er
ich
ilkin
rch, S
wcastl
niver
ty of N
e 20
2002). They are present in the cytosol, mitochondria, ER and
nucleus with different family members functioning in
Many newly synthesized proteins need assistance from
chaperones in order to fold correctly. 10–20% of new
Mechanisms of Ageing and Developmproteins associate with chaperones (Wickner et al., 1999).
For example, the Hsp70 machinery acts early in the life of
many proteins, binding to a string of about seven
* Corresponding author. Tel.: +44 191 256 3467; fax: +44 191 256 3445.
E-mail address: c.j.proctor@ncl.ac.uk (C.J. Proctor).
0047-6374/$ – see front matter # 2004 Elsevier Ireland Ltd. All rights reserved.
doi:10.1016/j.mad.2004.09.0311. Introduction
Many chaperones are also known as heat shock proteins
(Hsps), because they are synthesised in increased amounts
after brief exposure of cells to an elevated temperature.
However, they are present in cells at all times and are
upregulated by a variety of other stresses such as irradiation,
hyperoxia, viral infection and oxidative stress. They range in
molecular mass from
15 to 110 kDa and are divided into
groups based on both size and function, and include Hsp100,
Hsp90, Hsp70, Hsp60, Hsp40 and the small HSPs (Kregel,
different organelles. They have an affinity for the exposed
hydrophobic patches on incompletely folded proteins and
hydrolyse ATP, often binding and releasing their protein
with each cycle of ATP hydrolysis.
Chaperones have many cellular functions. They are
involved in the folding of nascent proteins, the refolding of
denatured proteins, the prevention of protein aggregation,
assisting the targeting of proteins for degradation by the
proteasome and lysosomes, have a role in apoptosis, and are
involved in modulating signals for immune and inflamma-
tory responses.Keywords: Chaperones; Stress response; Mathematical model; AgeingAbstract
Many molecular chaperones are also known as heat shock proteins because they are synthesised in increased amounts after brief exposure
of cells to elevated temperatures. They have many cellular functions and are involved in the folding of nascent proteins, the re-folding of
denatured proteins, the prevention of protein aggregation, and assisting the targeting of proteins for degradation by the proteasome and
lysosomes. They also have a role in apoptosis and are involved in modulating signals for immune and inflammatory responses. Stress-induced
transcription of heat shock proteins requires the activation of heat shock factor (HSF). Under normal conditions, HSF is bound to heat shock
proteins resulting in feedback repression. During stress, cellular proteins undergo denaturation and sequester heat shock proteins bound to
HSF, which is then able to become transcriptionally active.
The induction of heat shock proteins is impaired with age and there is also a decline in chaperone function. Aberrant/damaged proteins
accumulate with age and are implicated in several important age-related conditions (e.g. Alzheimer’s disease, Parkinson’s disease, and
cataract). Therefore, the balance between damaged proteins and available free chaperones may be greatly disturbed during ageing. We have
developed a mathematical model to describe the heat shock system. The aim of the model is two-fold: to explore the heat shock system and its
implications in ageing; and to demonstrate how to build a model of a biological system using our simulation system (biology of ageing e-
science integration and simulation (BASIS)).
# 2004 Elsevier Ireland Ltd. All rights reserved.Modelling the actions of chap
Carole J. Proctora,*, Csaba So˝tib, R
Daryl P. Shanleya, Darren J. W
aHenry Wellcome Laboratory for Biogerontology Resea
University of Newcastle, Ne
bDepartment of Medical Chemistry, Semmelweis U
cSchool of Mathematics and Statistics, Universi
Available onlinones and their role in ageing
ard J. Boysc, Colin S. Gillespiea,
sonc, Thomas B.L. Kirkwooda
chool of Clinical and Medical Sciences-Gerontology,
e upon Tyne NE4 6BE, UK
sity, P.O. Box 260, H-1444 Budapest 8, Hungary
ewcastle, Newcastle upon Tyne NE1 7RU, UK
October 2004
www.elsevier.com/locate/mechagedev
ent 126 (2005) 119–131

a la
are
on
simulations and to change parameter values.
ing athe major route of removal of proteins. Ubiquitination is
mediated by a cascade of enzyme activities. Ubiquitin
is expressed constitutively in all cells and expression is
upregulated upon exposure to stress. The fate of proteins that
accumulate during exposure of cells to stress is dependent on
the interplay of chaperones and the ubiquitin–proteasome
system.
Chaperones generally inhibit apoptosis (Samali and
Orrenius, 1998). Hsp27, Hsp70 and Hsp90 are predomi-
nantly anti-apoptotic. For example Hsp70 and many other
Hsps can overcome both caspase-dependent and caspase-
independent apoptotic stimuli (Nylandsted et al., 2000;
Verbeke et al., 2001). On the other hand, there are examples
of positive involvement of Hsps in apoptotic signalling
(Punyiczki and Fesus, 1998).
