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Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology

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Computational Systems Biology in Medicine and Biotechnology

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2399))

Abstract

The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

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Authors and Affiliations

  1. Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, Córdoba, Córdoba, Argentina

    Ana Georgina Flesia & Paula Sofia Nieto

  2. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro de Investigaciones y Estudios de Matemática (CIEM, CONICET), Ciudad Universitaria, Córdoba, Argentina

    Ana Georgina Flesia

  3. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Física Enrique Gaviola (IFEG, CONICET-UNC), Ciudad Universitaria, Córdoba, Argentina

    Paula Sofia Nieto

  4. Laboratory of Cardiovascular Science, and Experimental Gerontology Section, Translational Gerontology Branch, National Institute on Aging, NIH, Baltimore, MD, USA

    Miguel A. Aon

  5. Universidad Nacional de Córdoba, Facultad de Ciencias Exactas, Físicas y Naturales, Instituto de Ciencia y Tecnología de los Alimentos (ICTA) and Catedra de Química Biológica. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Investigaciones Biológicas y Tecnológicas (IIByT, CONICET-UNC), Vélez Sarsfield 1611, Ciudad Universitaria, Córdoba, Argentina

    Jackelyn Melissa Kembro

Authors
  1. Ana Georgina Flesia
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  2. Paula Sofia Nieto
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  3. Miguel A. Aon
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  4. Jackelyn Melissa Kembro
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Corresponding author

Correspondence to Jackelyn Melissa Kembro .

Editor information

Editors and Affiliations

  1. Laboratory of Cardiovascular Science, National Institute on Aging, NIH, Baltimore, MD, USA

    Sonia Cortassa

  2. Translational Gerontology Branch, Laboratory of Cardiovascular Science, National Institute on Aging, NIH, Baltimore, MD, USA

    Miguel A. Aon

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Flesia, A.G., Nieto, P.S., Aon, M.A., Kembro, J.M. (2022). Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology. In: Cortassa, S., Aon, M.A. (eds) Computational Systems Biology in Medicine and Biotechnology. Methods in Molecular Biology, vol 2399. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-1831-8_13

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  • DOI: https://doi.org/10.1007/978-1-0716-1831-8_13

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  • Publisher Name: Humana, New York, NY

  • Print ISBN: 978-1-0716-1830-1

  • Online ISBN: 978-1-0716-1831-8

  • eBook Packages: Springer Protocols

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