1
|
Wang T, Zou X. Dynamic analysis of a drug resistance evolution model with nonlinear immune response. Math Biosci 2024; 374:109239. [PMID: 38906526 DOI: 10.1016/j.mbs.2024.109239] [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: 01/14/2024] [Revised: 06/03/2024] [Accepted: 06/10/2024] [Indexed: 06/23/2024]
Abstract
Recent studies have utilized evolutionary mechanisms to impede the emergence of drug-resistant populations. In this paper, we develop a mathematical model that integrates hormonal treatment, immunotherapy, and the interactions among three cell types: drug-sensitive cancer cells, drug-resistant cancer cells and immune effector cells. Dynamical analysis is performed, examining the existence and stability of equilibria, thereby confirming the model's interpretability. Model parameters are calibrated using available prostate cancer data and literature. Through bifurcation analysis for drug sensitivity under different immune effector cells recruitment responses, we find that resistant cancer cells grow rapidly under weak recruitment response, maintain at a low level under strong recruitment response, and both may occur under moderate recruitment response. To quantify the competitiveness of sensitive and resistant cells, we introduce the comprehensive measures R1 and R2, respectively, which determine the outcome of competition. Additionally, we introduce the quantitative indicators CIE1 and CIE2 as comprehensive measures of the immune effects on sensitive and resistant cancer cells, respectively. These two indicators determine whether the corresponding cancer cells can maintain at a low level. Our work shows that the immune system is an important factor affecting the evolution of drug resistance and provides insights into how to enhance immune response to control resistance.
Collapse
Affiliation(s)
- Tengfei Wang
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.
| | - Xiufen Zou
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.
| |
Collapse
|
2
|
Vibishan B, B V H, Dey S. A resource-based mechanistic framework for castration-resistant prostate cancer (CRPC). J Theor Biol 2024; 587:111806. [PMID: 38574968 DOI: 10.1016/j.jtbi.2024.111806] [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: 09/18/2023] [Revised: 02/04/2024] [Accepted: 03/25/2024] [Indexed: 04/06/2024]
Abstract
Cancer therapy often leads to the selective elimination of drug-sensitive cells from the tumour. This can favour the growth of cells resistant to the therapeutic agent, ultimately causing a tumour relapse. Castration-resistant prostate cancer (CRPC) is a well-characterised instance of this phenomenon. In CRPC, after systemic androgen deprivation therapy (ADT), a subset of drug-resistant cancer cells autonomously produce testosterone, thus enabling tumour regrowth. A previous theoretical study has shown that such a tumour relapse can be delayed by inhibiting the growth of drug-resistant cells using biotic competition from drug-sensitive cells. In this context, the centrality of resource dynamics to intra-tumour competition in the CRPC system indicates clear scope for the construction of theoretical models that can explicitly incorporate the underlying mechanisms of tumour ecology. In the current study, we use a modified logistic framework to model cell-cell interactions in terms of the production and consumption of resources. Our results show that steady state composition of CRPC can be understood as a composite function of the availability and utilisation efficiency of two resources-oxygen and testosterone. In particular, we show that the effect of changing resource availability or use efficiency is conditioned by their general abundance regimes. Testosterone typically functions in trace amounts and thus affects steady state behaviour of the CRPC system differently from oxygen, which is usually available at higher levels. Our data thus indicate that explicit consideration of resource dynamics can produce novel and useful mechanistic understanding of CRPC. Furthermore, such a modelling approach also incorporates variables into the system's description that can be directly measured in a clinical context. This is therefore a promising avenue of research in cancer ecology that could lead to therapeutic approaches that are more clearly rooted in the biology of CRPC.
Collapse
Affiliation(s)
- B Vibishan
- Department of Biology, Indian Institute of Science Education and Research (IISER) Pune, Pune, Maharashtra, India.
| | - Harshavardhan B V
- Department of Biology, Indian Institute of Science Education and Research (IISER) Pune, Pune, Maharashtra, India; IISc Mathematics Initiative, Indian Institute of Science, Bangalore, Karnataka, India.
| | - Sutirth Dey
- Department of Biology, Indian Institute of Science Education and Research (IISER) Pune, Pune, Maharashtra, India.
| |
Collapse
|
3
|
Wang M, Scott JG, Vladimirsky A. Threshold-awareness in adaptive cancer therapy. PLoS Comput Biol 2024; 20:e1012165. [PMID: 38875286 PMCID: PMC11210878 DOI: 10.1371/journal.pcbi.1012165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 06/27/2024] [Accepted: 05/09/2024] [Indexed: 06/16/2024] Open
Abstract
Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative "cost" of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified cost threshold (or a "budget"). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such "threshold-aware" optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new "threshold-aware" policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.
Collapse
Affiliation(s)
- MingYi Wang
- Center for Applied Mathematics, Cornell University, Ithaca, New York, United States of America
| | - Jacob G. Scott
- Department of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, Ohio, United States of America
| | - Alexander Vladimirsky
- Department of Mathematics and Center for Applied Mathematics, Cornell University, Ithaca, New York, United States of America
| |
Collapse
|
4
|
Weaver DT, King ES, Maltas J, Scott JG. Reinforcement learning informs optimal treatment strategies to limit antibiotic resistance. Proc Natl Acad Sci U S A 2024; 121:e2303165121. [PMID: 38607932 PMCID: PMC11032439 DOI: 10.1073/pnas.2303165121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 02/23/2024] [Indexed: 04/14/2024] Open
Abstract
Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent, or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that it is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 [Formula: see text]-lactam antibiotics with which to treat the simulated Escherichia coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1,024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.
Collapse
Affiliation(s)
- Davis T. Weaver
- Case Western Reserve University School of Medicine, Cleveland, OH44106
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland, OH44106
| | - Eshan S. King
- Case Western Reserve University School of Medicine, Cleveland, OH44106
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland, OH44106
| | - Jeff Maltas
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland, OH44106
| | - Jacob G. Scott
- Case Western Reserve University School of Medicine, Cleveland, OH44106
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland, OH44106
- Department of Physics, Case Western Reserve University, Cleveland, OH44106
| |
Collapse
|
5
|
Alvarez FE, Viossat Y. Tumor containment: a more general mathematical analysis. J Math Biol 2024; 88:41. [PMID: 38446165 DOI: 10.1007/s00285-024-02062-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Revised: 02/07/2024] [Accepted: 02/11/2024] [Indexed: 03/07/2024]
Abstract
Clinical and pre-clinical data suggest that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.
Collapse
Affiliation(s)
- Frank Ernesto Alvarez
- CEREMADE, CNRS, Université Paris-Dauphine, Université PSL, Place du Maréchal De Lattre De Tassigny, 75016, Paris, France.
- GMM, INSA Toulouse, 135 Avenue de Rangueil, 31000, Toulouse, France.
| | - Yannick Viossat
- CEREMADE, CNRS, Université Paris-Dauphine, Université PSL, Place du Maréchal De Lattre De Tassigny, 75016, Paris, France
| |
Collapse
|
6
|
Yankeelov TE, Hormuth DA, Lima EA, Lorenzo G, Wu C, Okereke LC, Rauch GM, Venkatesan AM, Chung C. Designing clinical trials for patients who are not average. iScience 2024; 27:108589. [PMID: 38169893 PMCID: PMC10758956 DOI: 10.1016/j.isci.2023.108589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024] Open
Abstract
The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.
Collapse
Affiliation(s)
- Thomas E. Yankeelov
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Oncology, The University of Texas at Austin, Austin, TX 78712, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX 78712, USA
- Division of Diagnostic Imaging, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77030, USA
| | - David A. Hormuth
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX 78712, USA
| | - Ernesto A.B.F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
- Texas Advanced Computer Center, The University of Texas at Austin, Austin, TX 78712, USA
| | - Guillermo Lorenzo
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Civil Engineering and Architecture, University of Pavia, 27100 Pavia, Italy
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
| | - Lois C. Okereke
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
| | - Gaiane M. Rauch
- Department of Abdominal Imaging, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77030, USA
| | - Aradhana M. Venkatesan
- Department of Abdominal Imaging, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77030, USA
| | - Caroline Chung
- Department of Radiation Oncology, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77030, USA
| |
Collapse
|
7
|
Zhang L, Ma J, Liu L, Li G, Li H, Hao Y, Zhang X, Ma X, Chen Y, Wu J, Wang X, Yang S, Xu S. Adaptive therapy: a tumor therapy strategy based on Darwinian evolution theory. Crit Rev Oncol Hematol 2023; 192:104192. [PMID: 37898477 DOI: 10.1016/j.critrevonc.2023.104192] [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: 08/27/2022] [Revised: 04/07/2023] [Accepted: 10/22/2023] [Indexed: 10/30/2023] Open
Abstract
Cancer progression is a dynamic process of continuous evolution, in which genetic diversity and heterogeneity are generated by clonal and subclonal amplification based on random mutations. Traditional cancer treatment strategies have a great challenge, which often leads to treatment failure due to drug resistance. Integrating evolutionary dynamics into treatment regimens may be an effective way to overcome the problem of drug resistance. In particular, a potential treatment is adaptive therapy, which strategy advocates containment strategies that adjust the treatment cycles according to tumor evolution to control the growth of treatment-resistant cells. In this review, we first summarize the shortcomings of traditional tumor treatment methods in evolution and then introduce the theoretical basis and research status of adaptive therapy. By analyzing the limitations of adaptive therapy and exploring possible solutions, we can broaden people's understanding of adaptive therapy and provide new insights and strategies for tumor treatment.
