Microenvironment-enhanced invasive tumor growth via cellular automaton simulations

Liang Long; Jiao Yang

doi:10.7498/aps.64.058706

Abstract

Emergence of invasive and metastatic behavior in malignant tumors can often lead to fatal outcomes for patients. The collective malignant tumor behavior resulting from the complex tumor-host interactions and the interactions between the tumor cells are currently poorly understood. Progress towards such an understanding necessarily requires an interdisciplinary and collaborative effort. In this paper, we review a state-of-art simulation technique, i.e., a cellular automaton (CA) model which has been developed by the authors over the past few years to investigate microenvironment-enhanced invasive growth of avascular solid tumors. This CA model incorporates a variety of microscopic-scale tumor-host interactions, including the degradation of the extracellular matrix by the malignant cells, nutrient-driven cell migration, pressure build-up due to the deformation of the microenvironment by the growing tumor and its effect on the local tumor-host interface stability. Moreover, the effects of cell-cell adhesion on tumor growth are also explicitly taken into account. A number of bench-mark collective invasion behaviors have been successfully reproduced via the CA model, including the emergence of elongated invasion branches characterized by homotype attraction and least resistance path, development of rough tumor surface in a high-pressure confined environment, as well as reduced invasion due to strong cell-cell adhesion. Such simulated bench-mark behaviors strongly indicate the validity and predictive power of the CA model. In addition, the CA model allows one to investigate the role of various different microenvironment factors in the progression of the neoplasm, in particular, the promotion and enhancement of tumor malignancy. As an example, a “phase diagram” that summarizes the dependency of tumor invasive behavior on extracellular matrix (ECM) rigidity (density) and strength of cell-cell adhesion is constructed based on comprehensive simulations. In this simple phase diagram, a clear transition from non-invasive to invasive behaviors of the tumor can be achieved by increasing ECM rigidity and/or decreasing the strength of cell-cell adhesion. This model, when properly combined with clinical data, in principle enables one to broaden the conclusions drawn from existing medical data, suggest new experiments, test hypotheses, predict behavior in experimentally unobservable situations, be employed for early detection and prognosis, and to suggest optimized treatment strategy for individual patient.

Keywords:

Authors and contacts

Liang Long¹,
Jiao Yang^1,2

1.
Department of Physics, Arizona State University, AZ 85287, USA;
2.
Materials Science and Engineering, Arizona State University, AZ 85287, USA

