Supplementary Material
Bacterial heat shock response
The heat shock response is a protective mechanism which helps the bacterium to tackle the
increased levels of misfolded protein in the cell during a temperature up-shift. The heat shock
response is controlled by regulation of the synthesis, activity and degradation of the alternative
sigma factor, σ32. The synthesis of σ32 is regulated both at the level of transcription and
translation (Erickson et al. 1987; Morita et al. 1999). The regulatory region of rpoH is complex
and contains at least four promoters: P1, P3, P4 and P5. The synthesis rate of σ32 at the
transcriptional level is regulated by the differential activation of these promoters (Erickson and
Gross 1989). The secondary structure of the mRNA of σ32 regulates the synthesis rates at the
level of translation. During the temperature up-shift, the translation of rpoH (gene that codes for
32) mRNA increases immediately due to the change in the secondary structure of the mRNA
(Morita et al. 1999), resulting in a fast 10-fold increase in the concentration of 32.
The degradation and activity of 32 are regulated by the chaperones and proteases it transcribes
(Liberek and Georgopoulos 1993; Yura et al. 1993; Arsene et al. 2000). The chaperones
sequester 32 away from RNA polymerase and thus reduce the activity of 32 (Gamer et al. 1996).
The chaperone bound 32 is also presented to certain proteases like FtsH which degrade 32
(Tomoyasu et al. 1995). The other proteases induced during heat-shock (stress conditions) also
directly degrade 32 and thus affect the level of 32 within the cell (Kanemori et al. 1997). At
steady state, the level of 32 within the cell is a result of the balance between the various
mechanisms acting to regulate the synthesis, activity and degradation of 32.
1
Model development
The schematic of the bacterial heat-shock response developed in the present work is shown in
Figure SI.1. The model developed is a modification of the frame work developed by Kurata et al.
(2006). The different steps involved in the adaptation of the cell to heat-shock conditions have
been modeled and analyzed as a control system. The synthesis, activity and degradation of 32
(during a temperature up-shift) are modeled as a feed-forward / feedback control system within
the cell. The major objective of the control system is to maintain the folded state of cellular
proteins. Three levels of control were considered, one feed-forward control and two feedback
controls. The increase in the synthesis of 32 is considered as the feed-forward control which
responds proportionally to the extent of heat-shock. Sequestration of 32 by DnaK and chaperone
mediated degradation of 32 were considered as the two feedback controls. The efficiency of the
feedback controls depends on the availability of the chaperones in the cell.
However, the model developed requires modifications to explain some of the recent observations
in the literature. Kurata et al. (2006), considered only one of the major chaperones, DnaK and a
protease, FtsH, belonging to the 32 circuit in their model. However, literature observation
indicates that it is the network of chaperones which coordinates the heat-shock response and not
a single chaperone. It was also observed that GroEL chaperone team plays a major role in downregulating 32 activity and refolding misfolded cellular proteins (Guisbert et al. 2004). The
synergistic role played by HslVU and other ATP- dependent proteases in the degradation of 32
and other abnormal proteins in the cell has also been observed (Kanemori et al. 1997). Hence, in
the model proposed in this work, the GroEL chaperone team and the ATP-dependent protease
2
HslVU, which were observed to play a major role in regulating the level of 32 in the cell and in
handling the misfolding proteins in the cell, were included.
Further, the parameter values used in the model proposed by Kurata et al. (2006) were tuned to
explain the mechanisms proposed and the rationale on their selection is not explained. Any
extension of this model requires fine tuning of model parameters to obtain physiological
simulation results. So the model parameters were independently identified from different sources
in the literature (values of model parameters and their sources are presented in main manuscript
Table 3 of Appendix A).
Simulation Results for the Bacterial Heat-shock response
The model equations were simulated using the “DASSL” solver. The simulations were carried
out for the various experimental conditions by altering a few of the model parameters. The list of
experimental conditions with its appropriate change in parameter values is shown in Table SI.1.
The set of model equations with their appropriate initial conditions were initially simulated for
about 400 minutes for the variables to reach steady state. At this point, the test conditions were
simulated by changing a few of the model parameters. The results of the model simulations are
explained in the following sections.
