1
|
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
|
2
|
Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity. J Math Biol 2023; 86:30. [PMID: 36637504 PMCID: PMC9839821 DOI: 10.1007/s00285-022-01859-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 09/14/2022] [Accepted: 12/16/2022] [Indexed: 01/14/2023]
Abstract
May and Leonard (SIAM J Appl Math 29:243-253, 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.
Collapse
|
3
|
Mononen T, Kuosmanen T, Cairns J, Mustonen V. Understanding cellular growth strategies via optimal control. J R Soc Interface 2023; 20:20220744. [PMID: 36596459 PMCID: PMC9810423 DOI: 10.1098/rsif.2022.0744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 12/05/2022] [Indexed: 01/05/2023] Open
Abstract
Evolutionary prediction and control are increasingly interesting research topics that are expanding to new areas of application. Unravelling and anticipating successful adaptations to different selection pressures becomes crucial when steering rapidly evolving cancer or microbial populations towards a chosen target. Here we introduce and apply a rich theoretical framework of optimal control to understand adaptive use of traits, which in turn allows eco-evolutionarily informed population control. Using adaptive metabolism and microbial experimental evolution as a case study, we show how demographic stochasticity alone can lead to lag time evolution, which appears as an emergent property in our model. We further show that the cycle length used in serial transfer experiments has practical importance as it may cause unintentional selection for specific growth strategies and lag times. Finally, we show how frequency-dependent selection can be incorporated to the state-dependent optimal control framework allowing the modelling of complex eco-evolutionary dynamics. Our study demonstrates the utility of optimal control theory in elucidating organismal adaptations and the intrinsic decision making of cellular communities with high adaptive potential.
Collapse
Affiliation(s)
- Tommi Mononen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Teemu Kuosmanen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Johannes Cairns
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
| | - Ville Mustonen
- Department of Computer Science, Organismal and Evolutionary Biology Research Programme, University of Helsinki, Helsinki 00014, Finland
- Institute of Biotechnology, University of Helsinki, Helsinki 00014, Finland
| |
Collapse
|
4
|
Browning AP, Ansari N, Drovandi C, Johnston APR, Simpson MJ, Jenner AL. Identifying cell-to-cell variability in internalization using flow cytometry. J R Soc Interface 2022; 19:20220019. [PMID: 35611619 PMCID: PMC9131125 DOI: 10.1098/rsif.2022.0019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 04/21/2022] [Indexed: 12/23/2022] Open
Abstract
Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.
Collapse
Affiliation(s)
- Alexander P. Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| | - Niloufar Ansari
- Drug Delivery, Disposition and Dynamics, Monash Institute of Pharmaceutical Sciences, Monash University, 399 Royal Parade, Parkville, Victoria 3052, Australia
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| | - Angus P. R. Johnston
- Drug Delivery, Disposition and Dynamics, Monash Institute of Pharmaceutical Sciences, Monash University, 399 Royal Parade, Parkville, Victoria 3052, Australia
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| | - Adrianne L. Jenner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| |
Collapse
|
5
|
Nikolaev YA, Loiko NG, Demkina EV, Borzenkov IA, Kanapatskii TA, El’-Registan GI. Highly Persistent Strains of Hydrocarbon-Oxidizing Bacteria as a Base for Increasing the Viable Cell Numbers during Long-Term Storage. Microbiology (Reading) 2021. [DOI: 10.1134/s0026261721060126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
|
6
|
Verstraete L, Van den Bergh B, Verstraeten N, Michiels J. Ecology and evolution of antibiotic persistence. Trends Microbiol 2021; 30:466-479. [PMID: 34753652 DOI: 10.1016/j.tim.2021.10.001] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 10/03/2021] [Accepted: 10/05/2021] [Indexed: 12/22/2022]
Abstract
Bacteria have at their disposal a battery of strategies to withstand antibiotic stress. Among these, resistance is a well-known mechanism, yet bacteria can also survive antibiotic attack by adopting a tolerant phenotype. In the case of persistence, only a small fraction within an isogenic population switches to this antibiotic-tolerant state. Persistence depends on the ecological niche and the genetic background of the strains involved. Furthermore, it has been shown to be under direct and indirect evolutionary pressure. Persister cells play a role in chronic infections and the development of resistance, and therefore a better understanding of this phenotype could contribute to the development of effective antibacterial therapies. In the current review, we discuss how ecological and evolutionary forces shape persistence.
