Cells can enter into a dormant state when faced with unfavorable conditions. However, how cells enter into and recover from this state is still poorly understood. Here, we study dormancy in different eukaryotic organisms and find it to be associated with a significant decrease in the mobility of organelles and foreign tracer particles. We show that this reduced mobility is caused by an influx of protons and a marked acidification of the cytoplasm, which leads to widespread macromolecular assembly of proteins and triggers a transition of the cytoplasm to a solid-like state with increased mechanical stability. We further demonstrate that this transition is required for cellular survival under conditions of starvation. Our findings have broad implications for understanding alternative physiological states, such as quiescence and dormancy, and create a new view of the cytoplasm as an adaptable fluid that can reversibly transition into a protective solid-like state.https://doi.org/10.7554/eLife.09347.001
Most organisms live in unpredictable environments, which can often lead to nutrient shortages and other conditions that limit their ability to grow. To survive in these harsh conditions, many organisms adopt a dormant state in which their metabolism slows down to conserve vital energy. When the environmental conditions improve, the organisms can return to their normal state and continue to grow.
The interior of cells is known as the cytoplasm. It is very crowded and contains many molecules and compartments called organelles that carry out a variety of vital processes. The cytoplasm has long been considered to be fluid-like in nature, but recent evidence suggests that in bacterial cells it can solidify to resemble a soft glass-type material under certain conditions. When cells become dormant they stop dividing and reorganise their cytoplasm in several ways; for example, the water content drops and many essential proteins form storage compartments. However, it was not clear how cells regulate the structure of the cytoplasm to enter into or exit from dormancy.
Now, Munder et al. analyse the changes that occur in the cytoplasm when baker’s yeast cells enter a dormant state. The experiments show that when yeast cells are deprived of energy – as happens during dormancy – the cytoplasm becomes more acidic than normal. This limits the ability of molecules and organelles to move around the cytoplasm. Similar results were also seen in other types of fungi and an amoeba. Munder et al. found that this increase in acidity during dormancy causes many proteins to interact with each other and form large clumps or filament structures that result in the cytoplasm becoming stiffer.
A separate study by Joyner et al. found that when yeast cells are starved of sugar, two large molecules are less able to move around the cell interior. Together, the findings of the studies suggest that the interior of cells can undergo a transition from a fluid-like to a more solid-like state to protect the cells from damage when energy is in short supply. The next challenge is to understand the molecular mechanisms that cause the physical properties of the cytoplasm to change under different conditions.https://doi.org/10.7554/eLife.09347.002
The cytoplasm of living cells is highly dynamic and yet exquisitely organized. Maintenance of this state requires a constant input of energy and a metabolism that is far from thermodynamic equilibrium. However, organisms typically live in unpredictable environments and frequently experience conditions that are not optimal for growth and reproduction. Under such conditions, cells must protect themselves by entering into a non-dividing state, generally referred to as dormancy (Lennon and Jones, 2011).
Dormancy is defined as a state of reversible cell cycle arrest with reduced metabolic activity and changes in cellular organization (Lennon and Jones, 2011). It often involves execution of a developmental program, which culminates in the formation of specialized cell types such as spores, seeds, or cysts. These cell types can endure long periods of nutrient starvation, low temperatures, and even desiccation. Dormancy is also accompanied by extensive changes in cellular architecture, some of which are drastic. For instance, dormant cells have a very low water content, their cytoplasm is densely packed, and they show strongly diminished intracellular dynamics (Ablett et al., 1999; Cowan et al., 2003; Dijksterhuis et al., 2007; Parry et al., 2014). However, how cells enter into and recover from such a state is still unresolved.
The current paradigm of cellular biochemistry is based on studies in dilute solutions, often performed with only a handful of proteins. Findings made in such dilute regimes have been extrapolated to the cellular interior. In recent years awareness has been increasing that the cellular environment is very different from such dilute regimes. One reason for this is that the cytoplasm is densely packed with macromolecules. The overall concentration of macromolecules in the cytoplasm is estimated to be around 200–350 mg/ml (Ellis, 2001; Zimmerman and Trach, 1991), which amounts to a volume fraction of up to 40%. This dense packing of macromolecules is referred to as macromolecular crowding. How macromolecules remain soluble at such high concentrations inside a cell is unknown, but it presumably involves a fine balance of attractive and repulsive interactions between the different cytoplasmic components.
The highly crowded conditions inside a cell generate an environment with specific physical properties. These properties have traditionally been explored by following the diffusive behavior of tracer particles or organelles. Such particle-tracking approaches have led to the realization that intracellular diffusion is anomalous in cells (Dix and Verkman, 2008; Hall and Hoshino, 2010; Luby-Phelps, 2000; Tolić-Nørrelykke et al., 2004). Based on these findings, proposals have been made about the physical nature of the cytoplasm, which has either been described as a hydrogel (Fels et al., 2009) or, more recently, as a liquid at the transition to a glass-like state (Parry et al., 2014). Because many metabolic reactions and signaling processes take place in the cytoplasm, changes in its physicochemical properties should have far-reaching effects on cellular function and survival.
Recent findings indicate that the organization of the cytoplasm can change considerably, in particular under stress conditions such as starvation. In energy-depleted yeast cells, many proteins and RNAs assemble into microscopically visible structures (Laporte et al., 2008; Narayanaswamy et al., 2009; Noree et al., 2010; O'Connell et al., 2012; Sagot et al., 2006). These structures may constitute storage depots for proteins and RNAs (Daignan-Fornier and Sagot, 2011; Laporte et al., 2008; Sagot et al., 2006). Indeed, several metabolic enzymes assemble into filamentous structures in response to starvation, and the formation of these filaments leads to enzymatic inactivation (Petrovska et al., 2014). Importantly, the enzymes contained in these filaments can be reused, when cells escape from dormancy. This suggests that cells may regulate the structure of the cytoplasm to enter into and exit from a metabolically inactive state.
In this study, we demonstrate that, in acidic environments, entry into dormancy is triggered by an influx of protons that promotes a transition of the cytoplasm from a fluid- to a solid-like state through widespread assembly of proteins into higher-order structures. We show that this transition arrests the movement of organelles and foreign tracer particles. We provide further evidence that this state of reduced intracellular mobility is required for survival of energy depletion stress. Thus, we propose that organisms have global control mechanisms in place to fine-tune the material properties of the cytoplasm, allowing them to enter into a protective solid-like state, when challenged by extreme environmental conditions.
To investigate how eukaryotic cells enter into a dormant state, we focused on budding yeast, a single-celled organism, which can enter into dormancy upon depletion of energy (De Virgilio, 2012; Gray et al., 2004; Neiman, 2011; Valcourt et al., 2012). Because a strong reduction in intracellular dynamics is a hallmark of dormant cells (Cowan et al., 2003; Dijksterhuis et al., 2007; Mastro et al., 1984; Parry et al., 2014), we first compared the mobility of different cellular organelles in dividing and dormant yeast cells (Huh et al., 2003). Induction of a dormant state was achieved by treating yeast cells with 2-deoxyglucose (2-DG, an inhibitor of glycolysis) and antimycin A (an inhibitor of mitochondrial respiration), a treatment that decreases cellular ATP levels by more than 95% (Serrano, 1977). Using single particle tracking (SPT) and mean squared displacement (MSD) analysis we found a striking reduction in intracellular movements upon energy depletion (Figure 1A and B).
Tracking of endogenous particles provides only limited information on the material properties of the cytoplasm, because they are often membrane-associated and/or move by active transport. Therefore, foreign tracer particles are better suited as probes of the subcellular environment. However, direct injection methods of foreign particles, as they have been developed for mammalian cells, are not feasible for yeast cells because of their small size. We therefore adopted a technique that relies on a genetically encoded viral capsid protein (µNS), which has been used successfully in bacteria (Parry et al., 2014). We could show that GFP-µNS self-assembles into distinct particles in the yeast cytoplasm (Figure 1—figure supplement 1, Video 1). These particles have bead-like properties with a size-dependent MSD and generalized diffusion coefficient (Figure 1—figure supplement 2 and 3), indicating that they are a valuable tool to study the properties of the yeast cytoplasm. Using GFP-µNS particles and SPT, we found that energy depletion caused a similar reduction in the mobility of these foreign particles (Figure 1C). Thus, we conclude that upon energy depletion, the cytoplasm of budding yeast transitions into a state with strongly reduced dynamics.
In higher eukaryotes, ATP-driven processes exert fluctuating forces on the cytoplasm, which lead to random movements of particles and thus cytoplasmic mixing (Brangwynne et al., 2008, 2009; Guo et al., 2014). These effects are predominantly driven by motor proteins, which are linked to the cytoskeleton. However, in contrast to mammalian cells, yeast cells have a cell wall, and thus only a rudimentary cytoskeleton, which is primarily based on actin. Importantly, the actin cytoskeleton of yeast disassembles upon starvation (Sagot et al., 2006), suggesting that this event may be responsible for the reduced particle mobility by removing tracks for motor-based mixing. To test this, we depolymerized the actin cytoskeleton by adding the drug latrunculin A (LatA) to dividing yeast cells. Indeed, GFP-µNS particle mobility was reduced, but the effect was much less pronounced than under conditions of energy depletion (Figure 2A). Next, we treated yeast cells with the drug nocodazole to inhibit microtubule-based motor movements. Again, we only observed marginal effects on particle mobility (Figure 2B). This indicates that a lack of active motor-driven movements can only partially explain the reduced particle mobility.
