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Govindaraj V, Sarma S, Karulkar A, Purwar R, Kar S. Transcriptional Fluctuations Govern the Serum-Dependent Cell Cycle Duration Heterogeneities in Mammalian Cells. ACS Synth Biol 2022; 11:3743-3758. [PMID: 36325971 DOI: 10.1021/acssynbio.2c00347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Mammalian cells exhibit a high degree of intercellular variability in cell cycle period and phase durations. However, the factors orchestrating the cell cycle duration heterogeneities remain unclear. Herein, by combining cell cycle network-based mathematical models with live single-cell imaging studies under varied serum conditions, we demonstrate that fluctuating transcription rates of cell cycle regulatory genes across cell lineages and during cell cycle progression in mammalian cells majorly govern the robust correlation patterns of cell cycle period and phase durations among sister, cousin, and mother-daughter lineage pairs. However, for the overall cellular population, alteration in the serum level modulates the fluctuation and correlation patterns of cell cycle period and phase durations in a correlated manner. These heterogeneities at the population level can be fine-tuned under limited serum conditions by perturbing the cell cycle network using a p38-signaling inhibitor without affecting the robust lineage-level correlations. Overall, our approach identifies transcriptional fluctuations as the key controlling factor for the cell cycle duration heterogeneities and predicts ways to reduce cell-to-cell variabilities by perturbing the cell cycle network regulations.
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Affiliation(s)
| | - Subrot Sarma
- Department of Chemistry, IIT Bombay, Powai, Mumbai 400076, India
| | - Atharva Karulkar
- Department of Biosciences and Bioengineering, IIT Bombay, Powai, Mumbai 400076, India
| | - Rahul Purwar
- Department of Biosciences and Bioengineering, IIT Bombay, Powai, Mumbai 400076, India
| | - Sandip Kar
- Department of Chemistry, IIT Bombay, Powai, Mumbai 400076, India
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Hughes FA, Barr AR, Thomas P. Patterns of interdivision time correlations reveal hidden cell cycle factors. eLife 2022; 11:e80927. [PMID: 36377847 PMCID: PMC9822260 DOI: 10.7554/elife.80927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Accepted: 11/14/2022] [Indexed: 11/16/2022] Open
Abstract
The time taken for cells to complete a round of cell division is a stochastic process controlled, in part, by intracellular factors. These factors can be inherited across cellular generations which gives rise to, often non-intuitive, correlation patterns in cell cycle timing between cells of different family relationships on lineage trees. Here, we formulate a framework of hidden inherited factors affecting the cell cycle that unifies known cell cycle control models and reveals three distinct interdivision time correlation patterns: aperiodic, alternator, and oscillator. We use Bayesian inference with single-cell datasets of cell division in bacteria, mammalian and cancer cells, to identify the inheritance motifs that underlie these datasets. From our inference, we find that interdivision time correlation patterns do not identify a single cell cycle model but generally admit a broad posterior distribution of possible mechanisms. Despite this unidentifiability, we observe that the inferred patterns reveal interpretable inheritance dynamics and hidden rhythmicity of cell cycle factors. This reveals that cell cycle factors are commonly driven by circadian rhythms, but their period may differ in cancer. Our quantitative analysis thus reveals that correlation patterns are an emergent phenomenon that impact cell proliferation and these patterns may be altered in disease.
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Affiliation(s)
- Fern A Hughes
- Department of Mathematics, Imperial College LondonLondonUnited Kingdom
- MRC London Institute of Medical SciencesLondonUnited Kingdom
| | - Alexis R Barr
- MRC London Institute of Medical SciencesLondonUnited Kingdom
- Institute of Clinical Sciences, Imperial College LondonLondonUnited Kingdom
| | - Philipp Thomas
- Department of Mathematics, Imperial College LondonLondonUnited Kingdom
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Nozoe T, Kussell E. Cell Cycle Heritability and Localization Phase Transition in Growing Populations. PHYSICAL REVIEW LETTERS 2020; 125:268103. [PMID: 33449732 PMCID: PMC8528515 DOI: 10.1103/physrevlett.125.268103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Accepted: 10/27/2020] [Indexed: 06/12/2023]
Abstract
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate the existence of a phase transition, which can be continuous or first order, by which a nonzero fraction of the population becomes localized at a minimal division time. Just below the transition, we demonstrate the coexistence of localized and delocalized age-structure phases and the power law decay of correlation functions. Above it, we observe the self-synchronization of cell cycles, collective divisions, and the slow "aging" of population growth rates.