Collapse
Affiliation(s)
- L Verstraete
- Centre of Microbial and Plant Genetics, KU Leuven, Leuven, Belgium; Center for Microbiology, Flanders Institute for Biotechnology, Leuven, Belgium
| | - B Van den Bergh
- Centre of Microbial and Plant Genetics, KU Leuven, Leuven, Belgium; Center for Microbiology, Flanders Institute for Biotechnology, Leuven, Belgium
| | - N Verstraeten
- Centre of Microbial and Plant Genetics, KU Leuven, Leuven, Belgium; Center for Microbiology, Flanders Institute for Biotechnology, Leuven, Belgium
| | - J Michiels
- Centre of Microbial and Plant Genetics, KU Leuven, Leuven, Belgium; Center for Microbiology, Flanders Institute for Biotechnology, Leuven, Belgium.
| |
Collapse
|
7
|
Sharp JA, Burrage K, Simpson MJ. Implementation and acceleration of optimal control for systems biology. J R Soc Interface 2021; 18:20210241. [PMID: 34428951 PMCID: PMC8385371 DOI: 10.1098/rsif.2021.0241] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.
Collapse
Affiliation(s)
- Jesse A Sharp
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia.,Department of Computer Science, University of Oxford, Oxford OX2 6GG, UK
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| |
Collapse
|
8
|
Bhattacharya S, Mohanty A, Achuthan S, Kotnala S, Jolly MK, Kulkarni P, Salgia R. Group Behavior and Emergence of Cancer Drug Resistance. Trends Cancer 2021; 7:323-334. [PMID: 33622644 PMCID: PMC8500356 DOI: 10.1016/j.trecan.2021.01.009] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 01/25/2021] [Accepted: 01/26/2021] [Indexed: 02/06/2023]
Abstract
Drug resistance is a major impediment in cancer. Although it is generally thought that acquired drug resistance is due to genetic mutations, emerging evidence indicates that nongenetic mechanisms also play an important role. Resistance emerges through a complex interplay of clonal groups within a heterogeneous tumor and the surrounding microenvironment. Traits such as phenotypic plasticity, intercellular communication, and adaptive stress response, act in concert to ensure survival of intermediate reversible phenotypes, until permanent, resistant clones can emerge. Understanding the role of group behavior, and the underlying nongenetic mechanisms, can lead to more efficacious treatment designs and minimize or delay emergence of resistance.
Collapse
Affiliation(s)
- Supriyo Bhattacharya
- Translational Bioinformatics, Center for Informatics, Department of Computational and Quantitative Medicine, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Atish Mohanty
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Srisairam Achuthan
- Center for Informatics, Division of Research Informatics, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Sourabh Kotnala
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Mohit Kumar Jolly
- Center for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - Prakash Kulkarni
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Ravi Salgia
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA.
| |
Collapse
|
9
|
Browning AP, Warne DJ, Burrage K, Baker RE, Simpson MJ. Identifiability analysis for stochastic differential equation models in systems biology. J R Soc Interface 2020; 17:20200652. [PMID: 33323054 PMCID: PMC7811582 DOI: 10.1098/rsif.2020.0652] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 11/24/2020] [Indexed: 12/26/2022] Open
Abstract
Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.
Collapse
Affiliation(s)
- Alexander P. Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - David J. Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, Australia
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Ruth E. Baker
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| |
Collapse
|