Yeast typically live in acidic environments. The standard laboratory growth media therefore have a pH of around 5.5 (see materials and methods for details). However, the cytosolic pH is kept in the neutral range by proton-translocating ATPases such as Pma1, which use a large amount of energy to continuously pump protons out of the cell, thus preventing cytosolic acidification (Orij et al., 2011). In agreement with this, previous studies have reported that energy depletion leads to a drop in cytosolic pH (pHc) (Dechant et al., 2010; Orij et al., 2012). Indeed, using a ratiometric, pH-sensitive variant of GFP (Mahon, 2011) (Figure 2—figure supplement 1), we observed a significant pHc decrease from around 7.3 to around 5.8 in yeast cells that were energy-depleted in normal growth medium of pH 5.5 (Figure 2C). If this drop in pHc was responsible for the reduced particle mobility, it should be possible to prevent particle immobilization by keeping the pHc in the neutral range. Indeed, when yeast cells were energy-depleted in growth medium of neutral pH, cytosolic acidification could be prevented (Figure 2C) and the reduction in particle mobility was much less pronounced (Figure 2D). Thus, we conclude that strong energy depletion leads to a rapid drop in cytosolic pH, which in turn causes reduced particle mobility.
We next tested whether direct manipulation of the cytosolic pH in the presence of an energy source is sufficient to induce reduced particle mobility. The protonophore DNP rapidly carries protons across the cell membrane and effectively equilibrates the intracellular with the extracellular pH (Dechant et al., 2010; Petrovska et al., 2014). This allowed us to manipulate the intracellular pH by keeping cells in DNP-containing buffers of different pH (Figure 3A, left panel). Cells exposed to DNP-containing buffers generally showed a reduced particle mobility, when compared to cells growing in medium (see Figure 1C), most likely because of direct effects of DNP on metabolism. However, the particle mobility was much more strongly reduced at pHc 6 and 5.5 than at pH 7.0 (Figure 3A, right panel). To exclude possible secondary effects of DNP, we also used a mild membrane-permeable acid (sorbic acid) to alter pHc (Orij et al., 2009) and found that it had a similar effect on cytosolic pH (Figure 3B, left panel) and on particle mobility (Figure 3B, right panel). These experiments were performed in the presence of glucose as an energy source, suggesting that the pHc change acts downstream of ATP depletion.
Our experimental setup allows for rapid changes of the intracellular proton concentration by almost two orders of magnitude (from 7.4 to 5.5). To test whether such pronounced pH fluctuations affect cell viability, we exposed yeast cells to repeated pHc changes in a microfluidic chamber. Remarkably, pH changes of this magnitude did not affect the viability of yeast (Video 2). Moreover, when yeast cells were acidified with DNP, reduced particle mobility manifested within minutes, and it was readily reversed on a similar time scale (Video 3). Thus, pH-induced changes are readily reversible and well tolerated by yeast.
Next, we tested whether other eukaryotic organisms undergo similar changes. We focused on another fungus, fission yeast, and a protist, the social amoeba Dictyostelium discoideum. As S. cerevisiae, both organisms can enter into a dormant state (Jímenez et al., 1988; Sajiki et al., 2009), form spores upon starvation (Egel et al., 1994; Xu et al., 2004) and undergo cytosolic pH fluctuations in response to energy depletion (Gross et al., 1983; Karagiannis and Young, 2001). Consistent with this, both organisms showed reduced GFP-µNS particle mobility in an energy- and pH-dependent manner (Figure 3C and D). Thus, we conclude that the pH-induced reduction in particle mobility is not limited to budding yeast, but also extends to other, distantly related organisms.
Our findings so far show that the mobility of particles is reduced upon energy depletion and acidification of the cytoplasm. In Figure 4A, we show the MSDs and their subdiffusive scaling for different experimental conditions. Particles of all sizes were included in the analysis. We see a dramatic decrease in particle mobility for energy depleted and acidified cells. To gain more insight into the rheological properties of the cytoplasm, which might explain this behavior, we performed a comprehensive analysis of the particle trajectories. From a rheological point of view, the cytoplasm can be considered as an active viscoelastic material (Guo et al., 2014; Mizuno et al., 2007). The motion of an inert tracer particle in the cytoplasm results from the balance between stochastic driving forces and opposing material forces. Due to a possible non-thermal origin of stochastic forces in living cells, in general, a combination of passive and active microrheology experiments is required to quantify the material properties of the cytoplasm (Guo et al., 2014; Mizuno et al., 2007). However, active microrheology experiments in yeast are challenging, because of its small size and stiff outer cell wall. Nonetheless, a detailed analysis of particle trajectories in the passive microrheology approach provides first pointers towards changes in the physical properties of the cytoplasm. One example is the power spectral density (PSD) of particle displacements, which is related to the power spectrum of stochastic forces and the material properties (Guo et al., 2014). The PSD can be calculated as a Fourier transform of the MSD and can, for our data in all conditions, be well approximated by a power law dependence (see Figure 4—figure supplement 1). We find that the exponent is smaller for acidified and energy-depleted cells. For a viscoelastic material driven by thermal fluctuations, a decrease in would correspond to a transition from a fluid to a more solid-like state (Squires and Mason, 2010). Although we demonstrate that active cytoskeleton-dependent forces do not strongly affect mobility of particles, and we expect no active motion to occur in energy-depleted cells, the thermal nature of driving forces remains an assumption and therefore limits our interpretation of the PSD data. To obtain further insight into particle diffusion, we turn to the analysis of the displacement data on the level of individual trajectories and suggest a statistical model for the observed particle motion.
It has been suggested that the trajectories of tracer particles in cells (Jeon et al., 2011; Tejedor et al., 2010) and hydrogels (Stempfle et al., 2014) can be well described by the model of fractional Brownian motion (fBm). In contrast to ordinary Brownian motion, the displacements in fBm are correlated in time. Positively correlated displacements lead to superdiffusion, whereas negative correlations lead to subdiffusion. As for ordinary Brownian motion, the distribution of displacements of individual particles performing subdiffusive fBm is Gaussian, but the width of the distribution increases with the lag time sub-linearly (Hofling and Franosch, 2013). Here, is the subdiffusion exponent, is the dimension of space, and is the generalized diffusion constant. The subscripts indicate the diffusivities of individual particle trajectories. We show that our displacement data are consistent with the model of fBm: For sufficiently long individual trajectories, the cumulative distribution functions (CDF) of displacements are well described by CDFs of the corresponding Gaussian distributions (Figure 4—figure supplement 2). Also consistent with the model of fBm, the combined (ensemble) distributions of all particle displacements measured for different lag times collapse onto each other after rescaling the displacements as (Figure 4B). The value of is read out from the scaling of the MSD for the corresponding experimental condition (see Figure 4A). Remarkably, the shape of this distribution is not Gaussian. However, if we additionally rescale the displacements of each trajectory by its corresponding generalized diffusivity , the combined distributions collapse onto a Gaussian distribution with unit variance (Figure 4—figure supplement 3). This collapse shows that the non-Gaussian shape of the combined distribution is a result of the variation in individual particle diffusivities (see materials and methods for details). The variability of generalized diffusivities could be due to differences in particle sizes, but it could also reflect variations in the properties of the particles’ microenvironments. Indeed, we find that even for particles of similar sizes the diffusivities vary strongly for all size groups (see Figure 1—figure supplement 3), suggesting that the heterogeneity of the particle microenvironment has a strong impact on particle mobility.
To further test how the microenvironment of the particles changes upon energy depletion and acidification, we analyzed the correlations in the displacements of particles. Negative displacement correlations are the origin of subdiffusive fBm. Indeed, we found that subsequent particle displacements were negatively correlated (see Figure 4—figure supplement 4 and material and methods for the definition of the correlation function). Interestingly, such negative correlations are a hallmark of particle motion in an elastic environment; particles surrounded by elastic structures tend to be pushed back to their original position. The further the particle is initially displaced, the stronger are the forces pushing it back in the subsequent time interval, which results in stronger negative correlations. Indeed, we find on average that the restoring motion is opposite to the initial step and is linearly proportional to the initial displacement length (Figure 4C). In general, the slope of this linear dependence changes from 0 for viscous fluid to -1/2 for an elastic material (Weeks and Weitz, 2002). In our data, the magnitude of the slope b increases from to upon energy depletion and acidification (Figure 4C and Figure 4—figure supplement 5). This result is consistent with the idea that energy depletion and acidification increase the stiffness of the particles’ microenvironments and that the cytoplasm transitions from a fluid-like to a more solid-like state under these conditions.
We next tested whether the transition of the cytoplasm to a more solid-like state, as proposed by our particle analysis, also manifests in global changes in the mechanical properties of cells. To experimentally address this question, we mechanically phenotyped budding yeast cells. This required enzymatic removal of the rigid cell wall, which provides mechanical stability to yeast cells, by a process known as spheroplasting. Spheroplasted budding yeast cells were investigated using atomic force microscopy (AFM, [Radmacher, 2007]), the standard in cell mechanical characterization, and real-time deformability cytometry (RT-DC, [Otto et al., 2015]), a novel microfluidic technique with 100000 times higher throughput. The AFM-based indentation experiments, performed with 10 µm-sized spherical probes to test whole cell mechanics, revealed that acidified cells were about 2.5 times as stiff as control cells (Figure 5A and Figure 5—figure supplement 1). Importantly, the apparent elastic modulus we measured for spheroplasted cells was three orders of magnitude lower than for yeast cells surrounded by a cell wall (Figure 5—figure supplement 1), thus clearly showing that the cell wall had been completely removed. However, cells are usually viscoelastic, and the apparent elastic modulus, as extracted using the Hertz model, reflects their combined elastic and viscous response. To test whether the observed 2.5-fold increase in the apparent elastic modulus of spheroplasts at low pH could also be caused by a strong increase in the viscous resistance to deformation, we extracted the viscosity of the cells from the AFM indentation-retraction curves similar to a recently published method (Rebelo et al., 2013; for details see Methods section). We found that the viscosity even decreased from pH 7.4 to pH 6.0 (Figure 5—figure supplement 2). Together, the analysis of apparent elastic modulus and viscosity unambiguously demonstrates that the cell body transitions from a compliant, more viscous material to a stiffer, more elastic material at low pH.
