Modeling epigenetic regulation of PRC1 protein accumulation in the cell cycle

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

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

The cell cycle is the fundamental process of cell populations, it is regulated by environmental cues and by intracellular checkpoints. Cell cycle variability in clonal cell population is caused by stochastic processes such as random partitioning of cellular components to progeny cells at division and random interactions among biomolecules in cells. One of the important biological questions is how the dynamics at the cell cycle scale, which is related to family dependencies between the cell and its descendants, affects cell population behavior in the long-run. We address this question using a “mechanistic” model, built based on observations of single cells over several cell generations, and then extrapolated in time. We used cell pedigree observations of NIH 3T3 cells including FUCCI markers, to determine patterns of inheritance of cell-cycle phase durations and single-cell protein dynamics. Based on that information we developed a hybrid mathematical model, involving bifurcating autoregression to describe stochasticity of partitioning and inheritance of cell-cycle-phase times, and an ordinary differential equation system to capture single-cell protein dynamics. Long-term simulations, concordant with in vitro experiments, demonstrated the model reproduced the main features of our data and had homeostatic properties. Moreover, heterogeneity of cell cycle may have important consequences during population development. We discovered an effect similar to genetic drift, amplified by family relationships among cells. In consequence, the progeny of a single cell with a short cell cycle time had a high probability of eventually dominating the population, due to the heritability of cell-cycle phases. Patterns of epigenetic heritability in proliferating cells are important for understanding long-term trends of cell populations which are either required to provide the influx of maturing cells (such as hematopoietic stem cells) or which started proliferating uncontrollably (such as cancer cells).

All cells in multicellular organisms obey orchestrated sequences of signals to ensure developmental and homeostatic fitness under a variety of external stimuli. However, there also exist self-perpetuating stem-cell populations, the function of which is to provide a steady supply of differentiated progenitors that in turn ensure persistence of organism functions. This “cell production engine” is an important element of biological homeostasis. A similar process, albeit distorted in many respects, plays a major role in cancer development; here the robustness of homeostasis contributes to difficulty in eradication of malignancy. An important role in homeostasis seems to be played by generation of heterogeneity among cell phenotypes, which then can be shaped by selection and other genetic forces. In the present paper, we present a model of a cultured cell population, which factors in relationships among related cells and the dynamics of cell growth and important proteins regulating cell division. We find that the model not only maintains homeostasis, but that it also responds to perturbations in a manner that is similar to that exhibited by the Wright-Fisher model of population genetics. The model-cell population can become dominated by the progeny of the fittest individuals, without invoking advantageous mutations. If confirmed, this may provide an alternative mode of evolution of cell populations.