Collapse
Affiliation(s)
- Lei Zhang
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Jianli Ma
- Department of Radiotherapy, Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Lei Liu
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Guozheng Li
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Hui Li
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Yi Hao
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Xin Zhang
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Xin Ma
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Yihai Chen
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Jiale Wu
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Xinheng Wang
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Shuai Yang
- Harbin Medical University Cancer Hospital, Harbin, 150040, China
| | - Shouping Xu
- Harbin Medical University Cancer Hospital, Harbin, 150040, China.
| |
Collapse
|
8
|
Weaver DT, King ES, Maltas J, Scott JG. Reinforcement Learning informs optimal treatment strategies to limit antibiotic resistance. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.12.523765. [PMID: 36711676 PMCID: PMC9882109 DOI: 10.1101/2023.01.12.523765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 β-lactam antibiotics with which to treat the simulated E. coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.
Collapse
Affiliation(s)
- Davis T. Weaver
- Case Western Reserve University School of Medicine, Cleveland, OH, 44106, USA
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland OH, 44106, USA
| | - Eshan S. King
- Case Western Reserve University School of Medicine, Cleveland, OH, 44106, USA
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland OH, 44106, USA
| | - Jeff Maltas
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland OH, 44106, USA
| | - Jacob G. Scott
- Case Western Reserve University School of Medicine, Cleveland, OH, 44106, USA
- Translational Hematology Oncology Research, Cleveland Clinic, Cleveland OH, 44106, USA
- Department of Physics, Case Western Reserve University, Cleveland, OH, 44106, USA
| |
Collapse
|
9
|
Strobl MAR, Gallaher J, Robertson-Tessi M, West J, Anderson ARA. Treatment of evolving cancers will require dynamic decision support. Ann Oncol 2023; 34:867-884. [PMID: 37777307 PMCID: PMC10688269 DOI: 10.1016/j.annonc.2023.08.008] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Revised: 08/01/2023] [Accepted: 08/21/2023] [Indexed: 10/02/2023] Open
Abstract
Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.
Collapse
Affiliation(s)
- M A R Strobl
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa; Translational Hematology and Oncology Research, Lerner Research Institute, Cleveland Clinic Foundation, Cleveland, USA
| | - J Gallaher
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa
| | - M Robertson-Tessi
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa
| | - J West
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa
| | - A R A Anderson
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa.
| |
Collapse
|
10
|
Chahoud J, Anderson AR, Zhang J, Brown J, Gatenby RA. Evolutionary Dynamics and Intermittent Therapy for Metastatic Cancers. J Clin Oncol 2023; 41:4469-4471. [PMID: 37418680 PMCID: PMC10553063 DOI: 10.1200/jco.23.00647] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 06/09/2023] [Indexed: 07/09/2023] Open
Abstract
Mathematical models show that the induction period of intermittent cancer therapy drives cancer toward resistance
Collapse
Affiliation(s)
- Jad Chahoud
- Department of Genitourinary Oncology, H. Lee Moffitt Cancer Center, Tampa, FL
| | | | - Jingsong Zhang
- Department of Genitourinary Oncology, H. Lee Moffitt Cancer Center, Tampa, FL
| | - Joel Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL
| | - Robert A. Gatenby
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL
- Department of Radiology, Department of Integrated Mathematical Oncology H. Lee Moffitt Cancer Center, Tampa, FL
| |
Collapse
|
11
|
Wang M, Li G, Peng L, Hong L. Towards Optimal Control of Amyloid Fibrillation. Bull Math Biol 2023; 85:99. [PMID: 37688714 DOI: 10.1007/s11538-023-01205-9] [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: 12/02/2022] [Accepted: 08/25/2023] [Indexed: 09/11/2023]
Abstract
Epigallocatechin-3-gallate, as a representative amyloid inhibitors, has shown a promising ability against A[Formula: see text] fibrillation by directly degradating the mature fibrils. Most previous studies have been focusing on its functional mechanisms, meanwhile its optimal dosage has been seldom considered. To solve this critical issue, we refer to the generalized Logistic model for amyloid fibrillation and inhibition and adopt the optimal control theory to balance the effectiveness and cost (or toxicity) of inhibitors. The optimal control trajectory of inhibitors is analytically solved, based on which the influence of model parameters, the difference between the optimal control strategy and several other traditional drug dosing strategies are systematically compared and validated through experiments. It is found that the strategy of multiple-times adding is more suitable for a long-term disease treatment, while single high-dose therapy is preferred for a short-term treatment. We hope our findings can shed light on the rational usage of amyloid inhibitors in clinic.
Collapse
Affiliation(s)
- Mengshou Wang
- School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China
| | - Gao Li
- Fujian Engineering Research Center of New Chinese Lacquer Material, College of Material and Chemical Engineering, Minjiang University, Fuzhou, 350108, People's Republic of China
- Institute of Oceanography, Minjiang University, Fuzhou, 350108, People's Republic of China
| | - Liangrong Peng
- College of Mathematics and Data Science, Minjiang University, Fuzhou, 350108, People's Republic of China
| | - Liu Hong
- School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China.
| |
Collapse
|
12
|
Gallaher J, Strobl M, West J, Gatenby R, Zhang J, Robertson-Tessi M, Anderson AR. Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics. Cancer Res 2023; 83:2775-2789. [PMID: 37205789 PMCID: PMC10425736 DOI: 10.1158/0008-5472.can-22-2558] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Revised: 03/11/2023] [Accepted: 05/17/2023] [Indexed: 05/21/2023]
Abstract
Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores. SIGNIFICANCE Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.
Collapse
Affiliation(s)
- Jill Gallaher
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida
| | - Maximilian Strobl
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida
| | - Jeffrey West
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida
| | - Robert Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida
- Department of Radiology, Moffitt Cancer Center, Tampa, Florida
| | - Jingsong Zhang
- Department of Genitourinary Oncology, Moffitt Cancer Center, Tampa, Florida
| | - Mark Robertson-Tessi
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida
| | | |
Collapse
|
13
|
Masud MA, Kim JY, Kim E. Effective dose window for containing tumor burden under tolerable level. NPJ Syst Biol Appl 2023; 9:17. [PMID: 37221258 DOI: 10.1038/s41540-023-00279-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Accepted: 05/05/2023] [Indexed: 05/25/2023] Open
Abstract
A maximum-tolerated dose (MTD) reduces the drug-sensitive cell population, though it may result in the competitive release of drug resistance. Alternative treatment strategies such as adaptive therapy (AT) or dose modulation aim to impose competitive stress on drug-resistant cell populations by maintaining a sufficient number of drug-sensitive cells. However, given the heterogeneous treatment response and tolerable tumor burden level of individual patients, determining an effective dose that can fine-tune competitive stress remains challenging. This study presents a mathematical model-driven approach that determines the plausible existence of an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells while maintaining the tumor volume below a threshold tolerable tumor volume (TTV). We use a mathematical model that explains intratumor cell competition. Analyzing the model, we derive an EDW determined by TTV and the competitive strength. By applying a fixed endpoint optimal control model, we determine the minimal dose to contain cancer at a TTV. As a proof of concept, we study the existence of EDW for a small cohort of melanoma patients by fitting the model to longitudinal tumor response data. We performed identifiability analysis, and for the patients with uniquely identifiable parameters, we deduced patient-specific EDW and minimal dose. The tumor volume for a patient could be theoretically contained at the TTV either using continuous dose or AT strategy with doses belonging to EDW. Further, we conclude that the lower bound of the EDW approximates the minimum effective dose (MED) for containing tumor volume at the TTV.
Collapse
Affiliation(s)
- M A Masud
- Natural Product Informatics Research Center, Korea Institute of Science and Technology (KIST), Gangneung, 25451, Republic of Korea
| | - Jae-Young Kim
- Graduate School of Analytical Science and Technology (GRAST), Chungnam National University, Daejeon, 34134, Republic of Korea
| | - Eunjung Kim
- Natural Product Informatics Research Center, Korea Institute of Science and Technology (KIST), Gangneung, 25451, Republic of Korea.
| |
Collapse
|
14
|
Copperman J, Gross SM, Chang YH, Heiser LM, Zuckerman DM. Morphodynamical cell state description via live-cell imaging trajectory embedding. Commun Biol 2023; 6:484. [PMID: 37142678 PMCID: PMC10160022 DOI: 10.1038/s42003-023-04837-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 04/10/2023] [Indexed: 05/06/2023] Open
Abstract
Time-lapse imaging is a powerful approach to gain insight into the dynamic responses of cells, but the quantitative analysis of morphological changes over time remains challenging. Here, we exploit the concept of "trajectory embedding" to analyze cellular behavior using morphological feature trajectory histories-that is, multiple time points simultaneously, rather than the more common practice of examining morphological feature time courses in single timepoint (snapshot) morphological features. We apply this approach to analyze live-cell images of MCF10A mammary epithelial cells after treatment with a panel of microenvironmental perturbagens that strongly modulate cell motility, morphology, and cell cycle behavior. Our morphodynamical trajectory embedding analysis constructs a shared cell state landscape revealing ligand-specific regulation of cell state transitions and enables quantitative and descriptive models of single-cell trajectories. Additionally, we show that incorporation of trajectories into single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, (ii) better separation of phenotypes, and (iii) more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable to the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications.