The increase in stiffness was independently confirmed by RT-DC measurements, which showed that the mechanical deformability of yeast cells was significantly reduced upon cytosolic acidification (Figure 5B). In the RT-DC assay, we also noticed that acidification was associated with differences in cell size, with acidified yeast being smaller (equivalent diameter: 3.503 +/- 0.012 microns; mean +/- SEM; N = 2938) than control cells (equivalent diameter: 3.724 +/- 0.014 microns; mean +/- SEM; N = 2354) (Figure 5B). Overall, these whole cell measurements show that acidification changes the mechanical properties of the cells in line with a transition of the cytoplasm to a more elastic, solid-like state, which is accompanied by a reduction in cell volume.
Our findings so far can be explained in two ways: First, cytosolic acidification could lead to a regulatory cell volume decrease, including water loss and increased macromolecular crowding (Mourão et al., 2014). Second, acidification could trigger the formation of macromolecular assemblies, which provide increased mechanical stability to the cytoplasm. In this case, the cell volume reduction could be a result of the exclusion of water from these assemblies (Cameron et al., 2006; Cameron and Fullerton, 2014; Fullerton et al., 2006; Thirumalai et al., 2012).
To investigate which scenario might apply, we performed a series of experiments with budding and fission yeast. First, we determined the volume of budding yeast cells using an image-based approach (see materials and methods for details). We found that the cell volume was reduced in a pH-dependent manner. After 30 min at pH 5.5, the cell volume was reduced by ~7% (Figure 5—figure supplement 3). Cell volume changes can also be induced by altering the osmotic strength of the growth medium with sorbitol (Miermont et al., 2013). Thus, we exposed yeast to different sorbitol concentrations to determine the concentration at which the cell volume was similar to that of acidified yeast. We found that at a sorbitol concentration of 0.8 M the cell volume decrease was of the same magnitude (Figure 5—figure supplement 3). As a next step, we compared the particle mobility of osmotically compressed and acidified yeast showing a similar decrease in cell volume. We found that under both conditions particle motion was strongly reduced (Figure 5—figure supplement 4). However, in osmotically compressed cells particles of all sizes still performed small movements. These movements could also be detected when yeast cells were exposed to a sorbitol concentration of 1 M, which triggers an even more pronounced cell volume reduction of ~30%. In contrast, particle motion was abolished in acidified yeast (Figure 5—figure supplement 4). This suggests that a regulatory cell volume decrease cannot fully explain the reduced particle dynamics of acidified yeast. To further investigate this, we compared the diffusivity of a mCherry-GFP fusion protein (54 kDa) in energy-depleted, acidified and sorbitol-treated cells. The diffusion of mCherry-GFP was not affected in acidified or energy-depleted yeast (Figure 5—figure supplement 5), but strongly decreased in cells subjected to high levels of osmotic compression. This indicates the presence of a fluid phase that allows unimpaired diffusion of small macromolecules such as mCherry-GFP in cells exposed to low pH or energy depletion conditions. Thus, cytosolic acidification and osmotic compression seem to induce qualitatively different states of the cytoplasm.
We next analyzed the mechanical stability of fission yeast cells. Fission yeast has an elongated shape, which is supported by the cell wall. However, when the cell wall is removed, fission yeast cells rapidly round up into a spherical shape (Kelly and Nurse, 2011; Sipiczki et al., 1985). This process requires the cytoplasm to be in a fluid-like state, and it is most likely driven by the osmotic pressure of the cytoplasm and by the passive tendency of the cell to minimize its surface to volume ratio. Remarkably, when we spheroplasted energy-depleted yeast cells, they did not relax into spheres, but maintained their initial rod-like shape (Figure 5C and D, Video 4). This effect was not due to incomplete removal of the cell wall (Figure 5—figure supplement 6, 7 and 8, Video 6). Importantly, for wall-free cells, maintenance of the rod-like shape was pH-dependent and could also be induced by reducing the cytosolic pH with DNP (Figure 5C and D, Video 5).
To investigate whether rod-shaped spheroplasts would eventually round up into spheres, we observed them for extended times by time-lapse microscopy. However, the spheroplasts maintained their elongated shape for several hours and did not show signs of rounding up (Video 4 and 5). Given this remarkable cellular phenotype, we tested whether the cells are still alive and get softer when energy is provided and the internal pH rebounds to neutral values. Indeed, when acidified yeast cells were re-exposed to medium, the cells quickly became spherical and started to enter the cell cycle (Figure 5—figure supplement 9, Video 7). Importantly, this rounding up process occurred in the presence of 1 M sorbitol, which was used to osmotically stabilize the cells. Under these conditions, yeast cells experience a substantial reduction in cell volume (Figure 5—figure supplement 3), suggesting that an increase in molecular crowding alone does not generate enough mechanical stability to keep the cells in a rod-like shape. Rather, these findings support our idea that cellular stiffening may involve the formation of rigid cytoplasmic structures, which dissolve when energy-depleted yeast re-adjust their cytosolic pH to neutral values. Thus, we conclude that the cytoplasm of energy-depleted cells undergoes a pH-dependent transition from a fluid- to a solid-like state, which may be accompanied by the formation of structures that significantly increase the mechanical stability of cells.
Which cytoplasmic structures could be underlying this remarkable change in cellular rigidity? A large number of in vitro studies have shown that the solubility of proteins drops precipitously, when the pH of the solution approaches their isoelectric points (Tanford and De, 1961). Under these conditions, proteins interact with each other to form higher-order assemblies, which macroscopically manifest as structures with solid-like properties (Boye et al., 1996; Matsudomi et al., 1991; Parker et al., 2005; Renard and Lefebvre, 1992). Thus, we reasoned that the densely packed cytoplasm of yeast cells undergoes a similar transition on a global scale.
To investigate this possibility, we first analyzed the distribution of the isoelectric points of all proteins in the yeast proteome. In agreement with previous work (Weiller et al., 2004), we found that the isoelectric points of yeast proteins are largely excluded from the neutral pH range and cluster into two peaks, one in the acidic and one in the basic range (Figure 6A). Importantly, the acidic peak overlaps with the pH that cells experience under starvation conditions. This suggests that many proteins have a reduced net charge in energy-depleted cells (Chan et al., 2006) and thus become less soluble. This is in agreement with previous results, where it was shown that starvation triggers the assembly of many proteins into higher-order structures (Narayanaswamy et al., 2009; Noree et al., 2010; Petrovska et al., 2014). Importantly, protein complexes remain intact in energy-depleted cells, as shown by the fact that the different proteins in a hetero-complex colocalize in the same structures (Figure 6—figure supplement 1). This suggests that the proteins assemble into structures in a native-like state, ensuring that this step is readily reversible. To investigate whether protein assembly and reduced particle mobility are temporally linked, we exposed yeast cells to pH manipulations in a microfluidic chamber and followed assembly and particle movement by fluorescence microscopy. Indeed, we found that these two events coincided (Video 8), suggesting a causal relationship.
Given these observations, we reasoned that many proteins might be able to form structures in a pH-dependent manner. Widespread formation of macromolecular protein assemblies could lead to considerable changes in the cellular architecture, and could trigger the formation of a percolated filamentous-colloidal network that would obstruct the movement of particles and provide mechanical stability to the cell. To investigate this possibility, we tested a set of 70 proteins that had previously been shown to assemble into higher-order structures upon starvation (Narayanaswamy et al., 2009; Noree et al., 2010). We found that the majority of these proteins formed structures upon acidification, whereas such structures were less abundant or absent at neutral pH (Figure 6B and C) or in 1 M sorbitol (Figure 6—figure supplement 2). Similar structures were observed in dormant yeast spores (Figure 6B), which reportedly have a pH in the acidic range (Aon and Cortassa, 1997; Barton et al., 1980). Thus, we conclude that many proteins assemble into higher-order structures in energy-depleted and acidified cells and that this causes extensive changes in the organization and material properties of the cytoplasm.
A hallmark of dormant cells is that they can survive extended periods of energy depletion. We therefore wondered whether pH-induced formation of a solid-like cytoplasm promotes cellular survival. Indeed, when energy-depleted budding yeast cells were kept in the presence of neutral medium to prevent cytoplasmic acidification, they rapidly lost viability (Figure 7A). Moreover, when we fixed the pHc in the acidic or neutral range in energy-depleted cells, only acidified S. cerevisiae (Figure 7B) and S. pombe (Figure 7C) cells survived. Thus, we conclude that the change in the physical properties of the cytoplasm is protective and that yeast cells use a simple physicochemical signal—the pH of the cytosol—to signal a depletion of energy and to regulate entry into a dormant state.
