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

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.

From the seminal discovery of proteoglycogen and glycogenin to emerging knowledge and research on glycogen biology.

Although the discovery of glycogen in the liver, attributed to Claude Bernard, happened more than 160 years ago, the mechanism involved in the initiation of glucose polymerization remained unknown. The discovery of glycogenin at the core of glycogen's structure and the initiation of its glucopolymerization is among one of the most exciting and relatively recent findings in Biochemistry. This review focuses on the initial steps leading to the seminal discoveries of proteoglycogen and glycogenin at the beginning of the 1980s, which paved the way for subsequent foundational breakthroughs that propelled forward this new research field. We also explore the current, as well as potential, impact this research field is having on human health and disease from the perspective of glycogen storage diseases. Important new questions arising from recent studies, their links to basic mechanisms involved in the de novo glycogen biogenesis, and the pervading presence of glycogenin across the evolutionary scale, fueled by high throughput -omics technologies, are also addressed.

The fractal organization of ultradian rhythms in avian behavior.

Living systems exhibit non-randomly organized biochemical, physiological, and behavioral processes that follow distinctive patterns. In particular, animal behavior displays both fractal dynamics and periodic rhythms yet the relationship between these two dynamic regimens remain unexplored. Herein we studied locomotor time series of visually isolated Japanese quails sampled every 0.5 s during 6.5 days (>106 data points). These high-resolution, week-long, time series enabled simultaneous evaluation of ultradian rhythms as well as fractal organization according to six different analytical methods that included Power Spectrum, Enright, Empirical Mode Decomposition, Wavelet, and Detrended Fluctuation analyses. Time series analyses showed that all birds exhibit circadian rhythms. Although interindividual differences were detected, animals presented ultradian behavioral rhythms of 12, 8, 6, 4.8, 4 h and/or lower and, irrespective of visual isolation, synchronization between these ultradian rhythms was observed. Moreover, all birds presented similar overall fractal dynamics (for scales ∼30 s to >4.4 h). This is the first demonstration that avian behavior presents fractal organization that predominates at shorter time scales and coexists with synchronized ultradian rhythms. This chronobiological pattern is advantageous for keeping the organism's endogenous rhythms in phase with internal and environmental periodicities, notably the feeding, light-dark and sleep-wake cycles.

High resolution, week-long, locomotion time series from Japanese quail in a home-box environment.

Temporal and spatial patterns of locomotion reflect both resting periods and the movement from one place to another to satisfy physiological and behavioural needs. Locomotion is studied in diverse areas of biology such as chronobiology and physiology, as well as in biomathematics. Herein, the locomotion of 24 visually-isolated Japanese quails in their home-box environment was recorded continuously over a 6.5 days at a 0.5 s sampling rate. Three time series are presented for each bird: (1) locomotor activity, (2) distance ambulated, and (3) zone of the box where the bird is located. These high resolution, week-long, time series consisting of 1.07×10(6) data points represent, to our knowledge, a unique data set in animal behavior, and are publically available on FigShare. The data obtained can be used for analyzing dynamic changes of daily or several day locomotion patterns, or for comparison with existing or future data sets or mathematical models across different taxa.

Complex oscillatory redox dynamics with signaling potential at the edge between normal and pathological mitochondrial function.

The time-keeping properties bestowed by oscillatory behavior on functional rhythms represent an evolutionarily conserved trait in living systems. Mitochondrial networks function as timekeepers maximizing energetic output while tuning reactive oxygen species (ROS) within physiological levels compatible with signaling. In this work, we explore the potential for timekeeping functions dependent on mitochondrial dynamics with the validated two-compartment mitochondrial energetic-redox (ME-R) computational model, that takes into account (a) four main redox couples [NADH, NADPH, GSH, Trx(SH)2], (b) scavenging systems (glutathione, thioredoxin, SOD, catalase) distributed in matrix and extra-matrix compartments, and (c) transport of ROS species between them. Herein, we describe that the ME-R model can exhibit highly complex oscillatory dynamics in energetic/redox variables and ROS species, consisting of at least five frequencies with modulated amplitudes and period according to power spectral analysis. By stability analysis we describe that the extent of steady state-as against complex oscillatory behavior-was dependent upon the abundance of Mn and Cu, Zn SODs, and their interplay with ROS production in the respiratory chain. Large parametric regions corresponding to oscillatory dynamics of increasingly complex waveforms were obtained at low Cu, Zn SOD concentration as a function of Mn SOD. This oscillatory domain was greatly reduced at higher levels of Cu, Zn SOD. Interestingly, the realm of complex oscillations was located at the edge between normal and pathological mitochondrial energetic behavior, and was characterized by oxidative stress. We conclude that complex oscillatory dynamics could represent a frequency- and amplitude-modulated H2O2 signaling mechanism that arises under intense oxidative stress. By modulating SOD, cells could have evolved an adaptive compromise between relative constancy and the flexibility required under stressful redox/energetic conditions.

Ultrasensitive behavior in the synthesis of storage polysaccharides in cyanobacteria.

The glycogen synthetic pathway operates ultrasensitively as a function of the ADPglucose pyrophosphorylase (ADPGlcPPase) allosteric effectors, 3-phosphoglycerate and Pi, in permeabilized cells of the cyanobacterium Anabaena PCC 7120. In vitro data previously showed that the ultrasensitive behavior of ADPGlcPPase depends upon cross-talk between the two allosteric effectors, the enzyme's response being additionally modulated by molecular crowding [D.F. Gómez Casatiet al. (2000) Biochem J 350:139-147]. In the present work we show, experimentally and with a mathematical model, that alpha-1,4-glucan synthesis is also ultrasensitive in cells due to the propagation of the switch-like behavior of ADPGlcPPase to the synthetic pathway. Amplifications of up to 20-fold in storage-polysaccharide synthesis can be achieved with a modest 6.7-fold increase in 3-phosphoglycerate in the presence of 5 mM Pi in contrast to the 30-fold necessary in its absence. This is the first time that this phenomenon has been reported to occur in the glycogen synthetic pathway of a photosynthetic prokaryote. The implications of the results for plant cell physiology during light-dark transitions are discussed.

Coherent and robust modulation of a metabolic network by cytoskeletal organization and dynamics.

In order to investigate the influence of cytoskeletal organization and dynamics on cellular biochemistry, a mathematical model was formulated based on our own experimental evidence. The model couples microtubular protein (MTP) dynamics to the glycolytic pathway and its branches: the Krebs cycle, ethanolic fermentation, and the pentose phosphate (PP) pathway. Results show that the flux through glycolysis coherently and coordinately increases or decreases with increased or decreased levels of polymerized MTP, respectively. The rates of individual enzymatic steps and metabolite concentrations change with the polymeric status of MTP throughout the metabolic network. Negative control is exerted by the PP pathway on the glycolytic flux, and the extent of inhibition depends inversely on the polymerization state of MTP, i.e. a high degree of polymerization relieves the negative control. The stability of the model's steady state dynamics for a wide range of variation of metabolic parameters increased with the degree of polymerized MTP. The findings indicate that the organization of the cytoskeleton bestows coherence and robustness to the coordination of cellular metabolism.