Biophysical properties of Saccharomyces cerevisiae and their relationship with HOG pathway activation.
ABSTRACT Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyperosmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.

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Page 1
ORIGINAL PAPER
Biophysical properties of Saccharomyces cerevisiae
and their relationship with HOG pathway activation
Jo ¨rg Schaber•Miquel A`ngel Adrover•Emma Eriksson•Serge Pelet•
Elzbieta PetelenzKurdziel•Dagmara Klein•Francesc Posas•
Mattias Gokso ¨r•Mathias Peter•Stefan Hohmann•Edda Klipp
Received: 11 January 2010/Revised: 18 March 2010/Accepted: 12 May 2010/Published online: 19 June 2010
? The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract
mechanical cell properties are important for predictive
mathematical modeling of cellular processes. The concepts
of turgor, cell wall elasticity, osmotically active volume,
and intracellular osmolarity have been investigated for
decades, but a consistent rigorous parameterization of these
concepts is lacking. Here, we subjected several data sets
of minimum volume measurements in yeast obtained
after hyperosmotic shock to a thermodynamic modeling
framework. We estimated parameters for several relevant
biophysical cell properties and tested alternative hypotheses
Parameterizedmodelsof biophysicaland
abouttheseconceptsusingamodeldiscriminationapproach.
In accordance with previous reports, we estimated an aver
age initial turgor of 0.6 ± 0.2 MPa and found that turgor
becomes negligible at a relative volume of 93.3 ± 6.3%
corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At
high stress levels (4 Osm/l), plasmolysis may occur. We
found that the volumetric elastic modulus, a measure of cell
wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimina
tion analysis suggests that other thermodynamic quantities
affecting the intracellular water potential, for example the
matrix potential, can be neglected under physiological con
ditions. The parameterized turgor models showed that acti
vation of the osmosensing high osmolarity glycerol (HOG)
signaling pathway correlates with turgor loss in a 1:1 rela
tionship. This finding suggests that mechanical properties of
the membrane trigger HOG pathway activation, which can
be represented and quantitatively modeled by turgor.
M. A`. Adrover, E. Eriksson, S. Pelet, E. PetelenzKurdziel have
contributed equally to this work.
Electronic supplementary material
article (doi:10.1007/s0024901006120) contains supplementary
material, which is available to authorized users.
The online version of this
J. Schaber ? E. Klipp (&)
Theoretical Biophysics, Humboldt University,
Invaliden Str. 42, 10115 Berlin, Germany
email: edda.klipp@rz.huberlin.de
M. A`. Adrover ? F. Posas
Cell Signaling Unit, Departament de Cie `ncies Experimentals i de
la Salut, Universitat Pompeu Fabra (UPF),
08003 Barcelona, Spain
E. Eriksson ? M. Gokso ¨r
Department of Physics, University of Gothenburg,
412 96 Gothenburg, Sweden
S. Pelet ? M. Peter
Institute of Biochemistry, ETH, Zurich, Switzerland
E. PetelenzKurdziel ? D. Klein ? S. Hohmann
Department of Cell and Molecular Biology/Microbiology,
University of Gothenburg, Box 462, 405 30 Go ¨teborg, Sweden
Present Address:
D. Klein
Clinical R&D Laboratory, Oxoid, Microbiology,
Basingstoke, Thermo Fisher Scientific, Perth, UK
J. Schaber (&)
Institute for Experimental Internal Medicine, Medical Faculty,
Otto von Guericke University, Leipziger Str. 44,
39120 Magdeburg, Germany
email: schaber@med.ovgu.de
Present Address:
E. Eriksson
SP Technical Research Institute of Sweden,
Brinellgatan 4, Box 857, 501 15 Bora ˚s, Sweden
123
Eur Biophys J (2010) 39:1547–1556
DOI 10.1007/s0024901006120
Page 2
Keywords
Volumetric elastic modulus ? High osmolarity glycerol
(HOG) signaling ? Plasmolysis ? Model discrimination ?
Yeast
Turgor ? Cell wall elasticity ?
Introduction
All living cells maintain an osmotic pressure gradient
between their interior and the extracellular environment.