References

[1]	Coffey D S 1998 Nat. Med. 4 882
[2]	Anderson A R A 2005 Math. Med. Biol. 22 163
[3]	Anderson A R A, Weaver A M, Cummings P T, Quaranta V 2006 Cell 127 905
[4]	Deisboeck T S, Berens M E, Kansal A R, Torquato S, Stemmer-Rachamimov A O, Chiocca E A 2001 Cell Prolif. 34 115
[5]	Fidler I J 2003 Nat. Rev. Cancer 3 453
[6]	Frieboes H B, Zheng X, Sun C-H, Tromberg B, Gatenby R, Cristini V 2006 Cancer Res. 66 1597
[7]	Hanahan D, Weinberg R A 2000 Cell 100 57
[8]	Kerbel R S 1990 Adv. Cancer Res., edited by George F. Vande Woude and George Klein (Waltham, Massachusetts: Academic Press) pp87–-132
[9]	Liotta L A, Kohn E C 2003 Nat. Genet. 33 10
[10]	Gatenby R A 1996 Eur. J. Cancer 32A 722
[11]	Fearon E R, Vogelstein B 1990 Cell 61 759
[12]	Jiao Y, Torquato S 2011 PLoS Comput. Biol. 7 e1002314
[13]	Jiao Y, Torquato S 2012 AIP Adv. 2 011003
[14]	Anderson A R A, Chaplain M a J 1998 Bull. Math. Biol. 60 857
[15]	Anderson A R A, Quaranta V 2008 Nat. Rev. Cancer 8 227
[16]	Brú A, Casero D 2006 J. Theor. Biol. 243 171
[17]	Byrne H M 2010 Nat. Rev. Cancer 10 221
[18]	Byrne H M, Alarcon T, Owen M R, Webb S D, Maini P K 2006 Philos. Trans. R. Soc. Lond. Math. Phys. Eng. Sci. 364 1563
[19]	Gatenby R A, Maini P K 2003 Nature 421 321
[20]	Guiot C, Pugno N, Delsanto P P, Deisboeck T S 2007 Phys. Biol. 4 P1
[21]	Helmlinger G, Netti P A, Lichtenbeld H C, Melder R J, Jain R K 1997 Nat. Biotechnol. 15 778
[22]	Hogan M C, Lee A, Solberg L A, Thomé S D 2002 Am. J. Hematol. 70 55
[23]	KANSAL A R, TORQUATO S, HARSH IV G R, CHIOCCA E A, DEISBOECK T S 2000 J. Theor. Biol. 203 367
[24]	KANSAL A R, TORQUATO S, CHIOCCA E A, DEISBOECK T S 2000 J. Theor. Biol. 207 431
[25]	T P Padera, Kadambi A, Di Tomaso E, Carreira C M, Brown E B, Boucher Y, Choi N C, Mathisen D, Wain J, Mark E J, Munn L L, Jain R K 2002 Science 296 1883
[26]	Paszek M J, Zahir N, Johnson K R, Lakins J N, Rozenberg G I, Gefen A, Reinhart-King C A, Margulies S S, Dembo M, Boettiger D, Hammer D A, Weaver V M 2005 Cancer Cell 8 241
[27]	Torquato S 2011 Phys. Biol. 8 015017
[28]	Schrödinger E 1992 What Is Life?: With Mind and Matter and Autobiographical Sketches (Cambridge, UK: Cambridge University Press)
[29]	Fernandez-Gonzalez R, Simoes S de M, Röper J-C, Eaton S, Zallen J A 2009 Dev. Cell 17 736
[30]	Wozniak M A, Chen C S 2009 Nat. Rev. Mol. Cell Biol. 10 34
[31]	Boey S K, Boal D H, Discher D E 1998 Biophys. J. 75 1573
[32]	Coughlin M F, Stamenović D 2003 Biophys. J. 84 1328
[33]	Gordon D, Bernheim-Groswasser A, Keasar C, Farago O 2012 Phys. Biol. 9 026005
[34]	Totsukawa G, Wu Y, Sasaki Y, Hartshorne D J, Yamakita Y, Yamashiro S, Matsumura F 2004 J. Cell Biol. 164 427
[35]	Friedl P, Bröcker E-B 2000 Cell. Mol. Life Sci. CMLS 57 41
[36]	Grinnell F, Petroll W M 2010 Annu. Rev. Cell Dev. Biol. 26 335
[37]	Vaziri A, Gopinath A 2008 Nat. Mater. 7 15
[38]	Carlsson A E 2006 Biophys. J. 90 413
[39]	Yamaoka H, Matsushita S, Shimada Y, Adachi T 2012 Biomech. Model. Mechanobiol. 11 291
[40]	Lecuit T, Lenne P-F, Munro E 2011 Annu. Rev. Cell Dev. Biol. 27 157
[41]	Carlsson A E 2011 New J. Phys. 13 073009
[42]	Buenemann M, Levine H, Rappel W-J, Sander L M 2010 Biophys. J. 99 50
[43]	Zaman M H, Kamm R D, Matsudaira P, Lauffenburger D A 2005 Biophys. J. 89 1389
[44]	Cirit M, Krajcovic M, Choi C K, Welf E S, Horwitz A F, Haugh J M 2010 PLoS Comput Biol 6 e1000688
