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Fig. 12.7 (a) Protonophore
concentration decreases
during continuous dilution of
Saccharomyces cerevisiae
culture. (b) Escalating
consequences over multiple
scales (0.1-10,000 s)
In terms of the kinetics of mitochondrial processes, it is quite remarkable that
these organelles are characteristically associated with an extremely dynamic poten-
tiality (as determined by their rapid metabolic responses in vitro after extraction
from organisms). However, in vivo they behave quite differently and their changing
properties and functions during an oscillation cycle are evidently constrained
(Lloyd and Edwards
1984
; Marques et al.
1987
). We have suggested that inside
cells or organisms mitochondria not only display rapid kinetics but also have slower
oscillatory modes that suggest that “they dance to a tune that is played by a piper
performing elsewhere in the cell”. In situ, the mitochondrion is enslaved to the
slower beat of the nucleo-cytosolic system.
12.8 The Multi-Oscillatory State
The use of membrane inlet mass spectrometry to monitor dissolved gas levels
(O
2
,CO
2
and H
2
S; Fig.
12.8
) directly in the continuous culture at 12 s interval
sampling time showed a predominant large-amplitude period of approximately
13.6 h, with superimposed 40 min, and an intermittent 4-min oscillation (Roussel
and Lloyd
2007
). A metabolic attractor was constructed using more than 36,000
points collected at 15 s intervals from a single experiment, lasting for 3 months.
Computation of the leading Lyapounov exponent (0.752
0.004 h
1
; 95 % confi-
dence), which is clearly demarcated from 0, indicated the dynamics on this attractor
was chaotic. This chaotic behaviour was further supported by the Poincar
´
plots of
data taken from a time frame of weeks during the 40-min cycle, while amplitude
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