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Fassoni AC, Diaz CV, de Carvalho Braga D, Santos JLG. Dynamics and bifurcations in a model of chronic myeloid leukemia with optimal immune response windows. J Math Biol 2024; 89:35. [PMID: 39177819 DOI: 10.1007/s00285-024-02135-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Revised: 05/28/2024] [Accepted: 07/28/2024] [Indexed: 08/24/2024]
Abstract
Chronic Myeloid Leukemia is a blood cancer for which standard therapy with Tyrosine-Kinase Inhibitors is successful in the majority of patients. After discontinuation of treatment half of the well-responding patients either present undetectable levels of tumor cells for a long time or exhibit sustained fluctuations of tumor load oscillating at very low levels. Motivated by the consequent question of whether the observed kinetics reflect periodic oscillations emerging from tumor-immune interactions, in this work, we analyze a system of ordinary differential equations describing the immune response to CML where both the functional response against leukemia and the immune recruitment exhibit optimal activation windows. Besides investigating the stability of the equilibrium points, we provide rigorous proofs that the model exhibits at least two types of bifurcations: a transcritical bifurcation around the tumor-free equilibrium point and a Hopf bifurcation around a biologically plausible equilibrium point, providing an affirmative answer to our initial question. Focusing our attention on the Hopf bifurcation, we examine the emergence of limit cycles and analyze their stability through the calculation of Lyapunov coefficients. Then we illustrate our theoretical results with numerical simulations based on clinically relevant parameters. Besides the mathematical interest, our results suggest that the fluctuating levels of low tumor load observed in CML patients may be a consequence of periodic orbits arising from predator-prey-like interactions.
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MESH Headings
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/immunology
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/drug therapy
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/pathology
- Humans
- Mathematical Concepts
- Computer Simulation
- Models, Immunological
- Protein Kinase Inhibitors/therapeutic use
- Protein Kinase Inhibitors/pharmacology
- Models, Biological
- Tumor Burden/immunology
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Affiliation(s)
- Artur César Fassoni
- Instituto de Matemática e Computação, Universidade Federal de Itajubá, Itajubá, Brazil.
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2
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Malik V, Radhakrishnan N, Kaul SC, Wadhwa R, Sundar D. Computational Identification of BCR-ABL Oncogenic Signaling as a Candidate Target of Withaferin A and Withanone. Biomolecules 2022; 12:biom12020212. [PMID: 35204712 PMCID: PMC8961606 DOI: 10.3390/biom12020212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Revised: 12/28/2021] [Accepted: 01/03/2022] [Indexed: 01/09/2023] Open
Abstract
Withaferin-A (Wi-A), a secondary metabolite extracted from Ashwagandha (Withania somnifera), has been shown to possess anticancer activity. However, the molecular mechanism of its action and the signaling pathways have not yet been fully explored. We performed an inverse virtual screening to investigate its binding potential to the catalytic site of protein kinases and identified ABL as a strong candidate. Molecular docking and molecular dynamics simulations were undertaken to investigate the effects on BCR-ABL oncogenic signaling that is constitutively activated yielding uncontrolled proliferation and inhibition of apoptosis in Chronic Myeloid Leukemia (CML). We found that Wi-A and its closely related withanolide, Withanone (Wi-N), interact at both catalytic and allosteric sites of the ABL. The calculated binding energies were higher in the case of Wi-A at catalytic site (−82.19 ± 5.48) and allosteric site (−67.00 ± 4.96) as compared to the clinically used drugs Imatinib (−78.11 ± 5.21) and Asciminib (−54.00 ± 6.45) respectively. Wi-N had a lesser binding energy (−42.11 ± 10.57) compared to Asciminib at the allosteric site. The interaction and conformational changes, subjected to ligand interaction, were found to be similar to the drugs Imatinib and Asciminib. The data suggested that Ashwagandha extracts containing withanolides, Wi-A and Wi-N may serve as natural drugs for the treatment of CML. Inhibition of ABL is suggested as one of the contributing factors of anti-cancer activity of Wi-A and Wi-N, warranting further in vitro and in vivo experiments.