Dynamics of 32, DnaK, GroEL and total folded proteins in the cell during the heat-shock
response
The level of the major components of the model during heat-shock was analyzed by model
simulations. Model simulations were carried out for temperature shift from 30 to 37º C and 30 to
42º C. Heat-shock is normally assumed to set in at 42º C, for which there is sufficient literature
data. In this work, for inducing the recombinant protein temperature shift from 30-37º C was
3
used. Therefore, the temperature shift simulations were carried out at two different levels (3042oC and 30-37oC), to simulate the ‘normal’ heat-shock response and the heat-shock response
under mild temperature shift conditions (30 to 37º C), which is often adapted for the expression
of recombinant proteins (Ramalingam et al. 2007). The 32 levels were found to follow the
classical profiles of transient induction and increased steady state values as shown in Figure
SI.2a. The corresponding increased levels of the chaperones DnaK and GroEL was also depicted
by the model simulations (Figure SI.3). The total folded protein levels were found to decrease
after the temperature shift and then increase back to steady state values as shown in Figure SI.2b.
These profiles were found to qualitatively match with the profiles observed in the literature.
Strauss et al. (1987) observed a similar profile for 32 levels in the cell during heat-shock
conditions. Most of the literature on heat-shock response has focused on a temperature shift from
30ºC to 42ºC and the information on the change in the chaperone and folded protein levels were
reported for this temperature shift. However, Arnvig et al. (2000) has observed that the DnaK
levels show a similar increase during the temperature shift from 30ºC to 37ºC. The model
simulations were also able to predict these results.
Analysis of 32 dynamics and activity in protease mutant strains
The level of 32 during the mild heat-shock conditions in different protease mutants was
analyzed by model simulations. It was observed that for the current set of model parameters, the
initial transience of the 32 level was found to be altered in the HslVU protease mutant strain
while the steady-state values of 32 was altered in the FtsH protease mutant strain (Figures SI.4a
and SI.5a). The final activity of 32, reflected as the level of chaperones it transcribes (GroEL
used as an example), was found to be similar in either of the single mutants (Figures SI.4b and
4
SI.5b). However, in the double-protease mutant, the initial transient response and the final steady
state value of 32 was found to be higher, resulting in a significantly enhanced level of the
chaperone (Figure SI.6). This also indicated that the activity of the transcription factor was
considerably enhanced.
The simulations for the protease mutant strains have shown the importance of having the
chaperone-assisted and chaperone-independent degradation pathways for regulating 32 level and
activity. The simulation also demonstrates the need for the cell to possess multiple pathways for
regulating the activity of the transcription factors.
Kanemori et al. (1997) studied the role of HslVU and other ATP-dependent proteases on the
heat-shock response by studying in-vivo turnover of 32. They have observed that the doubleprotease mutants were found to exhibit a significant enhancement in the heat-shock response due
the stabilization of 32 compared to the single-protease mutants. These results were qualitatively
predicted by the present model. This also justifies the need for the development of a complete
mechanistic model for the heat-shock response in Escherichia coli as the reduced model proposed
by Kurata et al. (2006) does not explain some of the important observations in the literature.
Effect of the chaperone co-expression on the 32 level and activity
Alternate mechanism of regulation of the activity of the transcription factor is by the chaperones,
which sequester the 32 and either present it to proteases or inactivate it. The presence of
multiple pathways for the chaperone mediated inactivation of 32 was observed in the literature
(Guisbert et al. 2004). To investigate this further, the model equations were simulated by
increasing the level of either or both of the chaperone teams in the cell.
5
The change in the level and activity of 32 was simulated during the co-expression of either or
both the chaperone teams. A decrease in the level of 32 was observed during the co-expression
of either of the chaperone teams (Figure SI.7). The decrease in activity of 32 was confirmed by
analyzing the level of the other chaperone (i.e., DnaK chaperone levels during GroEL chaperone
co-expression and vice versa, Figure SI.8). The decrease in the level of 32 was even more
pronounced during the co-expression of both the chaperones (Figure SI.7).