Many biochemical reactions inside a cell take place in the cytoplasm. Thus, changes in the physical or chemical properties of the cytoplasm will have far-reaching consequences for cellular metabolism and survival. Here, we demonstrate that adaptive changes in the cytosolic pH alter the material properties of the cytoplasm and arrest the diffusion of cellular organelles and foreign tracer particles (see schematic in Figure 7D). We further show that pH-controlled macromolecular assembly drives a transition of the cytoplasm to a solid-like state, which provides protection and increased mechanical stability.
Many previous studies have demonstrated a role for energy in controlling intracellular dynamics. In eukaryotic cells, ATP-driven motor proteins carry organelles and other cargo along cytoskeletal tracks to specific subcellular locations, thus regulating the distribution of cytoplasmic components (Hirokawa et al., 2009; Roberts et al., 2013). Recent findings also indicate that the movements of motor proteins generate random fluctuating forces, which drive diffusive-like non-thermal motion (Brangwynne et al., 2008, 2009; Guo et al., 2014). These non-thermal force fluctuations facilitate the mixing of the cytoplasm and thus are important for cellular function. As a consequence, energy depletion in mammalian cells causes a cessation of motor movements and thus a strong impairment of intracellular motion, with a significant impact on the distribution of macromolecules in the cytoplasm.
The diffusion of a particle in the cytoplasm is the result of two opposing forces: fluctuating forces of thermal or non-thermal origin, which transfer energy onto the particle, thus propelling its motion, and opposing material forces that restrict the movement of a particle and result from interactions of the particle with cytoplasmic components. Studies so far have largely focused on the driving forces of particle motion, and most prominently those that are dependent on ATP (Brangwynne et al., 2008, 2009; Guo et al., 2014; Parry et al., 2014). However, we now show that changes in the material properties of the cytoplasm can also significantly affect particle motion. These changes occur in an energy-dependent manner, indicating that energy not only regulates motor-driven diffusive processes, but also has an impact on the organization of the cytoplasm. In the organisms we investigate, these changes are largely independent of the cytoskeleton, but reflect the collective effects of many cytosolic proteins that assemble into higher-order structures.
The chemistry and physics of proteins has been under investigation for many decades. For example, it is a well-known fact that changes in the salt concentration can have a strong impact on protein solubility. One parameter with particularly strong effects on protein solubility is the pH. When the pH of a solution approaches a protein’s isoelectric point, the solubility of the protein drops to a minimum (Tanford and De, 1961). The reason is that under these conditions proteins attain a low net charge and thus are subject to weaker repulsive interactions. As a consequence, attractive interactions dominate, which—provided that the protein is present at a high enough concentration—can trigger the assembly of proteins into higher-order structures.
The pH-driven assembly of proteins can result in the formation of large structures with solid-like properties (Boye et al., 1996; Matsudomi et al., 1991; Parker et al., 2005; Renard and Lefebvre, 1992). Thus, on the macroscopic level, protein assembly can exhibit signs of a phase transition. Although this tendency of proteins to form higher-order structures is well known, this knowledge has not yet been applied to the understanding of living organisms. One reason may be the widespread but misleading assumption that the physicochemical properties of the cytoplasm are invariant. However, in recent years, an increasing number of reports have shown that key physical and chemical parameters of the cytoplasm can fluctuate, especially under conditions of stress. In the case of cytosolic proton concentrations, these fluctuations can span almost two orders of magnitude (our study and Imai and Ohno, 1995; Orij et al., 2009; Valli et al., 2005). Given that the cytoplasm is highly crowded with proteins, it is not surprising that pH changes of this scale have strong effects on the physical properties and the dynamics of the cytoplasm.
Previous studies have analyzed the distribution of the isoelectric points in the proteome (Chan et al., 2006; VanBogelen et al., 1999; Weiller et al., 2004). These studies found that only few proteins have isoelectric points in the neutral pH range and that most proteins only become electrically neutral when the pH shifts to the acidic or basic range. Importantly, proteins become more insoluble when their net charge decreases. Thus, to maintain maximum proteome solubility, cells have to keep the cytosolic pH in the neutral range. However, when the pH of the cytosol becomes more acidic, as during starvation, a large fraction of the proteome will become less soluble. Consistent with this, we could previously show that cytosolic acidification triggers the assembly of a group of metabolic enzymes into higher-order structures and that assembly inactivates their enzymatic activities (Petrovska et al., 2014). Here, we provide evidence that many more proteins assemble into microscopically visible structures upon acidification (Figure 6B and C), and we propose that assembly of these and probably many other proteins promotes a transition of the cytoplasm to a more solid-like state. Importantly, pH-dependent assembly of proteins does not seem to go along with protein denaturation, as the proteins in these assemblies retain their native structure (Petrovska et al., 2014) and oligomeric states (Figure 6—figure supplement 2). This ensures that assembly formation can readily be reversed and that the cytoplasm can rapidly recover from pH-induced alterations, thus allowing swift reentry into the cell cycle. Most importantly, protein assembly and the solid-like state of the cytoplasm protect cells from the adverse effects of energy depletion stress (Figure 7). We do not yet know why these processes are protective, but we favor a combination of different explanations, such as energy conservation (Bernstein et al., 2006), regulation of metabolism (Petrovska et al., 2014), and potentially protection of macromolecules from damage.
One of the hallmarks of dormant cells is a loss of water. Although we do not determine the water content of energy-depleted and acidified cells, we find that acidification goes along with a significant reduction of the cellular volume, which is consistent with a loss of water. Previous studies have shown that protein assembly leads to the exclusion of water (Cameron et al., 2006; Cameron and Fullerton, 2014; Fullerton et al., 2006; Thirumalai et al., 2012). The released water becomes osmotically available and can be lost to the surrounding environment, inducing a compaction of the cytoplasm and a change in cell volume. Thus, we propose that the observed cellular shrinkage is to a large degree caused by the formation of cytoplasmic structures and a subsequent release of water.
Additional evidence for this scenario comes from a study that characterized the cytoplasm as a material with distinctive gel-like properties (Fels et al., 2009). The authors of this study found that the cytoplasm of mammalian cells behaves like a hydrogel, which can swell and shrink depending on its water content. Importantly, changes in the cytosolic pH could modulate swelling and shrinking (Fels et al., 2009). This suggests that the cytoplasm with its many macromolecular components is inherently pH sensitive, a property, which may have been exploited repeatedly during evolution as a strategy for adaptation or survival. In fact, the germination of spores goes along with a drastic increase in water content (Cowan et al., 2003; Dijksterhuis et al., 2007) and spores consistently have a pH in the acidic range (Aon and Cortassa, 1997; Barton et al., 1980; Busa and Crowe, 1983; Setlow and Setlow, 1980; van Beilen and Brul, 2013). However, what is still unclear is how water is released from forming spores and re-enters into spores upon germination. Given our findings, we propose that the dehydration/rehydration cycle of spores is at least partially driven by changes in the cytosolic pH. A regulatory cell volume decrease with increased macromolecular crowding may also contribute to the water loss in dormant cells (Mourão et al., 2014). Dissection of this important problem will require the use of sophisticated biophysical, biochemical, and genetic approaches.
We show that the cytoplasm of energy-depleted cells transitions from a fluid- to a solid-like state. This transition was evident for the cytoplasm (as determined by particle tracking) and on the level of the entire cell (as determined by cellular deformability assays). This is, to our knowledge, the first viscous and elastic characterization of S. cerevisiae spheroplasts by AFM-indentation. The elastic modulus (on the order of 1 kPa) is several orders of magnitude lower than what has been reported for intact yeast cells surrounded by a rigid cell wall (about 500 kPa; [Pillet et al., 2014]). A similar difference in stiffness between spheroplasts and intact cells with a rigid cell wall has previously been found in E. coli (Sullivan et al., 2007). The increased mechanical stiffness at low pH was independently confirmed by a new microfluidic technique (RT-DC). The transition from a compliant, more viscous cytoplasm to a stiff, elastic cytoplasm in energy-depleted yeast cells is in agreement with a model in which many proteins assemble into a dense network, thus restricting the diffusion of large particles. This network could have the overall physical properties of a glass, as recently proposed for bacteria (Parry et al., 2014). Future studies will have to determine the molecular mechanisms and physical causes promoting the formation of a solid-like cytoplasm.
In contrast to mammalian cells, yeast cells are much smaller in size. This may explain why yeast rely more strongly on thermal diffusion for macromolecular dispersal. However, this also means that yeast cells have to alter the material properties of the cytoplasm to restrict diffusion during dormancy. We believe this is achieved by promoting a pH-controlled transition to a solid-like state, which significantly changes the fluidity of the cytoplasm. Acidification of the cellular interior of yeast seems to occur through an influx of protons from the outside, suggesting that this transition is dependent on an acidic environment, which may be generated through the normal metabolic activity of yeast. Thus, we predict that single-celled organisms make extensive use of the pH responsiveness of the cytoplasm in order to protect themselves and regulate their metabolism. However, even multicellular organisms such as marine brine shrimp can enter into a dormant state in a pH-dependent manner (Busa and Crowe, 1983). Importantly, in this organism dormancy is induced through protons that are released from intracellular stores (Covi et al., 2005), indicating that dependence on outside pH could be a peculiarity of yeast. Moreover, cytosolic pH changes have also been observed when organisms such as yeast and Dictyostelium are challenged with other types of stresses, such as heat stress or osmotic stress (Pintsch et al., 2001; Weitzel et al., 1985; 1987). Thus, global control over the material properties of the cytoplasm through simple physicochemical signals such as the pH could be a frequently used means to regulate cellular function in fluctuating environments.