[45]	Kabla A J, 2011 arXiv11084286 Phys. Q-Bio.
[46]	Sun L, Chang Y F 2003 Journal of Huazhong Normal University: Natural Sciences 37 491 (in Chinese) [孙亮, 常云峰 2003 华中师范大学学报：自然科学版 37 491]
[47]	Manning M L, Foty R A, Steinberg M S, Schoetz E-M 2010 Proc. Natl. Acad. Sci. 107 12517
[48]	Drasdo D, Höhme S 2005 Phys. Biol. 2 133
[49]	Szabó B, Szöllösi G J, Gönci B, Jurányi Z, Selmeczi D, Vicsek T 2006 Phys. Rev. E 74 061908
[50]	Yang X, Manning M L, Marchetti M C 2014 Soft Matter 10 6477
[51]	Gatenby R A, Gawlinski E T 1996 Cancer Res. 56 5745
[52]	Owen M R, Byrne H M, Lewis C E 2004 J. Theor. Biol. 226 377
[53]	Zhou Y 2012 Ph. D. Thesis (Shanghai: Fudan University) (in Chinese) [周瑜 2012 博士学位论文 (上海:复旦大学)]
[54]	Schmitz J E, Kansal A R, Torquato S 2002 Comput. Math. Methods Med. 4 223
[55]	Alarcón T, Byrne H M, Maini P K 2004 J. Theor. Biol. 229 395
[56]	Gavaghan D J, Brady J M, Behrenbruch C P, Highnam R P, Maini P K 2002 Comput. Math. Methods Med. 4 3
[57]	Gevertz J L, Torquato S 2006 J. Theor. Biol. 243 517
[58]	Gevertz J L, Gillies G T, Torquato S 2008 Phys. Biol. 5 036010
[59]	Gevertz J, Torquato S 2009 Phys. Rev. E 80 051910
[60]	Bellomo N, Preziosi L 2000 Math. Comput. Model. 32 413
[61]	Scalerandi M, Sansone B C, Condat C A 2001 Phys. Rev. E 65 011902
[62]	Scalerandi M, Sansone B C 2002 Phys. Rev. Lett. 89 218101
[63]	Kim Y, Friedman A 2010 Bull. Math. Biol. 72 1029
[64]	McElwain D L S, Pettet G J 1993 Bull. Math. Biol. 55 655
[65]	Chen C Y, Byrne H M, King J R 2001 J. Math. Biol. 43 191
[66]	Roose T, Netti P A, Munn L L, Boucher Y, Jain R K 2003 Microvasc. Res. 66 204
[67]	Gatenby R A, Gawlinski E T, Gmitro A F, Kaylor B, Gillies R J 2006 Cancer Res. 66 5216
[68]	Gerisch A, Chaplain M A J 2008 J. Theor. Biol. 250 684
[69]	Macklin P, Lowengrub J 2007 J. Theor. Biol. 245 677
[70]	Gardner M 1970 Sci. Am. 223 120
[71]	Raabe D 1998 in Comput. Mater. Sci. (Weinheim Germany: Wiley-VCH Verlag GmbH & Co. KGaA) pp201–-224
[72]	Jiao Y, Torquato S 2013 Phys. Rev. E 87 052707
[73]	Wolfram S 1983 Rev. Mod. Phys. 55 601
[74]	Torquato S 2002 Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Berlin, Heidelberg: Springer Science & Business Media) pp189-192
[75]	Gevertz J L, Torquato S 2008 PLoS Comput Biol 4 e1000152
[76]	Burridge K, Chrzanowska-Wodnicka M 1996 Annu. Rev. Cell Dev. Biol. 12 463
[77]	Sarntinoranont M, Rooney F, Ferrari M 2003 Ann. Biomed. Eng. 31 327
[78]	Gordon V D, Valentine M T, Gardel M L, Andor-Ardó D, Dennison S, Bogdanov A A, Weitz D A, Deisboeck T S 2003 Exp. Cell Res. 289 58
[79]	La L, Cn R, Sh B 1983 Lab. Investig. J. Tech. Methods Pathol. 49 636
[80]	Boyle J O, Hakim J, Koch W, van der Riet P, Hruban R H, Roa R A, Correo R, Eby Y J, Ruppert J M, Sidransky D 1993 Cancer Res. 53 4477
[81]	Stetler-Stevenson W G, Aznavoorian S, Liotta L A 1993 Annu. Rev. Cell Biol. 9 541
[82]	Lawrence J A, Steeg P S 1996 World J. Urol. 14 124
[83]	Cai Y 2011 Ph. D. Thesis (Shanghai: Fudan University) (in Chinese) [蔡彦 2011博士学位论文 (上海：复旦大学)]
[84]	Gevertz J L 2011 Comput. Math. Methods Med. 2011 e830515
[85]	Enderling H, Chaplain M A J, Anderson A R A, Vaidya J S 2007 J. Theor. Biol. 246 245
[86]	Jiao Y, Berman H, Kiehl T-R, Torquato S 2011 PLoS One 6 e27323
[87]	Gevertz J 2012 Phys. Rev. E 85 041914

