Modeling epigenetic regulation of PRC1 protein accumulation in the cell cycle

Abstract

BackgroundEpigenetic regulation contributes to many important processes in biological cells. Examples include developmental processes, differentiation and maturation of stem cells, evolution of malignancy and other. Cell cycle regulation has been subject of mathematical modeling by a number of authors that resulted in many interesting models and application of analytic techniques ranging from stochastic processes to partial differential equations and to integral, functional and operator equations. In this paper we address the question of how the regulation of protein contents influences the long-term dynamics of the population. To accomplish this, we follow the philosophy of a 1984 model by Kimmel et al., but adjust the details to fit the experimental data on protein PRC1 from a more recent paper.ResultsWe built a model of cell cycle dynamics of the PRC1 and fitted it to the data made available by Cohen and his co-authors. We have run the model for a large number of cell generations, recording the PRC1 contents in all cells of the resulting pedigree, at constant time intervals. During cell division the PRC1 is unequally divided between daughter cells. The picture emerging from simulations of Data set 1 is that of a very well-tuned regulatory circuit that provides a stable distribution of PRC1 contents and interdivision times. Data set 2 seems qualitatively different, with more variation in cell cycle duration.ConclusionsThe main question we address is whether the regulatory feedbacks deduced from single cell cycle data provide epigenetic regulation of cell characteristics in long run. PRC1 is a good candidate because of its role in setting timing of division. Findings of the current paper include tight regulation of the cell cycle (particularly the timing of the cell cycle) even that PRC1 is only one of the players in cell dynamics. Understanding that association, even close, does not necessarily imply causation, we consider this an interesting and important result.ReviewersThis article was reviewed by Ollivier Hyrien, Anna Marciniak-Czochra and Alberto d’Onofrio.

Mathematical modelling reveals unexpected inheritance and variability patterns of cell cycle parameters in mammalian cells

“…As we described in ref. [4], we fitted experimental trajectories of individual cells to a model in the form of a system of ordinary differential equations (ODE) and calculated correlations among production parameters, duration of phases of cell cycle and initial levels of proteins. Each cell in the population is described by seven parameters with cell-dependent stochastic values.…”

“…Simulation was started from a single ancestor cell with defined or randomly sampled parameters, and the fates of cells from the resulting populations have been recorded. During cell division, the proteins are unequally distributed among progeny cells [4]. Direct measurement of the extent to which division of proteins is unequal is difficult due to degradation of the FUCCI markers in late M phase.…”

“…We address this question using a “mechanistic” model, built based on observations of single cells over several cell generation, and then extrapolated in time. We follow a paradigm recently expressed among others by Sandler et al [3] and Dolbniak et al [4] stating that stochastic processes in cells are associated with fluctuations in mRNA [5], protein production and degradation [6, 7], noisy partition of cellular components at division [8], and other cell processes. Variability within a clonal population of cells originates from such stochastic processes, which may be amplified or reduced by deterministic factors [9].…”

“…Models involving cell cycle duration stochasticity followed, with the most recent one being ref. [4]. The latter model is a precursor of the present one, yet with a more limited scope and based only on literature data.…”

Automated deep lineage tree analysis using a Bayesian single cell tracking approach

“…Heterogeneity in cell populations may originate from deterministic or stochastic processes. For example, the observed distribution of cell cycle durations in a population of cells is governed either by stochastic processes, inherited in a deterministic fashion, or some combination of both [3][4][5][6] (Figure 1A). Previous studies have shown poor correlations within lineages when observing direct ancestral relationships, but remain correlated with immediate relatives 4,7,8 .…”