The chaperone co-expression simulation also predicts that the increase in the cellular folding
machinery leads to increased capacity of the cell to tackle stressful conditions and thus a reduced
activation of the stress-response network. This is also clear from the analysis of the total folded
protein level in the cell during chaperone co-expression (Figure SI.9).
The mathematical model developed for the bacterial heat-shock response in the present work,
explains the following observations. As has been extensively observed in the literature (Strauss et
al. 1987; Yura and Nakahigashi 1999) the cytoplasmic heat-shock response in Escherichia coli is
governed by the regulation of the synthesis and activity of the alternative sigma factor, 32.
However, the robustness in the regulation of the synthesis and activity is brought about by a
complex control architecture involving multiple key chaperones and proteases in the cell. The
major aim of the heat-shock response is the maintenance of the proper folding of the cellular
proteins. The disturbance to the proper folding of the cellular proteins comes from multiple
sources and this disturbance has to be first sensed for the corrective measure to be taken.
The capability of the cell to induce a heat-shock-like response during the misfolding of several
cellular and foreign proteins is well documented (Yura et al. 1993; Kanemori et al. 1994). The
cell can sense disturbances from multiple sources and translate them to the heat-shock-like
6
response only through the chaperones and proteases. Further, the major chaperones and protease
in the cell have distinct and partially overlapping substrate specificities. Thus, the presence of
multiple chaperones and protease in heat-shock response network becomes essential for
articulating the versatility of the response.
References
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Lett 84:3005-3008.
Arsene F, Tomoyasu T, Bukau B (2000) The heat-shock response of Escherichia coli. Int J Food
Microbiol 55:3-9.
Erickson JW, Vaughn V, Walter WA, Neidhardt FC, Gross CA (1987) Regulation of the
promoters and transcripts of rpoH, the Escherichia coli heat-shock regulatory gene. Genes Dev
1:419-432.
Erickson JW, Gross CA (1989) Identification of the σE subunit of Escherichia coli RNA
polymerase: a second alternative sigma factor involved in high temperature gene expression.
Genes Dev 3:1462-1471.
Gamer J, Multhaup G, Tomoyasu T, McCarty JS, Rudiger S, Schonfeld HJ, Schirra C, Bujard H,
Bukau B (1996) A cycle of binding and release of the DnaK, DnaJ and GrpE chaperones
regulates the activity of the Escherichia coli heat-shock transcription factor σ32. EMBO J
15(3):607-617.
Guisbert E, Herman C, Lu CZ, Gross CA (2004) A chaperone network controls the heat-shock
response in Escherichia coli. Genes Dev 18:2812-2821.
Kanemori M, Nishihara K, Yanagi H, Yura T (1997) Synergistic role of HslVU and other ATPdependent proteases in controlling the in vivo turnover of 32 and abnormal proteins in
Escherichia coli. J Bacteriol 179(23):7219-7225.
Kanemori M, Mori H, Yura Y (1994) Induction of heat-shock proteins by abnormal proteins
results from stabilization and not increased synthesis of 32in Escherichia coli. J Bacteriol
176(18):5648-5653.
Kurata H, El-Samad H, Iwasaki R, Ohtake H, Doyle JC, Grigorova I, Gross CA, Khammash M
(2006) Module based analysis of robustness tradeoffs in the heat-shock response system. PloS
Comput Biol 2(7):663-675.
Liberek K, Georgopoulos C (1993) Auto regulation of the Escherichia coli heat-shock response
by the DnaK and DnaJ heat-shock proteins. Proc Nat Acad Sci USA 90:11019-11023.
Morita M, Kanemori M, Yanagi H, Yura T (1999) Heat-Induced Synthesis of 32 in Escherichia
coli: Structural and Functional Dissection of rpoH mRNA Secondary Structure. J Bacteriol
181(2):401-410.
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Ramalingam S, Gautam P, Mukherjee KJ, Jayaraman G (2007) Effects of post-induction feed
strategies on secretory production of recombinant streptokinase in Escherichia coli. Biochem
Eng J 33:33-41.
Strauss DB, Walter WA, Gross CA (1987) The heat-shock response of Escherichia coli is
regulated by changes in the concentration of 32. Nature 329:348–351.
