Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

BMC Systems Biology

Ruth E Baker¹  DL Sean McElwain²  David I Leavesley²  Kerry J Manton²  Parvathi Haridas²  Matthew J Simpson²  Katrina K Treloar² 

[1] Centre for Mathematical Biology, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK;Tissue Repair and Regeneration Program, Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia

关键词: Mathematical model;    Circular barrier assay;    Cell–to–cell adhesion;    Cell proliferation;    Cell migration;    Cancer;    Melanoma;   

Others  :  1141706
DOI  :  10.1186/1752-0509-7-137

 received in 2013-09-11, accepted in 2013-12-05,  发布年份 2013

【 摘 要 】

Background

The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell–to–cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell–to–cell adhesion, despite the fact that cell–to-cell adhesion is thought to play an important role.

Results

We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell–to–cell adhesion strength, q, and cell proliferation rate, λ, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and λ. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell–to–cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D=161−243μm²hour⁻¹, q=0.3−0.5 (low to moderate strength) and λ=0.0305−0.0398hour⁻¹, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony.

Conclusions

Our systematic approach to identify the cell diffusivity, cell–to–cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

【 授权许可】

   
2013 Treloar et al.; licensee BioMed Central Ltd.

【 图 表 】

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【 参考文献 】

• [1]Maini P, McElwain DS, Leavesley D: Traveling wave model to interpret a wound–healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng 2004, 10:475-482.
• [2]Swanson K, Bridge C, Murray J, Alvord E: Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sci 2003, 216:1-10.
• [3]Weinberg R: The biology of cancer. USA: Garland Publishing; 2006.
• [4]Ciarletta P, Foret L, BA M: The radial growth phase of malignant melanoma: multi–phase modelling, numerical simulations and linear stability analysis. J R Soc Interface 2011, 8:345-368.
• [5]Frieboes H, Edgerton M, Fruehauf J, Rose F, Worrall L, Gatenby R, Ferrari M, Cristini V: Prediction of drug response in breast cancer using integrative experimental/computational modeling. Cancer Res 2009, 69:4484-4492.
• [6]Gerlee P SN: The impact of phenotypic switching on glioblastoma growth and invasion. PLoS Comput Biol 2012, v8:e1002556.
• [7]Simpson M, Treloar K, Binder B, Haridas P, Manton K, Leavesley D, McElwain D, Baker R: Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. J R Soc Interface 2013, 10:20130007.
• [8]Bonaventure J, Domingues M, Larue L: Cellular and molecular mechanisms controlling the migration of melanocytes and melanoma cells. Nat Genet 2013, 26:316-325.
• [9]Garbe C, Peris K, Hauschild A, Saiag P, Middleton M, Spatz A, Grob J, Malvehy J, Newton-Bishop J, Stratigos A, Pehamberger H, Eggermont A: Diagnosis and treatment of melanoma. European consensus–based interdisciplinary guideline – Update 2012. Eur J Cancer 2012, 48:2375-2390.
• [10]Su D, Zhang Q, Wang X, He P, Zhu Y, Zhao J, Rennert O, YA S: Two types of human malignant melanoma cell lines revealed by expression patterns of mitochondrial and survival–apoptosis genes: implications for malignant melanoma therapy. Mol Cancer Ther 2009, 8:1292-1304.