This gradient is counterbalanced by a hydrostatic pressure,
called turgor, which is especially prominent in plants and
unicellular organisms, most notably fungi. The concept of
turgor has been debated for many years (Burstro ¨m 1971). It
is recognized that turgor plays a vital role in growth
(Cosgrove 1981; Zimmermann 1978; Marechal and Gervais
1994), cell structure (Cosgrove 1993; Morris et al. 1986;
Zhongcan and Helfrich 1987; Munns et al. 1983), and
membrane transport processes (Zimmermann 1978; Lande
et al. 1995; Kamiya et al. 1963; Soveral et al. 2008) and
that it may be sensed by the cells as an indicator of external
osmotic changes (Tamas et al. 2000; Coster et al. 1976;
Schmalstig and Cosgrove 1988; Reiser et al. 2003).
Therefore, quantifying cell wall and membrane properties,
and thus the resulting turgor pressure, has been the aim of
numerous studies (Cosgrove 1981; Morris et al. 1986;
Munns et al. 1983; Kamiya et al. 1963; Coster et al. 1976;
Smith et al. 1998, 2000a, b, c; Marechal et al. 1995;
Gervais et al. 1996a; Cosgrove 2000). Parameterized
models of turgor pressure, based on cell wall and mem
brane properties are especially important for quantitative
mathematical models describing the interdependence
between water transport and signaling processes (Schaber
and Klipp 2008; Klipp et al. 2005; Gennemark et al. 2006;
Kargol and Kargol 2003a, 2003).
At present, it is not possible to directly measure turgor
in yeast. However, the socalled linear elastic theory
states that the change in turgor pressure P is proportional
to a relative change in membrane enclosed cell volume
Vm, i.e.,
dP ¼ edVm
Vm;
ð1Þ
where e is a proportionality factor, called volumetric elastic
modulus or bulk modulus. This factor can be viewed as a
measure of the elasticity of the cell wall. Thus, the turgor
pressure can be derived from cell volume measurements
that have been performed repeatedly on yeast cells under
different experimental conditions (Munns et al. 1983;
Smith et al. 2000a, b, c; Touhami et al. 2003; Wei et al.
2001; Martinez de Maranon et al. 1996; Arnold and Lacy
1977). However, the results obtained for turgor pressure
were highly inconsistent, with variations spanning up to
three orders of magnitude from 0.05 (Martinez de Maranon
et al. 1996) to 2.9 (Arnold and Lacy 1977) MPa.
The concepts of turgor, cell wall elasticity, osmotically
active volume and intracellular osmolarity have never been
quantified and parameterized together in a consistent
framework, nor challenged by alternative concepts (Smith
et al. 2000c; Martinez de Maranon et al. 1996; Gervais
et al. 1996b). Moreover, the few reports in which turgor
and/or cell wall elasticity were quantitatively determined
usednonphysiologicalexperimental
example, one study used prestressed cells (Marechal et al.
1995) and in two others, the cells were suspended in dis
tilled water before volume measurements (Smith et al.
2000b, c).
The objective of this study was to derive parameterized
models of turgor and other biophysical properties of
the cell, for example the volumetric elastic modulus, in
Saccharomyces cerevisiae. We developed a modeling frame
work that includes the concepts of turgor pressure, intra and
extracellular osmotic pressure, and membrane and volume
properties and, for the first time, also other thermodynamic
quantities, for example the matrix potential, in a consistent
manner. By reformulating submodules while keeping
the overall framework consistent, we could test several
hypotheses describing the relationship between cell volume
and changes in the intracellular water potential. Verification
of these hypotheses was based on four independent data
sets. To ensure a wide applicability of the selected model,
the conditions for generating each data set were slightly
different. We also correlated cell volume measurements
with Hog1 phosphorylation levels and Hog1GFP nuclear
localization to investigate the physiological consequences
of turgor loss under hyperosmotic stress in a quantitative
fashion. Hog1 is the yeast p38 stressactivated protein
kinase whose phosphorylation level and subcellular locali
zation are controlled by an osmosensing signaling pathway
(Hohmann 2002). We found a 1:1 relationship between
turgor loss and HOG pathway activation. A loss of turgor
relates to HOG pathway activation such that when turgor
becomes zero because of application of a hyperosmotic
solution the HOG pathway is maximally activated. This
finding suggests that the extent of HOG pathway activation
is directly linked to some mechanical property of the
membrane, which can be represented and quantitatively
modeled by the loss of turgor pressure.
conditions. For
Materials and methods
Descriptions and units of all variables and parameters are
listed in Table 1.
1548 Eur Biophys J (2010) 39:1547–1556
123
Page 3
Modeling framework
We assume that the change in osmotically active volume
Vosis equal to the water flux across the cell membrane,
which is driven by differences in chemical water potentials
inside and outside the cell. Based on these thermodynamic
principles (for details refer to the ‘‘Supplementary mate
rial’’) we developed a model describing the minimal vol
ume of yeast cells attained after osmotic shock, Vap
included several new aspects that are depicted in Fig. 1.