S. cerevisiae was grown at 25°C or 30°C in yeast extract peptone dextrose (YPD), synthetic complete (S-complete) or synthetic dropout (SD) medium. Standard pH of SD media is around pH 5.5. S. pombe was grown in either YE5 or EMM5 (standard pH is 6.0) medium at 30°C. D. discoideum was grown in AX medium (ForMedium, standard pH 6.0-6.5) at 23°C under light. A list of all S. cerevisiae strains used in this study can be found in Supplementary file 1. S. pombe wild type strain L972 was used for spheroplasting and spotting experiments. The same strain was transformed with plasmid pDUAL2HFG-µNS-sfGFP for particle tracking experiments. D. discoideum wild type strain AX2-214 (DictyBase) transformed with plasmid pDM353-µNS-GFP (Veltman et al., 2009) was used for particle tracking experiments.
The intracellular pH of S. cerevisiae and S. pombe cells was adjusted by incubation in phosphate buffers of different pH in the presence of 2 mM 2,4-dinitrophenol (DNP) as described previously (Dechant et al., 2010; Petrovska et al., 2014). DNP was added to the buffers from a 0.2 M (100x) stock solution in methanol. Alternatively, cytosolic acidification was achieved by incubation in SD medium containing 1, 2, or 6 mM sorbic acid. D. discoideum cells were pH adjusted by treatment with either 4 mM sorbic acid or 0.2 mM DNP in LoFlo medium (pH 5.5). For generation of pH calibration curves, cells were treated with 75 µM monensin, 10 µM nigericin, 10 mM 2-deoxyglucose and 10 mM NaN3 in buffers of pH 5.0, 5.5, 6.0. 6.5, 7.0, 7.5, and 8.0 containing 50 mM MES, 50 mM HEPES, 50 mM KCl, 50 mM NaCl, 0.2 M ammonium acetate as described previously (Brett et al., 2005).
S. cerevisiae and S. pombe cells were energy-depleted by incubation in SD medium or EMM medium, respectively, without glucose containing 20 mM 2-deoxyglucose (2-DG, inhibition of glycolysis) and 10 µM antimycin A (inhibition of mitochondrial ATP production). This treatment causes a more than 95% reduction in cellular ATP (Serrano, 1977). D. discoideum cells were energy-depleted with 40 mM 2-DG and 200 µM azide in Soerensen-phosphate buffer (pH 6.0).
To test the influence of the actin cytoskeleton on particle mobility, cells were treated with 100 µM latrunculin A (LatA) in SD medium for 30 min prior to imaging. To test the role of the microtubule cytoskeleton, cells were treated with 15 µg/ml nocodazole in SD medium for 1 hr prior to imaging.
S. cerevisiae spheroplasts were generated by incubating cells in PBS containing 1 M sorbitol (Sigma), 1% glucose and 0.25 mg/mL Zymolyase 100T (USBiological) at 25°C for at least one hour under shaking. S. pombe spheroplasts were generated, with minor adaptations, as described previously (Kelly and Nurse, 2011). Shortly, cells were incubated in buffers of different pH (depending on experiment) in the presence of 1.2 M sorbitol (Sigma), 0.5 mg/mL Zymolyase 100T (USBiological) and 2.5 mg/mL lysing enzymes from Trichoderma harzianum (Sigma).
Wild type S. pombe L972 cells were grown in liquid EMM medium containing 0.5% glucose at 30°C overnight shaking at 200 rpm, diluted and re-grown to mid-log phase the next day. Cells were harvested by centrifugation, washed twice with medium or buffer containing 1.2 M sorbitol and applied to a 4-chamber glass-bottom dish (Greiner BIO-ONE) coated with concanavalin-A. For energy depletion experiments, cells were energy-depleted as described above prior to loading to the dish. Unbound cells were washed off with EMM medium or phosphate buffers containing 1.2 M sorbitol. Bound cells were covered with 400 µl of phosphate buffer of different pH containing 1.2 M sorbitol and either 2 mM DNP (pH experiment) or 20 mM 2-DG and 10 µM antimycin A (energy depletion experiment). Cells were imaged for five frames before addition of 40 µl cell wall digesting enzymes (final concentrations: 0.5 mg/ml Zymolyase 100T, 2.5 mg/ml lysing enzymes from Trichoderma harzianum). Spheroplasting and rounding up of cells was followed by time-lapse bright-field microscopy with a DeltaVision (Applied Precision) microscope (Olympus IX70 stand, Olympus UPlanSApo 20x objective, CoolSnap HQ2 camera).
S. cerevisiae wild type strain W303, or S. pombe wild type strain L972 were grown overnight, diluted to OD600 ~ 0.1 the next morning and regrown to OD600 ~0.5. Cells were harvested and resuspended in either phosphate buffers of pH 6.0 or pH 7.0, respectively, containing 2 mM DNP (S. cerevisiae and S. pombe) or in S-medium without glucose containing 20 mM 2-DG and 10 µM antimycin A (S. cerevisiae). Cells were then incubated under shaking at 25°C. Samples were taken after 2, 24 and 48 hr, cells were washed once with H2O and subsequently spotted on YPD as five-fold serial dilutions.
For cytosolic pH measurements a codon-optimized version of the ratiometric fluorescent protein pHluorin2 (Mahon, 2011) was integrated into the W303 ADE+ genome at the trp locus. The protein was expressed under control of a GPD promoter. A pH calibration curve was obtained as described previously (Brett et al., 2005), except that we used a microscopy-based fluorescence readout. Briefly, cells were incubated in buffers of different pH-containing proton carriers (75 μM monensin, 10 μM nigericin) and inhibitors (10 mM 2-deoxyglucose) to rapidly deplete cells of energy and allow for complete equilibration of the intracellular and extracellular pH. Cells were immobilized in 4-chamber dishes (Greiner BIO-ONE) with concanavalin A and imaged using DAPI/FITC (Excitation: DAPI; Emission: FITC) and FITC/FITC (Excitation and emission: FITC) filter sets on a DeltaVision (Applied Precision) microscope (Olympus IX70 stand, Osram Mercury short arc HBO light source, 100x Olympus UPlanSApo objective, CoolSnap HQ2 camera). Six different Z-stacks each with 6 planes (Z-resolution 0.5 µm) were recorded for each pH condition. Imaging settings were: 10% excitation intensity, 0.1 s exposure time, 512x512 pixels, 2x2 binning. After background subtraction, the mean DAPI/FITC to FITC/FITC ratio was calculated from the intensity readouts of both channels and plotted against pH to obtain a calibration curve. Subsequent pH measurements were calculated from a fourth degree polynomial fit to the calibration curve. Time series of pH measurements were obtained using identical imaging settings and a CellASIC (Millipore) microfluidics flow setup combined with CellASIC ONIX Y04C microfluidic plates.
For particle tracking experiments, samples were prepared in 4-chamber glass-bottom dishes (Greiner BIO-ONE). Dishes were coated with concanavalin A coating solution for at least 30 min. Subsequently the coating solution was removed and the glass surface washed with H2O twice before adding 1 ml of a log phase yeast culture (OD600 = 0.5). Cells were allowed to settle onto the glass surface for 10 min. The supernatant was then removed and cells sticking to the surface were washed with appropriate medium or buffer twice. This normally results in a single layer of yeast cells that stick tightly to the glass surface. For control experiments cells were then incubated in 500 µl of S-complete medium for 30 min before imaging. When treated with DNP or sorbic acid cells were incubated in 500 µl of appropriate buffer or medium for 30 min before imaging. For energy depletion experiments, cells were incubated in energy depletion medium for 2 hr before imaging.
Imaging was done on different microscope setups depending on requirements for image acquisition rate and camera chip size. Data with a time resolution of 5 s were recorded on a Deltavision (Applied Precision) microscope (Olympus IX70 stand, Osram Mercury short arc HBO light source, Olympus UPlanSApo 100x oil objective, CoolSnap HQ2 camera, resulting pixel size (x, y) = 65 nm). Z stacks with 10 focal planes were collected at each time point. Imaging settings were: 10% excitation intensity, 0.08 s exposure time, 1024x1024 pixels, total imaging time 10 min. All data with a time resolution of 1 s were recorded on an Andor spinning disk confocal microscope (Olympus IX81 stand, Andor iXon+ EMCCD camera, resulting pixel size (x, y) = 81 nm). Z-stacks with 16 focal planes were collected at each time point. Imaging settings were: 40% laser intensity, minimum possible exposure time (~16 ms), 512x512 pixels, total imaging time 20 s. Data with 10 millisecond time resolution was recorded on an Andor Spinning disk setup (Olympus IX71 stand, Olympus UPlanSApo 60x silicon oil objective, resulting pixel size (x, y) = 108 nm). Imaging was done in a single focal plane of 764x1190 pixels, which allowed us to track a reasonable number of particles at this frame rate in a single experiment. Imaging settings were: 15% laser intensity, 10 milliseconds exposure time, total imaging time of 10 s.
