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Giannakou M, Waclaw B. Resonant noise amplification in a predator-prey model with quasi-discrete generations. Sci Rep 2024; 14:16783. [PMID: 39039177 PMCID: PMC11263699 DOI: 10.1038/s41598-024-67098-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Accepted: 07/08/2024] [Indexed: 07/24/2024] Open
Abstract
Predator-prey models have been shown to exhibit resonance-like behaviour, in which random fluctuations in the number of organisms (demographic noise) are amplified when their frequency is close to the natural oscillatory frequency of the system. This behaviour has been traditionally studied in models with exponentially distributed replication and death times. Here we consider a biologically more realistic model, in which organisms replicate quasi-synchronously such that the distribution of replication times has a narrow maximum at some T > 0 corresponding to the mean doubling time. We show that when the frequency of replication f = 1 / T is tuned to the natural oscillatory frequency of the predator-prey model, the system exhibits oscillations that are much stronger than in the model with Poissonian (non-synchronous) replication and death. These oscillations lead to population instability and the extinction of one of the species much sooner than in the case of Poissonian replication. The effect can be explained by resonant amplification of coloured noise generated by quasi-synchronous replication events.
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Affiliation(s)
- M Giannakou
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128, Mainz, Germany
| | - B Waclaw
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
- Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry PAS, Kasprzaka 44/52, 01-224, Warsaw, Poland.
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Cheng YC, Stein S, Nardone A, Liu W, Ma W, Cohen G, Guarducci C, McDonald TO, Jeselsohn R, Michor F. Mathematical Modeling Identifies Optimum Palbociclib-fulvestrant Dose Administration Schedules for the Treatment of Patients with Estrogen Receptor-positive Breast Cancer. CANCER RESEARCH COMMUNICATIONS 2023; 3:2331-2344. [PMID: 37921419 PMCID: PMC10652811 DOI: 10.1158/2767-9764.crc-23-0257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Revised: 07/12/2023] [Accepted: 10/31/2023] [Indexed: 11/04/2023]
Abstract
Cyclin-dependent kinases 4/6 (CDK4/6) inhibitors such as palbociclib are approved for the treatment of metastatic estrogen receptor-positive (ER+) breast cancer in combination with endocrine therapies and significantly improve outcomes in patients with this disease. However, given the large number of possible pairwise drug combinations and administration schedules, it remains unclear which clinical strategy would lead to best survival. Here, we developed a computational, cell cycle-explicit model to characterize the pharmacodynamic response to palbociclib-fulvestrant combination therapy. This pharmacodynamic model was parameterized, in a Bayesian statistical inference approach, using in vitro data from cells with wild-type estrogen receptor (WT-ER) and cells expressing the activating missense ER mutation, Y537S, which confers resistance to fulvestrant. We then incorporated pharmacokinetic models derived from clinical data into our computational modeling platform. To systematically compare dose administration schedules, we performed in silico clinical trials based on integrating our pharmacodynamic and pharmacokinetic models as well as considering clinical toxicity constraints. We found that continuous dosing of palbociclib is more effective for lowering overall tumor burden than the standard, pulsed-dose palbociclib treatment. Importantly, our mathematical modeling and statistical analysis platform provides a rational method for comparing treatment strategies in search of optimal combination dosing strategies of other cell-cycle inhibitors in ER+ breast cancer. SIGNIFICANCE We created a computational modeling platform to predict the effects of fulvestrant/palbocilib treatment on WT-ER and Y537S-mutant breast cancer cells, and found that continuous treatment schedules are more effective than the standard, pulsed-dose palbociclib treatment schedule.
