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Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect
Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observation...
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| Published in: | PLoS biology 2019-08, Vol.17 (8), p.e3000399 |
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| description | Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors. |
| doi_str_mv | 10.1371/journal.pbio.3000399 |
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However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. 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This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 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Academic</collection><collection>PubMed Central (Full Participant titles)</collection><collection>Open Access: DOAJ - Directory of Open Access Journals</collection><collection>PLoS Biology</collection><jtitle>PLoS biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Johnson, Kaitlyn E</au><au>Howard, Grant</au><au>Mo, William</au><au>Strasser, Michael K</au><au>Lima, Ernesto A B F</au><au>Huang, Sui</au><au>Brock, Amy</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect</atitle><jtitle>PLoS biology</jtitle><addtitle>PLoS Biol</addtitle><date>2019-08-05</date><risdate>2019</risdate><volume>17</volume><issue>8</issue><spage>e3000399</spage><pages>e3000399-</pages><issn>1545-7885</issn><issn>1544-9173</issn><eissn>1545-7885</eissn><notes>new_version</notes><notes>ObjectType-Article-1</notes><notes>SourceType-Scholarly Journals-1</notes><notes>ObjectType-Feature-2</notes><notes>content type line 23</notes><notes>The authors have declared that no competing interests exist.</notes><abstract>Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.</abstract><cop>United States</cop><pub>Public Library of Science</pub><pmid>31381560</pmid><doi>10.1371/journal.pbio.3000399</doi><orcidid>https://orcid.org/0000-0001-8255-9024</orcidid><orcidid>https://orcid.org/0000-0003-4731-7251</orcidid><orcidid>https://orcid.org/0000-0002-9219-8784</orcidid><orcidid>https://orcid.org/0000-0001-8011-0012</orcidid><orcidid>https://orcid.org/0000-0001-8512-6814</orcidid><orcidid>https://orcid.org/0000-0002-3545-4665</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Biology Biology and Life Sciences Biomedical engineering Brain cancer Breast cancer Cancer therapies Cell Count - methods Cell culture Cell death Cell growth Cell Line, Tumor Cell number Cell proliferation Cell Proliferation - physiology Computer simulation Cooperation Ecological effects Ecology Ecology and Environmental Sciences Ecosystem Ecosystems Engineering Evolution Gene expression Genetics Growth kinetics Growth patterns Growth rate Humans Immune response Kinetics Longitude Lymphocytes B Mathematical models Medicine and Health Sciences Models, Biological Models, Theoretical Mutation Neoplasms - metabolism Nutrients Parameter estimation Population Population growth Population number Research and Analysis Methods Stochastic models Stochasticity Tumor cells Tumors |
| title | Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect |
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