Cited By

[1]	Coffey D S 1998 Nat. Med. 4 882
[2]	Anderson A R A 2005 Math. Med. Biol. 22 163
[3]	Anderson A R A, Weaver A M, Cummings P T, Quaranta V 2006 Cell 127 905
[4]	Deisboeck T S, Berens M E, Kansal A R, Torquato S, Stemmer-Rachamimov A O, Chiocca E A 2001 Cell Prolif. 34 115
[5]	Fidler I J 2003 Nat. Rev. Cancer 3 453
[6]	Frieboes H B, Zheng X, Sun C-H, Tromberg B, Gatenby R, Cristini V 2006 Cancer Res. 66 1597
[7]	Hanahan D, Weinberg R A 2000 Cell 100 57
[8]	Kerbel R S 1990 Adv. Cancer Res., edited by George F. Vande Woude and George Klein (Waltham, Massachusetts: Academic Press) pp87–-132
[9]	Liotta L A, Kohn E C 2003 Nat. Genet. 33 10
[10]	Gatenby R A 1996 Eur. J. Cancer 32A 722
[11]	Fearon E R, Vogelstein B 1990 Cell 61 759
[12]	Jiao Y, Torquato S 2011 PLoS Comput. Biol. 7 e1002314
[13]	Jiao Y, Torquato S 2012 AIP Adv. 2 011003
[14]	Anderson A R A, Chaplain M a J 1998 Bull. Math. Biol. 60 857
[15]	Anderson A R A, Quaranta V 2008 Nat. Rev. Cancer 8 227
[16]	Brú A, Casero D 2006 J. Theor. Biol. 243 171
[17]	Byrne H M 2010 Nat. Rev. Cancer 10 221
[18]	Byrne H M, Alarcon T, Owen M R, Webb S D, Maini P K 2006 Philos. Trans. R. Soc. Lond. Math. Phys. Eng. Sci. 364 1563
[19]	Gatenby R A, Maini P K 2003 Nature 421 321
[20]	Guiot C, Pugno N, Delsanto P P, Deisboeck T S 2007 Phys. Biol. 4 P1
[21]	Helmlinger G, Netti P A, Lichtenbeld H C, Melder R J, Jain R K 1997 Nat. Biotechnol. 15 778
[22]	Hogan M C, Lee A, Solberg L A, Thomé S D 2002 Am. J. Hematol. 70 55
[23]	KANSAL A R, TORQUATO S, HARSH IV G R, CHIOCCA E A, DEISBOECK T S 2000 J. Theor. Biol. 203 367
[24]	KANSAL A R, TORQUATO S, CHIOCCA E A, DEISBOECK T S 2000 J. Theor. Biol. 207 431
[25]	T P Padera, Kadambi A, Di Tomaso E, Carreira C M, Brown E B, Boucher Y, Choi N C, Mathisen D, Wain J, Mark E J, Munn L L, Jain R K 2002 Science 296 1883
[26]	Paszek M J, Zahir N, Johnson K R, Lakins J N, Rozenberg G I, Gefen A, Reinhart-King C A, Margulies S S, Dembo M, Boettiger D, Hammer D A, Weaver V M 2005 Cancer Cell 8 241
[27]	Torquato S 2011 Phys. Biol. 8 015017
[28]	Schrödinger E 1992 What Is Life?: With Mind and Matter and Autobiographical Sketches (Cambridge, UK: Cambridge University Press)