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Affiliation(s)
- Vidhi Malik
- DAILAB, Department of Biochemical Engineering & Biotechnology, Indian Institute of Technology (IIT)-Delhi, Hauz Khas, New Delhi 110-016, India; (V.M.); (N.R.)
| | - Navaneethan Radhakrishnan
- DAILAB, Department of Biochemical Engineering & Biotechnology, Indian Institute of Technology (IIT)-Delhi, Hauz Khas, New Delhi 110-016, India; (V.M.); (N.R.)
| | - Sunil C. Kaul
- AIST-INDIA DAILAB, DBT-AIST International Center for Translational & Environmental Research (DAICENTER), National Institute of Advanced Industrial Science & Technology (AIST), Tsukuba 305-8565, Japan; (S.C.K.); (R.W.)
| | - Renu Wadhwa
- AIST-INDIA DAILAB, DBT-AIST International Center for Translational & Environmental Research (DAICENTER), National Institute of Advanced Industrial Science & Technology (AIST), Tsukuba 305-8565, Japan; (S.C.K.); (R.W.)
| | - Durai Sundar
- DAILAB, Department of Biochemical Engineering & Biotechnology, Indian Institute of Technology (IIT)-Delhi, Hauz Khas, New Delhi 110-016, India; (V.M.); (N.R.)
- School of Artificial Intelligence, Indian Institute of Technology (IIT) Delhi, New Delhi 110-016, India
- Correspondence: ; Tel.: +91-11-2659-1066
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3
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G. Lindström HJ, Friedman R. The effects of combination treatments on drug resistance in chronic myeloid leukaemia: an evaluation of the tyrosine kinase inhibitors axitinib and asciminib. BMC Cancer 2020; 20:397. [PMID: 32380976 PMCID: PMC7204252 DOI: 10.1186/s12885-020-06782-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2019] [Accepted: 03/23/2020] [Indexed: 02/06/2023] Open
Abstract
BACKGROUND Chronic myeloid leukaemia is in principle a treatable malignancy but drug resistance is lowering survival. Recent drug discoveries have opened up new options for drug combinations, which is a concept used in other areas for preventing drug resistance. Two of these are (I) Axitinib, which inhibits the T315I mutation of BCR-ABL1, a main source of drug resistance, and (II) Asciminib, which has been developed as an allosteric BCR-ABL1 inhibitor, targeting an entirely different binding site, and as such does not compete for binding with other drugs. These drugs offer new treatment options. METHODS We measured the proliferation of KCL-22 cells exposed to imatinib-dasatinib, imatinib-asciminib and dasatinib-asciminib combinations and calculated combination index graphs for each case. Moreover, using the median-effect equation we calculated how much axitinib can reduce the growth advantage of T315I mutant clones in combination with available drugs. In addition, we calculated how much the total drug burden could be reduced by combinations using asciminib and other drugs, and evaluated which mutations such combinations might be sensitive to. RESULTS Asciminib had synergistic interactions with imatinib or dasatinib in KCL-22 cells at high degrees of inhibition. Interestingly, some antagonism between asciminib and the other drugs was present at lower degrees on inhibition. Simulations revealed that asciminib may allow for dose reductions, and its complementary resistance profile could reduce the risk of mutation based resistance. Axitinib, however, had only a minor effect on T315I growth advantage. CONCLUSIONS Given how asciminib combinations were synergistic in vitro, our modelling suggests that drug combinations involving asciminib should allow for lower total drug doses, and may result in a reduced spectrum of observed resistance mutations. On the other hand, a combination involving axitinib was not shown to be useful in countering drug resistance.
