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).

A mathematical model as a tool to identify microRNAs with highest impact on transcriptome changes.

BACKGROUND: Rapid changes in the expression of many messenger RNA (mRNA) species follow exposure of cells to ionizing radiation. One of the hypothetical mechanisms of this response may include microRNA (miRNA) regulation, since the amounts of miRNAs in cells also vary upon irradiation. To address this possibility, we designed experiments using cancer-derived cell lines transfected with luciferase reporter gene containing sequences targeted by different miRNA species in its 3'- untranslated region. We focus on the early time-course response (1 h past irradiation) to eliminate secondary mRNA expression waves. RESULTS: Experiments revealed that the irradiation-induced changes in the mRNA expression depend on the miRNAs which interact with mRNA. To identify the strongest interactions, we propose a mathematical model which predicts the mRNA fold expression changes, caused by perturbation of microRNA-mRNA interactions. Model was applied to experimental data including various cell lines, irradiation doses and observation times, both ours and literature-based. Comparison of modelled and experimental mRNA expression levels given miRNA level changes allows estimating how many and which miRNAs play a significant role in transcriptome response to stress conditions in different cell types. As an example, in the human melanoma cell line the comparison suggests that, globally, a major part of the irradiation-induced changes of mRNA expression can be explained by perturbed miRNA-mRNA interactions. A subset of about 30 out of a few hundred miRNAs expressed in these cells appears to account for the changes. These miRNAs play crucial roles in regulatory mechanisms observed after irradiation. In addition, these miRNAs have a higher average content of GC and a higher number of targeted transcripts, and many have been reported to play a role in the development of cancer. CONCLUSIONS: Our proposed mathematical modeling approach may be used to identify miRNAs which participate in responses of cells to ionizing radiation, and other stress factors such as extremes of temperature, exposure to toxins, and drugs.