Temporal Partitioning of the Yeast Cellular Network - Systems Biology of Metabolic and Signaling Networks - page 333

temperature (25 C and 36 C), strange attractor-like behaviour with clear bifurca-
tion points was observed.
In order to reveal the “scale-invariant” (fractal or self-similar) features of the
multi-oscillator, well-established approaches previously applied to time series were
employed (Aon et al. 2008 ). Thus, Relative Dispersional Analyses (RDA) of both
the O 2 and CO 2 data indicated that the observed multi-oscillatory dynamics corre-
spond to statistical fractals, as judged by the perfect correlation between oscillators
in the 13-h, 40-min and 4-min time domains. Thus, double-log plots exhibit an
inverse power relationship with a fractal dimension D f ( ¼ 1.0) implying that RD is
constant with scale (i.e. the time series looks statistically self-similar at all scales).
Long-term memory on timescales from minutes to hour is implicit in this
oscillatory behaviour. Power Spectral Analysis (PSA) also indicated an inverse
power law proportional to 1/ f β , and the value of

1.95 is close to that character-
istic of coloured noise, and again is as expected for the time series of a system that
displays deterministic chaos. The fractal nature of a chaotic time series has been
explained previously (Lloyd and Lloyd 1995 ). Moreover, and most significantly,
these characteristics indicate a functional scale-free statistically self-similar net-
work that operates simultaneously on several timescales (Aon et al. 2008 )soasto
provide coherence between time domains. A computational model indicated that
both in yeast and cardiomyocytes, underlying mechanisms of scale-free behaviour
are similar. This scale-free behaviour is supported by wavelet analyses of NAD(P)
H fluorimetry data sampled at 100 Hz (Fig. 12.9 ) and revealed how the
multioscillatory states correlated during the respiratory oscillation (Sasidharan
et al. 2012 ). In analysis we revealed a 4-, 12- and 20-min signals, whose amplitude
was modulated according to phase.
The 4-min period had not been observed previously in continuous cultures of
yeast, but may be related to oscillatory autofluorescence emission from NAD(P)H
in both mitochondrial and cytosolic compartments observed in contiguous single-
layered films of cells perfused with buffer-containing glucose (Aon et al. 2007 ).
Two-photon excitation of cells loaded with appropriate fluorescent probes indicated
oscillations in inner mitochondrial membrane potential ( ΔΨ m ) and superoxide
radical anions (O 2 • ) with definite phase relationships with the nicotinamide
nucleotide redox states. The inner membrane anion channel has a peripheral
benzodiazepine receptor, and an inhibitor, 4-Chlorodiazepam, attenuates the oscil-
lation both of the redox state and of the O 2 • as had previously been shown in
cardiomyocytes (Aon et al. 2003 ; Brown et al. 2008 ). This out-of-phase relationship
was lost after inhibitor treatment and washout. Superoxide dismutase addition was
ineffective at blocking the oscillations indicating that the signalling function of this
O 2 • serves intracellular rather than an intercellular role (Aon et al. 2008 ). Thereby,
yeast mitochondrial populations function as a network of coupled oscillators
through metabolite-linked communication (Cortassa et al. 2011 ). Inhibiting mito-
chondrial respiration at the level of cytochrome oxidase with H 2 S abates all
oscillatory frequencies including the 40-min-period ultradian clock, therefore
providing proof-of-principle that multi-scale timekeeping is an emergent property
of the overall network involved in metabolism, growth and proliferation in yeast, as

β ¼