Supplementary Information for “Analysis of Osmoadaptation System in Budding Yeast
Suggests that Regulated Degradation of Glycerol Synthesis Enzyme is Key to Near-Perfect
Adaptation”
Anilkumar K. Patel, K.V. Venkatesh*, Sharad Bhartiya*
Department of Chemical Engineering, Indian Institute of Technology Bombay,
Mumbai, India – 400 076
+91-22-25767223
+91-22- 5726895
*Authors to whom any correspondence should be made
E-mail: anilpatel@iitb.ac.in; bhartiya@che.iitb.ac.in; venks@che.iitb.ac.in
Indexes for the Supplementary Information
Title
Page No.
S1: Description of Variables (Table S1)
2
S2: Initial Conditions for wild type and mutants (Tables S2 and S3)
3-4
S3: Description of Parameters (Table S4 and S5)
5-8
S4: Implementation of Simulation for various invoked conditions Table S6 9-11
S5. Derivation of Steady State Error equation (Eqn.A1-Eqn.A15)
12-13
S1: Description of Variable
Table S1
Variable
Description
Unit
E
Normalised error in Turgor pressure
Dimensionless
𝞹t
Turgor pressure
J/m3
𝞹i
Internal Osmotic Pressure
J/m3
G
Intracellular Glycerol
mM
OsmT
Intracellular Total Osmolyte
mM
V
Total Volume of cell
m3
Hog1PP
Dually phosphorylated Hog1 in nucleus
µM
mRNA
Common pool of mRNA in cytosol which are up-
µM
regulated by Hog1PP
E
Common pool of GPD1,GPP2 and other glycerol µM
synthesis enzymes
PTP
PTP concentration assumed to be identical to E
for wild type
µM
S2: Initial Conditions for wild type and mutants
Table S2: Initial conditions for wild type
Variable
Value
Unit
Reference/Remarks
Hog1PP0
0.0300
µM
In (Schaber et al., 2012) Initial Hog1PP and
Hog1P are .0068 µM and .0471 µM and. As
we have not quantified Hog1P we have taken
higher initial value of Hog1PP compare to the
value reported them them.
mRNA0
0.0030
µM
In (Klipp et al., 2005) model, total mRNA of
GPD1 is around .0015 µM
E0, PTP0
0.4920
µM
Obtained by initial steady state condition of
enzyme balance equation
OsmT0
601
mM
(Parmar et al., 2009)
(Klipp et al., 2005)
G0
240.5581
mM
In (Schaber et al., 2012) it is 180 mM, however
they have chosen lesser initial internal osmotic
pressure (1.265 MP)compare to the value given
by (Parmar et al., 2009) and (Klipp et al.,
2005)(see below). We obtained this value
assuming initial glycerol as 40 % of total
osmolyte (i.e. OsmT). This assumption is
consistent with (Schaber et al., 2012)
V0
6.5*10-17
m3
(Parmar et al., 2009)
𝞹i0
1.5*106
J/m3
(Parmar et al., 2009)
𝞹t0
0.875*106
J/m3
(Parmar et al., 2009)
𝞹e0
0.625*106
J/m3
(Parmar et al., 2009)
Table S3: Initial conditions for mutants
Mutant/variable
Hog1PP
mRNA
E
πi
G
µM
µM
µM
M.Pa.
mM
V/VWT
OsmT
mM
FPS1 over
0.0602
0.006
0.9871
1.3867
176.954
0.9521 555.9481
FPS1 absent
0.0296
0.003
0.4863
1.9401 473.6328
1.1861 777.8469
PTP over
0.0233
0.0023
0.3825
1.4521 213.8769
0.9797 582.1891
PTP absent
0.0303
0.003
0.4969
1.5019 241.6161
1.0008 602.1617
KD,E,Case2
0.0797
0.008
0.1307
1.3602
161.856
0.9409 545.3657
KDE,Case3
0.1295
0.013
0.0637
1.2933 123.1038
0.9126 518.5194
Notes: (1) VWT is volume of wild type, (2) For three mutants mentioned section 3.6, the initial
conditions are identical to the case of wild type. (3) For KD,E case1, the initial conditions are same
as in wild type.