Collapse
Affiliation(s)
- Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
| | - Sean M Gross
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA
| | - Young Hwan Chang
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA
| | - Laura M Heiser
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA.
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA.
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR, 97239, USA.
| |
Collapse
|
15
|
Lee ND, Kaveh K, Bozic I. Clonal interactions in cancer: integrating quantitative models with experimental and clinical data. Semin Cancer Biol 2023; 92:61-73. [PMID: 37023969 DOI: 10.1016/j.semcancer.2023.04.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 02/16/2023] [Accepted: 04/03/2023] [Indexed: 04/08/2023]
Abstract
Tumors consist of different genotypically distinct subpopulations-or subclones-of cells. These subclones can influence neighboring clones in a process called "clonal interaction." Conventionally, research on driver mutations in cancer has focused on their cell-autonomous effects that lead to an increase in fitness of the cells containing the driver. Recently, with the advent of improved experimental and computational technologies for investigating tumor heterogeneity and clonal dynamics, new studies have shown the importance of clonal interactions in cancer initiation, progression, and metastasis. In this review we provide an overview of clonal interactions in cancer, discussing key discoveries from a diverse range of approaches to cancer biology research. We discuss common types of clonal interactions, such as cooperation and competition, its mechanisms, and the overall effect on tumorigenesis, with important implications for tumor heterogeneity, resistance to treatment, and tumor suppression. Quantitative models-in coordination with cell culture and animal model experiments-have played a vital role in investigating the nature of clonal interactions and the complex clonal dynamics they generate. We present mathematical and computational models that can be used to represent clonal interactions and provide examples of the roles they have played in identifying and quantifying the strength of clonal interactions in experimental systems. Clonal interactions have proved difficult to observe in clinical data; however, several very recent quantitative approaches enable their detection. We conclude by discussing ways in which researchers can further integrate quantitative methods with experimental and clinical data to elucidate the critical-and often surprising-roles of clonal interactions in human cancers.
Collapse
Affiliation(s)
- Nathan D Lee
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America
| | - Kamran Kaveh
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America
| | - Ivana Bozic
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America; Herbold Computational Biology Program, Fred Hutchinson Cancer Center, Seattle, Washington, United States of America.
| |
Collapse
|
16
|
West J, Adler F, Gallaher J, Strobl M, Brady-Nicholls R, Brown J, Roberson-Tessi M, Kim E, Noble R, Viossat Y, Basanta D, Anderson ARA. A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation. eLife 2023; 12:e84263. [PMID: 36952376 PMCID: PMC10036119 DOI: 10.7554/elife.84263] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 02/27/2023] [Indexed: 03/24/2023] Open
Abstract
Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.
Collapse
Affiliation(s)
- Jeffrey West
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Fred Adler
- Department of Mathematics, University of UtahSalt Lake CityUnited States
- School of Biological Sciences, University of UtahSalt Lake CityUnited States
| | - Jill Gallaher
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Maximilian Strobl
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Renee Brady-Nicholls
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Joel Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Mark Roberson-Tessi
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Eunjung Kim
- Natural Product Informatics Research Center, Korea Institute of Science and TechnologyGangneungRepublic of Korea
| | - Robert Noble
- Department of Mathematics, University of LondonLondonUnited Kingdom
| | - Yannick Viossat
- Ceremade, Université Paris-Dauphine, Université Paris Sciences et LettresParisFrance
| | - David Basanta
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Alexander RA Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| |
Collapse
|
17
|
Cho H, Lewis AL, Storey KM, Byrne HM. Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types. J Theor Biol 2023; 559:111377. [PMID: 36470468 DOI: 10.1016/j.jtbi.2022.111377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Revised: 10/25/2022] [Accepted: 11/29/2022] [Indexed: 12/12/2022]
Abstract
The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously. Each design is tested on data generated from the Lotka-Volterra model with noise added, to determine efficacy in an ideal sense. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model - i.e., its ability to fit data for initial ratios other than those to which it was calibrated - is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.
Collapse
Affiliation(s)
- Heyrim Cho
- Department of Mathematics, University of California, Riverside, CA, United States of America
| | - Allison L Lewis
- Department of Mathematics, Lafayette College, Easton, PA, United States of America
| | - Kathleen M Storey
- Department of Mathematics, Lafayette College, Easton, PA, United States of America.
| | - Helen M Byrne
- Department of Mathematics, University of Oxford, Oxford, UK
| |
Collapse
|
18
|
Taleb NN, West J. Working with Convex Responses: Antifragility from Finance to Oncology. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25020343. [PMID: 36832709 PMCID: PMC9955868 DOI: 10.3390/e25020343] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 01/23/2023] [Accepted: 01/25/2023] [Indexed: 06/07/2023]
Abstract
We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define "antifragility" as a mathematical property for local beneficial convex responses and the generalization of "fragility" as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.
Collapse
Affiliation(s)
| | - Jeffrey West
- Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL 33612, USA
| |
Collapse
|
19
|
Deris A, Sohrabi-Haghighat M. Abiraterone-Docetaxel scheduling for metastatic castration-resistant prostate cancer based on evolutionary dynamics. PLoS One 2023; 18:e0282646. [PMID: 36893142 PMCID: PMC9997888 DOI: 10.1371/journal.pone.0282646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 02/20/2023] [Indexed: 03/10/2023] Open
Abstract
Patients with metastatic castration-resistant prostate cancer (mCRPC) are divided into three groups based on their response to Abiraterone treatment: best responder, responder, and non-responder. In the latter two groups, successful outcomes may not be achieved due to the development of drug-resistant cells in the tumor environment during treatment. To overcome this challenge, a secondary drug can be used to control the population of drug-resistant cells, potentially leading to a longer period of disease inhibition. This paper proposes using a combination of Docetaxel and Abiraterone in some polytherapy methods to control both the overall cancer cell population and the drug-resistant subpopulation. To investigate the competition and evolution of mCRPC cancer phenotypes, as in previous studies, the Evolutionary Game Theory (EGT) has been used as a mathematical modeling of evolutionary biology concepts.
Collapse
|
20
|
Yue R, Dutta A. Computational systems biology in disease modeling and control, review and perspectives. NPJ Syst Biol Appl 2022; 8:37. [PMID: 36192551 PMCID: PMC9528884 DOI: 10.1038/s41540-022-00247-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 09/05/2022] [Indexed: 02/02/2023] Open
Abstract
Omics-based approaches have become increasingly influential in identifying disease mechanisms and drug responses. Considering that diseases and drug responses are co-expressed and regulated in the relevant omics data interactions, the traditional way of grabbing omics data from single isolated layers cannot always obtain valuable inference. Also, drugs have adverse effects that may impair patients, and launching new medicines for diseases is costly. To resolve the above difficulties, systems biology is applied to predict potential molecular interactions by integrating omics data from genomic, proteomic, transcriptional, and metabolic layers. Combined with known drug reactions, the resulting models improve medicines' therapeutical performance by re-purposing the existing drugs and combining drug molecules without off-target effects. Based on the identified computational models, drug administration control laws are designed to balance toxicity and efficacy. This review introduces biomedical applications and analyses of interactions among gene, protein and drug molecules for modeling disease mechanisms and drug responses. The therapeutical performance can be improved by combining the predictive and computational models with drug administration designed by control laws. The challenges are also discussed for its clinical uses in this work.
Collapse
Affiliation(s)
- Rongting Yue
- Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Way, Storrs, CT, 06269, USA.
| | - Abhishek Dutta
- Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Way, Storrs, CT, 06269, USA
| |
Collapse
|
21
|
Zhang H, Lei J. Optimal treatment strategy of cancers with intratumor heterogeneity. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:13337-13373. [PMID: 36654050 DOI: 10.3934/mbe.2022625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Intratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic interaction between normal, drug-sensitive and drug-resistant cells in response to cancer treatment. Based on the proposed model, we first study the analytical conclusions, namely the nonnegativity and boundedness of solutions, and the existence and stability of steady states. Furthermore, to investigate the optimal treatment that minimizes both the cancer cells count and the total dose of drugs, we apply the Pontryagin's maximum(or minimum) principle (PMP) to explore the combination therapy strategy with either quadratic control or linear control functionals. We establish the existence and uniqueness of the quadratic control problem, and apply the forward-backward sweep method (FBSM) to solve the optimal control problems and obtain the optimal therapy scheme.
