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*, SharadBhartiya*

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: ; ;

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
?t / Turgor pressure / J/m3
?i / 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-regulated by Hog1PP / µM
E / Common pool of GPD1,GPP2 and other glycerol synthesis enzymes / µM
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)
?i0 / 1.5*106 / J/m3 / (Parmar et al., 2009)
?t0 / 0.875*106 / J/m3 / (Parmar et al., 2009)
?e0 / 0.625*106 / J/m3 / (Parmar et al., 2009)

Table S3: Initial conditions for mutants

Mutant/variable / Hog1PP / mRNA / E / πi / G / V/VWT / OsmT
µM / µM / µM / M.Pa. / mM / 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 conditionsareidentical 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 / Remarks
R / Gas Constant / 8.314 / J/mol/K
T / Temperature / 303.15 / K
KHOG_b / Basal Hog1 activation rate / 5.29·10-4 / µM /sec / Obtained from initial steady state conditions of Hog1PP
Ph0 / Basal Phosphotase / 0.1 / µM / (Schaber et al., 2012)
Krna / Synthesis rate constant for mRNA / 0.800 / sec-1 / Obtained from initial steady state conditions of mRNA
KD,rna / Degradation rate constant for mRNA / 8.00 / sec-1 / (Klipp et al., 2005)
KE / Synthesis rate constant for E / 0.0205 / sec-1 / (Klipp et al., 2005)
KD,E0 / Degradation rate- constant for E under unstressed condition / 1.25·10-4 / sec-1 / (Klipp et al., 2005)
KT,G / Glycerol transportation rate / 0.74·10-3 / sec-1 / 5·10-3sec-1 in
(Klipp et al., 2005)
0.228·10-3 sec-1 in
(Schaber et al., 2012)
KG / Rate constant for synthesis of glycerol / 0.54 / mM/sec glycerol /(µM of Enzyme) / Obtained from Initial steady state condition of glycerol balance equation
nFPS / Sensitivity of FPS1 channel opening by turgor pressure / 4 / Dimensionless / (Parmar et al., 2009)
(Klipp et al., 2005)
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 / Constant for linear relation between turgor pressure and volume change / (0.37·V0)-1 / 1/m3 / Obtained from volume-turgor relation in
(Parmar et al., 2009)
(Klipp et al., 2005)
Vos / Volume of cell which is available for change due to osmotic stress / 0.600·V / m3 / (Parmar et al., 2009)
(Klipp et al., 2005)
V?t0 / 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)

Parameter / Description / Value / Unit / Assumption/Justification
n1 / Sensitivity of activation of Hog1PP by e (i.e. by error in turgor pressure) / 2.5 / Dimensionless / The phosphorelay module in the upstream of MAPK cascade is ultrasensitive with respect to changes in turgor pressure (Klipp 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 for Hog1PP activation rate in the Hill equation of error (Eq 1) / 0.35 / Dimensionless / Assumed that at the 35% reduction in the turgor pressure, the Hog1 activation rate is 50% of the maximum rate.
KHOG / Maximum Hog1 activation rate by normalised error in turgor pressure / 0.01 / sec-1 / See more details below this table
KD,HOG / Rate constant for basal deactivation of Hog1PP by basal phosphotase / 0.11 / (µMsec)-1 / Assumed that
(KD,HOG *Ph_tase) is comparable to maximum Hog1 activation rate (KHOG)
Hog1T0 / Total Hog1initially / 0.54 / µM / Assumed 18 times Hog1PP0
KD,HOG,PTP / Maximum deactivation rate of Hog1PP by PTP / 0.011 / sec-1 / Assumed equal to rate constant for basal deactivation of Hog1PP i.e. Kd,HOG
n2 / Sensitivity of deactivation of Hog1PP by PTP / 2 / Dimensionless
kmPTP / Half saturation constant for Hog1PP deactivation rate in Hill equation of fold change in PTP (Eq 1) / 4.92 / mM / We assumed that after 10 fold increase in PTP, the deactivation rate of Hog1PP by PTP becomes 50 % of the maximum
KmHOG / Half saturation constant of effect of Hog1PP on glycerol synthesis rate / 0.015 / µM / There is a lack of experimental data which can be useful in estimation of this parameter. Therefore we arbitrarily set it 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

where [NaCl] is concentration of NaCl in M

  1. Mutant Simulations:

Table S6: List of mutants and their implementation in the model

Mutant / Equation used in Wild type / Modification/Remark
FPS1 over-expressing mutant / Glycerol transport:
/ New equation:
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
Unregulated FPS1 / Same as above / New equation,nFPS= 0
ΔPTP mutant: / Hog1PP deactivation by PTP is

Where f is hill equation / New equation
PTP over-expressing mutant / Hill equation of PTP in Hog1PP balance:
/ PTPover=
New equation:

Un regulated protein degradation simulation / Protein degradation rate constant:(i.e., Eqn. 10)

Where f is multiplication of two hill function / f=0 and KD,E0 ( sec-1) value for three cases
1) KD,E0 (i.e., 1.8750·10-4)
2)10· KD,E0 (i.e., 1.8750·10-3)
3)33.33·KD,E0 (i.e., 6.2500·10-3)
Nontransciptional-Glycerol Synthesis absent / Equation of glycerol synthesis:
/ The induced effect of Hog1PP on glycerol synthesis is removed by keeping the Hog1PP effect constant.
Modified equation:
Transciptional-Glycerol Synthesis absent / Equation of glycerol synthesis: / The induced effect of enzyme on glycerol synthesis is removed by keeping the enzyme effect constant.
Modified equation:
Both transcriptional and non-transcriptional effect of Glycerol Synthesis are absent / Equation of glycerol synthesis: / The induced effect of enzyme and and Hog1PP on glycerol synthesis are removed by keeping the enzyme effect and Hog1PP constant.
Modified equation:
  1. Ramp Input simulations (Figure 10):

?e =3.14·106 J/met3which is external osmotic pressure equivalent to 0.75 M NaCl

(seeequation of external osmotic pressure in variable table). We increased ?efor a certain time before it was kept constant, thus following condition was applied,

For e(t>=0) following implementation was done;

If (t<tc) ?e =0.625·106+R?e·t

else ?e =3.14·106

where t is time, tc is time (sec) after which ?e was kept constant. R?e is fixed rate of increase of ?e. We invoked three combinations based on tc and R?e which are following,

Case 1: R?e= 9.314·102 J/(m3·sec), tc=45 minutes

Case 2: R?e= 4.654·102 J/(m3·sec), tc= 90 minutes

Case 3: R?e= 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.

(A1)

(A2)

(A3)

(A4)

(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. Hog1T). 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.

(A6)

(A7)

We know that internal osmotic pressure at steady state can be written as

(A8)

(A9)

To make contribution of glycerol distinct from non-glycerol osmolyte we can rewrite Eqn.A8 as following

(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.

(A11)

(A12)

By substitution of Eqn.A12 into Eqn.A11 equation, following equation can be obtained.

(A13)

where, (A14)

By substitution of Eqn.A13 into Eqn.1 (error of turgor pressure) and after reorientation, following equation can be obtained.

(A15)