Tomoyasu T, Gamer J, Bukau B, Kanemori M, Mori H, Rutman AJ, Oppenheim AB, Yura T,
Yamanaka K, Niki H, Hiraga S, Ogura T (1995) Escherichia coli FtsH is a membrane-bound,
ATP-dependent protease which degrades the heat-shock transcription factor 32. EMBO J
14:2551 –2560.
Yura T, Nagai H, Mori H (1993) Regulation of the heat-shock response in bacteria. Annu Rev
Microbiol 47:321–350.
Yura T, Nakahigashi K (1999) Regulation of heat-shock response. Curr Opin Microbiol 2:153158.
Table SI.1.
Values of parameters for the different experimental conditions simulated by the
bacterial heat-shock response model
S No Condition
Parameter Values
1
Normal Condition 30oC
 = 1; Kx5 = 75 min-1
2
Temperature Shift 30-37o C
 = 5; Kx5 = 150 min-1
3
Temperature Shift 30-42o C
 = 10; Kx5 = 225 min-1
4
HslVU Mutant
 = 5; Kx5 = 150 min-1; Km4 = 0;
5
FtsH Mutant
 = 5; Kx5 = 150 min-1; Km5 = 0;
6
HslVU, FtsH Double Mutant
 = 5; Kx5 = 150 min-1; Km4 = 0;
Km5 = 0;
7
DnaK Co-expression
 =1; Kx5 = 75 min-1; Km2 = 60 min-1;
8
GroEL Co-expression
 =1; Kx5 = 75 min-1; Km3 = 90 min-1;
9
DnaK and GroEL Co-expression  = 1; Kx5 = 75 min-1;Km2 = 60 min-1;
Km3 = 90 min-1;
8
Figure SI.1 Schematic of the Bacterial Heat Shock Response proposed in this study
32 Synthesis and
Stability  Level of 32
Heat shock, Accumulation of misfolded
proteins , Ethanol stress
Temperature induced
enhancement in the
levels of σ32
Sequestration of σ32 by
DnaK chaperone team
FtsH mediated degradation
of DnaK bound σ32
Degraded 32
J -32 complex
32
Association of σ32 with
RNA polymerase to form
the holoenzyme
RNAP
Chaperone assisted folding of
unfolded cellular proteins
DnaK/J/GrpE
GroEL/GroES
Temperature
induced misfolding
of cellular proteins
Pfold
T
E32
Synthesis of heat
shock proteins by the
holoenzyme Eσ32
Punfold
FtsH
HslVU (ClpQP)
GroEL mediated inactivation of σ32
HslVU mediated degradation of σ32
Degraded 32
FtsH and HslVU
mediated degradation of
unfolded proteins
Folded protein
Degraded
protein
9
3.00E-07
0.005
a
0.0045
Folded Protein (M)
2.50E-07
Sigma32 (M)
2.00E-07
1.50E-07
1.00E-07
0.004
0.0035
0.003
Temp Shift 30-37ºC
0.0025
Temp Shift 30-42ºC
0.002
Temp Shift 30-37ºC
5.00E-08
0.00E+00
-0.5
0
0.5
Figure SI.2.
1
1.5
Time (hr)
2
2.5
3
b
0.0015
Temp Shift 30-42ºC
0.001
-0.5
3.5
0
0.5
1
1.5
Time (hr)
2
2.5
3
3.5
Sigma32 levels and total folded protein levels at two different
temperature shift conditions
3.50E-05
5.00E-05
a
3.00E-05
4.50E-05
b
4.00E-05
3.50E-05
GroEL (M)
DnaK (M)
2.50E-05
2.00E-05
1.50E-05
2.50E-05
2.00E-05
1.50E-05
1.00E-05
Temp Shift 30-37ºC
Temp Shift 30-37ºC
1.00E-05
Temp Shift 30-42ºC
5.00E-06
Temp Shift 30-42ºC
5.00E-06
0.00E+00
-0.5
0
0.5
Figure SI.3.