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MESH Headings
- Antineoplastic Combined Chemotherapy Protocols/pharmacology
- Axitinib/administration & dosage
- Cell Line, Tumor
- Computer Simulation
- Dasatinib/administration & dosage
- Drug Discovery/methods
- Drug Resistance, Neoplasm/genetics
- Drug Synergism
- Humans
- Imatinib Mesylate/administration & dosage
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/drug therapy
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/genetics
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/metabolism
- Mutation
- Niacinamide/administration & dosage
- Niacinamide/analogs & derivatives
- Pyrazoles/administration & dosage
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Affiliation(s)
| | - Ran Friedman
- Department of Chemistry and Biomedical Sciences, Linnæus University, Kalmar, 391 82 Sweden
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4
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Aliper A, Jellen L, Cortese F, Artemov A, Karpinsky-Semper D, Moskalev A, Swick AG, Zhavoronkov A. Towards natural mimetics of metformin and rapamycin. Aging (Albany NY) 2017; 9:2245-2268. [PMID: 29165314 PMCID: PMC5723685 DOI: 10.18632/aging.101319] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 11/02/2017] [Indexed: 12/14/2022]
Abstract
Aging is now at the forefront of major challenges faced globally, creating an immediate need for safe, widescale interventions to reduce the burden of chronic disease and extend human healthspan. Metformin and rapamycin are two FDA-approved mTOR inhibitors proposed for this purpose, exhibiting significant anti-cancer and anti-aging properties beyond their current clinical applications. However, each faces issues with approval for off-label, prophylactic use due to adverse effects. Here, we initiate an effort to identify nutraceuticals-safer, naturally-occurring compounds-that mimic the anti-aging effects of metformin and rapamycin without adverse effects. We applied several bioinformatic approaches and deep learning methods to the Library of Integrated Network-based Cellular Signatures (LINCS) dataset to map the gene- and pathway-level signatures of metformin and rapamycin and screen for matches among over 800 natural compounds. We then predicted the safety of each compound with an ensemble of deep neural network classifiers. The analysis revealed many novel candidate metformin and rapamycin mimetics, including allantoin and ginsenoside (metformin), epigallocatechin gallate and isoliquiritigenin (rapamycin), and withaferin A (both). Four relatively unexplored compounds also scored well with rapamycin. This work revealed promising candidates for future experimental validation while demonstrating the applications of powerful screening methods for this and similar endeavors.
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Affiliation(s)
- Alexander Aliper
- Insilico Medicine, Inc, Research Department, Baltimore, MD 21218, USA
| | - Leslie Jellen
- Insilico Medicine, Inc, Research Department, Baltimore, MD 21218, USA
| | - Franco Cortese
- Biogerontology Research Foundation, Research Department, Oxford, United Kingdom
- Department of Biomedical and Molecular Science, Queen's University School of Medicine, Queen's University, Kingston, ON K7L 3N6, Canada
| | - Artem Artemov
- Insilico Medicine, Inc, Research Department, Baltimore, MD 21218, USA
| | | | - Alexey Moskalev
- Laboratory of Molecular Radiobiology and Gerontology, Institute of Biology of Komi Science Center of Ural Branch of Russian Academy of Sciences, Syktyvkar, 167982, Russia
| | | | - Alex Zhavoronkov
- Insilico Medicine, Inc, Research Department, Baltimore, MD 21218, USA
- Biogerontology Research Foundation, Research Department, Oxford, United Kingdom
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5
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Grimbs A, Shrestha A, Rezk ASD, Grimbs S, Hakeem Said I, Schepker H, Hütt MT, Albach DC, Brix K, Kuhnert N, Ullrich MS. Bioactivity in Rhododendron: A Systemic Analysis of Antimicrobial and Cytotoxic Activities and Their Phylogenetic and Phytochemical Origins. FRONTIERS IN PLANT SCIENCE 2017; 8:551. [PMID: 28450876 PMCID: PMC5390042 DOI: 10.3389/fpls.2017.00551] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Accepted: 03/27/2017] [Indexed: 05/20/2023]
Abstract
The exceptional diversity of the genus Rhododendron has a strong potential for identification, characterization, and production of bioactive lead compounds for health purposes. A particularly relevant field of application is the search for new antibiotics. Here, we present a comparative analysis of nearly 90 Rhododendron species targeted toward the search for such candidate substances. Through a combination of phytochemical profiles with antimicrobial susceptibility and cytotoxicity, complemented by phylogenetic analyses, we identify seven potentially antimicrobial active but non-cytotoxic compounds in terms of mass-to-charge ratios and retention times. Exemplary bioactivity-guided fractionation for a promising Rhododendron species experimentally supports in fact one of these candidate lead compounds. By combining categorical correlation analysis with Boolean operations, we have been able to investigate the origin of bioactive effects in further detail. Intriguingly, we discovered clear indications of systems effects (synergistic interactions and functional redundancies of compounds) in the manifestation of antimicrobial activities in this plant genus.