S3: Description of Parameters:
Table S4: Parameters obtained either from Literature or calculated from balance equation
for initial steady state conditions:
Parameter Description
Value
Unit
R
Gas Constant
8.314
J/mol/K
T
Temperature
303.15
K
KHOG_b
Basal Hog1 activation
5.29·10-4
µM /sec
Remarks
Obtained from initial steady
state conditions of Hog1PP
rate
Ph0
Basal Phosphotase
0.1
µM
(Schaber et al., 2012)
Krna
Synthesis rate constant
0.800
sec-1
Obtained from initial steady
state conditions of mRNA
for mRNA
KD,rna
Degradation
rate
8.00
sec-1
(Klipp et al., 2005)
0.0205
sec-1
(Klipp et al., 2005)
1.25·10-4
sec-1
(Klipp et al., 2005)
0.74·10-3
sec-1
5·10-3 sec-1 in
constant for mRNA
KE
Synthesis rate constant
for E
KD,E0
Degradation
rate-
constant for E under
unstressed condition
KT,G
Glycerol transportation
(Klipp et al., 2005)
rate
0.228·10-3 sec-1 in
(Schaber et al., 2012)
KG
Rate
constant
for
0.54
mM/sec
glycerol Obtained from Initial steady
/(µM of Enzyme)
synthesis of glycerol
state condition of glycerol
balance equation
nFPS
Sensitivity
channel
of
FPS1
opening
4
Dimensionless
(Parmar et al., 2009)
(Klipp et al., 2005)
by
turgor pressure
Kp
Constant for rate of
increase of cell volume
by osmotic pressure
balance
9.3·10-23
m2/(J*sec)
(Parmar et al., 2009)
(Klipp et al., 2005)
C1
1/m3
Constant for linear
relation between turgor
Obtained from volume-turgor
relation in
(0.37·V0)-1
(Parmar et al., 2009)
pressure and volume
(Klipp et al., 2005)
change
Vos
Volume of cell which
0.600·V
m3
(Parmar et al., 2009)
(Klipp et al., 2005)
is available for change
due to osmotic stress
V𝞹t0
Volume of cell at
which turgor pressure
of cell is zero
0.378·V
m3
(Parmar et al., 2009)
(Klipp et al., 2005)
Table S5: Description of parameters trained (mainly for activation of Hog1), with data of
(Muzzy et al, 2009)
Value Unit
Parameter Description
n1
2.5
Dimensionless
Assumption/Justification
Sensitivity
of
The phosphorelay module in the
activation
of
upstream of MAPK cascade is
Hog1PP by e (i.e.
ultrasensitive with respect to
by error in turgor
changes in turgor pressure (Klipp
pressure)
et al., 2005). To capture this
property in the Hog1PP which is
final effector molecule in the
downstream, we assumed this
parameter as ultra-sensitive with
respect to error in turgor pressure
Km1
Half
saturation
constant
0.35
Dimensionless
Assumed
that
at
the
35%
for
reduction in the turgor pressure,
Hog1PP activation
the Hog1 activation rate is 50%
rate
of the maximum rate.
in
the
Hill
equation of error
(Eq 1)
KHOG
Maximum
Hog1
0.01
sec-1
See more details below this table
0.11
(µM sec)-1
Assumed that
activation rate by
normalised error in
turgor pressure
KD,HOG
Rate constant for
basal
Hog1T0
deactivation
(KD,HOG * Ph_tase) is comparable
of Hog1PP by basal
to maximum Hog1 activation rate
phosphotase
(KHOG)
Total Hog1initially
KD,HOG,PTP Maximum
0.54
µM
Assumed 18 times Hog1PP0
0.011
sec-1
Assumed equal to rate constant
deactivation rate of
for basal deactivation of Hog1PP
Hog1PP by PTP
i.e. Kd,HOG
n2
Sensitivity
of
deactivation
of
2
Dimensionless
4.92
mM
Hog1PP by PTP
kmPTP
Half
saturation
constant
for
We assumed that after 10 fold
increase in PTP, the deactivation
Hog1PP
rate of Hog1PP by PTP becomes
deactivation rate in
50 % of the maximum
Hill
equation
of
fold change in PTP
(Eq 1)
KmHOG
Half
saturation
0.015
µM
There is a lack of experimental data
constant of effect of
which can be useful in estimation of this
Hog1PP on glycerol
parameter. Therefore we arbitrarily set it
synthesis rate
to 50 % of initial Hog1PP.