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Affiliation(s)
- Takashi Nozoe
- Department of Biology, New York University, 12 Waverly Place, New York, New York 10003, USA
| | - Edo Kussell
- Department of Biology, New York University, 12 Waverly Place, New York, New York 10003, USA
- Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA
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Mura M, Feillet C, Bertolusso R, Delaunay F, Kimmel M. Mathematical modelling reveals unexpected inheritance and variability patterns of cell cycle parameters in mammalian cells. PLoS Comput Biol 2019; 15:e1007054. [PMID: 31158226 PMCID: PMC6564046 DOI: 10.1371/journal.pcbi.1007054] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2018] [Revised: 06/13/2019] [Accepted: 04/26/2019] [Indexed: 01/12/2023] Open
Abstract
The cell cycle is the fundamental process of cell populations, it is regulated by environmental cues and by intracellular checkpoints. Cell cycle variability in clonal cell population is caused by stochastic processes such as random partitioning of cellular components to progeny cells at division and random interactions among biomolecules in cells. One of the important biological questions is how the dynamics at the cell cycle scale, which is related to family dependencies between the cell and its descendants, affects cell population behavior in the long-run. We address this question using a “mechanistic” model, built based on observations of single cells over several cell generations, and then extrapolated in time. We used cell pedigree observations of NIH 3T3 cells including FUCCI markers, to determine patterns of inheritance of cell-cycle phase durations and single-cell protein dynamics. Based on that information we developed a hybrid mathematical model, involving bifurcating autoregression to describe stochasticity of partitioning and inheritance of cell-cycle-phase times, and an ordinary differential equation system to capture single-cell protein dynamics. Long-term simulations, concordant with in vitro experiments, demonstrated the model reproduced the main features of our data and had homeostatic properties. Moreover, heterogeneity of cell cycle may have important consequences during population development. We discovered an effect similar to genetic drift, amplified by family relationships among cells. In consequence, the progeny of a single cell with a short cell cycle time had a high probability of eventually dominating the population, due to the heritability of cell-cycle phases. Patterns of epigenetic heritability in proliferating cells are important for understanding long-term trends of cell populations which are either required to provide the influx of maturing cells (such as hematopoietic stem cells) or which started proliferating uncontrollably (such as cancer cells). All cells in multicellular organisms obey orchestrated sequences of signals to ensure developmental and homeostatic fitness under a variety of external stimuli. However, there also exist self-perpetuating stem-cell populations, the function of which is to provide a steady supply of differentiated progenitors that in turn ensure persistence of organism functions. This “cell production engine” is an important element of biological homeostasis. A similar process, albeit distorted in many respects, plays a major role in cancer development; here the robustness of homeostasis contributes to difficulty in eradication of malignancy. An important role in homeostasis seems to be played by generation of heterogeneity among cell phenotypes, which then can be shaped by selection and other genetic forces. In the present paper, we present a model of a cultured cell population, which factors in relationships among related cells and the dynamics of cell growth and important proteins regulating cell division. We find that the model not only maintains homeostasis, but that it also responds to perturbations in a manner that is similar to that exhibited by the Wright-Fisher model of population genetics. The model-cell population can become dominated by the progeny of the fittest individuals, without invoking advantageous mutations. If confirmed, this may provide an alternative mode of evolution of cell populations.