We made a distinction between the commonly measured
volume that is enclosed by the cell wall, which we refer to
as the apparent volume Vap, and the membraneenclosed
cytoplasmic volume, Vm, where osmotic and hydrostatic
pressures are defined. Vmcomprises the osmotically active
volume Vosand the minimal solid cytosolic volume Vb, i.e.,
Vm= Vos? Vb. We assume that for osmotic shocks higher
than a critical value of cpl
value of Vap
wall (Vap), i.e., plasmolysis occurs, giving rise to the
min, which
eor volumes lower than a critical
pl, the membrane (Vm) detaches from the cell
periplasmic volume Vpl, such that Vap= Vm? Vpl. Fur
thermore, we define Vm
becomes zero and Vm
as the volume where negative
hydrostatic effects and/or matrix potential effects become
important, corresponding to hyperosmotic shock levels of
cP=0
and cs
thresholds that affect the rate of water outflow, i.e.,
shrinkage. Between Vm
reciprocal function of external osmolarity, also called the
van’t Hoff relationship (Noble 1969) (Eq. S6 in ‘‘Supple
mentary material’’). Based on these concepts, we derived a
formula for the apparent minimum volume after osmotic
shock Vap
larities and volumes:
?
PVmin
ap
aPCRTþ ce
where c0
‘‘Supplementary material’’), Vap
P=0as the volume at which the turgor
s
ee, respectively (Fig. 1). The latter two are
P=0and Vm
sapparent cell volume is a
minas a function of turgor pressure PVmin
ap, osmo
Vmin
ap¼ Vbþ Vplþ
ci
0V0
ap? Vb? Vpl
?
0
stressþ ce
ð2Þ
iis the initial internal osmolarity (Eq. S4 in
0is the initial apparent cell
Table 1 Summary of quantities used in the main text
QuantityUnit Description
Vap
Vap
Vap
Vm
Vos
Vpl
% initial volume Apparent cell volume, enclosed by the cell wall
0
% initial volume Initial Vap
Minimal Vapattained after hyperosmotic shock
Cell volume, enclosed by the plasma membrane
min
% initial volume
% initial volume
% initial volume Osmotically active volume
% initial volume Periplasmic volume. We tested three alternative models of Vplas a function of cstress
‘‘Supplementary material’’)
e
(see
Vb
Vm
Vm
Vap
c0
c0
cstress
cP=0
cs
cpl
P0
PVmin
ap
% initial volumeSolid cytosolic volume
P=0
% initial volumeVolume, when turgor becomes zero
s
% initial volumeVolume below which negative hydrostatic or matrix potential effects are important
pl
% initial volumeApparent volume where plasmolysis occurs
i
Osm/lInitial internal osmolarity.
e
Osm/l Initial external osmolarity
e
Osm/l Applied osmotic stress
e
Osm/l
cstress
cstress
cstress
Initial turgor at the initial turgid cell volume of 100%
e
corresponding to Vm
corresponding to Vm
corresponding to Vap
P=0
e
Osm/l
e
s
e
Osm/l
e pl
MPa
MPa Turgor at Vap
‘‘Supplementary material’’) and the twosided model (Eq. S8 in ‘‘Supplementary material’’)
(Fig. 2)
min. In general, there are two alternatives, i.e., the onesided model (Eq. S7 in
e
MPaVolumetric elastic modulus, describing the elasticity of the cell wall, relating relative volume
change to hydrostatic pressure, i.e., turgor
es
MPaProportionality factor, relating relative volume change to the matrix potential or other effects
negatively influencing the intracellular water potential
R
J K1mol1
Gas constant
T
aPC
K Temperature
Conversion factor relating pressure to osmolarity, e.g., for relating MPa and Osm/l it is 103
Dimensionless
Eur Biophys J (2010) 39:1547–1556 1549
123
Page 4
volume, R is the gas constant, T is the temperature, aPCis a
dimensionless conversion factor, c0
osmolarity, and cstress
is the applied osmotic stress.
eis the initial external
e
Turgor pressure and matrix potential
Thermodynamic quantities other than turgor and osmolar
ity, that can affect the cellular water potential, are usually
ignored. For example, a specific fraction of the intracellular
water might be bound to colloidal surfaces by electrostatic
interactions. This water is not freely available in solution,
which lowers the total intracellular water potential by a
value that is termed the matrix potential (Griffin 1981). In
addition, it is possible that the cytoskeleton mechanically
counteracts cell shrinkage such that the cell has an inherent
tendency to reswell in a spongelike fashion. This effect
would also reduce the total intracellular water potential.