Collapse
Affiliation(s)
- Haifeng Zhang
- Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
| | - Jinzhi Lei
- School of Mathematical Sciences, Center for Applied Mathematics, Tiangong University, Tianjin 300387, China
| |
Collapse
|
22
|
Zhang J, Cunningham J, Brown J, Gatenby R. Evolution-based mathematical models significantly prolong response to abiraterone in metastatic castrate-resistant prostate cancer and identify strategies to further improve outcomes. eLife 2022; 11:e76284. [PMID: 35762577 PMCID: PMC9239688 DOI: 10.7554/elife.76284] [Citation(s) in RCA: 32] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 06/01/2022] [Indexed: 11/15/2022] Open
Abstract
Background Abiraterone acetate is an effective treatment for metastatic castrate-resistant prostate cancer (mCRPC), but evolution of resistance inevitably leads to progression. We present a pilot study in which abiraterone dosing is guided by evolution-informed mathematical models to delay onset of resistance. Methods In the study cohort, abiraterone was stopped when PSA was <50% of pretreatment value and resumed when PSA returned to baseline. Results are compared to a contemporaneous cohort who had >50% PSA decline after initial abiraterone administration and met trial eligibility requirements but chose standard of care (SOC) dosing. Results 17 subjects were enrolled in the adaptive therapy group and 16 in the SOC group. All SOC subjects have progressed, but four patients in the study cohort remain stably cycling (range 53-70 months). The study cohort had significantly improved median time to progression (TTP; 33.5 months; p<0.001) and median overall survival (OS; 58.5 months; hazard ratio, 0.41, 95% confidence interval (CI), 0.20-0.83, p<0.001) compared to 14.3 and 31.3 months in the SOC cohort. On average, study subjects received no abiraterone during 46% of time on trial. Longitudinal trial data demonstrated the competition coefficient ratio (αRS/αSR) of sensitive and resistant populations, a critical factor in intratumoral evolution, was two- to threefold higher than pre-trial estimates. Computer simulations of intratumoral evolutionary dynamics in the four long-term survivors found that, due to the larger value for αRS/αSR, cycled therapy significantly decreased the resistant population. Simulations in subjects who progressed predicted further increases in OS could be achieved with prompt abiraterone withdrawal after achieving 50% PSA reduction. Conclusions Incorporation of evolution-based mathematical models into abiraterone monotherapy for mCRPC significantly increases TTP and OS. Computer simulations with updated parameters from longitudinal trial data can estimate intratumoral evolutionary dynamics in each subject and identify strategies to improve outcomes. Funding Moffitt internal grants and NIH/NCI U54CA143970-05 (Physical Science Oncology Network).
Collapse
Affiliation(s)
- Jingsong Zhang
- Department of Genitourinary Oncology, Moffitt Cancer Center and Research InstituteTampaUnited States
| | - Jessica Cunningham
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research InstituteTampaUnited States
| | - Joel Brown
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research InstituteTampaUnited States
- Department of Biological Sciences, University of Illinois at ChicagoChicagoUnited States
| | - Robert Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research InstituteTampaUnited States
- Cancer Biology and Evolution Program, Moffitt Cancer Center and Research InstituteTampaUnited States
| |
Collapse
|
23
|
Hamilton PT, Anholt BR, Nelson BH. Tumour immunotherapy: lessons from predator-prey theory. Nat Rev Immunol 2022; 22:765-775. [PMID: 35513493 DOI: 10.1038/s41577-022-00719-y] [Citation(s) in RCA: 31] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/04/2022] [Indexed: 12/15/2022]
Abstract
With the burgeoning use of immune-based treatments for cancer, never has there been a greater need to understand the tumour microenvironment within which immune cells function and how it can be perturbed to inhibit tumour growth. Yet, current challenges in identifying optimal combinations of immunotherapies and engineering new cell-based therapies highlight the limitations of conventional paradigms for the study of the tumour microenvironment. Ecology has a rich history of studying predator-prey dynamics to discern factors that drive prey to extinction. Here, we describe the basic tenets of predator-prey theory as applied to 'predation' by immune cells and the 'extinction' of cancer cells. Our synthesis reveals fundamental mechanisms by which antitumour immunity might fail in sometimes counterintuitive ways and provides a fresh yet evidence-based framework to better understand and therapeutically target the immune-cancer interface.
Collapse
Affiliation(s)
| | - Bradley R Anholt
- Department of Biology, University of Victoria, Victoria, British Columbia, Canada
| | - Brad H Nelson
- Deeley Research Centre, BC Cancer, Victoria, British Columbia, Canada. .,Department of Biochemistry and Microbiology, University of Victoria, Victoria, British Columbia, Canada. .,Department of Medical Genetics, University of British Columbia, Vancouver, British Columbia, Canada.
| |
Collapse
|
24
|
Bayer P, Gatenby RA, McDonald PH, Duckett DR, Staňková K, Brown JS. Coordination games in cancer. PLoS One 2022; 17:e0261578. [PMID: 35061724 PMCID: PMC8782377 DOI: 10.1371/journal.pone.0261578] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Accepted: 12/03/2021] [Indexed: 11/19/2022] Open
Abstract
We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.
Collapse
Affiliation(s)
- Péter Bayer
- Toulouse School of Economics, Toulouse, France
- Institute for Advanced Study in Toulouse, Toulouse, France
| | - Robert A. Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
| | - Patricia H. McDonald
- Department of Cancer Physiology, Moffitt Cancer Center, Tampa, Florida United States of America
| | - Derek R. Duckett
- Department of Drug Discovery, Moffitt Cancer Center, Tampa, Florida, United States of America
| | - Kateřina Staňková
- Delft Institute of Applied Mathematics, Delft University, Delft, Netherlands
| | - Joel S. Brown
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, Illinois, United States of America
| |
Collapse
|
25
|
Gedye C, Navani V. Find the path of least resistance: Adaptive therapy to delay treatment failure and improve outcomes. Biochim Biophys Acta Rev Cancer 2022; 1877:188681. [PMID: 35051527 DOI: 10.1016/j.bbcan.2022.188681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 01/01/2022] [Accepted: 01/11/2022] [Indexed: 11/15/2022]
Abstract
Cytotoxic chemotherapy and targeted therapies help people with advanced cancers, but for most, treatment fails. Cancer heterogeneity is one cause of treatment failure, but also suggests an opportunity to improve outcomes; reconceptualising cancer therapy as an ecological problem offers the strategy of adaptive therapy. If an agent is active against a patient's cancer, instead of traditional continuous dosing at the maximum tolerated dose until treatment failure, the patient and their oncologist may instead choose to pause treatment as soon as the cancer responds. When tumour burden increases, the cancer is rechallenged with the same agent in hope of delivering another response, ideally before symptoms occur or quality-of-life is impacted. These 'loops' of 'pause/restart' allows an active treatment to be used strategically, to delay the development of evolutionary selection within the cancer, delaying the onset of treatment resistance, controlling the cancer for longer. Modelling predicts patients can navigate several 'loops', potentially increasing the utility of an active treatment by multiples, and early trials suggest at least doubling of progression-free survival. In this narrative review we confront how cancer heterogeneity limits treatment effectiveness, re-examine cancer as an ecological problem, review the data supporting adaptive therapy and outline the challenges and opportunities faced in clinical practice to implement this evolutionary concept. In an era where multiple novel active anti-neoplastic agents are being used with ancient inflexibile maximum tolerated dose for maximum duration approaches, adaptive dosing offers a personalised, n = 1 approach to cancer therapy selection.
Collapse
Affiliation(s)
- Craig Gedye
- Calvary Mater Newcastle, Waratah 2298, NSW, Australia; Clinical Trial Unit, Hunter Medical Research Institute, New Lambton Heights, NSW, Australia; School of Medicine and Public Health University of Newcastle, NSW, Australia.
| | - Vishal Navani
- Tom Baker Cancer Centre, University of Calgary, Calgary, AB, Canada.
| |
Collapse
|
26
|
Abstract
We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.
