Biomechanical and Nutrient Controls in the Growth of Mammalian Cell Populations

REFERENCES

• Adam , J. and Bellomo , N. ( 1997 ). A Survey of Models for Tumor-Immune System Dynamics . Boston : Birkhäauser .
   Google Scholar
• Alarcón , T. , Byrne , H. , and Maini , P. ( 2004 ). A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells . Journal of Theoretical Biology , 229 : 395 – 411 .
   Google Scholar
• Alber , M. , Kiskowski , M. , Glazier , J.A. , and Jiang , Y. ( 2002 ). In J. Rosenthal and D.S. Gilliam (Eds.), On Cellular Automaton Approaches to Modeling Biological Cells . In Mathematical Systems Theory in Biology, Communication, and Finance . New York : Springer , pp. 1 – 39 .
   Google Scholar
• Alberts , B. , Johnson , B. , et al. . ( 2002 ). The Cell () , 2nd Edition . New York : Garland Science Publishers .
   Google Scholar
• Alcaraz , J. , Buscemi , L. , et al. . ( 2003 ). Microrheology of human lung epithelial cells measured by atomic force . Biophysical Journal , 84 : 2071 – 2079 .
   PubMed Web of Science ®Google Scholar
• Ambrosi , D. and Mollica , F. ( 2002 ). On the mechanics of a growing tumor . International Journal of Engineering Science , 40 : 1297 – 1316 .
   Web of Science ®Google Scholar
• Anderson , A.R. ( 2000 ). Mathematical modeling of tumor invasion and metastasis . Journal of Theoretical Medicine , 2 : 129 – 154 .
   Google Scholar
• Anderson , A.R. , Chaplain , M.A.J. , and Rejniak , K.A. (Eds.). ( 2007 ). Single-Cell-Based Models in Biology and Medicine . Basel , Switzerland : Birkhäuser .
   Google Scholar
• Anderson , A.R. , Weaver , A. , Cummings , P. , and Quaranta , V. ( 2006 ). Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment . Cell , 127 : 905 – 915 .
   PubMed Web of Science ®Google Scholar
• Araujo , R. and McElwain , D. ( 2004 ). A history of the study of solid tumor growth: the contribution of mathematical models . Bulletin of Mathematical Biology , 66 : 1039 – 1091 .
   PubMed Web of Science ®Google Scholar
• Barthel , E. ( 2008 ). Adhesive elastic contacts: JKR and more . Journal of Physics D: Applied Physics , 41 : 163001 .
   Web of Science ®Google Scholar
• Bergers , G. and Benjamin , L.E. ( 2003 ). Tumorigenesis and the angiogenic switch . Nature Reviews Cancer , 3 : 401 – 410 .
   PubMed Web of Science ®Google Scholar
• Beysens , D. , Forgacs , G. , and Glazier , J.A. ( 2000 ). Cell sorting is analogous to phase ordering in fluids . Proceedings of the National Academy of Sciences of the USA , 97 : 9467 – 9471 .
   PubMed Web of Science ®Google Scholar
• Bischofs , I. and Schwarz , U. ( 2005 ). Effect of Poisson ratio on cellular structure formation . Physical Review Letters , 95 : 068102–1 – 068102–4 .
   Google Scholar
• Block , M. , Schoell , E. , and Drasdo , D. ( 2007 ). Classifying the growth kinetics and surface dynamics in growing cell populations . Physical Review Letters , 99 : 248101 – 248104 .
   PubMedGoogle Scholar
• Bru , A. , Pastor , J. , et al. . ( 1998 ). Super-rough dynamics of tumor growth . Physical Review Letters , 81 : 4008 – 4011 .
   Web of Science ®Google Scholar
• Bru , A. , Albertos , S. , et al. . ( 2003a ). The universal dynamics of tumor growth . Biophysical Journal , 85 : 2948 – 2961 .
   PubMed Web of Science ®Google Scholar
• Bru , A. , Albertos , S. , et al. . ( 2003b ). The universal dynamics of tumor growth . Biophysical Journal , 85 : 2948 – 2961 .
   PubMed Web of Science ®Google Scholar
• Byrne , H. and Drasdo , D. ( 2009 ). Individual-based and continuum models of growing cell populations: a comparison . Journal of Mathematical Biology , 58 : 657 – 687 .
   PubMed Web of Science ®Google Scholar
• Casciari , J. , Sotirchos , S. , and Sutherland , R. ( 1992 ). Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH . Journal of Cellular Physiology , 151 : 386 – 394 .
