhesions. Science, 315(5808):111,
2007.
[25] Anders E Carlsson and David Sept. Mathematical modeling of cell migration. Methods
in Cell Biology, 84:911, 2008.
[26] Anne J Ridley, Martin A Schwartz, Keith Burridge, Richard A Firtel, Mark H Ginsberg,
Gary Borisy, J Thomas Parsons, and Alan Rick Horwitz. Cell migration: integrating
signals from front to back. Science, 302(5651):1704, 2003.
[27] Arpita Upadhyaya and Alexander van Oudenaarden. Biomimetic systems for studying
actin-based motility. Current Biology, 13(18):R734, 2003.
[28] Richard Anthony Lewis Jones. Soft condensed matter, volume 6. Oxford University
Press, 2002.
[29] Yusuke T Maeda, Junya Inose, Miki Y Matsuo, Suguru Iwaya, and Masaki Sano. Ordered
patterns of cell shape and orientational correlation during spontaneous cell migration.
PLoS One, 3(11):e3734, 2008.
[30] Tianzhi Luo, Krithika Mohan, Vasudha Srivastava, Yixin Ren, Pablo A Iglesias, and
Douglas N Robinson. Understanding the cooperative interaction between myosin ii and
actin cross-linkers mediated by actin filaments during mechanosensation. Biophysical
Journal, 102(2):238, 2012.
[31] Erin L Barnhart, Kun-Chun Lee, Kinneret Keren, Alex Mogilner, and Julie A Theriot.
An adhesion-dependent switch between mechanisms that determine motile cell shape.
PLoS Biol, 9(5):e1001059, 2011.
[32] Yu-Li Wang. Reorganization of actin filament bundles in living broblasts. The Journal
of Cell Biology, 99(4):1478, 1984.
[33] Masoud Nickaeen, Igor L Novak, Stephanie Pulford, Aaron Rumack, Jamie Brandon,
Boris M Slepchenko, and Alex Mogilner. A free-boundary model of a motile cell explains
turning behavior. PLoS Computational Biology, 13(11):e1005862, 2017.
[34] Joel H Ferziger, Milovan Peric, and Robert L Street. Computational methods for
dynamics, volume 3. Springer, New York, 2002.
[35] Graham Horton and Stefan Vandewalle. A space-time multigrid method for parabolic
partial di
erential equations. SIAM Journal on Scientic Computing, 16(4):848, 1995.
[36] Dhruv K Vig, Alex E Hamby, and Charles W Wolgemuth. Cellular contraction can drive
rapid epithelial
ows. Biophysical Journal, 113(7):1613, 2017.
[37] Igor L Novak, Boris M Slepchenko, Alex Mogilner, and Leslie M Loew. Cooperativity
between cell contractility and adhesion. Physical Review Letters, 93(26):268109, 2004.
[38] Stephanie I Fraley, Yunfeng Feng, Anjil Giri, Gregory D Longmore, and Denis Wirtz.
Dimensional and temporal controls of three-dimensional cell migration by zyxin and
binding partners. Nature Communications, 3(1):1, 2012.
[39] E Tjhung, A Tiribocchi, D Marenduzzo, and ME Cates. A minimal physical model
captures the shapes of crawling cells. Nature Communications, 6(1):1, 2015.
[40] Carles Blanch-Mercader and J Casademunt. Spontaneous motility of actin lamellar
fragments. Physical Review Letters, 110(7):078102, 2013.
[41] Ido Lavi, Nicolas Meunier, Raphael Voituriez, and Jaume Casademunt. Motility and
morphodynamics of conned cells. Physical Review E, 101(2):022404, 2020.