Collapse
Affiliation(s)
- Péter Bayer
- Toulouse School of Economics, Toulouse, France
- Institute for Advanced Study in Toulouse, Toulouse, France
| | - Robert A Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
| | - Patricia H McDonald
- Department of Cancer Physiology, Moffitt Cancer Center, Tampa, Florida United States of America
| | - Derek R Duckett
- Department of Drug Discovery, Moffitt Cancer Center, Tampa, Florida, United States of America
| | - Kateřina Staňková
- Delft Institute of Applied Mathematics, Delft University, Delft, Netherlands
| | - Joel S Brown
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, Illinois, United States of America
| |
Collapse
|
27
|
Dynamic Phenotypic Switching and Group Behavior Help Non-Small Cell Lung Cancer Cells Evade Chemotherapy. Biomolecules 2021; 12:biom12010008. [PMID: 35053156 PMCID: PMC8773639 DOI: 10.3390/biom12010008] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 12/14/2021] [Accepted: 12/17/2021] [Indexed: 12/21/2022] Open
Abstract
Drug resistance, a major challenge in cancer therapy, is typically attributed to mutations and genetic heterogeneity. Emerging evidence suggests that dynamic cellular interactions and group behavior also contribute to drug resistance. However, the underlying mechanisms remain poorly understood. Here, we present a new mathematical approach with game theoretical underpinnings that we developed to model real-time growth data of non-small cell lung cancer (NSCLC) cells and discern patterns in response to treatment with cisplatin. We show that the cisplatin-sensitive and cisplatin-tolerant NSCLC cells, when co-cultured in the absence or presence of the drug, display dynamic group behavior strategies. Tolerant cells exhibit a 'persister-like' behavior and are attenuated by sensitive cells; they also appear to 'educate' sensitive cells to evade chemotherapy. Further, tolerant cells can switch phenotypes to become sensitive, especially at low cisplatin concentrations. Finally, switching treatment from continuous to an intermittent regimen can attenuate the emergence of tolerant cells, suggesting that intermittent chemotherapy may improve outcomes in lung cancer.
Collapse
|
28
|
Belkhir S, Thomas F, Roche B. Darwinian Approaches for Cancer Treatment: Benefits of Mathematical Modeling. Cancers (Basel) 2021; 13:4448. [PMID: 34503256 PMCID: PMC8431137 DOI: 10.3390/cancers13174448] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Revised: 08/27/2021] [Accepted: 08/29/2021] [Indexed: 02/07/2023] Open
Abstract
One of the major problems of traditional anti-cancer treatments is that they lead to the emergence of treatment-resistant cells, which results in treatment failure. To avoid or delay this phenomenon, it is relevant to take into account the eco-evolutionary dynamics of tumors. Designing evolution-based treatment strategies may help overcoming the problem of drug resistance. In particular, a promising candidate is adaptive therapy, a containment strategy which adjusts treatment cycles to the evolution of the tumors in order to keep the population of treatment-resistant cells under control. Mathematical modeling is a crucial tool to understand the dynamics of cancer in response to treatments, and to make predictions about the outcomes of these treatments. In this review, we highlight the benefits of in silico modeling to design adaptive therapy strategies, and to assess whether they could effectively improve treatment outcomes. Specifically, we review how two main types of models (i.e., mathematical models based on Lotka-Volterra equations and agent-based models) have been used to model tumor dynamics in response to adaptive therapy. We give examples of the advances they permitted in the field of adaptive therapy and discuss about how these models can be integrated in experimental approaches and clinical trial design.
Collapse
Affiliation(s)
- Sophia Belkhir
- CREEC/MIVEGEC, Université de Montpellier, CNRS, IRD, 34394 Montpellier, France; (S.B.); (F.T.)
- École Normale Supérieure de Lyon, Département de Biologie, Lyon CEDEX 07, 69342 Lyon, France
| | - Frederic Thomas
- CREEC/MIVEGEC, Université de Montpellier, CNRS, IRD, 34394 Montpellier, France; (S.B.); (F.T.)
| | - Benjamin Roche
- CREEC/MIVEGEC, Université de Montpellier, CNRS, IRD, 34394 Montpellier, France; (S.B.); (F.T.)
- Departamento de Etología, Fauna Silvestre y Animales de Laboratorio, Facultad de Medicina Veterinaria y Zootecnia, Universidad Nacional Autónoma de México (UNAM), Ciudad de México 01030, Mexico
| |
Collapse
|
29
|
Wölfl B, te Rietmole H, Salvioli M, Kaznatcheev A, Thuijsman F, Brown JS, Burgering B, Staňková K. The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer. DYNAMIC GAMES AND APPLICATIONS 2021; 12:313-342. [PMID: 35601872 PMCID: PMC9117378 DOI: 10.1007/s13235-021-00397-w] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/05/2021] [Indexed: 05/05/2023]
Abstract
Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.
Collapse
Affiliation(s)
- Benjamin Wölfl
- Department of Mathematics, University of Vienna, Vienna, Austria
- Vienna Graduate School of Population Genetics, Vienna, Austria
| | - Hedy te Rietmole
- Department of Molecular Cancer Research, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Monica Salvioli
- Department of Mathematics, University of Trento, Trento, Italy
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Artem Kaznatcheev
- Department of Biology, University of Pennsylvania, Philadelphia, USA
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Frank Thuijsman
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Joel S. Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL USA
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL USA
| | - Boudewijn Burgering
- Department of Molecular Cancer Research, University Medical Center Utrecht, Utrecht, The Netherlands
- The Oncode Institute, Utrecht, The Netherlands
| | - Kateřina Staňková
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
- Department of Engineering Systems and Services, Faculty of Technology, Policy and Management, Delft University of Technology, Delft, The Netherlands
| |
Collapse
|
30
|
Bussey KJ, Davies PCW. Reverting to single-cell biology: The predictions of the atavism theory of cancer. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2021; 165:49-55. [PMID: 34371024 DOI: 10.1016/j.pbiomolbio.2021.08.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 07/30/2021] [Accepted: 08/03/2021] [Indexed: 11/24/2022]
Abstract
Cancer or cancer-like phenomena pervade multicellular life, implying deep evolutionary roots. Many of the hallmarks of cancer recapitulate unicellular modalities, suggesting that cancer initiation and progression represent a systematic reversion to simpler ancestral phenotypes in response to a stress or insult. This so-called atavism theory may be tested using phylostratigraphy, which can be used to assign ages to genes. Several research groups have confirmed that cancer cells tend to over-express evolutionary older genes, and rewire the architecture linking unicellular and multicellular gene networks. In addition, some of the elevated mutation rate - a well-known hallmark of cancer - is actually self-inflicted, driven by genes found to be homologs of the ancient SOS genes activated in stressed bacteria, and employed to evolve biological workarounds. These findings have obvious implications for therapy.
Collapse
Affiliation(s)
- Kimberly J Bussey
- Precision Medicine, Midwestern University, Glendale, AZ, USA; The BEYOND Center for Fundamental Concepts in Science, Department of Physics, Arizona State University, Tempe, AZ, USA
| | - Paul C W Davies
- The BEYOND Center for Fundamental Concepts in Science, Department of Physics, Arizona State University, Tempe, AZ, USA.
| |
Collapse
|
31
|
Pressley M, Salvioli M, Lewis DB, Richards CL, Brown JS, Staňková K. Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems. Front Ecol Evol 2021. [DOI: 10.3389/fevo.2021.681121] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in human dominated landscapes - in recognizing the need for evolutionarily informed management strategies. The speed of evolution matters. Here, we employ game-theoretic modeling to compare time to progression with continuous maximum tolerable dose to that of adaptive therapy where treatment is discontinued when the population of cancer cells gets below half of its initial size and re-administered when the cancer cells recover, forming cycles with and without treatment. We show that the success of adaptive therapy relative to continuous maximum tolerable dose therapy is much higher if the population of cancer cells is defined by two cell types (sensitive vs. resistant in a polymorphic population). Additionally, the relative increase in time to progression increases with the speed of evolution. These results hold with and without a cost of resistance in cancer cells. On the other hand, treatment-induced resistance can be modeled as a quantitative trait in a monomorphic population of cancer cells. In that case, when evolution is rapid, there is no advantage to adaptive therapy. Initial responses to therapy are blunted by the cancer cells evolving too quickly. Our study emphasizes how cancer provides a unique system for studying rapid evolutionary changes within tumor ecosystems in response to human interventions; and allows us to contrast and compare this system to other human managed or dominated systems in nature.
Collapse
|
32
|
Buhler CK, Terry RS, Link KG, Adler FR. Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:6305-6327. [PMID: 34517535 PMCID: PMC10625481 DOI: 10.3934/mbe.2021315] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
When eradication is impossible, cancer treatment aims to delay the emergence of resistance while minimizing cancer burden and treatment. Adaptive therapies may achieve these aims, with success based on three assumptions: resistance is costly, sensitive cells compete with resistant cells, and therapy reduces the population of sensitive cells. We use a range of mathematical models and treatment strategies to investigate the tradeoff between controlling cell populations and delaying the emergence of resistance. These models extend game theoretic and competition models with four additional components: 1) an Allee effect where cell populations grow more slowly at low population sizes, 2) healthy cells that compete with cancer cells, 3) immune cells that suppress cancer cells, and 4) resource competition for a growth factor like androgen. In comparing maximum tolerable dose, intermittent treatment, and adaptive therapy strategies, no therapeutic choice robustly breaks the three-way tradeoff among the three therapeutic aims. Almost all models show a tight tradeoff between time to emergence of resistant cells and cancer cell burden, with intermittent and adaptive therapies following identical curves. For most models, some adaptive therapies delay overall tumor growth more than intermittent therapies, but at the cost of higher cell populations. The Allee effect breaks these relationships, with some adaptive therapies performing poorly due to their failure to treat sufficiently to drive populations below the threshold. When eradication is impossible, no treatment can simultaneously delay emergence of resistance, limit total cancer cell numbers, and minimize treatment. Simple mathematical models can play a role in designing the next generation of therapies that balance these competing objectives.