[29]	Fernandez-Gonzalez R, Simoes S de M, Röper J-C, Eaton S, Zallen J A 2009 Dev. Cell 17 736
[30]	Wozniak M A, Chen C S 2009 Nat. Rev. Mol. Cell Biol. 10 34
[31]	Boey S K, Boal D H, Discher D E 1998 Biophys. J. 75 1573
[32]	Coughlin M F, Stamenović D 2003 Biophys. J. 84 1328
[33]	Gordon D, Bernheim-Groswasser A, Keasar C, Farago O 2012 Phys. Biol. 9 026005
[34]	Totsukawa G, Wu Y, Sasaki Y, Hartshorne D J, Yamakita Y, Yamashiro S, Matsumura F 2004 J. Cell Biol. 164 427
[35]	Friedl P, Bröcker E-B 2000 Cell. Mol. Life Sci. CMLS 57 41
[36]	Grinnell F, Petroll W M 2010 Annu. Rev. Cell Dev. Biol. 26 335
[37]	Vaziri A, Gopinath A 2008 Nat. Mater. 7 15
[38]	Carlsson A E 2006 Biophys. J. 90 413
[39]	Yamaoka H, Matsushita S, Shimada Y, Adachi T 2012 Biomech. Model. Mechanobiol. 11 291
[40]	Lecuit T, Lenne P-F, Munro E 2011 Annu. Rev. Cell Dev. Biol. 27 157
[41]	Carlsson A E 2011 New J. Phys. 13 073009
[42]	Buenemann M, Levine H, Rappel W-J, Sander L M 2010 Biophys. J. 99 50
[43]	Zaman M H, Kamm R D, Matsudaira P, Lauffenburger D A 2005 Biophys. J. 89 1389
[44]	Cirit M, Krajcovic M, Choi C K, Welf E S, Horwitz A F, Haugh J M 2010 PLoS Comput Biol 6 e1000688
[45]	Kabla A J, 2011 arXiv11084286 Phys. Q-Bio.
[46]	Sun L, Chang Y F 2003 Journal of Huazhong Normal University: Natural Sciences 37 491 (in Chinese) [孙亮, 常云峰 2003 华中师范大学学报：自然科学版 37 491]
[47]	Manning M L, Foty R A, Steinberg M S, Schoetz E-M 2010 Proc. Natl. Acad. Sci. 107 12517
[48]	Drasdo D, Höhme S 2005 Phys. Biol. 2 133
[49]	Szabó B, Szöllösi G J, Gönci B, Jurányi Z, Selmeczi D, Vicsek T 2006 Phys. Rev. E 74 061908
[50]	Yang X, Manning M L, Marchetti M C 2014 Soft Matter 10 6477
[51]	Gatenby R A, Gawlinski E T 1996 Cancer Res. 56 5745
[52]	Owen M R, Byrne H M, Lewis C E 2004 J. Theor. Biol. 226 377
[53]	Zhou Y 2012 Ph. D. Thesis (Shanghai: Fudan University) (in Chinese) [周瑜 2012 博士学位论文 (上海:复旦大学)]
[54]	Schmitz J E, Kansal A R, Torquato S 2002 Comput. Math. Methods Med. 4 223
[55]	Alarcón T, Byrne H M, Maini P K 2004 J. Theor. Biol. 229 395
[56]	Gavaghan D J, Brady J M, Behrenbruch C P, Highnam R P, Maini P K 2002 Comput. Math. Methods Med. 4 3
[57]	Gevertz J L, Torquato S 2006 J. Theor. Biol. 243 517
[58]	Gevertz J L, Gillies G T, Torquato S 2008 Phys. Biol. 5 036010
