Deterministic dynamics control oscillations of bone marrow cell proliferation

Poincaré Maps and Aperiodic Oscillations in Leukemic Cell Proliferation Reveal Chaotic Dynamics

Biological systems are dynamic systems featuring two very common characteristics; Initial conditions and progression over time. Conceptualizing this on tumour models it can lead to important conclusions about disease progression, as well as the disease's "starting point". In the present study we tried to answer two questions: (a) which are the evolving properties of proliferating tumour cells that started from different initial conditions and (b) we have attempted to prove that cell proliferation follows chaotic orbits and it can be described by the use of Poincaré maps. As a model we have used the acute lymphoblastic leukemia cell line CCRF-CEM. Measurements of cell population were taken at certain time points every 24 h or 48 h. In addition to the population measurements flow cytometry studies have been conducted in order to examine the apoptotic and necrotic rate of the system and also the DNA content of the cells as they progress through. The cells exhibited a proliferation rate of nonlinear nature with aperiodic oscillatory behavior. In addition to that, the (positive) Lyapunov indices and the Poincaré representations in phase-space that we performed confirmed the presence of chaotic orbits. Several studies have dealt with the complex dynamic behaviour of animal populations, but few with cellular systems. This type of approach could prove useful towards the understanding of leukemia dynamics, with particular interest in the understanding of leukemia onset and progression.

Neutropenia dynamics in a case of T-LGL lymphoproliferation illustrate rapid turnover of granulocyte progenitors

OBJECTIVES

To elucidate the natural history of T-cell large granular lymphocyte (T-LGL) lymphoproliferation, we followed changes in associated fluctuating neutropenia for 3 years in an untreated patient presenting with the disease.

MATERIALS AND METHODS

We report a nonlinear mathematical analysis of irregular neutrophil fluctuation, using iterative data maps, to detect long-term regulation of the neutrophil population.

RESULTS

This geometric analysis indicated that variations of this sequence of neutrophil counts followed bounded deterministic dynamics around a fixed low level equilibrium, a situation similar to that previously observed for cultured mouse early bone marrow progenitor cells.

CONCLUSION

These findings illustrate how the deleterious effect of T-LGL on neutrophils is balanced, over periods of years, by pulses of compensatory neutrophil production, potentially accounting for the commonly observed prolonged indolent course of the disease.

Unmasking chaotic attributes in time series of living cell populations

Background

Long-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 Findings

Using 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/Significance

Theoretical 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.