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T. Amemiya et al.
level. However, only ambiguous oscillations will be observed if the degree of cell
synchronisation is low, which will be discussed below.
15.4 Dynamical Quorum Sensing and Kuramoto
Desynchronization
The cell-density dependent synchronisation behaviour in suspension culture systems
is called dynamical quorum sensing [42]. Quorum sensing is a phenomenon in which
microorganisms can sense a small, freely diffusible, and transient molecule, the
autoinducer, that accumulates to a critical concentration in a cell-density dependent manner in the extracellular environment [27]. In suspension culture, yeast cells
exhibit coherent oscillations at the population level by the exchange of a metabolite, acetaldehyde, pyruvate, H 2 S, or possibly ethanol [6, 9, 31, 43, 49]; however
these oscillations suddenly cease below the critical cell density, ca. 7 × 10
8 cells/ml.
Detailed mathematical analysis of the oscillatory behaviour revealed that individual
yeast cells have a coherent motion and stop oscillating in synchrony below the critical
cell density. This dynamical behaviour is phenomenologically similar to the Hopf
bifurcation in a single oscillator [21].
An intrinsically different type of transition to synchronised oscillatory behaviour
was observed in systems of immobilised yeast cells [60]. In the immobilised systems,
individual cells exhibited oscillations even at very low cell densities, ca. 1 ×
10
5 cells/ml, however collective oscillatory behaviour did not appear due to weak
coupling between cells at low densities. Whereas the collective coherent oscillations
appeared at high cell densities; thus, this collective oscillatory behaviour at population level is cell-density dependent. This type of transition from oscillations to
quiescence at the population level is called Kuramoto desynchronization [55, 57].
15.5 Glycolytic Oscillations in HeLa Cervical Cancer Cells
We have focused on the metabolic characteristics, namely, the Crabtree and/or
Warburg effects in yeast and cancer cells, and thus carried out experiments of
glycolytic oscillations in HeLa cells using systems of immobilised cells [5]. We
could observe their glycolytic oscillations in individual cell level for the first time
(Fig. 15.2).
Four characteristic behaviours in HeLa glycolytic oscillations can be summarised
as follows [5]: (i) starvation of glucose was indispensable for the oscillations, (ii)
starvation of both glucose and serum induced oscillations with longer periods and
larger amplitudes than those with only glucose starvation, (iii) the oscillations were
highly heterogeneous in terms of the number of oscillatory cells, periods of oscillations, and duration of oscillations in large populations of cells (N ≈ 700 − 900),
T. Amemiya et al.
level. However, only ambiguous oscillations will be observed if the degree of cell
synchronisation is low, which will be discussed below.
15.4 Dynamical Quorum Sensing and Kuramoto
Desynchronization
The cell-density dependent synchronisation behaviour in suspension culture systems
is called dynamical quorum sensing [42]. Quorum sensing is a phenomenon in which
microorganisms can sense a small, freely diffusible, and transient molecule, the
autoinducer, that accumulates to a critical concentration in a cell-density dependent manner in the extracellular environment [27]. In suspension culture, yeast cells
exhibit coherent oscillations at the population level by the exchange of a metabolite, acetaldehyde, pyruvate, H 2 S, or possibly ethanol [6, 9, 31, 43, 49]; however
these oscillations suddenly cease below the critical cell density, ca. 7 × 10
8 cells/ml.
Detailed mathematical analysis of the oscillatory behaviour revealed that individual
yeast cells have a coherent motion and stop oscillating in synchrony below the critical
cell density. This dynamical behaviour is phenomenologically similar to the Hopf
bifurcation in a single oscillator [21].
An intrinsically different type of transition to synchronised oscillatory behaviour
was observed in systems of immobilised yeast cells [60]. In the immobilised systems,
individual cells exhibited oscillations even at very low cell densities, ca. 1 ×
10
5 cells/ml, however collective oscillatory behaviour did not appear due to weak
coupling between cells at low densities. Whereas the collective coherent oscillations
appeared at high cell densities; thus, this collective oscillatory behaviour at population level is cell-density dependent. This type of transition from oscillations to
quiescence at the population level is called Kuramoto desynchronization [55, 57].
15.5 Glycolytic Oscillations in HeLa Cervical Cancer Cells
We have focused on the metabolic characteristics, namely, the Crabtree and/or
Warburg effects in yeast and cancer cells, and thus carried out experiments of
glycolytic oscillations in HeLa cells using systems of immobilised cells [5]. We
could observe their glycolytic oscillations in individual cell level for the first time
(Fig. 15.2).
Four characteristic behaviours in HeLa glycolytic oscillations can be summarised
as follows [5]: (i) starvation of glucose was indispensable for the oscillations, (ii)
starvation of both glucose and serum induced oscillations with longer periods and
larger amplitudes than those with only glucose starvation, (iii) the oscillations were
highly heterogeneous in terms of the number of oscillatory cells, periods of oscillations, and duration of oscillations in large populations of cells (N ≈ 700 − 900),