KHOG, The maximum Hog1 activation rate by normalised error in turgor pressure:
In the experiment of 0.4M NaCl shock (Muzzy et al., 2009), the maximum Hog1 activity is
0.45 unit. And the initial rate of increase of activity seen at time t=2 minute (shock applied at
t=0 minute) is around 0.0033 unit/sec. As in our model total Hog1 is 0.66 µM, the initial
activation rate becomes 0.2640 µM/minute (or 0.0044 µM/sec). During the initial 60 sec
after the shock, the deactivation rate of Hog1PP should not be very high compare to the basal
activation rate. Hence net increase in Hog1 activation is mainly by the error in turgor
pressure. Moreover the initial drop of volume in the experiment at time t=2 min is around
20% in the same experiment. According to our estimation based on turgor volume relation
given by (Klip et al., 2005) the equivalent drop of turgor pressure is 35 %. Since the 35%
error in the turgor pressure is the half saturation constant for the activation of Hog1 by error
in turgor pressure (see Km1 in the above table), the estimated activation rate 0.0044 µM/sec
would be 50% of maximum theoretical rate possible. Thus estimated maximum rate is
0.0088 µM/sec which is close to the value that we have used in the simulation i.e. 0.01
µM/sec.
S4: Implementation of Simulation for various invoked conditions
1. Step change of external osmotic pressure was set as following
 e (t  0)  0.625 106 J / m 3
 e (t  0)   0.625  3.35 [ NaCl ] 106 J / m 3
where [NaCl] is concentration of NaCl in M
2. Mutant Simulations:
Table S6: List of mutants and their implementation in the model
Mutant
Equation used in Wild type
FPS1 over-expressing Glycerol transport:
mutant
K T ,G
 t 


  to 
Modification/Remark
New equation: 3.25 KT ,G G
nFPS
G
Glycerol transport rate is increased
3.25 times rate for un stressed wild
type and also it is kept independent
of turgor pressure.
ΔFPS1 mutant
Same as above
New equation KT ,G  0
Unregulated FPS1
Same as above
New equation KT ,G G , nFPS = 0
ΔPTP mutant:
Hog1PP deactivation by
New equation K D , HOG , PTP  0
PTP is
K D , HOG , PTP Hog1PP f ( PTP)
Where f is hill equation
PTP over-expressing
Hill equation of PTP in
PTPover= 10 PTP0
mutant
Hog1PP balance:
New equation:
n2
PTP
PTP  KmPTP n 2
( PTP  PTPover )n 2
( PTP  PTPover ) n 2  KmPTP n 2
Protein degradation rate
f=0 and KD,E0 ( sec-1) value for three
n2
Un regulated protein
degradation simulation constant:(i.e., Eqn. 10)
cases
1) KD,E0 (i.e., 1.8750·10-4)
K D , E  K D , E 0 1  f  Osmex , E  
2)10· KD,E0 (i.e., 1.8750·10-3)
3)33.33·KD,E0 (i.e., 6.2500·10-3)
Where f is multiplication of
two hill function
Nontransciptional-
Equation of glycerol
The induced effect of Hog1PP on
Glycerol Synthesis
synthesis:
glycerol synthesis is removed by
absent
KG E
Hog1PP
KmHog1PP  Hog1PP
keeping the Hog1PP effect constant.
Modified equation:
KG E
Hog1PP0
KmHog1PP  Hog1PP0
Transciptional-
Equation of glycerol
The induced effect of enzyme on
Glycerol Synthesis
synthesis:
glycerol synthesis is removed by
absent
KG E
Hog1PP
KmHog1PP  Hog1PP
keeping the enzyme effect constant.
