The dynamics of intracellular water constrains glycolytic oscillations in Saccharomyces cerevisiae

We explored the dynamic coupling of intracellular water with metabolism in yeast cells. Using the polarity-sensitive probe 6-acetyl-2-dimethylaminonaphthalene (ACDAN), we show that glycolytic oscillations in the yeast S. cerevisiae BY4743 wild-type strain are coupled to the generalized polarization (GP) function of ACDAN, which measures the physical state of intracellular water. We analysed the oscillatory dynamics in wild type and 24 mutant strains with mutations in many different enzymes and proteins. Using fluorescence spectroscopy, we measured the amplitude and frequency of the metabolic oscillations and ACDAN GP in the resting state of all 25 strains. The results showed that there is a lower and an upper threshold of ACDAN GP, beyond which oscillations do not occur. This critical GP range is also phenomenologically linked to the occurrence of oscillations when cells are grown at different temperatures. Furthermore, the link between glycolytic oscillations and the ACDAN GP value also holds when ATP synthesis or the integrity of the cell cytoskeleton is perturbed. Our results represent the first demonstration that the dynamic behaviour of a metabolic process can be regulated by a cell-wide physical property: the dynamic state of intracellular water, which represents an emergent property.


Supporting Methods:
The generalized polarization (GP) function was originally introduced as an analytical method to quantitatively determine the relative amounts and temporal fluctuations of two distinct lipid phases when they coexist in a model membrane, for reviews see (1,2). This function was originally defined as: where I B and I R are the measured fluorescence intensities under conditions in which a wavelength (or a band of wavelengths) B (for blue shifted) and R (for red shifted) are both observed using a given excitation wavelength. Being a weighted difference, the values of the GP must fall within -1 and 1; the lower the value the greater the extent of relaxation (or bathochromic shift of the spectrum). This definition is formally identical to the classical definition of fluorescence polarization, in which B and R represent two orthogonal orientations of the observation polarizers in the fluorimeter. The advantage of the GP function for the analysis of the spectral properties of the DAN probes is derived from the well-known properties of the classical polarization function, which contains information on the interconversion between two different "states" of the emitting dipole of the fluorophore. In the original studies, the LAURDAN GP was shown to distinguish between the extent of water relaxation in solid-ordered (s o ) and liquid-disordered (l d ) phases in phospholipid membranes (1,2). In the GP function as used here, the two states correspond to the unrelaxed and relaxed environments sensed by the probes. Our approach to the study of intracellular water dynamics in yeast therefore constitutes a generalization of the use of the GP function (3,4). In this case, however, we explore fluctuations in water relaxation throughout the cell rather than in just membrane-associated water. The oscillations of the GP function in the cell ( Figure S1C) yielding the measured changes in the intensity of emission (quantum yield; Figure S1B) of the probes at any given wavelength can be explained only if solvent relaxation is the dominant mechanism. In the classical definition of GP, B and R correspond to 440 and 490 nm, respectively, of the ACDAN fluorescence emission spectrum (1,2).

Modelling the coupling of glycolytic oscillations with water dynamics
In order to put our experimental results in to a more rigid theoretical framework we use the Association-Induction hypothesis proposed by GN Ling (5). This hypothesis builds on the assumptions (i) that the bulk of water and various solutes are adsorbed on cellular proteins, (ii) that this adsorption is synchronized as a result of interactions of neighbouring adsorption sites (cooperativity), and (iii) that the cooperative adsorptions are controlled by a smaller number of molecular species referred to as cardinal adsorbents, which exert their control by interacting with certain key sites (cardinal sites) on the same proteins (5).
Here we give a brief outline of a recently developed model for the coupling of glycolytic oscillations with intracellular water dynamics. The model is based on an earlier model of glycolysis (6) using the generally accepted view that phosphofructokinase is a key enzyme in controlling the pace of glycolysis and that the enzyme shows cooperativity with respect to binding of ATP and is activated by its product ADP (6). However, instead of using the classical mass-action based Michaelis-Menten (or for cooperative enzymes Monod-Wyman-Changeux) approach, we use Yang-Ling isotherms (5,7,8) for describing the transformation of ATP to ADP and its coupling to the state of water, which is denoted p (for polarized). As opposed to the Monod-Wyman-Changeux and the related Koshland-Nemethy-Filmer models the Yang-Ling isotherm has a statistical-mechanical origin and is general.
The full description of the model will be presented elsewhere (manuscript in preparation), but briefly the equations are where v PFK is defined by: where V 1 is a maximum rate for the ATP-induced transition of water from a less to a more polarized state (p) and 1 and − 1 2 represent the dissociation constant and the nearest neighbour interaction energy for binding of ATP to fibrillary proteins, e.g. actin.
We now assume that the maximum activity of PFK (V) and the dissociation constant for binding of ATP ( ) depend on the variable p, i.e. V(p) and ( ). It is well-documented that for enzymes in viscous solutions the maximum activity and the binding constants of substrates change with crowding (9,10). For simplicity we assume that V is inversely proportional to p, while is proportional to p. However, other relations between the two parameters and p will yield similar behaviour. Furthermore, it is quite possible that many of the other parameters in equations S2-S3 may depend on p, but again this will only have qualitative effect on the behaviour of the model. In the current form of the model ATP, ADP , p and time t appear as dimensionless variables. The model was simulated using the Berkeley-Madonna software (Berkeley-Madonna, Berkeley, CA) Simulations of the model are shown in Figs. S16 and S17. The data in Fig. S16 reveal that ATP and p oscillate in phase as revealed by the phase plot in Fig. S16C. Note that this phase plot is similar to that of ATP and ACDAN fluorescence (Fig. S3C). Furthermore, reducing either the maximum velocity V 1 or increasing the rate constant k o will destroy the oscillations. This situation corresponds to that in Fig. 6 where the formation of actin filaments is inhibited by Latrunculin B. Changing the rate constant k o will change the steady-state level of p, which again will affect the amplitude and the frequency of the oscillations. A plot of the relative amplitude of oscillations of ATP against the steady-state value of p reveals a double Hopf bifurcation (Fig. S17), similar to the experimental Hopf bifurcation shown in Fig. 4A. Finally, the model predicts that simple mechanical coupling of p in a region where glycolytic oscillations occur to the polarization of water (p 1 ), in a region where glycolytic oscillations are absent, would result in a slight phase shift in the oscillations of p and p 1 (Fig. S18), which is confirmed experimentally (Fig S19).
It should be emphasized that the variables in the model constitute a network (11), and hence one cannot say that metabolic oscillations drive oscillations in the polarization of water or the other way around. Furthermore, in such a network one cannot study the individual components in isolation, e.g. by assuming that situations may exist in which one variable shows oscillations while others do not.
To investigate if the results obtained with the simple model (equations S2-S4) are general we also implemented the Yang-Ling approach to the coupling of the polarity of water to glycolytic oscillations on a detailed model of glycolysis adapted from Hald and Sørensen (12). The model, which involves 24 reactions and 32 chemical species, is shown in Fig. S20 and Fig. S21 shows two phase plots of p versus [ATP] and p versus [NADH], respectively. We note that the first phase plot is similar to those in Fig. S3C and S16C, showing that p is in phase with [ATP] as observed experimentally and with our simple model. While the simple model (equations S2-S4) does not involve NADH it is interesting to compare phase plots of p versus [NADH] in the detailed model ( Fig. S21B) with the corresponding plots of ACDAN versus NADH fluorescence (Fig. S3D). Both plots show that the oscillations of ACDAN GP are in antiphase with oscillations in NADH.