Collapse
Affiliation(s)
- Cassidy K. Buhler
- Department of Decision Sciences and MIS, Drexel University, 3220 Market St, Philadelphia, PA 19104, USA
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
| | - Rebecca S. Terry
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
- Department of Mathematics, Computer Science and Statistics, St. Lawrence University, 23 Romoda Drive, Canton, NY 13617, USA
| | - Kathryn G. Link
- Department of Mathematics, University of California, Davis, One Shields Avenue, CA 95616, USA
| | - Frederick R. Adler
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
- School of Biological Sciences, University of Utah, 257 S 1400 E, Salt Lake City, UT 84112, USA
| |
Collapse
|
33
|
Creemers JHA, Lesterhuis WJ, Mehra N, Gerritsen WR, Figdor CG, de Vries IJM, Textor J. A tipping point in cancer-immune dynamics leads to divergent immunotherapy responses and hampers biomarker discovery. J Immunother Cancer 2021; 9:jitc-2020-002032. [PMID: 34059522 PMCID: PMC8169479 DOI: 10.1136/jitc-2020-002032] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/06/2021] [Indexed: 11/04/2022] Open
Abstract
BACKGROUND Predicting treatment response or survival of cancer patients remains challenging in immuno-oncology. Efforts to overcome these challenges focus, among others, on the discovery of new biomarkers. Despite advances in cellular and molecular approaches, only a limited number of candidate biomarkers eventually enter clinical practice. METHODS A computational modeling approach based on ordinary differential equations was used to simulate the fundamental mechanisms that dictate tumor-immune dynamics and to investigate its implications on responses to immune checkpoint inhibition (ICI) and patient survival. Using in silico biomarker discovery trials, we revealed fundamental principles that explain the diverging success rates of biomarker discovery programs. RESULTS Our model shows that a tipping point-a sharp state transition between immune control and immune evasion-induces a strongly non-linear relationship between patient survival and both immunological and tumor-related parameters. In patients close to the tipping point, ICI therapy may lead to long-lasting survival benefits, whereas patients far from the tipping point may fail to benefit from these potent treatments. CONCLUSION These findings have two important implications for clinical oncology. First, the apparent conundrum that ICI induces substantial benefits in some patients yet completely fails in others could be, to a large extent, explained by the presence of a tipping point. Second, predictive biomarkers for immunotherapy should ideally combine both immunological and tumor-related markers, as a patient's distance from the tipping point can typically not be reliably determined from solely one of these. The notion of a tipping point in cancer-immune dynamics helps to devise more accurate strategies to select appropriate treatments for patients with cancer.
Collapse
Affiliation(s)
- Jeroen H A Creemers
- Department of Tumor Immunology, Radboudumc, Nijmegen, The Netherlands.,Oncode Institute, Nijmegen, The Netherlands
| | - W Joost Lesterhuis
- School of Biomedical Sciences and Telethon Kids Institute, University of Western Australia, Perth, Western Australia, Australia
| | - Niven Mehra
- Department of Medical Oncology, Radboudumc, Nijmegen, The Netherlands
| | | | - Carl G Figdor
- Department of Tumor Immunology, Radboudumc, Nijmegen, The Netherlands.,Oncode Institute, Nijmegen, The Netherlands
| | | | - Johannes Textor
- Department of Tumor Immunology, Radboudumc, Nijmegen, The Netherlands .,Data Science Department, Radboud University Institute for Computing and Information Sciences, Nijmegen, The Netherlands
| |
Collapse
|
34
|
A theoretical analysis of tumour containment. Nat Ecol Evol 2021; 5:826-835. [PMID: 33846605 DOI: 10.1038/s41559-021-01428-w] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 02/23/2021] [Indexed: 11/09/2022]
Abstract
Recent studies have shown that a strategy aiming for containment, not elimination, can control tumour burden more effectively in vitro, in mouse models and in the clinic. These outcomes are consistent with the hypothesis that emergence of resistance to cancer therapy may be prevented or delayed by exploiting competitive ecological interactions between drug-sensitive and drug-resistant tumour cell subpopulations. However, although various mathematical and computational models have been proposed to explain the superiority of particular containment strategies, this evolutionary approach to cancer therapy lacks a rigorous theoretical foundation. Here we combine extensive mathematical analysis and numerical simulations to establish general conditions under which a containment strategy is expected to control tumour burden more effectively than applying the maximum tolerated dose. We show that containment may substantially outperform more aggressive treatment strategies even if resistance incurs no cellular fitness cost. We further provide formulas for predicting the clinical benefits attributable to containment strategies in a wide range of scenarios and compare the outcomes of theoretically optimal treatments with those of more practical protocols. Our results strengthen the rationale for clinical trials of evolutionarily informed cancer therapy, while also clarifying conditions under which containment might fail to outperform standard of care.
Collapse
|
35
|
Kim E, Brown JS, Eroglu Z, Anderson AR. Adaptive Therapy for Metastatic Melanoma: Predictions from Patient Calibrated Mathematical Models. Cancers (Basel) 2021; 13:823. [PMID: 33669315 PMCID: PMC7920057 DOI: 10.3390/cancers13040823] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 02/11/2021] [Indexed: 02/07/2023] Open
Abstract
Adaptive therapy is an evolution-based treatment approach that aims to maintain tumor volume by employing minimum effective drug doses or timed drug holidays. For successful adaptive therapy outcomes, it is critical to find the optimal timing of treatment switch points in a patient-specific manner. Here we develop a combination of mathematical models that examine interactions between drug-sensitive and resistant cells to facilitate melanoma adaptive therapy dosing and switch time points. The first model assumes genetically fixed drug-sensitive and -resistant popul tions that compete for limited resources. The second model considers phenotypic switching between drug-sensitive and -resistant cells. We calibrated each model to fit melanoma patient biomarker changes over time and predicted patient-specific adaptive therapy schedules. Overall, the models predict that adaptive therapy would have delayed time to progression by 6-25 months compared to continuous therapy with dose rates of 6-74% relative to continuous therapy. We identified predictive factors driving the clinical time gained by adaptive therapy, such as the number of initial sensitive cells, competitive effect, switching rate from resistant to sensitive cells, and sensitive cell growth rate. This study highlights that there is a range of potential patient-specific benefits of adaptive therapy and identifies parameters that modulate this benefit.
Collapse
Affiliation(s)
- Eunjung Kim
- Natural Product Research Center, Korea Institute of Science and Technology, Gangneung 25451, Korea
| | - Joel S. Brown
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer and Research Institute, Tampa, FL 33612, USA;
| | - Zeynep Eroglu
- Cutaneous Oncology, H. Lee Moffitt Cancer and Research Institute, Tampa, FL 33612, USA;
| | - Alexander R.A. Anderson
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer and Research Institute, Tampa, FL 33612, USA;
| |
Collapse
|
36
|
Reckell T, Nguyen K, Phan T, Crook S, Kostelich EJ, Kuang Y. Modeling the synergistic properties of drugs in hormonal treatment for prostate cancer. J Theor Biol 2021; 514:110570. [PMID: 33422609 DOI: 10.1016/j.jtbi.2020.110570] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 11/07/2020] [Accepted: 12/23/2020] [Indexed: 11/28/2022]
Abstract
Prostate cancer is one of the most prevalent cancers in men, with increasing incidence worldwide. This public health concern has inspired considerable effort to study various aspects of prostate cancer treatment using dynamical models, especially in clinical settings. The standard of care for metastatic prostate cancer is hormonal therapy, which reduces the production of androgen that fuels the growth of prostate tumor cells prior to treatment resistance. Existing population models often use patients' prostate-specific antigen levels as a biomarker for model validation and for finding optimal treatment schedules; however, the synergistic effects of drugs used in hormonal therapy have not been well-examined. This paper describes the first mathematical model that explicitly incorporates the synergistic effects of two drugs used to inhibit androgen production in hormonal therapy. The drugs are cyproterone acetate, representing the drug family of anti-androgens that affect luteinizing hormones, and leuprolide acetate, representing the drug family of gonadotropin-releasing hormone analogs. By fitting the model to clinical data, we show that the proposed model can capture the dynamics of serum androgen levels during intermittent hormonal therapy better than previously published models. Our results highlight the importance of considering the synergistic effects of drugs in cancer treatment, thus suggesting that the dynamics of the drugs should be taken into account in optimal treatment studies, particularly for adaptive therapy. Otherwise, an unrealistic treatment schedule may be prescribed and render the treatment less effective. Furthermore, the drug dynamics allow our model to explain the delay in the relapse of androgen the moment a patient is taken off treatment, which supports that this delay is due to the residual effects of the drugs.