Modified equation:
KG E0
Both transcriptional
Equation of glycerol
Hog1PP
KmHog1PP  Hog1PP
The induced effect of enzyme and
and non-transcriptional synthesis:
and Hog1PP on glycerol synthesis
effect of Glycerol
are removed by keeping the enzyme
Synthesis are absent
KG E
Hog1PP
KmHog1PP  Hog1PP
effect and Hog1PP constant.
Modified equation:
KG E0
Hog1PP0
KmHog1PP  Hog1PP0
3. Ramp Input simulations (Figure 10):
𝞹e =3.14·106 J/met3 which is external osmotic pressure equivalent to 0.75 M NaCl
(see equation of external osmotic pressure in variable table). We increased 𝞹e for a certain time
before it was kept constant, thus following condition was applied,
 e (t 0)  0.625 106 J / m3
For
e (t>=0)
following implementation was done;
If (t<tc) 𝞹e =0.625·106+R𝞹e·t
else
𝞹e =3.14·106
where t is time, tc is time (sec) after which 𝞹e was kept constant. R𝞹e is fixed rate of increase of
𝞹e. We invoked three combinations based on tc and R𝞹e which are following,
Case 1: R𝞹e = 9.314·102 J/(m3·sec), tc=45 minutes
Case 2: R𝞹e = 4.654·102 J/(m3·sec), tc= 90 minutes
Case 3: R𝞹e = 2.328·102 J/(m3*sec), tc=180 minutes
S5. Derivation of Steady State error equation:
Eqn. A1 to Eqn. A5 below, are obtained by equating the differential equations of our reduced
model to zero.

 Hog1T K HOG
e n1
Hog1PPSS   n1 ss
n1 
K D, HOG
 ess  Km1 
mRNASS 
Krna
Hog1PPSS
K D,rna
(A1)
(A2)
ESS 
KE
mRNASS
K D, E
(A3)
GSS 
KG
ESS
KT , G
(A4)
 t , SS   i , SS   e, SS
(A5)
In the above equations we assumed that at the steady state conditions the total un activated
Hog1is large compare to the Hog1PP and hence it can be equated to the total Hog1 (i.e. Hog1 T).
Also the basal Hog1 activation rate constant is omitted. It should be noted that these
simplification does not defer the conclusion of our analysis and made only for sake of simplicity
in presenting the arguments. By substitution of Eqn.A1 into Eqn.A2 and Eqn.A3 into Eqn.A4,
following two equations can be obtained respectively.
mRNASS 
GSS 
K rna K HOG Hog1T
ess n1
K D ,rna
K D , HOG
ess n1  Km1n1
KG K E
mRNASS
KT K D, E
(A6)
(A7)
We know that internal osmotic pressure at steady state can be written as
 i ,SS  (OsmT R T )
nT (t ) 
N 0, X V0
V (t )
 G (t )
(A8)
(A9)
To make contribution of glycerol distinct from non-glycerol osmolyte we can rewrite Eqn.A8 as
following
 i ,SS  ( i , NG  GSS R T )
(A10)
where the first term on right hand side is contribution of osmolyte other than glycerol.
By substitution of Eqn.A10 into Eqn.A5 and Eqn.A6 into Eqn.A7, following two equations can
be obtained, respectively.
 t ,SS   i , NG  GSS R T   e,SS
GSS 
(A11)
KG K E K rna K HOG Hog1T
ess n1
KT ,G K D , E K D ,rna
K D , HOG
ess n1  Km1n1
(A12)
By substitution of Eqn.A12 into Eqn.A11 equation, following equation can be obtained.
1

ess n1
  e,SS
n1
n1 

e

km
ss
1 

 t ,SS   i , NG  
where,  
K D, E K D,rna
KE
K D, HOG
KT ,G
Krna K HOG Hog1T KG
(A13)
1
RT
(A14)
By substitution of Eqn.A13 into Eqn.1 (error of turgor pressure) and after reorientation,
following equation can be obtained.
essn1
    t 0   ess      e   t 0   i , NG 
essn1  Km1n1
(A15)