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Affiliation(s)
- Anne Grimbs
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Abhinandan Shrestha
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Ahmed S. D. Rezk
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Sergio Grimbs
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | | | | | - Marc-Thorsten Hütt
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Dirk C. Albach
- Institute for Biology and Environmental Sciences, Carl von Ossietzky University OldenburgOldenburg, Germany
| | - Klaudia Brix
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Nikolai Kuhnert
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
| | - Matthias S. Ullrich
- Department for Life Sciences and Chemistry, Jacobs University BremenBremen, Germany
- *Correspondence: Matthias S. Ullrich
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6
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He Q, Zhu J, Dingli D, Foo J, Leder KZ. Optimized Treatment Schedules for Chronic Myeloid Leukemia. PLoS Comput Biol 2016; 12:e1005129. [PMID: 27764087 PMCID: PMC5072565 DOI: 10.1371/journal.pcbi.1005129] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Accepted: 09/02/2016] [Indexed: 11/17/2022] Open
Abstract
Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substantial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies. However, the design of such combination therapies (timing, sequence, etc.) remains an open challenge. In this work we mathematically model the dynamics of CML response to combination therapy and analyze the impact of combination treatment schedules on treatment efficacy in patients with preexisting resistance. We then propose an optimization problem to find the best schedule of multiple therapies based on the evolution of CML according to our ordinary differential equation model. This resulting optimization problem is nontrivial due to the presence of ordinary different equation constraints and integer variables. Our model also incorporates drug toxicity constraints by tracking the dynamics of patient neutrophil counts in response to therapy. We determine optimal combination strategies that maximize time until treatment failure on hypothetical patients, using parameters estimated from clinical data in the literature. Targeted therapy using imatinib, nilotinib or dasatinib has become standard treatment for chronicle myeloid leukemia. A minority of patients, however, fail to respond to treatment or relapse due to drug resistance. One primary driving factor of drug resistance are point mutations within the driving oncogene. Laboratory studies have shown that different leukemic mutants respond differently to different drugs, so a promising way to improve treatment efficacy is to combine multiple targeted therapies. We build a mathematical model to predict the dynamics of different leukemic mutants with imatinib, nilotinib and dasatinib, and employ optimization techniques to find the best treatment schedule of combining the three drugs sequentially. Our study shows that the optimally designed combination therapy is more effective at controlling the leukemic cell burden than any monotherapy under a wide range of scenarios. The structure of the optimal schedule depends heavily on the mutant types present, growth kinetics of leukemic cells and drug toxicity parameters. Our methodology is an important step towards the design of personalized optimal therapeutic schedules for chronicle myeloid leukemia.
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Affiliation(s)
- Qie He
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN, USA
| | - Junfeng Zhu
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN, USA
| | - David Dingli
- Department of Hematology, Mayo Clinic, Rochester, MN, USA
| | - Jasmine Foo
- Department of Mathematics, University of Minnesota, Minneapolis, MN
| | - Kevin Zox Leder
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN, USA
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7
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Lindsay D, Garvey CM, Mumenthaler SM, Foo J. Leveraging Hypoxia-Activated Prodrugs to Prevent Drug Resistance in Solid Tumors. PLoS Comput Biol 2016; 12:e1005077. [PMID: 27560187 PMCID: PMC4999195 DOI: 10.1371/journal.pcbi.1005077] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Accepted: 07/25/2016] [Indexed: 11/21/2022] Open
Abstract