Table S1
Corresponding values of growth temperature, measurement temperature, ACDAN GP and oscillation frequency for the wild type BY4743 S. cerevisiae strain. A frequency of 0 s −1 means that no oscillations were obtained at the particular temperature.

Figure S2
Oscillations in NADH and Glucose 6-phosphate in S. cerevisiae cells grown at 30 °C. Yeast cells (10% w/v) were suspended at 25 °C in 100 mM potassium phosphate, pH 6.8 and oscillations were induced as described in Fig. S1. Measurements of intracellular glucose 6-phosphate were made by quenching the cells with boiling buffered ethanol and subsequently extracting the metabolites (13). The concentration of glucose 6-phosphate was then measured by addition of NADP + and glucose 6-phosphate dehydrogenase to the extract. The concentration of glucose 6-phosphate in the extract was determined from the concentration of formed NADPH using standard curves measured on solutions with known concentrations of glucose 6phosphate. In the estimation of the intracellular concentration of glucose 6-phosphate we assumed that 1 mg protein corresponds to a cytoplasmic volume of 3.7 µl.    Note that the cells grown on glycerol exhibit far more mitochondria and their respiration rate is more than twice that of cells grown on glucose. Images were obtained on a Leica DMRE epifluorescence microscope using a CoolLed illumination system (CoolLed, Andover, U.K.) through a 100X Leica oil-emission objective (NA = 1.4). Images of ACDAN fluorescence were obtained using a Leica Microsystems A4 filter cube, while images of MitoTracker Red were obtained using a Leica Microsystems Y3 filter cube. In the emission range 462 ± 24 nm there is no visible contribution of NADH fluorescence from the control cells upon excitation at 810 (g), 780nm (h) or 740nm (i) at the used settings. Intensity profiles reveal that the intensities in (g)-(i) are not above the background noise. A comparison of (j) and (e) reveals that in order to visualize NADH in unstained cells (j) the ACDAN signal becomes significantly oversaturated (e). The maximum laser power (i.e., the power output from the laser before interaction with filters and optics) are 790mW at 810nm, 740mW at 780nm and 675mW at 740nm. In (b)-(d) and (g)-(i) the used laser power was 40% of the maximum, while in (e) and (j) it was 60%. Scale bars are 10 µm.       Table S2. The ethanol production rate is normalized to that of the wild type strain. Calibration of the mass spectrometry ethanol signal showed that more than 80% of the added glucose is converted to ethanol in all strains. The dashed line is a linear regression to the data. It has a slope of 7.2×10 −3 and the R 2 value is 1.6×10 −3 .    Figure S15.

Figure S18
Phase plot of polarization of water in two different regions of the cell: one in which glycolytic oscillations occur (p) and another in which glycolytic oscillations are absent (p 1 ). The simulation assumes simple mechanical coupling of p to p 1 . Parameters as in Fig. S15.

Figure S19
Simultaneous measurements of oscillations in ACDAN (A) and Nile Red (B) fluorescence in the wild type strain S. cerevisiae BY4743 strain. A 10% (w/v) cell suspension in 100 mM potassium phosphate buffer, pH 6.8, was incubated at room temperature for 1 h with 10 µM ACDAN and 5 µM Nile red. Then the cells were washed twice and resuspended in the same buffer. ACDAN was excited at 365 nm and its emission was measured at 450 nm, while Nile red was excited at 550 nm with its emission measured at 630 nm. The plot in C is a phase plot of the two measurements. Yeasts were grown at 30 °C. Oscillations were induced by addition of first 30 mM glucose (arrow) and 60 s later 5 mM KCN. Measurement temperature was 25 °C.