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Affiliation(s)
- Yu-Chen Cheng
- Department of Data Science, Dana-Farber Cancer Institute, Boston, Massachusetts
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts
- Center for Cancer Evolution, Dana-Farber Cancer Institute, Boston, Massachusetts
| | - Shayna Stein
- Department of Data Science, Dana-Farber Cancer Institute, Boston, Massachusetts
| | - Agostina Nardone
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
| | - Weihan Liu
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
| | - Wen Ma
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
| | - Gabriella Cohen
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
| | - Cristina Guarducci
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
| | - Thomas O. McDonald
- Department of Data Science, Dana-Farber Cancer Institute, Boston, Massachusetts
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts
- Center for Cancer Evolution, Dana-Farber Cancer Institute, Boston, Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
| | - Rinath Jeselsohn
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston Massachusetts
- Center for Functional Cancer Epigenetics, Dana-Farber Cancer Institute, Boston, Massachusetts
- Breast Oncology Center, Dana-Farber Cancer Institute, Boston, Massachusetts
| | - Franziska Michor
- Department of Data Science, Dana-Farber Cancer Institute, Boston, Massachusetts
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts
- Center for Cancer Evolution, Dana-Farber Cancer Institute, Boston, Massachusetts
- Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, Massachusetts
- Broad Institute of Harvard and MIT, Cambridge, Massachusetts
- Ludwig Center at Harvard, Boston, Massachusetts
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Jafarpour F, Levien E, Amir A. Evolutionary dynamics in non-Markovian models of microbial populations. Phys Rev E 2023; 108:034402. [PMID: 37849168 DOI: 10.1103/physreve.108.034402] [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: 02/24/2023] [Accepted: 06/07/2023] [Indexed: 10/19/2023]
Abstract
In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.
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Affiliation(s)
- Farshid Jafarpour
- Institute for Theoretical Physics, Utrecht University, 3584 CC Utrecht, The Netherlands
| | - Ethan Levien
- Mathematics Department, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Ariel Amir
- Department of Complex Systems, Faculty of Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
- John A. Paulson, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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Jędrak J, Rubin M, Ochab-Marcinek A. Generalization of Powell's results to population out of steady state. Phys Rev E 2023; 108:024405. [PMID: 37723697 DOI: 10.1103/physreve.108.024405] [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: 12/06/2022] [Accepted: 07/27/2023] [Indexed: 09/20/2023]
Abstract
Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of exponential growth. Here we generalize these relationships to include an unsteady (transient) state for both the batch culture and the mother machine experiment. In particular, we derive a time-dependent Euler-Lotka equation (relating the generation-time distributions to the population growth rate) and a generalization of the inequality between the mean generation time and the population doubling time. To do this, we use a model proposed by Lebowitz and Rubinow, in which each cell is described by its age and generation time. We show that our results remain valid for a class of more complex models that use other state variables in addition to cell age and generation time, as long as the integration of these additional variables reduces the model to Lebowitz-Rubinow form. As an application of this formalism, we calculate the fitness landscapes for phenotypic traits (cell age, generation time) in a population that is not growing exponentially. We clarify that the known fitness landscape formula for the cell age as a phenotypic trait is an approximation to the exact time-dependent formula.
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Affiliation(s)
- Jakub Jędrak
- Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Marcin Rubin
- Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Anna Ochab-Marcinek
- Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warsaw, Poland
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Jia C, Singh A, Grima R. Cell size distribution of lineage data: analytic results and parameter inference. iScience 2021; 24:102220. [PMID: 33748708 PMCID: PMC7961097 DOI: 10.1016/j.isci.2021.102220] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Revised: 01/29/2021] [Accepted: 02/17/2021] [Indexed: 01/06/2023] Open
Abstract
Recent advances in single-cell technologies have enabled time-resolved measurements of the cell size over several cell cycles. These data encode information on how cells correct size aberrations so that they do not grow abnormally large or small. Here, we formulate a piecewise deterministic Markov model describing the evolution of the cell size over many generations, for all three cell size homeostasis strategies (timer, sizer, and adder). The model is solved to obtain an analytical expression for the non-Gaussian cell size distribution in a cell lineage; the theory is used to understand how the shape of the distribution is influenced by the parameters controlling the dynamics of the cell cycle and by the choice of cell tracking protocol. The theoretical cell size distribution is found to provide an excellent match to the experimental cell size distribution of E. coli lineage data collected under various growth conditions.
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Affiliation(s)
- Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, EH9 3JH, UK
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