If recorded, Z stacks were sum-projected using the Fiji image-processing package (Schindelin et al., 2012). All particle tracking was done with the MosaicSuite particle tracker (Sbalzarini and Koumoutsakos, 2005) a Fiji plugin freely available from http://mosaic.mpi-cbg.de. The following settings were used for tracking data with 5 s time resolution: particle radius: 7, cutoff: 0, percent: variable, link range: 3, displacement: 20. Data with 1 s time resolution was tracked with: particle radius: 8, cutoff: 0, percent: variable, link range: 1, displacement: 20. Data recorded with 10 ms time resolution was tracked with: particle radius: 8, cutoff: 0, percent: variable, link range: 1, displacement: 5. The MosaicSuite particle tracker also measures particle intensities (m0) during tracking. The mean intensity was computed from m0 for each trajectory and used as a proxy for particle size. Particle trajectories were binned into three roughly equally populated size bins (small, medium, large) to illustrate the dependence of the MSD on particle intensity. Computations and plotting were either done in R, making use of the plyr, reshape and ggplot2 (Wickham, 2009) packages or in MATLAB.
We imaged a list of 73 strains (see Supplementary file 1) from the yeast GFP collection (Huh et al., 2003) under conditions of high and low intracellular pH. Samples were prepared in 4-chamber glass bottom dishes as described for the single particle tracking experiments. Cells were incubated in phosphate buffers of pH 5.5 or pH 7.4, respectively, containing 2 mM DNP and 2% glucose for exactly 30 min before imaging. Imaging was done on a DeltaVision (Applied Precision) microscope (Olympus IX70 stand, Osram Mercury short arc HBO light source, Olympus UPlanSApo 100x oil objective, CoolSnap HQ2 camera). Z stacks with 14 focal planes were collected at 6 points for each sample. Imaging settings were: 50% excitation intensity, 0.1 s exposure time, 512x512 pixels, 2x2 binning. Imaging of protein assemblies in yeast spores was done with similar settings.
GFP-expressing yeast cells were used to determine the volume of cells using an imaging-based approach. Samples were prepared in 4-chamber glass bottom dishes as described for the single particle tracking experiments. In control experiments cells were subsequently incubated in 500 µl of S-complete medium for 30 min before imaging. For pH adjustment cells were incubated in 500 µl of phosphate buffers of pH 5.5, 6.5 or 7.4, respectively, containing 2 mM DNP and 2% glucose for exactly 30 min before imaging. For volume adjustment cells were incubated in S-complete medium containing 0.6, 0.8, 1 or 2 M sorbitol for exactly 30 min before imaging. Cells were imaged on an Andor spinning disk confocal microscope (Olympus IX81 stand, Olympus UPlanSApo 100x oil objective, Andor iXon+ EMCCD camera, resulting pixel size (x, y) = 81 nm). Z-stacks were obtained with z=210 nm resolution. Z stacks were projected to obtain 2D maximum intensity projections, which were then processed further for image segmentation and object detection. For image segmentation, objects smaller than 10 pixels were considered to be noise and removed, and a structural filter of ellipsoid shape was applied to detect the foreground of the cells. The background was identified by computing the distance transform matrix of the foreground. Using the watershed transform matrix, the background markers were turned into regional minima, and the foreground image was segmented to obtain individual cells. The mask for the individual cells was then used to select the corresponding Z stack, and the pixels above the stack threshold were considered as resulting from the GFP signal of the cell. Finally, the empty vacuolar regions were filled, and the resultant image was counted for total number of pixels above threshold to compute the total cellular volume. Image processing and analysis was done in MATLAB. To obtain an accurate measurement of the cell volume, budding and overlapping cells were not quantified.
The mobility of a mCherry-GFP fusion protein was measured using fluorescence recovery after photobleaching (FRAP). Prior to imaging, yeast cells were either pH adjusted in phosphate buffers of pH 5.5, 6.0 or 7.4, respectively, containing 2 mM DNP and 2% glucose, or treated with SD-medium containing 0.8, 1.0, 1.5 or 2.0 M sorbitol, respectively, or energy-depleted in SD-medium without glucose containing 20 mM 2-DG and 10 µM antimycin A. Cells were then immobilized on a cover slip with concanavalin A coating solution and imaged on an Andor spinning disc microscope (Nicon eclipse Ti stand, Nikon Plan Apo TIRF 100x oil objective, Andor iXon+ camera, resulting pixel size 70 nm) equipped with a FRAPPA unit (Andor). A single pixel region of interest was bleached with a 405 nm laser pulse (1 repeat, 40% intensity, dwell time 60 ms). Recovery from photobleaching was then recorded in a single focal plane with a time resolution of 5.4 ms (EM gain 200, laser intensity of 5%). Image analysis was carried out in FIJI.
AFM-based indentation experiments were performed using a Nanowizard I (JPK Instruments, Berlin) in combination with the CellHesion module. Tip-less silicone cantilevers (Arrow-TL1, Nanoworld, Switzerland) were equipped with a polystyrene bead of 10 µm diameter (microParticles GmbH, Germany) and calibrated prior to measurements using the thermal noise method. Cell-Tak (Corning, USA) was used for immobilization of spheroplasts (Gautier et al., 2015). To determine the stiffness of single spheroplasts (S. cerevisiae), the cantilever was positioned above individual cells and lowered with a speed of 10 µm/s. Force-distance curves were recorded (maximum force 2 nN) and analyzed using the JPK data processing software (JPK instruments): Force-distance data were corrected for the tip-sample separation (Radmacher, 2007) and fitted with the Hertz model for a spherical indenter (Sneddon, 1965). An effective probe radius was used according to the Hertz model for two spheres. A Poisson ratio of 0.5 was assumed. Experiments were carried out in phosphate buffer (containing 1 M sorbitol and 1% glucose) adjusted to pH 6.0 or pH 7.4 at room temperature both with and without DNP (see Figure 5 and Figure 5—figure supplements). Reporting an apparent elastic (Young’s) modulus acknowledges the fact that several assumptions of the Hertz model (isotropic, homogeneous, semi-infinite space) are not met; but this still serves well for quantitative comparison of cells in different pH conditions. The Hertz model also assumes an elastic material, but cells are viscoelastic and an observed increase in apparent elastic modulus could also be caused by an increase in viscous resistance to deformation. To directly determine the viscosity η of spheroplasted cells from the recorded force-distance data, we adapted a method proposed by (Rebelo et al., 2013). Briefly, this method extracts the viscosity η by comparing the dissipated energy during the indentation process, Wdiss, to the viscous work, Wv, which is modeled taking into account the indenter shape and indenter velocity. Wdiss corresponds to the area between the approach and retract force-distance curves, , where δ is the tip-sample-separation, or indentation, and the superscripts app and ret indicate the forces recorded during approach and retraction, respectively. The viscous work is the integral of the viscous force Fv, which is described by for a spherical indenter of radius R. Force-distance curves were smoothened using a median filter and a multi-exponential fit to compute the time-derivative of the indentation. Finally, the viscosity was calculated as , where . All calculations were implemented in Python.
Real-time deformability cytometry (RT-DC) has recently been introduced as a method for high-throughput cell mechanical characterization (Otto et al., 2015). Briefly, the experimental setup consists of an inverted microscope (Zeiss, Axiovert200M), a high-speed video camera (MC1362, Mikrotron) and a syringe pump (NemeSys, Cetoni), which are assembled around a microfluidic chip. The chip is made of polydimethylsiloxane using soft lithography and its geometry is defined by two reservoirs connected by a 300 μm long constriction with a 10 μm x 10 μm squared cross-section. When a cell suspension is driven through the narrow channel, cells experience a significant hydrodynamic stress and the resulting deformation is captured and analyzed in real-time using the high-speed camera. Deformation, D, is quantified by the circularity c: , where A is the projected surface area and l the perimeter of the cell inside the channel. The more a cell deviates from an ideal circular shape the larger is D. For simplicity, the size measure reported is the diameter of an equivalent circle with area A. A typical experiment requires a cell concentration of 106 cells/ml and a minimal absolute sample volume of 100 μl. Here, S. cerevisiae spheroplasts were resuspended in PBS-methylcellulose medium adjusted to different pH, containing 1 M sorbitol and 1% glucose. Cells were drawn into a 1 ml syringe and connected to polymer tubing, which had been cleaned using 70% ethanol and 200 nm sterile-filtered (Sigma Aldrich) deionized water. After connecting tubing to the syringe pump and microfluidic chip a flow was stabilized for 1 min. Here, measurements were carried out at a constant flow rate of 0.012 μl/s. For reference, data are also acquired inside the reservoirs to ensure no deformed cell shape in the absence of mechanical stress (data not shown).
The ensemble-averaged mean squared displacement (MSD) was calculated as
where is the number of particles, and and are the coordinates of particle at time .
The time-and-ensemble averaged MSD, , was computed as
where is the frameshift, is the number of particles and is the length of the particle trajectory. The maximum frameshift was limited to 1/3 of the full trajectory length. The subdiffusion exponent was estimated by fitting the time-and-ensemble averaged MSD to a power law between 0.2-2 s. Before fitting, the MSD was noise corrected assuming the positional noise of 11nm estimated from the power spectra. In this way, we obtained (DNP treated cells with external pH 6), (DNP treated cells with external pH 7.4), (energy depleted cells) and (log phase cells).