Experimental studies have shown that one key factor in driving the emergence of drug resistance in solid tumors is tumor hypoxia, which leads to the formation of localized environmental niches where drug-resistant cell populations can evolve and survive. Hypoxia-activated prodrugs (HAPs) are compounds designed to penetrate to hypoxic regions of a tumor and release cytotoxic or cytostatic agents; several of these HAPs are currently in clinical trial. However, preliminary results have not shown a survival benefit in several of these trials. We hypothesize that the efficacy of treatments involving these prodrugs depends heavily on identifying the correct treatment schedule, and that mathematical modeling can be used to help design potential therapeutic strategies combining HAPs with standard therapies to achieve long-term tumor control or eradication. We develop this framework in the specific context of EGFR-driven non-small cell lung cancer, which is commonly treated with the tyrosine kinase inhibitor erlotinib. We develop a stochastic mathematical model, parametrized using clinical and experimental data, to explore a spectrum of treatment regimens combining a HAP, evofosfamide, with erlotinib. We design combination toxicity constraint models and optimize treatment strategies over the space of tolerated schedules to identify specific combination schedules that lead to optimal tumor control. We find that (i) combining these therapies delays resistance longer than any monotherapy schedule with either evofosfamide or erlotinib alone, (ii) sequentially alternating single doses of each drug leads to minimal tumor burden and maximal reduction in probability of developing resistance, and (iii) strategies minimizing the length of time after an evofosfamide dose and before erlotinib confer further benefits in reduction of tumor burden. These results provide insights into how hypoxia-activated prodrugs may be used to enhance therapeutic effectiveness in the clinic. It has been suggested that one key factor driving the emergence of drug resistance is the spatial heterogeneity in the distribution of drug and oxygen throughout a tumor due to disorganized tumor vasculatures. Researchers have developed a class of novel drugs that penetrate to hypoxic regions where they are activated to kill tumor cells. The inclusion of these drugs, called hypoxia-activated prodrugs (HAPs) alongside standard therapies in combination may be the key to long-term tumor control or eradication. However, identifying the right timing and administration sequence of combination therapies is an extremely difficult task, and the time and human costs of clinical trials to investigate even a few options is often prohibitive. In this work we design a mathematical model based upon evolutionary principles to investigate the potential of combining HAPs with standard targeted therapy for a specific example in non-small cell lung cancer. We formulate novel toxicity constraints from existing clinical data to estimate the shape of the tolerated drug combination treatment space. We find that (i) combining these therapies delays resistance longer than any monotherapy schedule with either evofosfamide or erlotinib alone, and (ii) the best strategy for combination involves single doses of each drug sequentially administered in an alternating sequence. These model predictions of tumor dynamics during treatment provide insight into the role of the tumor microenvironment in combination therapy and identify treatment hypotheses for further experimental and clinical testing.
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Affiliation(s)
- Danika Lindsay
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota, United States of America
| | - Colleen M. Garvey
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, California, United States of America
| | - Shannon M. Mumenthaler
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, California, United States of America
- * E-mail: (SMM); (JF)
| | - Jasmine Foo
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota, United States of America
- * E-mail: (SMM); (JF)
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Badri H, Ramakrishnan J, Leder K. Minimizing metastatic risk in radiotherapy fractionation schedules. Phys Med Biol 2015; 60:N405-17. [PMID: 26509743 DOI: 10.1088/0031-9155/60/22/n405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells while keeping normal tissue damage below an acceptable level. A dynamic programming framework is utilized to determine the optimal fractionation scheme. We evaluated our approach on a breast cancer case using the heart and the lung as organs-at-risk (OAR). For small tumor [Formula: see text] values, hypo-fractionated schedules were optimal, which is consistent with standard models. However, for relatively larger [Formula: see text] values, we found the type of schedule depended on various parameters such as the time when metastatic risk was evaluated, the [Formula: see text] values of the OARs, and the normal tissue sparing factors. Interestingly, in contrast to standard models, hypo-fractionated and semi-hypo-fractionated schedules (large initial doses with doses tapering off with time) were suggested even with large tumor α/β values. Numerical results indicate the potential for significant reduction in metastatic risk.