For simplicity, we summarize these effects under the term
matrix potential (Ds in Eq. S1 of the ‘‘Supplementary
material’’). Quantitative descriptions of the matrix poten
tial are not available and elaborated models of mechanical
forces induced by volume changes (Stamenovic and
Coughlin 1999) are beyond the scope of this study.
Therefore, we include the effects summarized under the
term of the matrix potential in the model of the turgor
pressure PVmin
ap
with a simple mathematical description. In
this way, we obtain an expression for PVmin
matrix potential (assuming Vpl= 0 for VmC Vm
?
eln
VP¼0
m
for
0 for
Vmin
ap?Vpl
Vs
m
for
ap
including the
P=0):
PVmin
ap
Vmin
8
>
ap;Vpl;VP¼0
Vmin
ap
m
;Vs
m;e;es
?
Vmin
Vs
¼
??
ap?VP¼0
m?Vmin
Vmin
m
ap? Vpl\VP¼0
ap? Vpl\Vs
m
esln
??
m
>
>
>
:
<
ð3Þ
of
InFig. 2
min Vpl.
We tested Eq. 3 against the data, with and without the
term for matrix potential, which we refer to as the one
sided and the twosided models, respectively. We also
tested three hypotheses regarding the size of the periplas
mic volume Vpl, (a) Vpl= 0, (b) Vpl[0 with a constant
apparent volume Vap
material’’), and (c) Vpl[0 with a variable apparent volume
Vap
Inserting Eq. 3 into Eq. 2 yields an implicit expression
for Vap
model for turgor, matrix effect, and periplasmic volume.
When a solution exists, this solution is unique (see ‘‘Sup
plementary material’’).
PVmin
ap
isdisplayed asafunction
Vm= Vap
pl(Fig. 1; Eq. S10 in ‘‘Supplementary
pl(Eq. S11 in ‘‘Supplementary material’’).
minthat depends on various parameters of the specific
Fig. 1 Qualitative representation of cell volume concepts. Solid line:
Vap, the apparent cell wall enclosed volume. Dotted line: Vm, the
membrane enclosed volume. Vm
becomes zero and Vm
is the volume where negative hydrostatic
effects or matrix potential effects become important, corresponding to
hyperosmotic shock levels of cP=0
and cs
the stress and volume thresholds, respectively, where Vmdetaches
from Vap. Vplis the periplasmic volume. Vbis the minimum solid
cytosolic volume. Note, that it is not necessarily true that cs
Vm
membrane in different states after hyperosmotic shock
P=0is the volume at which the turgor
s
ee, respectively. cpl
eand Vap
plare
e\cpl
eand
s[Vap
pl. The diagrams of the cells illustrate the cell wall and the
Fig. 2 Illustration of turgor and matrix potential. Turgor (black line),
which has an initial value of P0at the initial turgid cell volume of
100%, is displayed on the positive yaxis. When the cell shrinks, the
turgor decreases to zero at the volume Vm
‘‘onesided turgor model’’. The matrix potential or other effects that
reduce the water potential are displayed on the negative yaxis. These
are assumed to become important below a specific threshold volume
Vm
the dashed line is referred to as the ‘‘twosided turgor model’’
P=0. This is referred to as the
s. The model represented by the solid line up to Vm
stogether with
1550 Eur Biophys J (2010) 39:1547–1556
123
Page 5
Model discrimination
Using Eq. 2 together with a model for Vpl(Eqs. S10, S11 in
‘‘Supplementary material’’) and a turgor model (Eq. 3;
Eqs. S7, S8 in ‘‘Supplementary material’’), a solution for
Vap
sured, Eq. 2 can be fitted to the data by estimating the
respective parameters (Table S1 in ‘‘Supplementary mate
rial’’), e.g., by minimizing the sum of squared residuals
(SSR)
X
where x = (x1, x2, …, xm) denote the parameters that are
to be estimated and that depend on the model (Table S1 in
‘‘Supplementary material’’), riis the standard deviation of
the measurements and n is the number of data points. For
the sake of simplicity, we assume that the measurement
errors are independently normally distributed. Thus, the
SSR becomes a maximumlikelihood estimator and we can
use the Akaike’s information criterion corrected for small
sample size (AICc) to rank and, thus, discriminate the
models according to their SSR and number of parameters
(Burnham and Anderson 2002):
?
where k is the number of parameters.