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Affiliation(s)
- Marzena Mura
- System Engineering Group, Silesian University of Technology, Gliwice, Poland
- Ardigen, Krakow, Poland
- * E-mail: (MM); (MK)
| | | | - Roberto Bertolusso
- Department of Statistics, Rice University, Houston, TX, United States of America
| | | | - Marek Kimmel
- System Engineering Group, Silesian University of Technology, Gliwice, Poland
- Department of Statistics, Rice University, Houston, TX, United States of America
- Department of Bioengineering, Rice University, Houston, TX, United States of America
- * E-mail: (MM); (MK)
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Chakrabarti S, Paek AL, Reyes J, Lasick KA, Lahav G, Michor F. Hidden heterogeneity and circadian-controlled cell fate inferred from single cell lineages. Nat Commun 2018; 9:5372. [PMID: 30560953 PMCID: PMC6299096 DOI: 10.1038/s41467-018-07788-5] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Accepted: 11/23/2018] [Indexed: 11/09/2022] Open
Abstract
The origin of lineage correlations among single cells and the extent of heterogeneity in their intermitotic times (IMT) and apoptosis times (AT) remain incompletely understood. Here we developed single cell lineage-tracking experiments and computational algorithms to uncover correlations and heterogeneity in the IMT and AT of a colon cancer cell line before and during cisplatin treatment. These correlations could not be explained using simple protein production/degradation models. Sister cell fates were similar regardless of whether they divided before or after cisplatin administration and did not arise from proximity-related factors, suggesting fate determination early in a cell's lifetime. Based on these findings, we developed a theoretical model explaining how the observed correlation structure can arise from oscillatory mechanisms underlying cell fate control. Our model recapitulated the data only with very specific oscillation periods that fit measured circadian rhythms, thereby suggesting an important role of the circadian clock in controlling cellular fates.
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Affiliation(s)
- Shaon Chakrabarti
- Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, 02215, MA, USA.,Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, 02115, MA, USA.,Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, 02138, MA, USA
| | - Andrew L Paek
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, 02115, MA, USA.,University of Arizona, Tucson, 85721 AZ, USA
| | - Jose Reyes
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, 02115, MA, USA
| | | | - Galit Lahav
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, 02115, MA, USA. .,Broad Institute of Harvard and MIT, Cambridge, 02139, MA, USA. .,Ludwig Center at Harvard, Boston, 02215, MA, USA.
| | - Franziska Michor
- Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, 02215, MA, USA. .,Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, 02115, MA, USA. .,Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, 02138, MA, USA. .,Broad Institute of Harvard and MIT, Cambridge, 02139, MA, USA. .,Ludwig Center at Harvard, Boston, 02215, MA, USA. .,Center for Cancer Evolution, Dana-Farber Cancer Institute, Boston, 02215, MA, USA.
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Jones ZW, Leander R, Quaranta V, Harris LA, Tyson DR. A drift-diffusion checkpoint model predicts a highly variable and growth-factor-sensitive portion of the cell cycle G1 phase. PLoS One 2018; 13:e0192087. [PMID: 29432467 PMCID: PMC5809023 DOI: 10.1371/journal.pone.0192087] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 01/17/2018] [Indexed: 11/28/2022] Open
Abstract
Even among isogenic cells, the time to progress through the cell cycle, or the intermitotic time (IMT), is highly variable. This variability has been a topic of research for several decades and numerous mathematical models have been proposed to explain it. Previously, we developed a top-down, stochastic drift-diffusion+threshold (DDT) model of a cell cycle checkpoint and showed that it can accurately describe experimentally-derived IMT distributions [Leander R, Allen EJ, Garbett SP, Tyson DR, Quaranta V. Derivation and experimental comparison of cell-division probability densities. J. Theor. Biol. 2014;358:129-135]. Here, we use the DDT modeling approach for both descriptive and predictive data analysis. We develop a custom numerical method for the reliable maximum likelihood estimation of model parameters in the absence of a priori knowledge about the number of detectable checkpoints. We employ this method to fit different variants of the DDT model (with one, two, and three checkpoints) to IMT data from multiple cell lines under different growth conditions and drug treatments. We find that a two-checkpoint model best describes the data, consistent with the notion that the cell cycle can be broadly separated into two steps: the commitment to divide and the process of cell division. The model predicts one part of the cell cycle to be highly variable and growth factor sensitive while the other is less variable and relatively refractory to growth factor signaling. Using experimental data that separates IMT into G1 vs. S, G2, and M phases, we show that the model-predicted growth-factor-sensitive part of the cell cycle corresponds to a portion of G1, consistent with previous studies suggesting that the commitment step is the primary source of IMT variability. These results demonstrate that a simple stochastic model, with just a handful of parameters, can provide fundamental insights into the biological underpinnings of cell cycle progression.