Collapse
Affiliation(s)
- Trevor Reckell
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| | - Kyle Nguyen
- Biomathematics Graduate Program, North Carolina State University, 2700 Katharine Stinson Drive, Raleigh, NC 27607, USA; Center for Research in Scientific Computation, North Carolina State University, 2700 Katharine Stinson Drive, Raleigh, NC 27607, USA
| | - Tin Phan
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| | - Sharon Crook
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| | - Eric J Kostelich
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| |
Collapse
|
37
|
Mehrabi F, Shamspur T, Mostafavi A, Hakimi H, Mohamadi M. Inclusion of sulfamethoxazole in a novel CuFe
2
O
4
nanoparticles/mesoporous silica‐based nanocomposite: Release kinetics and antibacterial activity. Appl Organomet Chem 2021. [DOI: 10.1002/aoc.6035] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Fatemeh Mehrabi
- Department of Chemistry Shahid Bahonar University of Kerman Kerman Iran
- Young Research Societies Shahid Bahonar University of Kerman Kerman Iran
| | - Tayebeh Shamspur
- Department of Chemistry Shahid Bahonar University of Kerman Kerman Iran
| | - Ali Mostafavi
- Department of Chemistry Shahid Bahonar University of Kerman Kerman Iran
| | - Hamid Hakimi
- Immunology of Infectious Diseases Research Center Rafsanjan University of Medical Sciences Rafsanjan Iran
- Department of Microbiology, Faculty of Medicine Rafsanjan University of Medical Sciences Rafsanjan Iran
| | - Maryam Mohamadi
- Pistachio Safety Research Center Rafsanjan University of Medical Sciences Rafsanjan Iran
| |
Collapse
|
38
|
Cunningham J, Thuijsman F, Peeters R, Viossat Y, Brown J, Gatenby R, Staňková K. Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer. PLoS One 2020; 15:e0243386. [PMID: 33290430 PMCID: PMC7723267 DOI: 10.1371/journal.pone.0243386] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 11/19/2020] [Indexed: 12/16/2022] Open
Abstract
In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an 'evolutionary stable therapy', within the context of the mathematical model that has been used to inform the first adaptive therapy clinical trial of mCRPC. The objective of this therapy is to maintain a stable polymorphic tumor heterogeneity of sensitive and resistant cells to therapy in order to prolong treatment efficacy and progression free survival. Optimal control analysis shows that an increasing dose titration protocol, a very common clinical dosing process, can achieve tumor stabilization for a wide range of potential initial tumor compositions and volumes. Furthermore, larger tumor volumes may counter intuitively be more likely to be stabilized if sensitive cells dominate the tumor composition at time of initial treatment, suggesting a delay of initial treatment could prove beneficial. While it remains uncertain if metastatic disease in humans has the properties that allow it to be truly stabilized, the benefits of a dose titration protocol warrant additional pre-clinical and clinical investigations.
Collapse
Affiliation(s)
- Jessica Cunningham
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Frank Thuijsman
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Ralf Peeters
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Yannick Viossat
- CEREMADE, Université Paris-Dauphine, Université PSL, Paris, France
| | - Joel Brown
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, Illinois, United States of America
| | - Robert Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Diagnostic Imaging and Interventional Radiology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
| | - Kateřina Staňková
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
| |
Collapse
|
39
|
Hansen E, Read AF. Modifying Adaptive Therapy to Enhance Competitive Suppression. Cancers (Basel) 2020; 12:E3556. [PMID: 33260773 PMCID: PMC7761372 DOI: 10.3390/cancers12123556] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Revised: 11/20/2020] [Accepted: 11/26/2020] [Indexed: 12/28/2022] Open
Abstract
Adaptive therapy is a promising new approach to cancer treatment. It is designed to leverage competition between drug-sensitive and drug-resistant cells in order to suppress resistance and maintain tumor control for longer. Prompted by encouraging results from a recent pilot clinical trial, we evaluate the design of this initial test of adaptive therapy and identify three simple modifications that should improve performance. These modifications are designed to increase competition and are easy to implement. Using the mathematical model that supported the recent adaptive therapy trial, we show that the suggested modifications further delay time to tumor progression and also increase the range of patients who can benefit from adaptive therapy.
Collapse
Affiliation(s)
- Elsa Hansen
- Department of Biology, Pennsylvania State University, University Park, PA 16802, USA
| | - Andrew F. Read
- Department of Biology, Pennsylvania State University, University Park, PA 16802, USA
- Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, PA 16802, USA;
- Department of Entomology, Pennsylvania State University, University Park, PA 16802, USA
| |
Collapse
|
40
|
Improving Convergence in Therapy Scheduling Optimization: A Simulation Study. MATHEMATICS 2020. [DOI: 10.3390/math8122114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The infusion times and drug quantities are two primary variables to optimize when designing a therapeutic schedule. In this work, we test and analyze several extensions to the gradient descent equations in an optimal control algorithm conceived for therapy scheduling optimization. The goal is to provide insights into the best strategies to follow in terms of convergence speed when implementing our method in models for dendritic cell immunotherapy. The method gives a pulsed-like control that models a series of bolus injections and aims to minimize a cost a function, which minimizes tumor size and to keep the tumor under a threshold. Additionally, we introduce a stochastic iteration step in the algorithm, which serves to reduce the number of gradient computations, similar to a stochastic gradient descent scheme in machine learning. Finally, we employ the algorithm to two therapy schedule optimization problems in dendritic cell immunotherapy and contrast our method’s stochastic and non-stochastic optimizations.
Collapse
|
41
|
Abstract
Despite the continuous deployment of new treatment strategies and agents over many decades, most disseminated cancers remain fatal. Cancer cells, through their access to the vast information of the human genome, have a remarkable capacity to deploy adaptive strategies for even the most effective treatments. We note there are two critical steps in the clinical manifestation of treatment resistance. The first, which is widely investigated, requires molecular machinery necessary to eliminate the cytotoxic effect of the treatment. However, the emergence of a resistant phenotype is not in itself clinically significant. That is, resistant cells affect patient outcomes only when they succeed in the second step of resistance by proliferating into a sufficiently large population to allow tumor progression and treatment failure. Importantly, proliferation of the resistant phenotype is by no means certain and, in fact, depends on complex Darwinian dynamics governed by the costs and benefits of the resistance mechanisms in the context of the local environment and competing populations. Attempts to target the molecular machinery of resistance have had little clinical success largely because of the diversity within the human genome-therapeutic interruption of one mechanism simply results in its replacement by an alternative. Here we explore evolutionarily informed strategies (adaptive, double-bind, and extinction therapies) for overcoming treatment resistance that seek to understand and exploit the critical evolutionary dynamics that govern proliferation of the resistant phenotypes. In general, this approach has demonstrated that, while emergence of resistance mechanisms in cancer cells to every current therapy is inevitable, proliferation of the resistant phenotypes is not and can be delayed and even prevented with sufficient understanding of the underlying eco-evolutionary dynamics.
Collapse
Affiliation(s)
- Robert A Gatenby
- Cancer Biology and Evolution Program
- Department of Radiology, Moffitt Cancer Center, Tampa, Florida 33612 USA
| | | |
Collapse
|
42
|
Gatenby RA, Brown JS. Integrating evolutionary dynamics into cancer therapy. Nat Rev Clin Oncol 2020; 17:675-686. [PMID: 32699310 DOI: 10.1038/s41571-020-0411-1] [Citation(s) in RCA: 90] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/18/2020] [Indexed: 12/28/2022]
Abstract
Many effective drugs for metastatic and/or advanced-stage cancers have been developed over the past decade, although the evolution of resistance remains the major barrier to disease control or cure. In large, diverse populations such as the cells that compose metastatic cancers, the emergence of cells that are resistant or that can quickly develop resistance is virtually inevitable and most likely cannot be prevented. However, clinically significant resistance occurs only when the pre-existing resistant phenotypes are able to proliferate extensively, a process governed by eco-evolutionary dynamics. Attempts to disrupt the molecular mechanisms of resistance have generally been unsuccessful in clinical practice. In this Review, we focus on the Darwinian processes driving the eco-evolutionary dynamics of treatment-resistant cancer populations. We describe a variety of evolutionarily informed strategies designed to increase the probability of disease control or cure by anticipating and steering the evolutionary dynamics of acquired resistance.
Collapse
Affiliation(s)
- Robert A Gatenby
- Cancer Biology and Evolution Program, Moffitt Cancer Center, Tampa, FL, USA.
- Integrated Mathematical Oncology Department, Moffitt Cancer Center, Tampa, FL, USA.
- Diagnostic Imaging Department, Moffitt Cancer Center, Tampa, FL, USA.
| | - Joel S Brown
- Cancer Biology and Evolution Program, Moffitt Cancer Center, Tampa, FL, USA
- Integrated Mathematical Oncology Department, Moffitt Cancer Center, Tampa, FL, USA
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL, USA
| |
Collapse
|
43
|
Angaroni F, Graudenzi A, Rossignolo M, Maspero D, Calarco T, Piazza R, Montangero S, Antoniotti M. An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments. Front Bioeng Biotechnol 2020; 8:523. [PMID: 32548108 PMCID: PMC7270334 DOI: 10.3389/fbioe.2020.00523] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Accepted: 05/01/2020] [Indexed: 12/17/2022] Open
Abstract
One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.