The power spectrum of displacements for a one-dimension signal is given by , where the angular brackets denote an average over the ensemble, and . For the two-dimensional tracking data, the total power spectrum is given by the sum of the power spectra of each component as . The integral is approximated using the built-in MATLAB function fft (Fast Fourier Transform). The tracking accuracy is estimated by considering the plateau of the power spectrum. The experimental power spectrum is given by , where is the power spectrum of the positional noise. This positional noise will manifest itself as a plateau in the power spectrum at high frequencies. We find that the plateau can be reproduced by generating Gaussian noise with standard deviation of 11 nm. The true power spectrum is obtained by subtracting the power spectrum of this estimated positional noise from the experimentally obtained power spectrum. Thereafter, the low-frequency regime (from 0.1 Hz to 5 Hz) was fitted to a power law in a least square sense. The low frequency regime was used for the fitting as this procedure minimizes potential additional errors from the tracking procedure.
To check whether the deviation of the slope of the PSD from the expected slope from Brownian motion is an artifact of the finite length of the trajectories or a result of correlations in the data, signifying a viscoelastic material state, the displacements of the individual trajectories were randomly reshuffled. This was done by randomly permuting the order of the displacements using the MATLAB function randperm. This way, subsequent displacements in the reshuffled trajectories are uncorrelated and the corresponding PSD should therefore scale as for Brownian motion. We find that this is indeed the case under all conditions (Figure 4—figure supplement 1).
We find that the time-averaged and ensemble-averaged MSD agrees well under all conditions, implying that the process is stationary (does not age) on the experimental time-scale (Figure 4—figure supplement 6). A statistical process that is consistent with our experimental observations (stationarity, subdiffusive scaling of the MSD, and an anomalous power-law scaling of the positional power spectrum (Weiss, 2013) is fractional Brownian motion (fBm). For fBm, the probability density function (PDF) of displacements is Gaussian, but the displacements are correlated, , where measures the strength of the fBm and may depend on particle size and the local microenvironment. As a consequence of the Gaussian property, the PDF is completely determined by its second moment, proportional to the MSD of the particle. The correlations cause the MSD to increase as a power law, where is the dimension of space, and is the subdiffusion exponent. From this expression we see that can be referred to as a generalized diffusion constant. In the following discussion, we consider the motion along the two coordinate axes as two independent realizations of the same random process. The motion is consequently analyzed as a one-dimensional process, .
For one-dimensional fBm the PDF of displacements of each individual particle is given by . The lengths of the individual trajectories are too short (~1000 time points) to provide a reliable estimate of the PDF on a single-particle level. A statistical measure that can be estimated also for small datasets (Weiss, 2013) is the cumulative distribution function (CDF). The CDF of a single particle trajectory is a measure for the probability that the particle makes a displacement not larger than (note that has both negative and positive values). To build a CDF at a given moment of time ( s) for an individual trajectory we just count the number of displacements which are smaller than and divide this number by the total number of displacements in a given trajectory. The CDFs are fitted to a Gaussian CDF with zero mean and variance given by the variance of the displacements in the array (see Figure 4—figure supplement 2). In addition, for each individual trajectory we can calculate the so-called non-Gaussian parameter , which vanishes for displacements with the Gaussian distribution. Indeed we see that for all experimental conditions this parameter is close to zero, see inset in Figure 4—supplement figure 2.
By rescaling the displacements by the lag time as , the PDF of displacements at different times can be collapsed to a single master curve . For an ensemble of particles performing fBm in a heterogeneous environment, the total master curve is given by . To obtain the master curve for the fBm process underlying the particle motion, we need to estimate the generalized diffusion constants of fBm for each trajectory. The strength of the fBm is obtained as , for a lag time s. As we see on Figure 4B the master curve perfectly fits the ensemble data for the PDF of particle displacements. Moreover, if we rescale displacements of each trajectory by the corresponding generalized diffusion constant, they should all collapse on a single Gaussian distribution with a unit variance, and this is what we show in Figure 4—figure supplement 3). For reference we also provide the unscaled PDFs of displacements for log phase and energy depleted cells for two lag times t=0.2 and 2.0 s, see Figure 4—figure supplement 3, right panel.
The directional correlation function of the displacements was calculated as , where is the lag-time, is an integer, is the change in particle position between time and and denotes the length of the vector . Averaging is performed over the ensemble of particles and time .
To quantify the strength of correlations we considered two displacements and during two consecutive time intervals of length (Weeks and Weitz, 2002). We then calculate the projection of the second displacement onto the direction of the preceding one, . If this value is negative, it indicates that the second displacement tends to move oppositely to the first. For small displacements, we expect this quantity to be a linear function of the initial particle displacement, . For a viscous material the slope vanishes, whereas for an elastic material the slope is and is independent of the lag time for which the displacements are calculated. To find out how depends on the magnitude of the initial displacement, we first extract all pairs of subsequent displacements at a certain lag time. Thereafter the projection is calculated for each pair of displacements. In order to consider the relation between the correlation and the initial displacement length , these lengths were binned in 38 equidistant bins. The correlation was averaged in each bin to obtain the correlation as a function of displacement length , see Figure 4C and Figure 4—figure supplement 5). The linear scaling of with and its independence on the lag time also rule out the localization error as a possible (dominating) source of negative correlations in the displacement data.
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Robert H SingerReviewing Editor; Albert Einstein College of Medicine, United States
In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.
[Editors’ note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]
Thank you for choosing to send your work entitled "A sol-gel transition of the cytoplasm driven by adaptive intracellular pH changes promotes entry into dormancy" for consideration at eLife. Your full submission has been evaluated by Vivek Malhotra (Senior editor) and two peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the decision was reached after discussions between the reviewers. Based on our discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.
While both reviewers found the work of interest and importance, they were unconvinced that the data supported the conclusions and felt there were numerous flaws in the experiments and analysis. One reviewer summarizes: "To me, there are two major problems. First, the authors seemed to propose a 'gel' transition originating from an increase in (presumably cross-linked?) protein filaments in the cytoplasm under starved/acidified conditions, but I find the evidence unconvincing. Second, the AFM and cell shape retention results (that the authors interpret as an increase of stiffness of the cytoplasm) could be due to the presence of residual cell wall." In view of these considerations, we do not feel that the manuscript warrants further consideration unless these concerns can be resolved.
This study shows that carbon starvation and acidification of the cytoplasm change the physical properties of the cytoplasm of yeast and Dictyostelium cells. Cytoplasmic acidification appears sufficient to reduce the motion of large tracer particles. It also increases survival rate under energy-depleted conditions (i.e., starvation), showcasing the biological significance of the findings. The authors propose that particle confinement under starvation is caused by the cytoplasm transitioning from a solution to a gel-like state. The topic is important and has large implications to our understanding of cellular dynamics and dormancy in eukaryotes. While the results are potentially exciting, there are major concerns with some interpretations and conclusions.
First, the proposed terms 'cytoplasmic freezing' are misleading. If what they observe was analogous to the cytoplasm freezing, all cellular components, including proteins, would reduce their motion as the dynamics of particles of all sizes are affected by temperature. This is not the case here as large particles are affected but not proteins (GFP). The size dependence is inconsistent with a cytoplasmic freezing, and this characterization should be avoided.
The evidence for a gel transition is not convincing. A gel suggests a meshwork. The authors argue that many proteins assemble into higher order structures under starvation, citing Noree et al. (2010), Narayanaswamy et al. (2009) and their own previous work. The Noree et al. (2010) paper talks about a wide genetic screen identifying metabolic proteins that form 4 distinct filaments, with some being induced by energy depletion, but others being unaffected or even reduced upon energy depletion. The Narayanaswamy et al. (2009) paper and Figure 6 here show mostly puncta forming, but puncta (compact aggregates) do not form gels. I agree that a few filaments form under energy-depleted/acidified conditions. But it is unclear that there are more of them under these conditions than under the normal situation, especially given the loss of cytoskeletal filaments under energy-depletion/acidification? To form a gel and trap probes, the cell would need a pervasive meshwork (cross-linked filaments), not just proteins that form higher-order structures.
Figure 4A: The method used to show that elasticity of the cytoplasm is increased under acidification is based on a model that explicitly assumes elasticity. The argument is circular.
Furthermore, in Figure 4A, the shift in power spectral density (PSD) is not sufficient to conclude elasticity, since there are other materials (e.g., dense colloidal suspensions, laponite) that would be expected to shift the PSD but are not elastic.
Additionally, a theoretical relationship between power spectrum and single-particle displacements is valid for long-time observations. To avoid distortions of the power spectrum (especially, in the low and high frequency parts) due to the finite length of the trajectories, one needs to test if the experimental time frame was long enough.
Paragraph two, subheading “Energy-depleted and acidified cells display increased mechanical stability”: It is stated that an increase in crowding implies an increase in elasticity. This is not necessarily true. What is the evidence for this statement?
In sum, there is insufficient evidence to propose a gel-like state, which implies a physical meshwork. In my opinion, it would be safer to propose a transition into a 'glassy' system (as in Parry et al., 2014). Broadly speaking, the glassy term can applicable to a wide range of out-of-equilibrium soft materials, including gels, foams, interacting or concentrated colloidal suspensions, etc. (Cipelletti and Ramos, Phys Condensed Matter, 2005).
There are also questions about the cell stiffness measurements. If S. pombe cells do indeed maintain their rod shape at low pH even after their cell wall has been removed, it would be an absolutely amazing result. This increases the burden of proof. An alternative and trivial explanation for the result is that the cells still have residual cell wall that contributes to the rod shape maintenance and stiffness of the cell. Perhaps enzymatic digestion of the cell wall is incomplete at low pH, which would not be surprising. To me, the maintenance of the rod shape actually argues that wall-free cells were not generated, casting doubt on the claim of increased stiffness. Complete removal of cell wall must be ascertained. Perhaps (round) spheroplasts could first be generated at neutral pH, and then re-shaped (e.g., to rod-like) by an external force (e.g., their pressure-based microfluidic device might do the trick). The authors could then test whether the new (non-round) shape is maintained after a switch to low pH even when the external force is relieved.
