(622c) Quantifying the Effect of Cell Population Heterogeneity on Proliferation Rates

Authors: 
Vargo, R. - Presenter, Rice University


The growth rates and the structure of regenerated tissues are modulated by many sub-processes acting at different length scales: (a) the bioreactor scale (mass transport and consumption of nutrients and growth factors), (b) the cell population scale (cell-cell and cell-substrate interactions), and (c) the single-cell scale (intracellular processes that modulate division and migration). A second overarching source of complexity spanning all three scales of the tissue regeneration process originates from cell population heterogeneity. Different cells of the same population may exhibit different phenotypes and this heterogeneity originates from three sources:

1. Unequal partitioning at cell division: With the exception of DNA, the amounts of most intracellular components of mother cells partition unequally between daughter cell. Variability in the number of regulatory molecules among daughter cells leads to different behavior. At each cell cycle, this process repeats itself, leading to further population variability. This type of heterogeneity will be called extrinsic.

2. Stochastic fluctuations of regulatory processes: Regulatory molecules typically exist in very small concentrations inside cells. Thus, the rates of reactions regulated by such molecules are subject to random fluctuations, and even cells with identical states may behave differently. This intrinsic heterogeneity originates from stochastic effects in cells with identical content.

3. Varying environmental conditions: Environmental conditions (nutrient or growth factor concentrations, ligand densities, temperature, pH, etc.) can vary significantly with time and location. Since the intracellular state strongly depends on the local environment, cells exposed to different environmental conditions will exhibit temporally and spatially varying behavior

The objective of this study is a quantitative characterization of the heterogeneity of the mammalian cell cycle in spatially uniform environmental conditions. Thus, we specifically seek here to study the combined effects of extrinsic and intrinsic heterogeneity on the distributions of cell division times. Presently, the majority of mammalian cell cycle models do not consider the stochastic nature of the reactions involved in cell division. These models assume that the temporal evolution of the concentration of each species is continuous and deterministic. However, molecules are discrete entities and reactions occur only when the reactant molecules collide. This is particularly important for cells that have an approximate volume of 10-12 L (10 mm diameter) and contain a small number of regulatory molecules.

Cyclin dependent kinases (Cdk) are the central molecules involved in the cell cycle. Their concentrations are high during DNA synthesis and mitosis, but fall to very low values during the G1 phase. Therefore, cell behavior is highly dependent on stochastic fluctuations when the concentrations of Cdk are at low levels and thus will affect transitions in the cell cycle.

This work utilized the Gillespie stochastic simulation algorithm and the chemical Langevin equation to investigate the stochastic dynamics of the core cell cycle model proposed by Tyson and Novak [2002]. Tyson and Novak hypothesized that there is a core cell cycle that is central to all eukaryotes and that the more complex cell cycle machinery observed in higher eukaryotes evolves from this core cell cycle. Their model accurately simulates the phenotypic behavior of the proteins involved in the cell cycle.

Our study investigates the effect of stochastic fluctuations on the dynamics of this system. Sensitivity analysis is also applied to identify the model parameters that are the key sources of heterogeneity. Even in a spatially homogeneous environment, an individual cell may have a different synthesis rate of a protein and degradation of another protein when compared to other cells in the population because of intrinsic and extrinsic noise. This variability in model parameters influences the dynamics of the system and, thus, the division time of a cell. The combined heterogeneity caused by stochastic fluctuations and/or rate distributions results in a distribution of division times within a cell population.

Future work will utilize this single-cell model to develop an equivalent discrete model that describes the dynamics of cell populations that build three-dimensional tissues. Classical discrete models (cellular automata) are phenomenological and do not provide an accurate description of the biological processes regulating cell division or migration. The present model will allow us to remove this restriction and will lead to discrete models that can accurately describe the dynamics of tissue growth in a spatially uniform environment.