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Affiliation(s)
- Hamidreza Badri
- Industrial and Systems Engineering, University of Minnesota, Minneapolis MN, USA
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9
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Lewis R, Guha R, Korcsmaros T, Bender A. Synergy Maps: exploring compound combinations using network-based visualization. J Cheminform 2015; 7:36. [PMID: 26236402 PMCID: PMC4521339 DOI: 10.1186/s13321-015-0090-6] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2015] [Accepted: 07/22/2015] [Indexed: 01/01/2023] Open
Abstract
Background The phenomenon of super-additivity of biological response to compounds applied jointly, termed synergy, has the potential to provide many therapeutic benefits. Therefore, high throughput screening of compound combinations has recently received a great deal of attention. Large compound libraries and the feasibility of all-pairs screening can easily generate large, information-rich datasets. Previously, these datasets have been visualized using either a heat-map or a network approach—however these visualizations only partially represent the information encoded in the dataset. Results A new visualization technique for pairwise combination screening data, termed “Synergy Maps”, is presented. In a Synergy Map, information about the synergistic interactions of compounds is integrated with information about their properties (chemical structure, physicochemical properties, bioactivity profiles) to produce a single visualization. As a result the relationships between compound and combination properties may be investigated simultaneously, and thus may afford insight into the synergy observed in the screen. An interactive web app implementation, available at http://richlewis42.github.io/synergy-maps, has been developed for public use, which may find use in navigating and filtering larger scale combination datasets. This tool is applied to a recent all-pairs dataset of anti-malarials, tested against Plasmodium falciparum, and a preliminary analysis is given as an example, illustrating the disproportionate synergism of histone deacetylase inhibitors previously described in literature, as well as suggesting new hypotheses for future investigation. Conclusions Synergy Maps improve the state of the art in compound combination visualization, by simultaneously representing individual compound properties and their interactions. The web-based tool allows straightforward exploration of combination data, and easier identification of correlations between compound properties and interactions.
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Affiliation(s)
- Richard Lewis
- Department of Chemistry, Centre for Molecular Informatics, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW UK
| | - Rajarshi Guha
- National Center for Advancing Translational Sciences, 9800 Medical Center Drive, Rockville, MD 20850 USA
| | - Tamás Korcsmaros
- TGAC, The Genome Analysis Centre, Norwich Research Park, Norwich, UK ; Gut Health and Food Safety Programme, Institute of Food Research, Norwich Research Park, Norwich, UK
| | - Andreas Bender
- Department of Chemistry, Centre for Molecular Informatics, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW UK
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Radivoyevitch T, Li H, Sachs RK. Etiology and treatment of hematological neoplasms: stochastic mathematical models. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2014; 844:317-46. [PMID: 25480649 DOI: 10.1007/978-1-4939-2095-2_16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
Abstract
Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.
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Affiliation(s)
- Tomas Radivoyevitch
- Epidemiology and Biostatistics, Case Western Reserve University, Cleveland, OH, USA,
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11
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Jabbour EJ, Cortes JE, Kantarjian HM. Tyrosine kinase inhibition: a therapeutic target for the management of chronic-phase chronic myeloid leukemia. Expert Rev Anticancer Ther 2013; 13:1433-52. [PMID: 24236822 PMCID: PMC4181370 DOI: 10.1586/14737140.2013.859074] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Chronic myeloid leukemia (CML) is a hematologic neoplasm with a progressive, ultimately terminal, disease course. In most cases, CML arises owing to the aberrant formation of a chimeric gene for a constitutively active tyrosine kinase. Inhibition of the signaling activity of this kinase has proved to be a highly successful treatment target, transforming the prognosis of patients with CML. New tyrosine kinase inhibitors continue to improve the management of CML, offering alternative options for those resistant to or intolerant of standard tyrosine kinase inhibitors. Here we review the pathobiology of CML and explore emerging strategies to optimize the management of chronic-phase CML, particularly first-line treatment.
