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Poincare Maps and Aperiodic Oscillations in Leukemic Cell Proliferation Reveal Chaotic Dynamics.

ABSTRACT: 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.

SUBMITTER: Adamopoulos K

PROVIDER: S-EPMC8700028 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundThe CRISPR-Cas systems of adaptive antivirus immunity are present in most archaea and many bacteria, and provide resistance to specific viruses or plasmids by inserting fragments of foreign DNA into the host genome and then utilizing transcripts of these spacers to inactivate the cognate foreign genome. The recent development of powerful genome engineering tools on the basis of CRISPR-Cas has sharply increased the interest in the diversity and evolution of these systems. Comparative genomic data indicate that during evolution of prokaryotes CRISPR-Cas loci are lost and acquired via horizontal gene transfer at high rates. Mathematical modeling and initial experimental studies of CRISPR-carrying microbes and viruses reveal complex coevolutionary dynamics.ResultsWe performed a bifurcation analysis of models of coevolution of viruses and microbial host that possess CRISPR-Cas hereditary adaptive immunity systems. The analyzed Malthusian and logistic models display complex, and in particular, quasi-chaotic oscillation regimes that have not been previously observed experimentally or in agent-based models of the CRISPR-mediated immunity. The key factors for the appearance of the quasi-chaotic oscillations are the non-linear dependence of the host immunity on the virus load and the partitioning of the hosts into the immune and susceptible populations, so that the system consists of three components.ConclusionsBifurcation analysis of CRISPR-host coevolution model predicts complex regimes including quasi-chaotic oscillations. The quasi-chaotic regimes of virus-host coevolution are likely to be biologically relevant given the evolutionary instability of the CRISPR-Cas loci revealed by comparative genomics. The results of this analysis might have implications beyond the CRISPR-Cas systems, i.e. could describe the behavior of any adaptive immunity system with a heritable component, be it genetic or epigenetic. These predictions are experimentally testable.Reviewers' reportsThis manuscript was reviewed by Sandor Pongor, Sergei Maslov and Marek Kimmel. For the complete reports, go to the Reviewers' Reports section.

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Poincare Maps and Aperiodic Oscillations in Leukemic Cell Proliferation Reveal Chaotic Dynamics.

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