   PubMed Web of Science ®Google Scholar
• Chaplain , M.A.J. ( 1996 ). Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development . Mathematical and Computational Modelling , 23 : 47 – 87 .
   Web of Science ®Google Scholar
• Chaplain , M. , Graziano , L. , and Preziosi , L. (2006). Mathematical modeling of the loss of tissue compression responsiveness and its role in solid tumor development. Mathematical Medicine and Biology , 23: 197–229.
   PubMedGoogle Scholar
• Chesla , S. , Selvaraj , P. , and Zhu , C. ( 1998 ). Measuring two-dimensional receptor-ligand binding kinetics by micropipette . Biophysical Journal , 75 : 1553 – 1557 .
   Google Scholar
• Chu , Y. , Dufour , S. , et al. . ( 2005 ). Johnson-Kendall-Roberts theory applied to living cells . Physical Review Letters , 94 ( 2 ): 028102 .
   Web of Science ®Google Scholar
• Cickovski , T. , Huang , C. , et al. . ( 2005 ). A framework for three-dimensional simulation of morphogenesis . IEEE/ACM Transactions on Computational Biology and Bioinformatics , 2 ( 3 ): 273 – 288 .
   Google Scholar
• Dallon , J. and Othmer , H. ( 2004 ). How cellular movement determines the collective force generated by the Dictyostelium discoideum slug . Journal of Theoretical Biology , 231 : 203 – 222 .
   Google Scholar
• Dhont , J. ( 1996 ). An Introduction to Dynamics of Colloids . Amsterdam : Elsevier .
   Google Scholar
• Dormann , S. and Deutsch , A. ( 2002 ). Modeling of self-organized avascular tumor growth with a hybrid cellular automaton . In Silico Biology , 2 : 0035 .
   Google Scholar
• Drasdo , D. ( 2003 ). On selected individual-based approaches to the dynamics of multicellular systems . In W. Alt , M. Griebel , and J. Lenz (Eds.), Multiscale Modeling . Basel , Switzerland : Birkhäuser , pp. 169 – 203 .
   Google Scholar
• Drasdo , D. ( 2005 ). Coarse graining in simulated cell populations . Advances in Complex Systems , 8 : 319 – 363 .
   Web of Science ®Google Scholar
• Drasdo , D. and Hoehme , S. ( 2003 ). Individual-based approaches to birth and death in avascular tumors . Mathematical and Computational Modelling , 37 : 1163 – 1175 .
   Google Scholar
• Drasdo , D. and Hoehme , S. ( 2005 ). A single-cell based model to tumor growth in-vitro: Monolayers and spheroids . Physical Biology , 2 : 133 – 147 .
   PubMed Web of Science ®Google Scholar
• Drasdo , D. , Hoehme , S. , and Block , M. ( 2007 ). On the role of physics in the growth and pattern formation of multi-cellular systems: What can we learn from individual-cell based models? Journal of Statistical Physics , 128 : 287 – 345 .
   Web of Science ®Google Scholar
• Drasdo , D. , Kree , R. , and McCaskill , J. ( 1995 ). Monte-Carlo approach to tissue-cell populations . Physical Review E , 52 : 6635 – 6657 .
   Google Scholar
• Drasdo , D. and Kruspe , M. ( 2005 ). Emergence of cell migration and aggregation strategies in a simulated evolutionary process . Advances in Complex Systems , 8 : 285 – 318 .
   Google Scholar
• Folkman , J. and Hochberg , M. ( 1973 ). Self-regulation of growth in three dimension . Journal of Experimental Medicine , 138 : 745 – 753 .
   PubMed Web of Science ®Google Scholar
• Forgacs , G. and Newman , S. ( 2005 ). Biological Physics of the Developing Embryo . Cambridge , UK : Cambridge University Press .
   Google Scholar
• Freyer , J.P. ( 1988 ). Role of necrosis in regulating the growth saturation of multicellular spheroids . Cancer Research , 48 : 2432 – 2439 .
   PubMed Web of Science ®Google Scholar
• Freyer , J. ( 1998 ). Decreased mitochondrial function in quiescent cells isolated from multicellular tumor spheroids . Journal of Cellular Physiology , 176 : 138 – 149 .
   Google Scholar
• Freyer , J.P. and Sutherland , R.M. ( 1985 ). A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth . Journal of Cellular Physiology , 124 : 516 – 524 .
   Google Scholar
• Freyer , J.P. and Sutherland , R.M. ( 1986 ). Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply . Cancer Research , 46 : 3504 – 3512 .
   PubMedGoogle Scholar
• Galle , J. , Aust , G. , et al. . ( 2006 ). Single-cell based mathematical models to the spatio-temporal pattern formation in multi-cellular systems . Cytometry Teil A , 69 : 704 – 710 .
