Unmasking Chaotic Attributes in Time Series of Living Cell Populations

Abstract

BackgroundLong-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth.Methodology/Principal FindingsUsing a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations.Conclusion/SignificanceTheoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled.

Characterization of cancer intracellular space using the K-S entropy for images

“…The experiment based on our proposed K-S entropy approach suggests the findings can be useful for the modeling and simulation of cancer using intracellular images, and they are consistent with the notion that fluctuations of cell populations can be chaotically controlled [19], [18].…”

“…It has been pointed out that theoretical models predict various cell population dynamics, from stable through pe-riodically oscillating to a chaotic regime; and periodic and stochastic fluctuations were found in various mammalian cells, but the underlying dynamics due to chaos has rarely been evidenced [18]. The experiment based on our proposed K-S entropy approach suggests the findings can be useful for the modeling and simulation of cancer using intracellular images, and they are consistent with the notion that fluctuations of cell populations can be chaotically controlled [19], [18].…”

Application of the stochastic Moran Model of population genetics to understanding the timing of a driver mutation in Myelodysplastic Syndrome (MDS)

“…According to molecular determinism, stochastic variability of the proliferating bone marrow cells can be reduced to complicated series of deterministic events including molecular switches, which are multistable by nature and which trigger proliferation and/or maturation decisions. This is distinct from older proposals involving chaotic dynamics (Raue et al 2010, Laurent et al 2010.…”

On the Chaos in Gene Networks

“…Currently, manifold phenomena are considered in this perspective, including sporadic epidemics 25 ; population irruptions among predators, rodents and insects 26À29 as well as among microorganisms 30 ; chaotic oscillation in proliferative activity of long-term cultivated cell lines 31,32 ; disturbances of the cardiac rhyme 33,34 ; development of renal hypertension 35 ; and aberrations in the dynamics of eukaryotic cell cycle. 14,16 Gene networks as an object of study are complex dynamic systems functioning in the living systems.…”