Collapse
Affiliation(s)
- Fabrizio Angaroni
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy
| | - Alex Graudenzi
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy
- Institute of Molecular Bioimaging and Physiology, Consiglio Nazionale delle Ricerche (IBFM-CNR), Segrate, Milan, Italy
| | - Marco Rossignolo
- Center for Integrated Quantum Science and Technologies, Institute for Quantum Optics, Universitat Ulm, Ulm, Germany
- Istituto Nazionale di Fisica Nucleare (INFN), Padova, Italy
| | - Davide Maspero
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy
- Institute of Molecular Bioimaging and Physiology, Consiglio Nazionale delle Ricerche (IBFM-CNR), Segrate, Milan, Italy
- Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy
| | - Tommaso Calarco
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), Jülich, Germany
| | - Rocco Piazza
- Department of Medicine and Surgery, University of Milano-Bicocca, Monza, Italy
- Hematology and Clinical Research Unit, San Gerardo Hospital, Monza, Italy
| | - Simone Montangero
- Istituto Nazionale di Fisica Nucleare (INFN), Padova, Italy
- Department of Physics and Astronomy “G. Galilei”, University of Padova, Padova, Italy
| | - Marco Antoniotti
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy
- Bicocca Bioinformatics Biostatistics and Bioimaging Centre - B4, Milan, Italy
| |
Collapse
|
44
|
Chamseddine IM, Frieboes HB, Kokkolaras M. Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles. Sci Rep 2020; 10:8294. [PMID: 32427977 PMCID: PMC7237449 DOI: 10.1038/s41598-020-65162-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Accepted: 04/26/2020] [Indexed: 12/31/2022] Open
Abstract
The pharmacokinetics of nanoparticle-borne drugs targeting tumors depends critically on nanoparticle design. Empirical approaches to evaluate such designs in order to maximize treatment efficacy are time- and cost-intensive. We have recently proposed the use of computational modeling of nanoparticle-mediated drug delivery targeting tumor vasculature coupled with numerical optimization to pursue optimal nanoparticle targeting and tumor uptake. Here, we build upon these studies to evaluate the effect of tumor size on optimal nanoparticle design by considering a cohort of heterogeneously-sized tumor lesions, as would be clinically expected. The results indicate that smaller nanoparticles yield higher tumor targeting and lesion regression for larger-sized tumors. We then augment the nanoparticle design optimization problem by considering drug diffusivity, which yields a two-fold tumor size decrease compared to optimizing nanoparticles without this consideration. We quantify the tradeoff between tumor targeting and size decrease using bi-objective optimization, and generate five Pareto-optimal nanoparticle designs. The results provide a spectrum of treatment outcomes - considering tumor targeting vs. antitumor effect - with the goal to enable therapy customization based on clinical need. This approach could be extended to other nanoparticle-based cancer therapies, and support the development of personalized nanomedicine in the longer term.
Collapse
Affiliation(s)
- Ibrahim M Chamseddine
- Deparment of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, USA.
- James Graham Brown Cancer Center, University of Louisville, Louisville, KY, USA.
- Center for Predictive Medicine, University of Louisville, Louisville, KY, USA.
| | - Michael Kokkolaras
- Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada.
- GERAD - Group for Research in Decision Analysis, Montreal, Quebec, Canada.
| |
Collapse
|
45
|
Gluzman M, Scott JG, Vladimirsky A. Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory. Proc Biol Sci 2020; 287:20192454. [PMID: 32315588 DOI: 10.1098/rspb.2019.2454] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Recent clinical trials have shown that adaptive drug therapies can be more efficient than a standard cancer treatment based on a continuous use of maximum tolerated doses (MTD). The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumour. But the adaptive treatment policies examined so far have been largely ad hoc. We propose a method for systematically optimizing adaptive policies based on an evolutionary game theory model of cancer dynamics. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation. We compare MTD-based treatment strategy with optimal adaptive treatment policies and show that the latter can significantly decrease the total amount of drugs prescribed while also increasing the fraction of initial tumour states from which the recovery is possible. We conclude that the use of optimal control theory to improve adaptive policies is a promising concept in cancer treatment and should be integrated into clinical trial design.
Collapse
Affiliation(s)
- Mark Gluzman
- Center for Applied Mathematics, Cornell University, Ithaca, NY, USA
| | - Jacob G Scott
- Department of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, OH, USA
| | - Alexander Vladimirsky
- Department of Mathematics and Center for Applied Mathematics, Cornell University, 561 Malott Hall, Ithaca, NY 14853-4201, USA
| |
Collapse
|
46
|
Review: Mathematical Modeling of Prostate Cancer and Clinical Application. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10082721] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer.
Collapse
|
47
|
Sharp JA, Browning AP, Mapder T, Baker CM, Burrage K, Simpson MJ. Designing combination therapies using multiple optimal controls. J Theor Biol 2020; 497:110277. [PMID: 32294472 DOI: 10.1016/j.jtbi.2020.110277] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Revised: 02/21/2020] [Accepted: 04/06/2020] [Indexed: 01/31/2023]
Abstract
Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.
Collapse
Affiliation(s)
- Jesse A Sharp
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia.
| | - Alexander P Browning
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia
| | - Tarunendu Mapder
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia
| | - Christopher M Baker
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia; School of Mathematics and Statistics, The University of Melbourne, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia; Department of Computer Science, University of Oxford, UK (Visiting Professor)
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology (QUT), Australia
| |
Collapse
|
48
|
Brady-Nicholls R, Nagy JD, Gerke TA, Zhang T, Wang AZ, Zhang J, Gatenby RA, Enderling H. Prostate-specific antigen dynamics predict individual responses to intermittent androgen deprivation. Nat Commun 2020; 11:1750. [PMID: 32273504 PMCID: PMC7145869 DOI: 10.1038/s41467-020-15424-4] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Accepted: 03/09/2020] [Indexed: 12/14/2022] Open
Abstract
Intermittent androgen deprivation therapy (IADT) is an attractive treatment for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose and limit toxicities. We simulate prostate-specific antigen (PSA) dynamics, with enrichment of PCa stem-like cell (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns correlate with longitudinal serum PSA measurements in 70 PCa patients. Learning dynamics from each treatment cycle in a leave-one-out study, model simulations predict patient-specific evolution of resistance with an overall accuracy of 89% (sensitivity = 73%, specificity = 91%). Previous studies have shown a benefit of concurrent therapies with ADT in both low- and high-volume metastatic hormone-sensitive PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who would benefit from concurrent docetaxel, demonstrating the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics.
Collapse
Affiliation(s)
- Renee Brady-Nicholls
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 USF Magnolia Drive, Tampa, FL, 33612, USA
| | - John D Nagy
- Department of Life Sciences, Scottsdale Community College, 9000 E. Chaparral Rd., Scottsdale, AZ, 85256, USA.,School of Mathematical and Statistical Sciences, Arizona State University, 900 S Palm Walk, Tempe, AZ, 85281, USA
| | - Travis A Gerke
- Department of Cancer Epidemiology, H. Lee Moffitt Cancer Center and Research Institute, 12902 USF Magnolia Drive, Tampa, FL, 33612, USA
| | - Tian Zhang
- Division of Medical Oncology, Department of Medicine, Duke Cancer Institute, 20 Duke Medicine Cir, Durham, NC, 27710, USA
| | - Andrew Z Wang
- Department of Radiation Oncology, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA
| | - Jingsong Zhang
- Department of Genitourinary Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, 33612, USA
| | - Robert A Gatenby
- Department of Radiology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, 33612, USA.
| | - Heiko Enderling
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 USF Magnolia Drive, Tampa, FL, 33612, USA.
| |
Collapse
|
49
|
West J, You L, Zhang J, Gatenby RA, Brown JS, Newton PK, Anderson ARA. Towards Multidrug Adaptive Therapy. Cancer Res 2020; 80:1578-1589. [PMID: 31948939 DOI: 10.1158/0008-5472.can-19-2669] [Citation(s) in RCA: 91] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Revised: 12/11/2019] [Accepted: 01/09/2020] [Indexed: 11/16/2022]
Abstract
A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.
Collapse
Affiliation(s)
- Jeffrey West
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida.
| | - Li You
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, the Netherlands
| | - Jingsong Zhang
- Department of Genitourinary Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida
| | - Robert A Gatenby
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida
| | - Joel S Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida.,Cancer Biology and Evolution Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida
| | - Paul K Newton
- Department of Aerospace & Mechanical Engineering and Mathematics, Norris Comprehensive Cancer Center, University of Southern California, Los Angeles, California
| | - Alexander R A Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida.
| |
Collapse
|
50
|
Akhmetzhanov AR, Kim JW, Sullivan R, Beckman RA, Tamayo P, Yeang CH. Modelling bistable tumour population dynamics to design effective treatment strategies. J Theor Biol 2019; 474:88-102. [DOI: 10.1016/j.jtbi.2019.05.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Revised: 05/05/2019] [Accepted: 05/07/2019] [Indexed: 12/16/2022]
|