The fitting was performed by differential evolution, a
global optimization method (Storn and Price 1997), and
the models were ranked according to the AICc (Eq. 4).
Additionally, for the best model, we performed a Monte–
Carlo analysis by resampling the data a hundred times
assuming a normal distribution with the respective stan
dard deviations for each data point. In this way, means
and confidence intervals for the estimated parameters
could be obtained.
mincan be numerically determined. When Vap
minis mea
SSRðxÞ ¼
n
i¼1
1
ri
Vmin
ap;iðxÞ ? Vmin
measured;i
??2;
AICc ¼ 2k þ n ln
2pSSR
n
?
þ 1
??
þ2kðk þ 1Þ
n ? k ? 1;
ð4Þ
Data sets
We collected three independent data sets (data sets 1–3 in
Fig. 3; Fig. S1 in ‘‘Supplementary material’’) and took one
data set from the literature (Marechal et al. 1995) (data set
4 in Fig. 3; Fig. S2 in ‘‘Supplementary material’’). The cell
volume was quantified immediately before and after the
hyperosmotic stress, ensuring that the minimum volume
after osmotic shock was measured. For our experiments we
used NaCl as an osmoticum, whereas in the data set from
literature yeast cells were subjected to a wide range
of glycerol concentrations (refer to Marechal et al. 1995
for details). Table 2 summarizes the different data sets.
Experimental details for data sets 1–3 are described in the
‘‘Supplementary material’’.
Results
Parameter fitting and model selection predicts turgor
pressure and other biophysical cell properties
We fitted Vap
alternative models for PVmin
different models (see Table S1 in ‘‘Supplementary mate
rial’’ for a complete listing). For each data set the best
model according to the AICc is described in Table 3. The
fitted and measured Vap
corresponding predicted turgor pressure.
minfrom Eq. 2 to four different data sets using
and Vpl, resulting in seven
m
minare displayed in Fig. 3, with the
Onesided turgor model is most appropriate
for physiological stress conditions
The three data sets produced for this study were all fitted
best by the onesided turgor model based on Eqs. 1 and 3,
where only the positive turgor pressure plays a role
(Fig. 2). Even though this is the generally accepted model
(Cosgrove 1981; Marechal and Gervais 1994; Klipp et al.
2005; Gennemark et al. 2006; Meikle et al. 1988), we
tested it with six other models, because to our knowledge it
has never been challenged by other models, nor rigorously
fitted to data. Thus, we show for the first time that effects
resisting cell shrinkage, for example the matrix potential or
mechanical forces, can be neglected under physiological
conditions. Consequently, when the turgor becomes zero
after an external osmotic shock of cP=0
the measured apparent volume Vapis well predicted by the
membrane enclosed volume Vm according to the van’t
Hoff’s equation (Eq. S6 in ‘‘Supplementary material’’).
This means that the cell wall tightly follows the shrinkage
of the membrane enclosed volume. Data set 4, which was
collected by applying extreme stress levels, also favored
the onesided turgor model. However, at 4 Osm/l plas
molysis was predicted, with a constant minimal apparent
volume Vap
e
(Table 1; Fig. 3),
plof 65%.
Estimated biophysical cell properties are similar
between experiments
Parameters estimated on the basis of the datasets give a
consistent picture of important biophysical cell properties.
For data sets 2 and 3, where single cell information was
available, we distinguished between small and large cells
and repeated the analysis to test whether cell size had an
effect on the results. We found no significant differences
between small and large cells with regard to the estimated
parameters, which is in agreement with earlier reports
(Martinez de Maranon et al. 1996). The solid volume Vb
was estimated to be between 33 and 49% of the initial
cell volume, which also corresponds to earlier reports
Eur Biophys J (2010) 39:1547–1556 1551
123
Page 6
(Marechal et al. 1995; Meikle et al. 1988). The initial
turgor estimated on the basis of the three data sets with
similar experimental conditions (data sets 1–3) was
0.6 ± 0.2 MPa on average, which confirmed results from
earlier studies (Smith et al. 2000c; Gervais et al. 1996a;
Meikle et al. 1988). The estimated membrane rigidity e was
the parameter that varied the most between experiments
and it turned out to be a sensitive, poorly determined
parameter, which is reflected by the relatively high stan
dard deviations. However, at least for the three directly
comparable data sets 1–3, the results were similar, giving
an average volumetric elastic modulus of 14.3 ± 10.4 MPa
ranging from 5.7 to 25.8 MPa.