6.00E-07
1
1.5
Time (hr)
2
2.5
3
3.5
0.00E+00
-0.5
6.00E-05
Wild Type Temp Shift (30-37ºC)
0.5
1
1.5
Time (hr)
2
2.5
3
3.5
b
5.00E-05
HslVU Mutant Temp Shift (30-37ºC)
4.00E-05
GroEL (M)
4.00E-07
0
DnaK and GroEL levels during temperature shift simulations
a
5.00E-07
Sigma32 (M)
3.00E-05
3.00E-07
3.00E-05
2.00E-07
2.00E-05
1.00E-07
1.00E-05
Wild Type Temp shift 30-37ºC
0.00E+00
-0.5
0.5
1.5
2.5
Time (hr)
Figure SI.4.
3.5
4.5
0.00E+00
-0.5
HslVU Mutant Temp Shift 30-37ºC
0
0.5
1
1.5
Time (hr)
2
2.5
3
3.5
Simulation results for HslVU mutant strain under mild heat-shock
conditions, sigma32 and GroEL levels
10
4.00E-05
a
3.50E-05
1.20E-07
3.00E-05
1.00E-07
2.50E-05
GroEL (M)
1.40E-07
8.00E-08
6.00E-08
Wild Type Temp Shift 30-37ºC
4.00E-08
b
2.00E-05
1.50E-05
1.00E-05
Wild Type Temp Shift 30-37º C
5.00E-06
FtsH Mutant Temp Shift 30-37º C
FtsH Mutant Temp Shift 30-37ºC
2.00E-08
0.00E+00
-0.5
0
0.5
Figure SI.5.
1
1.5
Time (hr)
2
2.5
3
0.00E+00
-0.5
3.5
0
0.5
1
1.5
Time (hr)
2
2.5
3
3.5
Simulation results for FtsH mutant strain under mild heat-shock
conditions, sigma32 and GroEL levels
7.00E-07
1.20E-04
6.00E-07
Wild Type Temp Shift 30-37ºC
1.00E-04
Double Mutant Temp Shift 30-37ºC
5.00E-07
8.00E-05
GroEL (M)
Sigma32 (M)
4.00E-07
3.00E-07
a
1.00E-07
0.00E+00
-0.5
0.5
1.5
2.5
3.5
Double Mutant Temp Shift 30-37ºC
2.00E-05
4.5
Time (hr)
Figure SI.6.
Wild Type Temp Shift 30-37ºC
6.00E-05
4.00E-05
2.00E-07
b
0.00E+00
-0.5
0
0.5
1
1.5
Time (hr)
2
2.5
3
Simulation results for FtsH and HslVU double mutant strain under mild
heat-shock conditions, sigma32 and GroEL levels
2.90E-08
2.70E-08
2.50E-08
Sigma32 (M)
Sigma32 (M)
1.60E-07
2.30E-08
2.10E-08
Normal
DnaK Coexpression
GroEL Coexpression
DnaK and GroEL coexpression
1.90E-08
1.70E-08
1.50E-08
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Time (hr)
Figure SI.7. Effect of coexpression of either DnaK chaperone team or GroEL
chaperone team or both the chaperone teams on the level of σ32. Normal
here represents the conditions when none of the chaperones were coexpressed.
11
3.5
1.20E-05
1.80E-05
1.60E-05
1.00E-05
1.40E-05
GroEL (M)
1.20E-05
6.00E-06
4.00E-06
2.00E-06
0.00E+00
-0.5
1.00E-05
8.00E-06
6.00E-06
Normal
0
0.5
Figure SI.8.
1
1.5
Time (hr)
2
Normal
DnaK Coexpression
4.00E-06
GroEL Coexpression
2.5
3
2.00E-06
3.5
0.00E+00
-0.5
0
0.5
1
1.5
Time (hr)
2
2.5
3
3.5
Level of DnaK chaperone team during GroEL chaperone coexpression
and level of GroEL chaperone team during DnaK chaperone
coexpression.
0.005
0.0045
Total Folded Protein (M)
DnaK (M)
8.00E-06
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
-0.5
Figure SI.9.
Mild Heat shock conditions
Mild heat shock condition + DnaK Coexpression
Mild Heat shock conditions + GroEL Coexpression
0
0.5
Time (hr)
1
Comparison of the total folded protein levels in the cell during mild
heat-shock conditions and during mild heat-shock conditions with
either DnaK or GroEL chaperone team coexpression
12