   Google Scholar
• Galle , J. , Löffler , M. , and Drasdo , D. (2005). Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro . Biophysical Journal , 88: 62–75.
   Google Scholar
• Gillies , R.J. and Gatenby , R.A. ( 2007 ). Hypoxia and adaptive landscapes in the evolution of carcinogenesis . Cancer and Metastasis Reviews , 26 : 311 – 317 .
   PubMed Web of Science ®Google Scholar
• Graner , F. and Glazier , J.A. ( 1992 ). Simulation of biological cell sorting using a two-dimensional extended Potts model . Physical Review Letters , 69 : 2013 – 2016 .
   PubMed Web of Science ®Google Scholar
• Hanahan , D. and Folkman , J. ( 1996 ). Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis . Cell , 86 : 353 – 364 .
   PubMed Web of Science ®Google Scholar
• Helmlinger , G. , Netti , P. , et al. . ( 1997 ). Solid stress inhibits the growth of multicellular tumor spheroids . Nature Biotechnology , 15 ( 8 ): 778 – 783 .
   PubMed Web of Science ®Google Scholar
• Hogeweg , P. ( 2000 ). Evolving mechanisms of morphogenesis: On the interplay between differential adhesion and cell differentiation . Journal of Theoretical Biology , 203 : 317 – 333 .
   PubMed Web of Science ®Google Scholar
• Huang , S. and Ingber , D. ( 1999 ). The structural and mechanical complexity of cell-growth control . Nature Cell Biology , 1 : E131 – E138 .
   PubMed Web of Science ®Google Scholar
• Ingber , D. ( 2005 ). Mechanical control of tissue growth: Function follows form . Proceedings of the National Academy of Sciences of the USA , 102 : 11571 – 11572 .
   PubMed Web of Science ®Google Scholar
• Johnson , K. , Kendall , K. , and Roberts , A. ( 1971 ). Surface energy and the contact of elastic solids . Proceedings of the Royal Society A , 324 : 301 – 313 .
   Google Scholar
• Kalliomäki , T.M. , McCallum , G. , et al. . ( 2008 ). Analysis of the effects of exposure to acute hypoxia on oxidative lesions and tumour progression in a transgenic mouse breast cancer model . BMC Cancer , 8 : 151 .
   Google Scholar
• Kreft , J. ( 2004 ). Biofilms promote altruism . Microbiology , 8 : 2751 – 2760 .
   Google Scholar
• Kreft , J. and Bonhoeffer , S. ( 2005 ). The evolution of groups of cooperating bacteria and the growth rate versus yield trade-off . Microbiology , 3 : 637 – 641 .
   Google Scholar
• Kunz-Schughart , L. ( 1999 ). Multicellular tumor spheroids: Intermediates between monolayer culture and in vivo tumor . Cell Biology International , 23 : 157 – 161 .
   PubMed Web of Science ®Google Scholar
• Landau , D. and Binder , K. ( 2000 ). A Guide to Monte Carlo Simulations in Statistical Physics . Cambridge , UK : Cambridge University Press .
   Google Scholar
• Lee , D.-S. and Rieger , H. ( 2006 ). Flow correlated percolation during vascular remodeling in growing tumor . Physical Review Letters , 96 : 4 – 7 .
   Google Scholar
• Lekka , M. , Laidler , P. , et al. . ( 1999 ). Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy . European Biophysics Journal , 28 ( 4 ): 312 – 316 .
   PubMed Web of Science ®Google Scholar
• Macklin , P. , McDougall , S. , et al. . ( 2009 ). Multiscale modeling and nonlinear simulation of vascular tumour growth . Journal of Mathematical Biology , 58 ( 4–5 ): 765 – 798 .
   PubMed Web of Science ®Google Scholar
• Mantzaris , N.V. , Webb , S. , and Othmer , H.G. ( 2004 ). Mathematical modeling of tumor-induced angiogenesis . Journal of Mathematical Biology , 49 : 111 – 187 .
   PubMed Web of Science ®Google Scholar
• Merks , R.M.H. and Glazier , J.A. ( 2005 ). A cell-centered approach to developmental biology . Physica A , 352 : 113 – 130 .
   Web of Science ®Google Scholar
• Mombach , J. and Glazier , J.A. ( 1996 ). Single cell motion in aggregates of embryonic cells . Physical Review Letters , 76 : 3032 – 3035 .
   Google Scholar
• Moreira , J. and Deutsch , A. ( 2002 ). Cellular automata models of tumour development—A critical review . Advances in Complex Systems , 5 : 247 – 267 .
