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.
Highlights
The process through which a cell replicates its DNA, doubles in size, and divides is known as the mitotic cell cycle [1] (Fig 1)
Using experimental data that separates intermitotic time (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
We present the mathematical basis of the DDT modeling approach, compare it to a frequently-used family of models known as exponentially-modified peak functions (EMPF) [58], and describe a custom numerical method that enables parameter estimation for multi-fold convolution models in the face of highly-concentrated distributions
Summary
The process through which a cell replicates its DNA, doubles in size, and divides is known as the mitotic cell cycle [1] (Fig 1). Many distinct checkpoint functions have been described [2, 3], including checkpoints that assess: (i) growth factor signaling (often referred to as the restriction point [4]; see Fig 1); (ii) licensing of DNA replication to prevent reduplication [5]; (iii) nutrient abundance [6]; (iv) DNA damage [3]; (v) sufficient size of the cell prior to mitosis [7]; and (vi) proper machinery for chromosomal alignment and segregation during mitosis [8] Hyperproliferative diseases, such as cancer, invariably suffer from defective cell cycle checkpoint function [2], usually caused by genetic mutations to important molecular regulators [9]. An improved understanding of the molecular mechanisms underlying cell cycle checkpoints and IMT variability may lead to novel therapeutics that can restore normal cell function and/ or slow or halt disease progression
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