On the basis of our general modeling framework and the
estimated parameters, we could derive several other inter
esting cell properties. The initial osmolarity within the cell
c0
of the outside medium. Thus, apparently, yeast can main
tain substantial osmotic gradients between the inside and
outside of the cell, which are equilibrated by turgor. The
volume at which turgor becomes zero was estimated to be
of 93.3 ± 6.3% on average for data sets 1–3. The corre
sponding external shock for the salt experiments was
0.4 ± 0.2 Osm/l, corresponding to a salt concentration of
roughly 0.2 M NaCl. As this is within the range of con
centrations in which saturation of HOG pathway activation
iwas estimated to be up to more than twice the osmolarity
Fig. 3 Best fit models and data. The data and the best fit model (solid
line) refer to the left yaxis. The dark gray region depicts the 95%
confidence region of the fitted model. The right yaxis refers to
the estimated turgor pressure (dashed line). The light gray region
depicts the 95% confidence region of the estimated turgor pressure.
The xaxis refers to concentrations of the respective stress agent. The
confidence regions were calculated on the basis of the confidence
intervals of the estimated parameters (Table 3). The four data sets
are described in the ‘‘Methods’’ sections and the ‘‘Supplementary
material’’
Table 2 Data sets used for model discrimination
No. MethodStrainMedium Agent
?CGrowth
c0
e(Osm/l)# n
Refs.
1Particle sizerW303 YPD NaCl30Early log0.26 16 This study
2 Single cells bright fieldBY4741 YNBNaCl20 Log 0.2711 This study
3 Single cells fluorescenceW303 SDNaCl 30Log 0.25 13 This study
4Single cells bright field CBS1171 WickerhamGlycerol 25 Stationary0.86 15Marechal et al. (1995)
c0
ewas measured for data sets 1–3 with an osmometer and calculated for data set 4 from Marechal et al. (1995), # is the number of data points
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is observed (Maeda et al. 1995), we hypothesized that the
initial HOG pathway response may be correlated with
turgor.
Loss of turgor correlates with HOG pathway activation
The exact biophysical mechanisms that trigger the activa
tion of the HOG pathway in yeast have not yet been
determined (Hohmann 2002), but there is evidence that the
turgor is one of the factors involved (Tamas et al. 2000;
Reiser et al. 2003). As our computational analysis provided
us with parameterized models of turgor pressure (Fig. 3;
Table 3), we tested whether there is a correlation between
the loss of turgor for different degrees of osmotic shock
and the extent of HOG pathway activation. Thus, in addi
tion to cell volume measurements, we collected two inde
pendent data sets reflecting the degree of HOG pathway
activation depending on the intensity of the hyperosmotic
stress. In the first data set, the extent of Hog1 nuclear
accumulation was measured, whereas the second data set
represents the extent of Hog1 phosphorylation in response
to different NaCl concentrations (Fig. 4, for details about
the measurements refer to the ‘‘Supplementary material’’).
By considering both Hog1 activation (Fig. 4) and the
predicted turgor (dotted line in Fig. 3) as a function of
applied osmotic stress, we could investigate Hog1 activa
tion as a function of predicted turgor (Fig. 5). With three
different parameterizations for the turgor model (from data
sets 1–3, data set 4 was disregarded, because it used a
different stress agent) and two different Hog1 activation
data sets, we obtained six turgorHog1 activation correla
tions, of which we display three in Fig. 5. The others are
displayed in the ‘‘Supplementary material’’ (Fig. S3).
