Validation of a Mathematical Model of Cancer Incorporating Spontaneous and Induced Evolution to Drug Resistance

This paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.

[1]  Sydney M. Shaffer,et al.  Rare cell variability and drug-induced reprogramming as a mode of cancer drug resistance , 2017, Nature.

[2]  Luis Menéndez-Arias,et al.  Editorial overview: Antivirals and resistance: Advances and challenges ahead , 2014, Current Opinion in Virology.

[3]  K. Borden,et al.  Mechanisms and insights into drug resistance in cancer , 2013, Front. Pharmacol..

[4]  Jordan Ma,et al.  Mechanism of action of antitumor drugs that interact with microtubules and tubulin. , 2012 .

[5]  C. Blank,et al.  Immune resistance orchestrated by the tumor microenvironment , 2006, Immunological reviews.

[6]  Claire J. Tomlin,et al.  A model of phenotypic state dynamics initiates a promising approach to control heterogeneous malignant cell populations , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[7]  Katarzyna A Rejniak,et al.  Limiting the Development of Anti-Cancer Drug Resistance in a Spatial Model of Micrometastases , 2016, bioRxiv.

[8]  Zahra Aminzare,et al.  Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model , 2014, 1412.0780.

[9]  Ami Radunskaya,et al.  Applications of dynamical systems in biology and medicine , 2015 .

[10]  M. Jordan,et al.  Mechanism of action of antitumor drugs that interact with microtubules and tubulin. , 2002, Current medicinal chemistry. Anti-cancer agents.

[11]  Tania C Sorrell,et al.  Responding to the emergence of antifungal drug resistance: perspectives from the bench and the bedside , 2018, Future microbiology.

[12]  J. Nyce,et al.  Drug-induced DNA hypermethylation: a potential mediator of acquired drug resistance during cancer chemotherapy. , 1997, Mutation research.

[13]  Mina J Bissell,et al.  The tumor microenvironment is a dominant force in multidrug resistance. , 2012, Drug resistance updates : reviews and commentaries in antimicrobial and anticancer chemotherapy.

[14]  Mitra Shojania Feizabadi Modeling multi-mutation and drug resistance: analysis of some case studies , 2017, Theoretical Biology and Medical Modelling.

[15]  George M Church,et al.  The human microbiome harbors a diverse reservoir of antibiotic resistance genes , 2010, Virulence.

[16]  Katarzyna A. Rejniak,et al.  Systems Biology of Tumor Microenvironment , 2016, Advances in Experimental Medicine and Biology.

[17]  Robert A. Gatenby,et al.  Environment-mediated drug resistance: a major contributor to minimal residual disease , 2009, Nature Reviews Cancer.

[18]  W P Lee,et al.  The role of reduced growth rate in the development of drug resistance of HOB1 lymphoma cells to vincristine. , 1993, Cancer letters.

[19]  Fei Li,et al.  Dose-Dependent Mutation Rates Determine Optimum Erlotinib Dosing Strategies for EGFR Mutant Non-Small Cell Lung Cancer Patients , 2015, PloS one.

[20]  Lurias,et al.  MUTATIONS OF BACTERIA FROM VIRUS SENSITIVITY TO VIRUS RESISTANCE’-’ , 2003 .

[21]  A. Saltelli,et al.  Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques , 2015, 1505.02350.

[22]  I. Tannock,et al.  Drug resistance and the solid tumor microenvironment. , 2007, Journal of the National Cancer Institute.

[23]  Ben S. Wittner,et al.  A Chromatin-Mediated Reversible Drug-Tolerant State in Cancer Cell Subpopulations , 2010, Cell.

[24]  A. Pisco,et al.  Non-genetic cancer cell plasticity and therapy-induced stemness in tumour relapse: ‘What does not kill me strengthens me' , 2015, British Journal of Cancer.

[25]  D. Axelrod,et al.  Effective chemotherapy of heterogeneous and drug-resistant early colon cancers by intermittent dose schedules: a computer simulation study , 2017, Cancer Chemotherapy and Pharmacology.

