A multiscale agent-based framework integrated with a constraint-based metabolic network model of cancer for simulating avascular tumor growth.

In recent years, many efforts have been made in the field of computational modeling of cancerous tumors, in order to obtain a better understanding and predictions of their growth patterns. Furthermore, constraint-based modeling of metabolic networks has become increasingly popular, which is appropriate for the systems-level reconstruction of cell physiology. The goal of the current study is to integrate a multiscale agent-based modeling framework with a constraint-based metabolic network model of cancer cells in order to simulate the three dimensional early growth of avascular tumors. In order to develop the integrated model, a previously published generic metabolic network model of cancer cells was introduced into a multiscale agent-based framework. This model is initiated with a single tumor cell. Nutrients can diffuse through the simulation space and the cells uptake or excrete metabolites, grow, proliferate or become necrotic based on certain defined criteria and flux values of particular reactions. The simulation was run for a period of 20 days and the plots corresponding to various features such as the growth profile and necrotic core evolution were obtained. These features were compared with the ones observed in other (experimental) studies. One interesting characteristic of our modeling is that it provides us with the ability to predict gene expression patterns through different layers of a tumor, which can have important implications, especially in drug target selection in the field of cancer therapy.

[1]  R. Mahadevan,et al.  The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. , 2003, Metabolic engineering.

[2]  K. Kato,et al.  Remarkable tolerance of tumor cells to nutrient deprivation: possible new biochemical target for cancer therapy. , 2000, Cancer research.

[3]  R. Tibshirani,et al.  Repeated observation of breast tumor subtypes in independent gene expression data sets , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Sayed-Amir Marashi,et al.  Biomedical applications of cell- and tissue-specific metabolic network models , 2017, J. Biomed. Informatics.

[5]  B. Palsson,et al.  Formulating genome-scale kinetic models in the post-genome era , 2008, Molecular systems biology.

[6]  Matthew G. Vander Heiden,et al.  Metabolic targets for cancer therapy , 2013, Nature Reviews Drug Discovery.

[7]  S Torquato,et al.  Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. , 2000, Journal of theoretical biology.

[8]  R. Deberardinis,et al.  The biology of cancer: metabolic reprogramming fuels cell growth and proliferation. , 2008, Cell metabolism.

[9]  T Vogelsaenger,et al.  Recent progress in modelling and simulation of three-dimensional tumor growth and treatment. , 1985, Bio Systems.

[10]  S. V. Sotirchos,et al.  Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids , 1992, Cell proliferation.

[11]  Joseph M. Martel,et al.  Three-Dimensional Holographic Refractive-Index Measurement of Continuously Flowing Cells in a Microfluidic Channel. , 2014, Physical review applied.

[12]  L. Kunz-Schughart,et al.  Three‐dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation , 1996, International journal of cancer.

[13]  D. Hanahan,et al.  Hallmarks of Cancer: The Next Generation , 2011, Cell.

[14]  J. Blenis,et al.  Identification of a small molecule inhibitor of 3-phosphoglycerate dehydrogenase to target serine biosynthesis in cancers , 2016, Proceedings of the National Academy of Sciences.

[15]  T. Yoshikawa,et al.  Glucose uptake in the human gastric cancer cell line, MKN28, is increased by insulin stimulation. , 1999, Cancer letters.

[16]  David S. Wishart,et al.  HMDB 3.0—The Human Metabolome Database in 2013 , 2012, Nucleic Acids Res..

[17]  Merisa Nisic,et al.  Circulating Tumor Cell Enrichment Based on Physical Properties , 2013, Journal of laboratory automation.

[18]  B. Palsson,et al.  How will bioinformatics influence metabolic engineering? , 1998, Biotechnology and bioengineering.

[19]  Sean Luke,et al.  MASON: A Multiagent Simulation Environment , 2005, Simul..

[20]  Michael A. Teitell,et al.  Live Cell Interferometry Quantifies Dynamics of Biomass Partitioning during Cytokinesis , 2014, PloS one.

[21]  Xiaobo Zhou,et al.  Computational Modeling of 3D Tumor Growth and Angiogenesis for Chemotherapy Evaluation , 2014, PloS one.

[22]  T. Deisboeck,et al.  Simulating non-small cell lung cancer with a multiscale agent-based model , 2007, Theoretical Biology and Medical Modelling.

[23]  S. V. Sotirchos,et al.  Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH , 1992, Journal of cellular physiology.

[24]  Erwin P. Gianchandani,et al.  The application of flux balance analysis in systems biology , 2010, Wiley interdisciplinary reviews. Systems biology and medicine.

[25]  V. P. Collins,et al.  Formation and growth of multicellular spheroids of human origin , 1983, International journal of cancer.

[26]  Eytan Ruppin,et al.  Computational evaluation of cellular metabolic costs successfully predicts genes whose expression is deleterious , 2013, Proceedings of the National Academy of Sciences.

