The impact of maturation time distributions on the structure and growth of cellular populations

Asma Alshehri; John Ford; Rachel Leander; Asma Alshehri; John Ford; Rachel Leander

doi:10.3934/mbe.2020098

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1855-1888. doi: 10.3934/mbe.2020098

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The impact of maturation time distributions on the structure and growth of cellular populations

1.
3404 Bakr Bin Mobashar Street, Taiba Box 8036, Jeddah 23833, KSA
2.
Department of Computer Science, Middle Tennessee State University, MTSU Box 48, Murfreesboro, TN 37132, USA
3.
Department of Mathematical Sciences, Middle Tennessee State University, MTSU Box 34, Murfreesboro, TN 37132, USA

Received: 30 September 2019 Accepted: 01 December 2019 Published: 18 December 2019

Here we study how the structure and growth of a cellular population vary with the distribution of maturation times from each stage. We consider two cell cycle stages. The first represents early G1. The second includes late G1, S, G2, and mitosis. Passage between the two reflects passage of an important cell cycle checkpoint known as the restriction point. We model the population as a system of partial differential equations. After establishing the existence of solutions, we characterize the maturation rates and derive the steady-state age and stage distributions as well as the asymptotic growth rates for models with exponential and inverse Gaussian maturation time distributions. We find that the stable age and stage distributions, transient dynamics, and asymptotic growth rates are substantially different for these two maturation models. We conclude that researchers modeling cellular populations should take care when choosing a maturation time distribution, as the population growth rate and stage structure can be heavily impacted by this choice. Furthermore, differences in the models' transient dynamics constitute testable predictions that can help further our understanding of the fundamental process of cellular proliferation. We hope that our numerical methods and programs will provide a scaffold for future research on cellular proliferation.

Keywords:

Citation: Asma Alshehri, John Ford, Rachel Leander. The impact of maturation time distributions on the structure and growth of cellular populations[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1855-1888. doi: 10.3934/mbe.2020098

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Abstract

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