• [11]Australian Institute of Health and Welfare and Australasian Associate of Cancer Registries, Cancer in Australia: an overview, 2012 (74, CAN 70, Canberra) Accessed: August 2013, [http://www.aihw.gov.au/WorkArea/DownloadAsset.aspx?id=60129542353 webcite]
• [12]Balch C, Gershenwald J, Soong S, Thompson J, Atkins M, Byrd D, Buzaid A, Cochran A, Coit D, Ding S, Eggermont A, Flaherty K, Gimotty P, Kirkwood J, McMasters K, Mihm M, Morton D, Sober A, Sondak V: Final version of 2009 AJCC melanoma staging and classification. J Clin Oncol 2009, 20:6199-6206.
• [13]Chatelain C, Ciarletta P, Ben Amar M: Morphological changes in early melanoma development: influence of nutrients, growth inhibitors and cell–adhesion mechanisms. J Theor Biol 2011, 290:46-59.
• [14]Eikenberry S, Thalhauser C, Kuang Y: Tumor–immune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma. PLoS Comput Biol 2009, 5:e1000362.
• [15]Soong S, Shaw H, Balch C, McCarthy W, Urist M, Lee J: Predicting survival and recurrence in localised melanoma: a multivariate approach. World J Surg 1992, 290:46-59.
• [16]Sherratt J, Murray J: Models of epidermal wound healing. Proc R Soc Lond B 1990, 241:29-36.
• [17]Murray J: Mathematical biology I: an introduction. Heidelberg: Springer-Verlag; 2002.
• [18]Sengers B, Please C, Oreffo R: Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration. J R Soc Interface 2007, 4:1107-1117.
• [19]Simpson M, Baker R, McCue S: Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models. Phys Rev E 2011, 83:021901. [Epub]
• [20]Treloar K, Simpson M, McCue S: Velocity–jump models with crowding effects. Phys Rev E 2011, 84:061920. [Epub]
• [21]Deroulers C, Aubert M, Badoual M, Grammaticos B: Modeling tumor cell migration: from microscopic to macroscopic models. Phys Rev E 2009, 79:031917.
• [22]Khain E, Katakowski M, Charteris N, Jiang F, Chopp M: Migration of adhesive glioma cells: Front propagation and fingering. Phys Rev E 2012, 88:28006.
• [23]Simpson M, Towne C, McElwain DS, Upton Z: Migration of breast cancer cells: understanding the roles of volume exclusion and cell-to-cell adhesion. Phys Rev E 2010, 82:041901.
• [24]Danen E, de Vries T, Morandini R, Ghanem G, Ruiter D, van Muijen G: E–cadherin expression in human melanoma. Melanoma Res 1996, 6:127-131.
• [25]Hsu M, Meier F, Nesbit M, Hsu J, Van Belle P Elder D: E–cadherin expression in melanoma cells restores keratinocyte-mediated growth control and down-regulates expression of invasion-related adhesion receptors. Am J Pathol 2000, 156:1515-1525.
• [26]Kreiseder B, Orel L, Bujnow C, Buschek S, Pflueger M, Schuett W, Hundsberger H, de Martin H Wiesner: α–Catulin downregulates E-cadherin and promotes melanoma progression and invasion. Int J Cancer 2013, 132:521-530.
• [27]Maret D, Gruzglin E, Sadr M, Siu V, Shan W, Koch A, Seidah N, Del Maestro R Colman: Surface expression of precursor N–cadherin promotes tumor cell invasion. Neoplasia 2010, 12:1066-1080.
• [28]McGary E, Lev D, Bar-Eli M: Cellular adhesion pathways and metastasis potential of human melanoma. Cancer Biol Ther 2002, 1:459-465.
• [29]Poser I, Dominquez D, de Herrerors A, Varnai A, Buettner R, Bosserhoff A: Loss of E–cadherin expression in melanoma cells involves up–regulation of the transcriptional repressor Snail. J Biol Chem 2001, 276:24661-24666.
• [30]Alber M, Kiskowski M, Glazier J, Jiang Y: On cellular automaton approaches to modeling biological cells. IMA V Math 2003, 134:1-39.