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Affiliation(s)
- Zack W. Jones
- Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, United States of America
| | - Rachel Leander
- Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, United States of America
| | - Vito Quaranta
- Department of Biochemistry, Vanderbilt University School of Medicine, Nashville, TN 37232, United States of America
| | - Leonard A. Harris
- Department of Biochemistry, Vanderbilt University School of Medicine, Nashville, TN 37232, United States of America
| | - Darren R. Tyson
- Department of Biochemistry, Vanderbilt University School of Medicine, Nashville, TN 37232, United States of America
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Gallaher J, Anderson ARA. Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance. Interface Focus 2014; 3:20130016. [PMID: 24511380 DOI: 10.1098/rsfs.2013.0016] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A tumour is a heterogeneous population of cells that competes for limited resources. In the clinic, we typically probe the tumour by biopsy, and then characterize it by the dominant genetic clone. But genotypes are only the first link in the chain of hierarchical events that leads to a specific cell phenotype. The relationship between genotype and phenotype is not simple, and the so-called genotype to phenotype map is poorly understood. Many genotypes can produce the same phenotype, so genetic heterogeneity may not translate directly to phenotypic heterogeneity. We therefore choose to focus on the functional endpoint, the phenotype as defined by a collection of cellular traits (e.g. proliferative and migratory ability). Here, we will examine how phenotypic heterogeneity evolves in space and time and how the way in which phenotypes are inherited will drive this evolution. A tumour can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumour with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cell's capacity to survive and propagate is determined by its combination of traits and interaction with the environment. With heterogeneity in phenotypes, the clone that will dominate is not always obvious as there are both local interactions and global pressures. Several combinations of phenotypes can coexist, changing the fitness of the whole. To understand some aspects of heterogeneity in a growing tumour, we build an off-lattice agent-based model consisting of individual cells with assigned trait values for proliferation and migration rates. We represent heterogeneity in these traits with frequency distributions and combinations of traits with density maps. How the distributions change over time is dependent on how traits are passed on to progeny cells, which is our main enquiry. We bypass the translation of genetics to behaviour by focusing on the functional end result of inheritance of the phenotype combined with the environmental influence of limited space.
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Affiliation(s)
- Jill Gallaher
- Department of Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL 33612 , USA
| | - Alexander R A Anderson
- Department of Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL 33612 , USA
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8
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von Neubeck C, Shankaran H, Geniza MJ, Kauer PM, Robinson RJ, Chrisler WB, Sowa MB. Integrated experimental and computational approach to understand the effects of heavy ion radiation on skin homeostasis. Integr Biol (Camb) 2013; 5:1229-43. [DOI: 10.1039/c3ib40071a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Claere von Neubeck
- German Cancer Consortium (DKTK), OncoRay - National Center for Radiation Research in Oncology, Medical Faculty and University Hospital Carl Gustav Carus, Technische Universität Dresden, Fetscherstrasse 74, 01307 Dresden, Germany
- German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
| | - Harish Shankaran
- Computational Biology and Bioinformatics, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Matthew J. Geniza
- Molecular and Cellular Biology Program, Oregon State University, Corvallis, OR, USA
| | - Paula M. Kauer
- Systems Toxicology, Pacific Northwest National Laboratory, P.O. Box 999, MS J4-02, Richland, WA 99352, USA. Fax: +1 509-371-7304; Tel: +1 509-371-6898
| | - R. Joe Robinson
- Systems Toxicology, Pacific Northwest National Laboratory, P.O. Box 999, MS J4-02, Richland, WA 99352, USA. Fax: +1 509-371-7304; Tel: +1 509-371-6898
| | - William B. Chrisler
- Systems Toxicology, Pacific Northwest National Laboratory, P.O. Box 999, MS J4-02, Richland, WA 99352, USA. Fax: +1 509-371-7304; Tel: +1 509-371-6898
| | - Marianne B. Sowa
- Systems Toxicology, Pacific Northwest National Laboratory, P.O. Box 999, MS J4-02, Richland, WA 99352, USA. Fax: +1 509-371-7304; Tel: +1 509-371-6898
