Rhythms, Clocks and Deterministic Chaos in Unicellular Organisms

Temporal metabolic partitioning of the yeast and protist cellular networks: the cell is a global scale-invariant (fractal or self-similar) multioscillator

“…It indicates that what affects function on one time-scale has effects on all, [98][99][100][101][102][103] which is an intrinsic property of fractal systems. 97 Physiological tuning of the chaotic attractor of metabolic origin shown in self-synchronized continuous cultures of yeast with several periods of 13 h, 40 min, and 4 min embedded 93 could potentially function as a source of multiple frequencies at the origin of ultradian (even circadian) rhythms.…”

An appreciation of the prescience of Don Gilbert (1930–2011): master of the theory and experimental unravelling of biochemical and cellular oscillatory dynamics

“…Deterministic chaos had previously been demonstrated in biological systems and in enzyme catalysed reactions in vitro (Olsen and Degn, 1977, 1978, 1985). Advantages may be discovered for such an “ergodic system” (one in which every point in the dynamic trajectory is visited), possibly providing opportunities for innovative performance (Lloyd and Lloyd, 1993, 1995; Lloyd, 2009; Lloyd et al, 2015). Gradual lowering of the pH of the yeast culture also results in the appearance of a strange attractor in the respiratory dynamics, one signature of chaotic behaviour (Murray and Lloyd, 2007).…”

Network dynamics: quantitative analysis of complex behavior in metabolism, organelles, and cells, from experiments to models and back

“…For example, periodicity in metabolic fluxes can be found under conditions of oxidative stress where mitochondrial ATP synthesis can oscillate in the order of seconds to a few minutes entraining ROS and metabolites from the tricarboxylic acid cycle, e.g., succinate (Figure ); in yeast, respiration may vary over time scales ranging from few minutes to several hours (see Figure 10); in sheep, prolactin secretion levels show seasonal timing throughout the year . In plants, oscillatory periodicity ranges from femtoseconds in photosynthetic events to infradian rhythms associated with seasonal and annual changes . Most animals experience seasonal changes in physiology and behavior such as annual rhythms in reproduction, immune function, metabolism, migration, and many others .…”

“…The convergence of trajectories to a subspace of the phase space constitutes an attractor of the system's dynamic behavior. Nonlinear systems display a wide repertoire of attractors in phase space, including limit cycles or closed loops (from oscillations), torus of ‘donut’ shape (quasiperiodic dynamics from superposition of different periods), and strange with fractal geometry (deterministic chaos) . Shifting dynamics between different types of attractor occur through bifurcations, i.e., abrupt changes in the stability of a system dynamics as reflected by a radically different qualitative behavior (e.g., steady, oscillatory, and chaotic) at critical values of the control (bifurcation) parameter (Figures and ).…”

“…Earth rotation and the subsequent daily variations in environmental parameters have a large impact on organisms, inspiring a classification of biological periodicities based on frequency according to the 24 h day/light cycle as: ultradian (<24 h), circadian (≈24 h) and infradian (>24 h), while longer processes can be associated to the yearly circannual cycle. Evolution in a periodic environment has led to the development of organisms finely tuned to exploit all possible advantages bestowed by rhythmic performance, spanning many decades measured in seconds 77,78 (Table 1).…”