Similarly, the authors need to rule out that the increased stiffness observed in energy-depleted/acidified budding yeast cells is not due to the presence of residual cell wall. Stiffness measurements could be performed on spheroplasts created under normal (log phase, neutral pH conditions when the cell wall is known to be completely digested) and then switched to energy-depleted or acidic conditions for stiffness measurements.
Figure 5—figure supplement 2: The statement about the reduction in cell volume is not convincing at this stage. A reduction in cell volume doesn't mean an increase in crowding, unless the reduction in cytoplasmic volume occurred very rapidly before there can be a change in cytoplasmic composition. Under their experimental conditions (30 min), the composition of the cytoplasm can change. Their microfluidic device allows them to measure the cytoplasmic volume immediately following acidification/energy depletion.
Also, what was the osmolality of the external media and buffers used? Can the authors exclude the possibility of an osmotic shock causing the difference in cytoplasmic volume? Also, could they clarify what 'relative cell volume' mean? How many cells were measured?
Figure 5—figure supplement 4: I am not sure what these FRAP curves are showing. Are they for a single cell or for many cells averaged? More importantly, there is no obvious difference in recovery time between the three conditions, contrary to what is stated. Furthermore, the FRAP data should be analyzed, and diffusion coefficients for GFP should be provided. And why was 2M of sorbitol used when the authors suggest that the difference in volume for DNP+pH5.5 cells is equivalent to the sorbitol 0.8 M condition? FRAP measurements under 0.8M sorbitol would be a fairer comparison.
What is the evidence for fractional Brownian motion? There are other types of motion where displacement distributions collapse after re-scaling. It is not clear what fractional Brownian motion brings to the story.
Is the starvation-induced acidification observed regardless of the pH of the external medium? Or is it only when the external medium is acidic? If it is the latter, it should be clearly stated.
Similarly, fission yeast and Dictyostelium are said to undergo cytosolic pH fluctuations in response to energy depletion. Is this true in any medium regardless of its pH or only in acidic media?
How do the MSD curves in Figure 3A and B compare to Figure 1C? If the authors' proposal is correct (reduction in particle dynamics associated with starvation is due to cytosolic acidification), shouldn't we expect the pH 7 condition in Figure 3 to look like the control (untreated/log-phase culture) in Figure 1C?
The article is well written and compelling for the most part. The numerous control experiments and the redundant mechanical measurements (microrheology and AFM indentation) support the sol to gel transition hypothesis. There are a few major flaws in the interpretation and presentation of the data that need addressing if the reader is to believe the authors' explanation of pH dependent fluctuations within the cytoplasm. My concerns are below.
1) The use of the term "cytoplamsic freezing" is really questionable. It is common in cell mechanics and active matter to find analogies to inanimate or inactive matter. The "soft glassy rheology" of the cytoskeleton is such an example. This is a good thing to do if there are truly fundamental characteristics shared between the two analogs. In the SGR case, great care was taken to show the analogy. Other examples in cell mechanics have been published to show in detail the analogy between cellular dynamics and some inanimate physical systems. In the submitted manuscript such a level of care is not taken, and the term "freezing" is used without any thought about what are the essential phenomena of freezing, and whether this gelation is anything like true freezing. If the authors believe that what they observe is truly a sol-gel transition associated with assembly of macromolecules in the cytoplasm, they should name the phenomenon accordingly. Their work will be taken more seriously by a broader audience if they let go of this name.
2) A lot of the particle tracking and MSD calculation is performed assuming thermal fluctuations are the driving force. This assumption allows connecting MSDs to material properties. A decent argument is made for this by showing that the depolymerization of actin and microtubules has little effect on their results. I do not know whether this argument is legitimate. Is it really true that no other non-equilibrium or biochemical driving forces can occur in the cytoplasm, other than those driven by the action of ATP on filament bound motors? The work by McIntosh and Schmidt from a few years ago sidestepped this question by comparing active microrheology (manually driven beads with E or B fields) to passive microrheology, and carefully measuring a driving spectrum. The recent paper by Guo and Weitz did something similar. I think this sort of thing would have to be done again here, and the outcome would have to show that the spectrum is indeed thermal, then a thermal analysis could be performed to link MSD to material properties.
Alternatively, the authors could just keep the same analysis and experiments that they have, and tone down their interpretation. I think that most of their story can be told without claiming that they can infer material properties from MSDs. They can just say that the MSDs say things are more "liquid-like" or "solid-like", and then focus on the general phenomena like the dramatic reduction in motion. The supplementary movies show this beautifully. Several years ago many high-profile papers were published that flippantly linked particle MSDs to material properties, which ultimately damaged the reputations of the authors. I think it is imperative that care is taken to prevent the same thing from occurring, for the sake of the authors and the broader research community.
To strengthen their story and focus on a transition in material properties from fluid-like to solid-like, more attention could be paid to the AFM indentation data. They use a Hertz model to fit their data. If they showed the F-d curve on a log-log scale and showed that the indent really scaled like F~d(3/2) (a fit on a lin-lin scale is not sufficient to convince the reader of the right power law), then this would be a first step that they really have a gel. They would also have to show that this could not be attributed to membrane tension, since a balloon filled with water will seem like a solid when indented from the outside. Again, I don't suggest new experiments, but perhaps extracting more compelling information about their current data.
3) The correlation analysis is seriously confusing. At first I thought I was looking at correlation functions, and concluded that the results made no sense. After re-reading the description of their analysis several times, I understood the steps taken by the authors to come up with Figure 4C and the associated supplementary figure. I think the authors need to include a few examples of the displacement autocorrelation functions (as a function of time), and show the process to come up with this correlation map as a function of displacement length.
[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]
Thank you for resubmitting your work entitled "A pH-driven transition of the cytoplasm from a fluid- to a solid-like state promotes entry into dormancy" for further consideration at eLife. Your revised article has been favorably evaluated by Vivek Malhotra (Senior editor), a Reviewing editor, and two reviewers. Both reviewers agree that the manuscript has been improved but there are some minor issues that need to be addressed before acceptance.
Both reviewers felt that some modifications to the text were warranted as outlined below. One felt that there were some technical concerns and improvements in clarity needed. The other suggests a further consideration be added to the Discussion. We feel that these should be accommodated in the final version.
The revised manuscript is vastly improved, and the additional results on the cell wall-free cells are simply amazing. However, I do have some technical concerns with some of the new analyses. These issues do not affect the major conclusions of the paper, but I believe that the authors should address them before publication.
Figure 4A. Why is α measured in the middle of the MSD? The center has fewer statistics, measurements involving the MSD should be made at the beginning where the statistics are the greatest.
Figure 4B and Figure 4—figure supplement 3 and Figure 4—figure supplement 2. I still think that the fractional Brownian motion (fBm) model doesn't bring much to the story (and disrupts the flow), and the evidence is not very strong. Also, a quantitative metric should be used to distinguish Gaussian from non-Gaussian (see equation 1 in Weeks et al., Science, 2000). This can be applied to individual trajectories. The particle size (since it is a mixture) should be considered in the rationale for scaling displacement distributions. What would they see if the distributions were scaled by the relative particle size instead?
It is confusing that Figure 4—figure supplement 5 shows a break in correlation linearity (consistent with caging and cage escape) whereas Figure 4C doesn't show the break (more consistent with purely elastic material). What are the experimental differences and what does it mean to their fBm model?
Figure 4—figure supplement 4. The shape of this correlation plot (a single negative correlation for the first displacement) is precisely what is expected for localization error. They could remove the plot altogether (going back to the support for the fBm model being quite weak). But if they want to show this, the authors should validate that this does not reflect localization error (imperfect localization of a static object will always give this correlation plot). The time scale of the negative correlation should be robust over experiments of different frame rates. If experiments of all frame rates produce anti-correlated displacements over one frame, the result is an artifact.
The authors have addressed all of my previous concerns and I recommend publication.https://doi.org/10.7554/eLife.09347.048
- Daniel Midtvedt
- Titus Franzmann
- Doris Richter
- Vasily Zaburdaev
- Simon Alberti
- Matthias Christoph Munder
- Matthias Christoph Munder
- Oliver Otto
- Maik Herbig
- Elke Ulbricht
- Paul Müller
- Anna Taubenberger
- Shovamayee Maharana
- Elisabeth Nüske
- Simon Alberti
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
We thank several members of the MPI-CBG and Christoph Weber from the MPI-PKS for critical reading of the manuscript. We are grateful to Eli Barkai and Daniela Frömberg for helpful discussions. We thank Cammie Lesser for the GFP-μNS plasmid. The light microscopy facility of the MPI-CBG is acknowledged for expert technical assistance. MM was supported by a DIGS-BB doctoral and a springboard-to-postdoc fellowship. SM was supported by a postdoctoral fellowship by the Alexander von Humboldt Foundation. JG was supported by an Alexander von Humboldt Professorship by the Alexander von Humboldt Foundation. We acknowledge founding by the Max Planck Society and the German Research Foundation (DFG, AL 1061/5-1).
- Robert H Singer, Reviewing Editor, Albert Einstein College of Medicine, United States
- Received: June 11, 2015
- Accepted: February 13, 2016
- Version of Record published: March 22, 2016 (version 1)
© 2016, Munder et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.