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Affiliation(s)
- Elias J Jabbour
- The University of Texas, MD Anderson Cancer Center, Houston, TX, USA
| | - Jorge E Cortes
- The University of Texas, MD Anderson Cancer Center, Houston, TX, USA
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13
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Bozic I, Reiter JG, Allen B, Antal T, Chatterjee K, Shah P, Moon YS, Yaqubie A, Kelly N, Le DT, Lipson EJ, Chapman PB, Diaz LA, Vogelstein B, Nowak MA. Evolutionary dynamics of cancer in response to targeted combination therapy. eLife 2013; 2:e00747. [PMID: 23805382 PMCID: PMC3691570 DOI: 10.7554/elife.00747] [Citation(s) in RCA: 420] [Impact Index Per Article: 38.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Accepted: 05/20/2013] [Indexed: 12/16/2022] Open
Abstract
In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics. DOI:http://dx.doi.org/10.7554/eLife.00747.001 As medicine becomes increasingly personalized, more and more emphasis is being placed on the development of therapies that target specific cancer-causing mutations. But while many of these drugs are effective in the short term, and do extend patient lives, tumors tend to evolve resistance to them within a few months. The key problem is that large tumors are genetically diverse. This means that for any given treatment, there is likely to be a small population of cells within the tumor that is resistant to the effects of the drug. When the drug is given to a patient, these cells will survive and multiply and this will lead ultimately to treatment failure. Given that a single drug is therefore highly unlikely to eradicate a tumor, combinations of two or more drugs may offer a higher chance of cure. This approach has been effective in the treatment of HIV as well as certain forms of leukemia. Here, Bozic et al. present a mathematical model designed to predict the effects of combination targeted therapies on tumors, based on the data obtained from 20 melanoma (skin cancer) patients. Their model revealed that if even 1 of the 6.6 billion base pairs of DNA present in a human diploid cell has undergone a mutation that confers resistance to each of two drugs, treatment with those drugs will not lead to sustained improvement for the majority of patients. This confirms the need to develop drugs that target distinct pathways. The model also reveals that combination therapy with two drugs given simultaneously is far more effective than sequential therapy where the drugs are used one after the other. Indeed, the model of Bozic et al. indicates that sequential treatment offers no chance of a cure, even when there are no cross-resistance mutations present, whereas combination therapy offers some hope of a cure, even in the presence of cross-resistance mutations. By emphasizing the need to develop drugs that target distinct pathways, and to administer them in combination rather than sequentially, the study by Bozic et al. offers valuable advice for drug development and the design of clinical trials, as well as for clinical practice. DOI:http://dx.doi.org/10.7554/eLife.00747.002
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Affiliation(s)
- Ivana Bozic
- Program for Evolutionary Dynamics , Harvard University , Cambridge , United States ; Department of Mathematics , Harvard University , Cambridge , United States
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14
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Radivoyevitch T, Hlatky L, Landaw J, Sachs RK. Quantitative modeling of chronic myeloid leukemia: insights from radiobiology. Blood 2012; 119:4363-71. [PMID: 22353999 PMCID: PMC3362357 DOI: 10.1182/blood-2011-09-381855] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2011] [Accepted: 02/13/2012] [Indexed: 11/20/2022] Open
Abstract
Mathematical models of chronic myeloid leukemia (CML) cell population dynamics are being developed to improve CML understanding and treatment. We review such models in light of relevant findings from radiobiology, emphasizing 3 points. First, the CML models almost all assert that the latency time, from CML initiation to diagnosis, is at most ∼10 years. Meanwhile, current radiobiologic estimates, based on Japanese atomic bomb survivor data, indicate a substantially higher maximum, suggesting longer-term relapses and extra resistance mutations. Second, different CML models assume different numbers, between 400 and 10(6), of normal HSCs. Radiobiologic estimates favor values>10(6) for the number of normal cells (often assumed to be the HSCs) that are at risk for a CML-initiating BCR-ABL translocation. Moreover, there is some evidence for an HSC dead-band hypothesis, consistent with HSC numbers being very different across different healthy adults. Third, radiobiologists have found that sporadic (background, age-driven) chromosome translocation incidence increases with age during adulthood. BCR-ABL translocation incidence increasing with age would provide a hitherto underanalyzed contribution to observed background adult-onset CML incidence acceleration with age, and would cast some doubt on stage-number inferences from multistage carcinogenesis models in general.
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MESH Headings
- Adult
- Humans
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/diagnosis
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/epidemiology
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/etiology
- Leukemia, Myelogenous, Chronic, BCR-ABL Positive/therapy
- Models, Biological
- Models, Theoretical
- Nuclear Weapons
- Radiation, Ionizing
- Radiobiology/methods
- Recurrence
- Survivors/statistics & numerical data
- Time Factors
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Affiliation(s)
- Tomas Radivoyevitch
- Department of Epidemiology and Biostatistics, Case Western Reserve University, Cleveland, OH, USA
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15
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Zhu GR, Ji O, Ji JM, Zhang YC, Wu Y, Yu H, Jiang PJ, Shen Q. Combining nilotinib and imatinib improves the outcome of imatinib-resistant blast phase CML. Acta Haematol 2012; 127:152-5. [PMID: 22286512 DOI: 10.1159/000333107] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2011] [Accepted: 08/22/2011] [Indexed: 12/11/2022]
Abstract
Imatinib resistance is an important hurdle in the treatment of chronic myeloid leukemia (CML), and CML patients with this drug resistance are often given a dismal prognosis. In this case report, an imatinib-refractory blast phase CML patient was treated with a combination of imatinib and nilotinib. A complete hematologic response was achieved within 3 months, the drug combination was well tolerated, and there was a relatively long bone-marrow complete remission. These results suggest that combining imatinib and nilotinib treatment may improve the outcome of imatinib-resistant CML patients in the blast phase. We hypothesize regarding the possible mechanism for the effectiveness of the drug combination by reviewing the recent literature.