• [31]Rejniak K, Anderson A: Single–cell–based models in biology and medicine. Birkhauser-Verlag, 2007: Mathematics and Biosciences in Interaction (MBI) series; ISBN 978-3-7643-8101-1..
• [32]Aubert M, Fereol S, Christov C, Grammaticos B: A cellular automation model for the migration of glioma cells. Phys Biol 2006, 3:93-100.
• [33]Drasdo D: Höhme: A single–cell–based model of tumor growth in vitro: monolayers and spheroids. Phys Biol 2005, 2:133-147.
• [34]Enderling H, Anderson A, Chaplain M, Beheshti A, Hlatky L, Hahnfeldt P: Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res 2009, 69:8814-8821.
• [35]Gerlee P, Anderson A: Evolution of cell motility in an individual–based model of tumour growth. J Theor Biol 2009, 259:67-83.
• [36]Graner F, Glazier J: Simulation of biological cell sorting using a two–dimensional extended potts model. Phys Rev Lett 1992, 69:2013-2017.
• [37]van Leeuwen I, Mirams G, Walter A, Fletcher A, Murray P, Osborne J, Varma S, Young S, Cooper J, Doyle B, Pitt-Francis J, Momtahan L, Pathmanathan P, Whiteley J, Chapman S, Gavaghan D, Jensen O, King J, Maini P, Waters S, Byrne H: An integrative computational model for intestinal tissue removal. Cell Prolif 2009, 42:617-636.
• [38]Rejniak K, Anderson A: Hybrid models of tumor growth. Wiley Interdiscip Rev Syst Biol Med 2010, 3:115-125.
• [39]Sottoriva A, Verhoeff J, Borovski T, McWeeney S, Naumov L, Medema J, Sloot P, Vermeulen L: Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res 2010, 70:46-56.
• [40]Deisboeck T, Wang Z, Macklin P: Multiscale cancer modeling. Annu Rev Biomed Eng 2011, 13:127-155.
• [41]Walker D, Southgate J: The virtual cell – a candidate coordinator for ‘middle–out’ modelling of biological systems. Brief Bioinforma 2009, 10:450-461.
• [42]Khain E, Sander L, Scheider-Mizell C: The role of cell–cell adhesion in wound healing. J Stat Phys 2007, 128:209-218.
• [43]Khain E, Schneider-Mizell C, Nowicki M, Chiocca A, Lawler S, Sander L: Pattern formation of glioma cells: effects of adhesion. Europhys Lett 2009, 88:28006.
• [44]Khain E, Katakowski M, Hopkins S, Szalad A, Zheng X, Jiang F, Chopp M: Collective behavior of brain tumor cells: the role of hypoxia. Phys Rev E 2012, 83:031920.
• [45]Kam Y, Guess C, Estrada L, Weidow B, Quaranta V: A novel circular invasion assay mimics in vivo invasive behavior of cancer cell lines and distinguishes single-cell motility in vitro. BMC Cancer 2008, 8:198-210. BioMed Central Full Text
• [46]Van Horssen R, Ten Hagen T: Crossing barriers: the new dimension of 2D cell migration assays. J Cell Physiol 2010, 226:288-290.
• [47]Li G, Satyamoorthy K, Herlyn M: N–cadherin–mediated intercellular interactions promote survival and migration of melanoma cells. Cancer Res 2001, 61:3819-3825.
• [48]Gray-Schopfer V, Wellbrock C, Marais R: Melanoma biology and new targeted therapy. Nature 2007, 445:851-857.
• [49]Pavey S, Johansson P, Packer L, Taylor J, Stark M, Pollock P, Walker G, Boyle G, Harper U, Cozzi S, Hansen K, Yudt L, Schmidt C, Hersey P, Ellem K, O’Rourke M, Parsons P, Meltzer P, Ringnér M, Hayward N: Microarray expression profiling in melanoma reveals a BRAF mutation signature. Oncogene 2004, 23:4060-4067.
• [50]Pope J, Morrison L, Moss D, Parsons P, Mary SR: Human malignant melanoma cell lines. Pathology 1979, 11:191-195.
• [51]Whitehead R, Little J: Tissue culture studies on human malignant melanoma. Pigment Cell 1973, 1:382-389.
