Skip to main content
bioRxiv
  • Home
  • About
  • Submit
  • ALERTS / RSS
Advanced Search
New Results

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Kaitlyn E. Johnson, Grant Howard, William Mo, Michael K. Strasser, Ernesto A. B. F. Lima, Sui Huang, Amy Brock
doi: https://doi.org/10.1101/585216
Kaitlyn E. Johnson
1Department of Biomedical Engineering, The University of Texas at Austin, Austin TX 78712
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Grant Howard
1Department of Biomedical Engineering, The University of Texas at Austin, Austin TX 78712
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
William Mo
1Department of Biomedical Engineering, The University of Texas at Austin, Austin TX 78712
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Michael K. Strasser
2Institute for Systems Biology, Seattle WA
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Ernesto A. B. F. Lima
4Institute for Computation Engineering and Sciences, the University of Texas at Austin, TX 78712
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Sui Huang
2Institute for Systems Biology, Seattle WA
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Amy Brock
1Department of Biomedical Engineering, The University of Texas at Austin, Austin TX 78712
3Department of Oncology, Livestrong Cancer Institute, Dell Medical School, The University of Texas at Austin, Austin TX 78712
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: amy.brock@utexas.edu
  • Abstract
  • Full Text
  • Info/History
  • Metrics
  • Supplementary material
  • Preview PDF
Loading

Abstract

Models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations from exponential growth only at higher densities due to limited resources such as space and nutrients. However, recent pre-clinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale 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 is 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 consider the small number of cells in this low-density regime and use the moment approach for stochastic parameter estimation to calibrate the stochastic 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 depends on cell number. 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 tumors and relapse.

Author Summary The growth kinetics of cancer cells at very low cell densities are of utmost clinical importance as the ability of a small number of newly transformed or surviving cells to grow exponentially and thus, to “take off” underlies tumor formation and relapse after treatment. Mathematical models of stochastic tumor cell growth typically assume a stochastic birth-death process of cells impacted by limited nutrients and space when cells reach high density, resulting in the widely accepted logistic growth model. Here we present an in-depth investigation of alternate growth models adopted from ecology to describe potential deviations from a simple cell autonomous birth-death model at low cell densities. We show that our stochastic modeling framework is robust and can be used to identify the underlying structure of stochastic growth trajectories from both simulated and experimental data taken from a controlled in vitro setting in which we can capture data from the relevant low cell density regime. This work suggests that the assumption of cell autonomous proliferation via a constant exponential growth rate at low cell densities may not be appropriate for all cancer cell growth dynamics. Consideration of cooperative behavior amongst tumor cells in this regime is critical for elucidating strategies for controlling tumor cell growth.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
Back to top
PreviousNext
Posted March 21, 2019.
Download PDF

Supplementary Material

Email

Thank you for your interest in spreading the word about bioRxiv.

NOTE: Your email address is requested solely to identify you as the sender of this article.

Enter multiple addresses on separate lines or separate them with commas.
Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect
(Your Name) has forwarded a page to you from bioRxiv
(Your Name) thought you would like to see this page from the bioRxiv website.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Share
Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect
Kaitlyn E. Johnson, Grant Howard, William Mo, Michael K. Strasser, Ernesto A. B. F. Lima, Sui Huang, Amy Brock
bioRxiv 585216; doi: https://doi.org/10.1101/585216
Digg logo Reddit logo Twitter logo Facebook logo Google logo LinkedIn logo Mendeley logo
Citation Tools
Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect
Kaitlyn E. Johnson, Grant Howard, William Mo, Michael K. Strasser, Ernesto A. B. F. Lima, Sui Huang, Amy Brock
bioRxiv 585216; doi: https://doi.org/10.1101/585216

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
  • Tweet Widget
  • Facebook Like
  • Google Plus One

Subject Area

  • Cancer Biology
Subject Areas
All Articles
  • Animal Behavior and Cognition (4087)
  • Biochemistry (8767)
  • Bioengineering (6481)
  • Bioinformatics (23348)
  • Biophysics (11751)
  • Cancer Biology (9150)
  • Cell Biology (13255)
  • Clinical Trials (138)
  • Developmental Biology (7417)
  • Ecology (11371)
  • Epidemiology (2066)
  • Evolutionary Biology (15090)
  • Genetics (10402)
  • Genomics (14012)
  • Immunology (9122)
  • Microbiology (22050)
  • Molecular Biology (8780)
  • Neuroscience (47381)
  • Paleontology (350)
  • Pathology (1420)
  • Pharmacology and Toxicology (2482)
  • Physiology (3704)
  • Plant Biology (8054)
  • Scientific Communication and Education (1431)
  • Synthetic Biology (2209)
  • Systems Biology (6016)
  • Zoology (1250)