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Affiliation(s)
- Guang-Rong Zhu
- Department of Hematology, First Affiliated Hospital of Nanjing University of Chinese Medicine, China
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16
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Werner B, Lutz D, Brümmendorf TH, Traulsen A, Balabanov S. Dynamics of resistance development to imatinib under increasing selection pressure: a combination of mathematical models and in vitro data. PLoS One 2011; 6:e28955. [PMID: 22216147 PMCID: PMC3245228 DOI: 10.1371/journal.pone.0028955] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2011] [Accepted: 11/17/2011] [Indexed: 12/20/2022] Open
Abstract
In the last decade, cancer research has been a highly active and rapidly evolving scientific area. The ultimate goal of all efforts is a better understanding of the mechanisms that discriminate malignant from normal cell biology in order to allow the design of molecular targeted treatment strategies. In individual cases of malignant model diseases addicted to a specific, ideally single oncogene, e.g. Chronic myeloid leukemia (CML), specific tyrosine kinase inhibitors (TKI) have indeed been able to convert the disease from a ultimately life-threatening into a chronic disease with individual patients staying in remission even without treatment suggestive of operational cure. These developments have been raising hopes to transfer this concept to other cancer types. Unfortunately, cancer cells tend to develop both primary and secondary resistance to targeted drugs in a substantially higher frequency often leading to a failure of treatment clinically. Therefore, a detailed understanding of how cells can bypass targeted inhibition of signaling cascades crucial for malignant growths is necessary. Here, we have performed an in vitro experiment that investigates kinetics and mechanisms underlying resistance development in former drug sensitive cancer cells over time in vitro. We show that the dynamics observed in these experiments can be described by a simple mathematical model. By comparing these experimental data with the mathematical model, important parameters such as mutation rates, cellular fitness and the impact of individual drugs on these processes can be assessed. Excitingly, the experiment and the model suggest two fundamentally different ways of resistance evolution, i.e. acquisition of mutations and phenotype switching, each subject to different parameters. Most importantly, this complementary approach allows to assess the risk of resistance development in the different phases of treatment and thus helps to identify the critical periods where resistance development is most likely to occur.
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Affiliation(s)
- Benjamin Werner
- Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, Plön, Germany.
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17
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Shieh MP, Mitsuhashi M, Lilly M. Moving on up: Second-Line Agents as Initial Treatment for Newly-Diagnosed Patients with Chronic Phase CML. Clin Med Insights Oncol 2011; 5:185-99. [PMID: 21792346 PMCID: PMC3140277 DOI: 10.4137/cmo.s6416] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
The treatment of chronic myelogenous leukemia (CML) was revolutionized by the development of imatinib mesylate, a small molecule inhibitor of several protein tyrosine kinases, including the ABL1 protein tyrosine kinase. The current second generation of FDA-approved ABL tyrosine kinase inhibitors, dasatinib and nilotinib, are more potent inhibitors of BCR-ABL1 kinase in vitro. Originally approved for the treatment of patients who were refractory to or intolerant of imatinib, dasatinib and nilotinib are now also FDA approved in the first-line setting. The choice of tyrosine kinase inhibitor (ie, standard or high dose imatinib, dasatinib, nilotinib) to use for initial therapy in chronic-phase CML (CML-CP) will not always be obvious. Therapy selection will depend on both clinical and molecular factors, which we will discuss in this review.
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Affiliation(s)
- Marie P Shieh
- Division of Hematology-Oncology, Department of Medicine, and Chao Family Comprehensive Cancer Center, University of California, Irvine, CA, USA
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