[59]	Gevertz J, Torquato S 2009 Phys. Rev. E 80 051910
[60]	Bellomo N, Preziosi L 2000 Math. Comput. Model. 32 413
[61]	Scalerandi M, Sansone B C, Condat C A 2001 Phys. Rev. E 65 011902
[62]	Scalerandi M, Sansone B C 2002 Phys. Rev. Lett. 89 218101
[63]	Kim Y, Friedman A 2010 Bull. Math. Biol. 72 1029
[64]	McElwain D L S, Pettet G J 1993 Bull. Math. Biol. 55 655
[65]	Chen C Y, Byrne H M, King J R 2001 J. Math. Biol. 43 191
[66]	Roose T, Netti P A, Munn L L, Boucher Y, Jain R K 2003 Microvasc. Res. 66 204
[67]	Gatenby R A, Gawlinski E T, Gmitro A F, Kaylor B, Gillies R J 2006 Cancer Res. 66 5216
[68]	Gerisch A, Chaplain M A J 2008 J. Theor. Biol. 250 684
[69]	Macklin P, Lowengrub J 2007 J. Theor. Biol. 245 677
[70]	Gardner M 1970 Sci. Am. 223 120
[71]	Raabe D 1998 in Comput. Mater. Sci. (Weinheim Germany: Wiley-VCH Verlag GmbH & Co. KGaA) pp201–-224
[72]	Jiao Y, Torquato S 2013 Phys. Rev. E 87 052707
[73]	Wolfram S 1983 Rev. Mod. Phys. 55 601
[74]	Torquato S 2002 Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Berlin, Heidelberg: Springer Science & Business Media) pp189-192
[75]	Gevertz J L, Torquato S 2008 PLoS Comput Biol 4 e1000152
[76]	Burridge K, Chrzanowska-Wodnicka M 1996 Annu. Rev. Cell Dev. Biol. 12 463
[77]	Sarntinoranont M, Rooney F, Ferrari M 2003 Ann. Biomed. Eng. 31 327
[78]	Gordon V D, Valentine M T, Gardel M L, Andor-Ardó D, Dennison S, Bogdanov A A, Weitz D A, Deisboeck T S 2003 Exp. Cell Res. 289 58
[79]	La L, Cn R, Sh B 1983 Lab. Investig. J. Tech. Methods Pathol. 49 636
[80]	Boyle J O, Hakim J, Koch W, van der Riet P, Hruban R H, Roa R A, Correo R, Eby Y J, Ruppert J M, Sidransky D 1993 Cancer Res. 53 4477
[81]	Stetler-Stevenson W G, Aznavoorian S, Liotta L A 1993 Annu. Rev. Cell Biol. 9 541
[82]	Lawrence J A, Steeg P S 1996 World J. Urol. 14 124
[83]	Cai Y 2011 Ph. D. Thesis (Shanghai: Fudan University) (in Chinese) [蔡彦 2011博士学位论文 (上海：复旦大学)]
[84]	Gevertz J L 2011 Comput. Math. Methods Med. 2011 e830515
[85]	Enderling H, Chaplain M A J, Anderson A R A, Vaidya J S 2007 J. Theor. Biol. 246 245
[86]	Jiao Y, Berman H, Kiehl T-R, Torquato S 2011 PLoS One 6 e27323
[87]	Gevertz J 2012 Phys. Rev. E 85 041914

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