We fitted a linear relationship between HOG pathway
activation and relative turgor for the three different
parameterized models, corresponding to data sets 1–3, and
the two different HOG pathway activation data sets (black
lines in Fig. 5) by a weighted orthogonal regression. Our
null hypothesis claimed a direct 1:1 linear relationship,
i.e., H0: a ? bx, with (a, b) = (100, 1) (gray lines in
Fig. 5). To test H0we computed confidence regions for
the estimated parameter pairs (a, b) by a Monte–Carlo
analysis. As can be seen from the insets in Fig. 5, in all
cases the hypothesized relationship (gray points) was
within the 95% confidence region of the actual estimated
parameter pair. Thus, the null hypothesis could not be
Table 3 Results of parameter fits of Eq. 2 for the best selected model according to the AICc
Data set 1Data set 2 Data set 3 Data set 4
#2224 Selected model
PVmin
Vpl
k
m
Onesided Onesided OnesidedOnesided
000 Constant Vap
4
pl
333
Vb
P0
e
Vap
c0
Vm
cP=0
cpl
49.0 ± 3.4 40.2 ± 5.533.0 ± 4.8 40.1 ± 11.1 Estimated parameters
0.5 ± 0.1 0.9 ± 0.2 0.5 ± 0.13.4 ± 1.0
25.8 ± 7.0 5.7 ± 2.011.4 ± 2.128.6 ± 11.3
pl
65.0 ± 5.9
i
0.4 ± 0.10.6 ± 0.10.5 ± 0.0 2.2 ± 0.4 Derived parameters
P=0
98.2 ± 3.1 86.1 ± 6.395.5 ± 6.8 88.9 ± 10.8
e
0.2 ± 0.10.5 ± 0.2 0.2 ± 0.11.9 ± 1.9
e
4.4 ± 2.2
For a complete description of parameters and units refer to Table 1
# Number of best selected model (Table S1 in ‘‘Supplementary material’’), PVmin
(Fig. 1; Eq. S10 in ‘‘Supplementary material’’), k: number of fitted parameters, Vb: solid base volume, P0: initial turgor, e: volumetric elastic
modulus, Vap
to equilibrate turgor, cpl
the data points were sampled from their respective standard deviations indicated in Figs. 3 and 4. The mean of parameters in the lower part are
derived from the mean parameters in the upper part
m: selected turgor model (Fig. 2; Eq. 3), Vpl: selected Vplmodel
plapparent volume where plasmolysis occurs, c0
e: applied external stress to reach Vap
i: initial internal osmolarity, Vm
pl. Estimated parameters are given as mean ± standard deviation from 100 fits where
P=0: volume at zero turgor, cP=0
e
: applied external stress
Fig. 4 Hog1 activation data. Circles: maximum Hog1 nuclear
concentration after osmotic shock. Squares: Hog1 phosphorylation
after 2 min of shock treatment. Data are scaled to the respective
measured maximum
Eur Biophys J (2010) 39:1547–15561553
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rejected. Moreover, the Kendallrank correlation coeffi
cient (Kendall and Gibbons 1990) was highly significant
in all cases (P\0.01).
Discussion
Parameterized models of biophysical and mechanical cell
properties become increasingly important for quantitative
and predictive descriptions of cellular behavior. Our
modeling framework, which included the concepts of tur
gor, membrane elasticity, intracellular osmolarity, osmoti
cally active volume, nonturgid volume, and solid cytosolic
volume in a coherent and thermodynamically accurate
way, enabled us to parameterize all these concepts con
sistently, by fitting the relevant parameters to experimental
data. In addition, it enabled us to discriminate between
alternative hypotheses for turgor and volume changes
by including alternative submodels within the general
framework. Even though the data sets were based on very
different techniques, the overall conclusions are strikingly
similar indicatingthatthe
description is both accurate and universal.
We confirmed previous reports, which suggested an
initial turgor pressure of around 0.6 MPa (Smith et al.
2000b; Meikle et al. 1988). Turgor pressures reported for
yeast differ substantially. Part of this variation might be
because they have never been rigorously fitted to data. In
our study, we obtained similar results for data sets 1–3.
However, the initial turgor estimated from data set 4 was
sixfold higher. We assume that this discrepancy is caused
by different growth phases of yeast cells employed in the
experiments. This explanation is supported by earlier
reports, in which differences in turgor between cells in
different physiological states were observed. Specifically,
a higher turgor pressure was reported for cells in sta
tionary phase (Smith et al. 2000c; Martinez de Maranon
et al. 1996). After examining different possible explana
tions (Eq. 3), we confirmed the hypothesis that turgor
pressure is significant only above a specific volume
threshold, below which it can be neglected, as previously
proposed (Cosgrove 1981; Marechal and Gervais 1994;
Klipp et al. 2005; Gennemark et al. 2006; Meikle et al.
1988). Other forces potentially affecting the water
potential, and therefore water flux within the cell, can be
neglected under the studied conditions of osmotic shock
up to 1.5 M NaCl.