[26]  Doron Levy,et al.  The dynamics of drug resistance: a mathematical perspective. , 2012, Drug resistance updates : reviews and commentaries in antimicrobial and anticancer chemotherapy.

[27]  Sojib Bin Zaman,et al.  A Review on Antibiotic Resistance: Alarm Bells are Ringing , 2017, Cureus.

[28]  Franziska Michor,et al.  Fitness Conferred by BCR-ABL Kinase Domain Mutations Determines the Risk of Pre-Existing Resistance in Chronic Myeloid Leukemia , 2011, PloS one.

[29]  P. Weiden,et al.  Vincristine neurotoxicity. , 1972, The New England journal of medicine.

[30]  P. Majumder,et al.  Temporally sequenced anticancer drugs overcome adaptive resistance by targeting a vulnerable chemotherapy-induced phenotypic transition , 2015, Nature Communications.

[31]  Sarah A Heerboth,et al.  Drug Resistance in Cancer: An Overview , 2014, Cancers.

[32]  Tae Min Kim,et al.  Heterogeneity of Genetic Changes Associated with Acquired Crizotinib Resistance in ALK-Rearranged Lung Cancer , 2013, Journal of thoracic oncology : official publication of the International Association for the Study of Lung Cancer.

[33]  Vittorio Cristini,et al.  Understanding Drug Resistance in Breast Cancer with Mathematical Oncology , 2014, Current Breast Cancer Reports.

[34]  Michael Dean,et al.  Tumour stem cells and drug resistance , 2005, Nature Reviews Cancer.

[35]  S. Legha,et al.  Vincristine Neurotoxicity , 1986, Medical toxicology.

[36]  P. Johnston,et al.  Cancer drug resistance: an evolving paradigm , 2013, Nature Reviews Cancer.

[37]  Amy Brock,et al.  Non-Darwinian dynamics in therapy-induced cancer drug resistance , 2013, Nature Communications.

[38]  S. Shackney,et al.  Growth rate patterns of solid tumors and their relation to responsiveness to therapy: an analytical review. , 1978, Annals of internal medicine.

[39]  Alexander Lorz,et al.  Emergence of drug tolerance in cancer cell populations: an evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation. , 2015, Cancer research.

[40]  Claude Preudhomme,et al.  Mutations in the ABL kinase domain pre-exist the onset of imatinib treatment. , 2003, Seminars in hematology.

[41]  Joseph M. Negri,et al.  The role of tumour–stromal interactions in modifying drug response: challenges and opportunities , 2013, Nature Reviews Drug Discovery.

[42]  Anna Sótér,et al.  Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio , 2011, Nature.

[43]  Eduardo D. Sontag,et al.  Mathematical Details on a Cancer Resistance Model , 2018, bioRxiv.

[44]  Eduardo D. Sontag,et al.  Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment , 2019, JCO clinical cancer informatics.

[45]  M. Gottesman Mechanisms of cancer drug resistance. , 2002, Annual review of medicine.

[46]  S. Wong,et al.  Epigenetic mechanisms of drug resistance: drug-induced DNA hypermethylation and drug resistance. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Mahmood Rasool,et al.  Sensitive Detection of Pre-Existing BCR-ABL Kinase Domain Mutations in CD34+ Cells of Newly Diagnosed Chronic-Phase Chronic Myeloid Leukemia Patients Is Associated with Imatinib Resistance: Implications in the Post-Imatinib Era , 2013, PloS one.

[48]  Richard F. Kefford,et al.  Preexisting MEK1P124 Mutations Diminish Response to BRAF Inhibitors in Metastatic Melanoma Patients , 2014, Clinical Cancer Research.

[49]  J. Turchi,et al.  Chemotherapy induced DNA damage response , 2013, Cancer biology & therapy.

[50]  Anil V. Rao,et al.  GPOPS-II , 2014, ACM Trans. Math. Softw..

[51]  Aleksandra Karolak,et al.  Microenvironmental Niches and Sanctuaries: A Route to Acquired Resistance. , 2016, Advances in experimental medicine and biology.