• [52]Kalluri R, Weinberg R: The basics of epithelial–mesenchymal transition. J Clin Invest 2009, 119:1420-1428.
• [53]Zeisberg M, Neilson E: Biomarkers for epithelial–mesenchymal transitions. J Clin Invest 2009, 119:1429-1437.
• [54]Khain E, Sander L: Generalized Cahn–Hilliard equation for biological applications. Phys Rev E 2008, 77:051129.
• [55]Codling E, Plank M, Benhamou S: Random walks models in biology. J R Soc Interface 2008, 5:813-834.
• [56]ImageJ user guide: research services branch, national institute of health Accessed: August 2013, [http://rsbweb.nih.gov/ij/docs/guide/146-29.html webcite]
• [57]Simpson M, Landman K, Hughes B: Cell invasion with proliferation mechanisms motivated by time–lapse data. Physica A 2010, 389:3779-3790.
• [58]Chowdhury D, Schadschneider A, Nishinari K: Physics of transport and traffic phenomena in biology: from molecular motors and cells to organisms. Phys Life Rev 2005, 2:318-652.
• [59]Søndergaard J, Nazarian R, Wang Q, Guo D, Hsueh T, Mok S, Sazegar H, MacConaill L, Barretina J, Kehoe S, Attar N, von Euw E, Zuckerman J, Chmielowski B, Comin-Anduix B, Koya R, Mischel P, Lo R, Ribas A: Research Differential sensitivity of melanoma cell lines with BRAFV600E mutation to the specific Raf inhibitor PLX4032. J Transl Med 2010, 8:1479-5876.
• [60]Sadeghi M, Seitz B, Hayashi S, LaBree L, McDonnell P: In vitro effects of mitomycin-c on human keratocytes. J Refract Surg 1998, 14:534-540.
• [61]McKenzie A, Campbell S, Howe A: Protein Kinase A activity and anchoring are required for ovarian cancer cell migration and invasion. PLoS ONE 2011, 6:e26552.
• [62]Treloar K, Simpson M: Sensitivity of edge detection methods for quantifying cell migration assays. PLoS ONE 2013, 8:e67389.
• [63]Hackett-Jones E, Landman K, Newgreen D, Zhang D: On the role of differential adhesion in gangliogenesis in the enteric nervous system. J Theor Biol 2011, 287:148-159.
• [64]Simpson M, Sharp J, Baker R: Distinguishing between mean–field, moment dynamics and stochastic descriptions of birth–death–movement processes. Physica A: Stat Mech Appl 2013, 395:236-246.
• [65]Decaestecker C, Debeir O, Van Ham P Kiss: Can anti-migratory drugs be screened in vitro? a review of 2d and 3d assays for the quantitative analysis of cell migration. Med Res Rev 2007, 27:149-176.
• [66]Deisboeck T, Berens M, Kansal A, Torquato S, Stemmer-Rachamimov A, Chiocca E: Pattern of self-organization in tumour systems: complex growth dynamics in a novel brain tumour spheroid model. Cell Prolif 2001, 34:115-134.
• [67]Lorensen W, Cline H: Marching cubes: a high resolution 3D surface construction algorithm. Comp Graph 1987, 752:163-169.
• [68]Friedrich J, Seidel C, Ebner R, Kunz-Schughart L: Spheroid–based drug screen: considerations and practical approach. Nat Protoc 2009, 4:309-324.
• [69]Kramer N, Walzl A, Unger C, Rosner M, Krupitza G, Hengstschlager M, Dolznig H: In vitro cell migration and invasion assays. Mutat Res 2013, 21:10-24.
• [70]Hanahan D, Weinberg R: Hallmarks of cancer: the next generation. Cell 2011, 144:646-674.
• [71]Frixen U, Behrens J, Sachs M, Eberle G, Voss B, Warda A, Löchner D, Birchmeier W: E–cadherin–mediated cell–cell adhesion prevents invasiveness of human carcinoma cells. J Cell Biol 1991, 113:173-85.
• [72]Image Aquisition Toolbox User Guide R2012b: Mathworks Accessed: August 2013, [http://www.mathworks.com.au/products/image/ webcite]