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9
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A law of large numbers result for a bifurcating process with an infinite moving average representation. Stat Probab Lett 2012. [DOI: 10.1016/j.spl.2011.09.012] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Quaranta V, Tyson DR, Garbett SP, Weidow B, Harris MP, Georgescu W. Trait variability of cancer cells quantified by high-content automated microscopy of single cells. Methods Enzymol 2009; 467:23-57. [PMID: 19897088 DOI: 10.1016/s0076-6879(09)67002-6] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
Mapping quantitative cell traits (QCT) to underlying molecular defects is a central challenge in cancer research because heterogeneity at all biological scales, from genes to cells to populations, is recognized as the main driver of cancer progression and treatment resistance. A major roadblock to a multiscale framework linking cell to signaling to genetic cancer heterogeneity is the dearth of large-scale, single-cell data on QCT-such as proliferation, death sensitivity, motility, metabolism, and other hallmarks of cancer. High-volume single-cell data can be used to represent cell-to-cell genetic and nongenetic QCT variability in cancer cell populations as averages, distributions, and statistical subpopulations. By matching the abundance of available data on cancer genetic and molecular variability, QCT data should enable quantitative mapping of phenotype to genotype in cancer. This challenge is being met by high-content automated microscopy (HCAM), based on the convergence of several technologies including computerized microscopy, image processing, computation, and heterogeneity science. In this chapter, we describe an HCAM workflow that can be set up in a medium size interdisciplinary laboratory, and its application to produce high-throughput QCT data for cancer cell motility and proliferation. This type of data is ideally suited to populate cell-scale computational and mathematical models of cancer progression for quantitatively and predictively evaluating cancer drug discovery and treatment.
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Affiliation(s)
- Vito Quaranta
- Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, Tennessee, USA; Vanderbilt Integrative Cancer Biology Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Darren R Tyson
- Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, Tennessee, USA; Vanderbilt Integrative Cancer Biology Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Shawn P Garbett
- Vanderbilt Integrative Cancer Biology Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Brandy Weidow
- Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, Tennessee, USA; Vanderbilt Integrative Cancer Biology Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Mark P Harris
- Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Walter Georgescu
- Vanderbilt Integrative Cancer Biology Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA; Department of Biomedical Engineering, Vanderbilt University Medical Center, Nashville, Tennessee, USA
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11
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Guyon J. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. ANN APPL PROBAB 2007. [DOI: 10.1214/105051607000000195] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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13
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Wein LM, Wu JT. Estimation of replicative senescence via a population dynamics model of cells in culture. Exp Gerontol 2001; 36:79-88. [PMID: 11162913 DOI: 10.1016/s0531-5565(00)00187-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
A simple mathematical model is developed for determining the time-varying fraction of senescent cells in culture in terms of the underlying probability distribution of the number of population doublings until senescence. This functional relationship is inverted, which allows for the estimation of the probability distribution of the number of population doublings until senescence given experimental data on the time-varying fraction of senescent cells. The relationship - in particular, the lag - between these two quantities is analyzed under the assumption that the number of population doublings until senescence follows the Weibull distribution. If the number of population doublings until senescence is geometrically distributed (i.e. the Weibull with shape parameter equal to one) then the cell culture appears immortal.
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Affiliation(s)
- L M Wein
- Sloan School of Management, E53-343, MIT, Cambridge, MA, USA.
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