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Experiments were performed with aerobically grown yeast cells from Saccharomyces carlsbergensis (ATCC 9080; American Type Culture Collection, Manassas, VA, USA) cultivated aerobically in a rotary shaker (180 rpm) in liquid semisynthetic minimal medium [22] at 28°C. The cells were grown until the glucose in the medium was just exhausted at the transition from the logarithmic to the stationary growth phase. After harvesting the cells by centrifugation at 5000g at 21°C and washing them with distilled water, the wet cells were suspended in 0.1 M KH2PO4 buffer, pH 6.5, as a 20% (weight/volume) suspension and stirred at 23°C until they showed NADH oscillations. This generally occurred after 3–5 h of starvation. After starvation the cells were aliquoted in 1.5 ml Eppendorf cups and kept at 0°C for at most 3 days until use. Prior to measuring signals of cell populations, the aliquoted cells were diluted in 0.1 M KH2PO4 buffer, pH 6.5 to densities in the range of = 0.8–0.001% (w/v) (i.e. 120106–0.1106 cells/ml) and well aerated by stirring the suspension for at least 5 min. Some experiments were conducted using cells of the yeast Saccharomyces cerevisiae diploid strain X2180. The cells were grown under aerobic conditions at 30°C in a rotary shaker (150 rpm) in a medium containing 10.0 g/l glucose, 6.7 g/l yeast nitrogen base (Bacto) and 100 mM potassium phthalate (Aldrich) at pH 5.0 until the glucose in the medium was exhausted. The yeast was harvested by centrifugation at 4066g for 3 min at 21°C, washed twice with 100 mM potassium phosphate buffer (Merck, Germany), pH 6.8 (centrifugation, 3 min at 4066g) and re-suspended in the same buffer to a cell density of 10% (w/v). The cells were starved in suspension by shaking (30°C, 150 rpm) for 3 h and handled then as S. carlsbergensis, but with 100 mM potassium phosphate buffer (pH 6.8). Immobilisation of yeast cells in the batch chamber: Single yeast cells were immobilised on polylysine-coated coverslips. To this purpose, the coverslips were washed with acetone and distilled water. Subsequently, 100l of a 0.1 mg/l poly-D-lysine solution were spread on the coverslips, which were then dried in an oven at 50°C. Before use, they were carefully washed with water again and dried. Finally, a dry coverslip was fixed at the bottom of the batch chamber mounted above the objective of the inverted microscope. The batch chamber consists of two parts between which the coated coverslip is clamped. 100l well-aerated yeast suspension of a chosen cell density were placed into the chamber (consequently, the number of cells in the chamber varied according to the cell densities studied). After 30 min all cells settled and adhered to the coverslip when their plasma membranes got in contact with the polylysine coating. After sedimentation the experiment was started. To induce anaerobiosis 3 mM potassium cyanide were added, followed by an addition of 52 mM glucose 10 min later, which triggered the glycolysis and induced oscillations in the cells.
The intracellular dynamics was monitored through the autofluorescence of NADH which serves as an indicator for the glycolytic activity [22]. NADH is an intracellular metabolite which is directly involved in the glycolysis. The NADH autofluorescence (absorption maximum at = 340 nm; emission maximum at = 460 nm [42]) from single yeast cells was measured with an inverted Nikon Ti Eclipse (Nikon GmbH, Germany) microscope, equipped with a 100/0.5–1.3 plan fluor lens and a position sensitive single photon counting photomultiplier tube as described previously [43]. For excitation of intracellular NADH a 8 MHz pulsed frequency-tripled Nd:vanadate laser tuned at 355 nm (HighQ Laser, Austria) was used. A dichroic mirror (z355rdc, AHF Analysentechnik, Germany) discriminated between excitation and emission. The emission light of yeast cells was filtered by a long-pass (LP 442 nm, Brightline, AHF, Germany) and a bandpass filter (FF01-440/40, Brightline, AHF, Germany) and detected by the photomultiplier. For all studied samples, the laser intensity was adjusted such that there was an incidence of 3,000–65,000 fluorescence photons/s at the detector, thus making sure that it operates under optimal conditions. The acquired photon positions were binned into frames of 512512 pixels, resulting in a resolution of 0.33m/pixel in the object space. The field of view had a diameter of 169m. The photon flux was integrated over 2 s time intervals, which was a sufficient sampling rate to analyse glycolytic oscillations with periods in a range of 24–70 s.
The global, collective signal of the whole population of yeast cells and the signal from individual cells were analysed separately. The immobilised yeast cells were randomly distributed on the coverslip. The collective signal was determined as the fluorescence light emitted from all cells in the entire area of observation. Therefore, all incident photons were summed up every second. For the analysis of single cell signals, the position of each cell in the population was determined and its area, in pixels, marked. At any time, the single cell fluorescence is the mean value of the intensity of the fluorescence signal detected in the area occupied by an individual cell(1)where is the number of incident photons originating from the area of the single cell. The temporal sequence of yields the time evolution of the fluorescence of an individual cell. For comparison, the amplitudes of the metabolic oscillations of the individual cells were normalised. Here, the norm was set by the oscillating amplitude of the cell in the population that showed the highest oscillatory amplitudes.
Analysis of synchronicity within populations: From the time series of each cell in a population, we subtracted the baseline to eliminate spurious drifts and trends. The baseline was computed as the walking average of the fluorescence data using a time window corresponding to one period of oscillation. After baseline subtraction, we obtained oscillations around zero and determined their frequencies by a fast Fourier transform. The standard deviation of the periods of oscillation of single cells was calculated as(2)where is the oscillation period of the th cell, is the averaged period, and is the number of cells. The noise in the time-series was filtered through a Fourier bandpass filter which cut off frequencies higher than 0.05 Hz and lower than 0.014 Hz. Thus, the frequencies of the glycolytic oscillations remained in the filtered time series . The phases of each oscillating cell (3)were computed trough the Hilbert transform(4)of the filtered single cell signal . The order parameter K, introduced by Shinomoto and Kuramoto [38],(5)and the time-averaged order parameter (6)were chosen for measuring the phase synchronisation. If the order parameter is close to 1 the coherence of oscillators in a population is high and if is 0 the cells oscillate at random phases. The standard deviation of (eq. 5) and the mean value are used to quantify the phase synchronisation in each measurement.
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