We found values for the volumetric elastic modulus e
between 6 and 29 MPa. We could not find any published
values of e for yeast. In a recent study, where yeast cells
were subjected to mechanical compression, values of
proposedmathematical
Fig. 5 TurgorHOG pathway activation relationship. The xaxes
are relative turgor (%) as predicted by the parameterized models
for different shocks of NaCl (dotted line in Fig. 3). The yaxes are
relative HOG pathway activation (%) according to different shocks
of NaCl (Fig. 4). The black lines are a fitted linear relationship
(y = a ? bx) based on a weighted orthogonal regression. The gray
lines represent the null hypothesis H0: y = 100  x, i.e., a direct
1:1 linear relationship between relative loss of turgor and relative
HOG pathway activation. The insets are plots of the (25, 50, 75,
90, 95%)confidence regions of the respective estimated parameter
pair (a, b) of a ? bx with the outermost line being the 95%
confidence region. The black points correspond to the black lines
in the plots, the gray points correspond to the gray lines. The
confidence regions are obtained by a Monte–Carlo analysis with
1,000 runs
1554Eur Biophys J (2010) 39:1547–1556
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Young’s modulus E for the cell wall of around 110 MPa
were reported (Smith et al. 2000a, c). Unfortunately, we
could not relate these values to our volumetric elastic
modulus, because those values for Young’s modulus E
were derived assuming a Poisson’s ratio m of 0.5 and,
hence, the formula E = 3e (1  2m) was not applicable.
We noted that cells in stationary phase (data set 4) are
estimated to be more rigid, i.e., have a higher volumetric
elastic modulus, but to a much lesser extent than in Smith
et al. (2000c). The cells used in data set 1 were grown to
saturation, i.e., beyond proliferation, before they were re
suspended in fresh medium for 1 h before measurements.
It is possible that they were still recovering from satura
tion phase and therefore had higher cell wall rigidity than
cells from data sets 2 and 3, which were measured at
logarithmic growth phase. This reflects that e is a function of
the physiological state of the cell. Thus, when turgor is being
modeled over longer time intervals than in this study, the
assumption of e being constant might be compromised.
Our modeling results support the notion of a rather
elastic cell wall, because the cell wall tightly follows the
cell membrane on shrinkage, and plasmolysis only occurs
under extremely high stresses. There is experimental evi
dence from mammalian cells that our model of an elastic
membrane/cell wall surrounding a viscous medium is an
oversimplification (Wang et al. 2001). However, our
model proved sufficient to explain our data. More com
plicated models were not supported by the data in respect
of the AICc. It is known that upon osmotic shock the actin
cytoskeleton in yeast depolymerizes (Brewster and Gustin
1994). This is in line with our results in which effects of the
skeleton, which we included into the model of the matrix
potential, were refuted by the model discrimination. A
recent compression study of mammalian cells also ruled
out the cytoskeleton as being responsible for the increase in
cell stiffness as the volume decreases (Zhou et al. 2009).
Other authors identified the concentration at which
plasmolysis occurs as approximately 1 Osm/l (Arnold and
Lacy 1977), but under different experimental conditions.
The predicted plasmolysis point of 65% in data set 4 was
higher than the lowest volumes measured in the other data
sets (44–54%, Fig. 3). Therefore, cells might have been at
the threshold of plasmolysis in those experiments. Because
no data were collected at higher stress levels this effect was
not distinguishable by model selection.
For the first time, we provide evidence that there is
direct link between loss of turgor upon osmotic shock and
HOG pathway activation, not only qualitatively but also
quantitatively. Moreover, the hypothesis of a direct 1:1
relationship between turgor loss and HOG pathway acti
vation could not be rejected. The physical basis of such a
direct relationship remains elusive, but could for example
be a change in Sln1 and Sho1 membrane protein
conformation as a function of membrane stretch or other
mechanical forces that relate to turgor.
Acknowledgments
ital version of data set 4, Rosie Perkins, Javier Macia, and Karlheinz
Schaber for useful suggestions on the manuscript, and Martina
Fro ¨hlich for measurement support. This work was supported via
several projects funded by the European Commission: QUASI
(Contract No. 503230 to SH, EK, FP and MP), CELLCOMPUT
(Contract No. 043310 to SH, EK and FP), UNICELLSYS (Contract
No. 201142 to SH, EK, FP, MP and MG), SYSTEMSBIOLOGY
(Contract No. 514169 to SH and EK), and AMPKIN (Contract No.
518181 to SH and MG). In addition work was funded by grants from
the Swedish Foundation for Strategic Research SSF (BioX to MG),
the Swedish Research Council (project grants to SH and MG), the
Carl Trygger Foundation (to MG), the Science Faculty, University of
Gothenburg (to SH and MG), and the Swiss systemsX.ch (to MP).
We thank Patrick Gervais for providing a dig
Open Access
Creative Commons Attribution Noncommercial License which per
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
This article is distributed under the terms of the
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