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

李雅普诺夫指数 自相关 小波 混乱的 计算机科学 白噪声 统计物理学 奥特典节律 生物系统 航程(航空) 噪音(视频) 人工智能 节奏 模式识别(心理学) 数学 统计 生物 物理 工程类 声学 图像(数学) 航空航天工程 电信
作者
Ana Georgina Flesia,Paula S. Nieto,Miguel A. Aon,Jackelyn Melissa Kembro
出处
期刊:Methods in molecular biology 卷期号:: 277-341 被引量:4
标识
DOI:10.1007/978-1-0716-1831-8_13
摘要

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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