[27]  Joseph D Butner,et al.  Simulating cancer growth with multiscale agent-based modeling. , 2015, Seminars in cancer biology.

[28]  T. Sauter,et al.  Constraint Based Modeling Going Multicellular , 2016, Front. Mol. Biosci..

[29]  Roderick Edwards,et al.  Theoretical Biology and Medical Modelling Open Access a Stochastic Model for Circadian Rhythms from Coupled Ultradian Oscillators , 2007 .

[30]  E. T. Gawlinski,et al.  A reaction-diffusion model of cancer invasion. , 1996, Cancer research.

[31]  P. Vaupel,et al.  Oxygen diffusivity in tumor tissue (DS-Carcinosarcoma) under temperature conditions within the range of 20–40°C , 1977, Pflügers Archiv.

[32]  G. Buettner,et al.  The rate of oxygen utilization by cells. , 2011, Free radical biology & medicine.

[33]  Sayed-Amir Marashi,et al.  Reconstruction of a generic metabolic network model of cancer cells. , 2014, Molecular bioSystems.

[34]  Alex H. Lang,et al.  Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics. , 2014, Cell reports.

[35]  Ronan M. T. Fleming,et al.  Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0 , 2007, Nature Protocols.

[36]  S. Webb,et al.  A cellular automaton model examining the effects of oxygen, hydrogen ions and lactate on early tumour growth , 2014, Journal of mathematical biology.

[37]  L. H. Gray,et al.  The Histological Structure of Some Human Lung Cancers and the Possible Implications for Radiotherapy , 1955, British Journal of Cancer.

[38]  T. Deisboeck,et al.  Development of a three-dimensional multiscale agent-based tumor model: simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. , 2006, Journal of theoretical biology.

[39]  Conan K. N. Li The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis , 1982, Cancer.

[40]  K Groebe,et al.  On the relation between size of necrosis and diameter of tumor spheroids. , 1996, International journal of radiation oncology, biology, physics.

[41]  B. Palsson The challenges of in silico biology , 2000, Nature Biotechnology.

[42]  Albert Lai,et al.  Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. , 2009, Cancer research.

[43]  A S Glicksman,et al.  Growth in solid heterogeneous human colon adenocarcinomas: comparison of simple logistical models , 1987, Cell and tissue kinetics.

[44]  Michael A Henson,et al.  Incorporating energy metabolism into a growth model of multicellular tumor spheroids. , 2006, Journal of theoretical biology.

[45]  J. Carlsson,et al.  Proliferation and viability in cellular spheroids of human origin. , 1978, Cancer research.

[46]  Jason A. Papin,et al.  Novel Multiscale Modeling Tool Applied to Pseudomonas aeruginosa Biofilm Formation , 2013, PloS one.

[47]  J. Carlsson,et al.  Relations between ph, oxygen partial pressure and growth in cultured cell spheroids , 1988, International journal of cancer.

[48]  A. Bonanno,et al.  Histologic coagulative tumour necrosis as a prognostic indicator of aggressiveness in renal, lung, thyroid and colorectal carcinomas: A brief review. , 2012, Oncology letters.

[49]  Hulin Wu,et al.  Multi-scale agent-based modeling on melanoma and its related angiogenesis analysis , 2013, Theoretical Biology and Medical Modelling.

[50]  Yousef Jamali,et al.  An agent based model of integrin clustering: Exploring the role of ligand clustering, integrin homo-oligomerization, integrin-ligand affinity, membrane crowdedness and ligand mobility , 2013, J. Comput. Phys..

[51]  V. Mootha,et al.  Metabolite Profiling Identifies a Key Role for Glycine in Rapid Cancer Cell Proliferation , 2012, Science.

[52]  Z Bajzer,et al.  Analysis of growth of multicellular tumour spheroids by mathematical models , 1994, Cell proliferation.

[53]  L. Norton A Gompertzian model of human breast cancer growth. , 1988, Cancer research.

[54]  Xiang-Sun Zhang,et al.  Two-stage flux balance analysis of metabolic networks for drug target identification , 2011, BMC Systems Biology.

[55]  Stefan Walenta,et al.  Metabolic Imaging in Multicellular Spheroids of Oncogene-transfected Fibroblasts , 2000, The journal of histochemistry and cytochemistry : official journal of the Histochemistry Society.

[56]  E. Milotti,et al.  Emergent Properties of Tumor Microenvironment in a Real-Life Model of Multicell Tumor Spheroids , 2010, PloS one.

[57]  P. Maini,et al.  A cellular automaton model for tumour growth in inhomogeneous environment. , 2003, Journal of theoretical biology.

[58]  Xiaobo Zhou,et al.  Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: Incorporating EGFR signaling pathway and angiogenesis , 2012, BMC Bioinformatics.

[59]  A. Burgard,et al.  Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization , 2003, Biotechnology and bioengineering.

[60]  Jeffrey D Orth,et al.  What is flux balance analysis? , 2010, Nature Biotechnology.