   Google Scholar
• Müller-Klieser , W. ( 2000 ). Tumor biology and experimental therapeutics . Critical Reviews in Oncology/Hematology , 36 : 123 – 139 .
   Google Scholar
• Nelson , C. , Jean , R. , et al. . ( 2005 ). Mechanical control of tissue growth: Function follows form . Proceedings of the National Academy of Sciences of the USA , 102 ( 9 ): 1571 – 11572 .
   Google Scholar
• Newman , T. (2005). Modeling multi-cellular systems using sub-cellular elements. Mathematical Bioscience Engineering , 2: 613–624.
   Google Scholar
• Palsson , E. and Othmer , H. ( 2000 ). A model for individual and collective cell movement in Dictyostelium discoideum . Proceedings of the National Academy of Sciences of the USA , 12 : 10448 – 10453 .
   Google Scholar
• Pfeuty , B. , David-Pfeuty , T. , and Kaneko , K. ( 2008 ). Underlying principles of cell fate determination during G 1 -phase of the mammalian cell cycle . Cell Cycle , 7 : 3246 – 3257 .
   PubMed Web of Science ®Google Scholar
• Preziosi , L. ( 2003 ). Cancer Modelling and Simulation . Boca Raton , FL : Chapman and Hall/CRC .
   Google Scholar
• Preziosi , L. and Tosin , A. ( 2009 ). Multiphase modeling of tumour growth and extracellular matrix interaction: Mathematical tools and applications . Journal of Mathematical Biology , 58 : 625 – 656 .
   PubMed Web of Science ®Google Scholar
• Radszuweit , M. , Block , M. , et al. . ( 2009 ). Comparing the growth kinetics of cell populations in two and three dimensions . Physical Review E, Statistical Nonlinear, and Soft Matter Physics , 79 ( 5 Pt. 1 ): 051907 .
   Google Scholar
• Ramis-Conde , I. , Chaplain , M.A.J. , Anderson , A.R. , and Drasdo , D. ( 2009 ). Multi-scale modeling of cancer cell intravasation: The role of cadherins in metastasis . Physical Biology , 6 : 16008 – 16020 .
   PubMed Web of Science ®Google Scholar
• Ramis-Conde , I. , Drasdo , D. , Chaplain , M.A.J. , and Anderson , A.R. ( 2008 ). Modelling the influence of the E-cadherin-β-catenin pathway in cancer cell invasion: a multiscale approach . Biophysical Journal , 95 : 155 – 165 .
   PubMed Web of Science ®Google Scholar
• Roose , T. , Chapman , S. , and Maini , P. ( 2007 ). Mathematical models of avascular tumour growth: a review . SIAM Review , 49 : 179 – 208 .
   Web of Science ®Google Scholar
• Rosen , P. and Misfeldt , D. ( 1980 ). Cell density determines epithelial migration in culture . Proceedings of the National Academy of Sciences of the USA , 77 : 4760 – 4763 .
   PubMedGoogle Scholar
• Schaller , G. and Meyer-Hermann , M. ( 2005 ). Multicellular tumor spheroid in an off-lattice voronoidelaunay cell model . Physical Review. E , 71 ( 5 ): 1 – 16 .
   Google Scholar
• Schienbein , M. , Franke , K. , and Gruler , H. ( 1994 ). Random walk and directed movement: Comparison between inert particles and self-organized molecular machines . Physical Review E , 49 : 5462 – 5471 .
   Google Scholar
• Shraiman , B. ( 2005 ). Mechanical feedback as a possible regulator of tissue growth . Proceedings of the National Academy of Sciences of the USA , 102 : 3318 – 3323 .
   PubMed Web of Science ®Google Scholar
• Stott , E. , Britton , N. , Glazier , J.A. , and Zajac , M. ( 1999 ). Stochastic simulation of benign avascular tumor growth using the Potts model . Mathematical and Computational Modelling , 30 : 183 – 198 .
   Web of Science ®Google Scholar
• Sutherland , R. , Freyer , J. , et al. . ( 1986 ). Cellular growth and metabolic adaptations to nutrient stress environments in tumor microregions . International Journal of Radiation Oncology*Biology*Physics , 12 : 611 – 615 .
   Google Scholar
• Ward , J. and King , J. ( 1997 ). Mathematical modelling of avascular-tumor growth . IMA Journal of Mathematics Applied in Medicine and Biology , 14 : 39 – 69 .
   PubMedGoogle Scholar
• Weinberg , R. ( 2007 ). The Biology of Cancer . New York : Garland Science Publishers .
   Google Scholar