The ‘‘protein homeostasis hypothesis of senescence’’ is
based on the balance between the amount of damaged
(denatured) proteins and the available capacity of molecular
chaperones to refold/repair them (So˝ti et al., 2003).
When the balance is
1. In favour of available chaperones (compensated stress):
cells may be arrested temporarily but divide normally
again after repair/refolding takes place.
2. In favour of damaged proteins (stress, senescence): cells
become irreversibly arrested. Strongly in favour of
damaged proteins (lethal stress): proteasome inhibition
leads to apoptosis.
3. Very strongly in favour of damaged proteins (supralethal
stress): complete loss of chaperone availability, ATP
depletion leads to necrosis (See Fig. 1 of So˝ti et al.,
2003.)
The level of chaperones in the cell increases after con-
ditions of stress. Stress-induced transcription requires act-
ivation of heat shock factor (HSF) that binds to the heat
shock promoter element (HSE) (Morimoto, 1998). There are
four known HSFs but only HSF1 is found in vertebrates.syst
MorUnIf a denatured protein cannot be refolded, then chaper-
es assist in its degradation. Chaperones and proteolytic
ems are often co-ordinately regulated (Mathew and
imoto, 1998). The ubiquitin–proteasome machinery iswithn assisting in protein refolding. Hsp60-like proteins form
rge barrel-shaped structure into which misfolded proteins
fed, preventing their aggregation and providing them
a favourable environment in which to attempt to refold.from
thehydrophobic amino acids before the protein leaves the
ribosome. Once a protein has been correctly folded, it can
later become misfolded as a result of a variety of stresses.
Misfolded proteins have exposed hydrophobic surfaces
which will clump together and then precipitate out of
solution. Chaperones play a role in dissolving protein
aggregates and precipitates (Glover and Lindquist, 1998).
They can also prevent aggregation of misfolded proteins
taking place by binding to the hydrophobic surface and
C.J. Proctor et al. / Mechanisms of Age120der normal growth conditions, HSF1 activity is repressed2. Molecular chaperones and ageing
There is an accumulation of damaged and denatured
proteins with age, especially in post-mitotic cells such as
neurons. In neurons, damaged protein may aggregate and
become resistant to degradation causing neurodegeneration.
Neuronal chaperones have been found to be localised in
neuronal plaques and fibrillary tangles and it has been
suggested that they were probably involved in an attempt to
sequester the b-amyloid and other damaged proteins (So˝ti
and Csermely, 2000; So˝ti and Csermely, 2003).
Chaperones have many exposed binding surfaces and so
are themselves very susceptible to oxidative damage which
may result in their functional decline. This is especially true
of long-lived chaperones such as crystalline. Although levels
of chaperones within cells do not decline with age, it has
been shown that the induction of heat shock protein after
stress is decreased in aged animals (So˝ti and Csermely,
2003). The level of HSF1 does not change with age but a
decrease in the activation and binding of its DNA binding
site has been observed in aged animals (Heydari et al.,
2000). However, levels of Hsp90 may also increase with age
which would suppress the activation of HSF1. There is also a
decline in proteasome activity with age which results in a
further increase in the amount of damaged proteins within
cells. The decline in Hsp induction and the increase inand exists either in the cytosol or nucleus in an inert mo-
nomeric state. HSF1 is maintained as a non-DNA-binding
inactive complex both by internal coiled-coil interactions
and by stoichiometric binding with Hsp90, Hsp70 and other
chaperones. The synergistic interaction between these ch-
aperones modulates HSF1 activity by feedback repression.
During and after stress, the cellular proteins undergo den-
aturation and/or polyubiquitination and sequester the cha-
perones bound to HSF1. The inactive HSF1 becomes free
and translocates into the nucleus if it was previously in the
cytosol (Verbeke et al., 2001). Activation of HSF1 is acc-
ompanied by the transition from an inert monomeric state to
a transcriptionally active trimer. The active trimers bind to
the DNA heat shock element (HSE) and stimulate tran-
scription of heat shock proteins.
In this paper we describe a model of the heat shock
system and the interaction of molecular chaperones with
denatured proteins. The model is then used to explore the
cellular conditions under which protein homeostasis can be
maintained and the conditions that lead to protein
aggregation. This model is one of a number of sub-models
which are currently being developed for the virtual ageing
cell as part of the biology of ageing e-science integration and
simulation (BASIS) system (Kirkwood et al., 2003). Further
details can be found on our web-site (www.basis.ncl.ac.uk),
where this model is available for users to run their own
nd Development 126 (2005) 119–131denatured protein, including damage to chaperones, all

sequester Hsp90 that is bound to heat shock factor-1 (HSF1)
eing aand so in our model we will only consider the Hsp90–HSF1
complex as a source of Hsp90 for denatured proteins and
ignore all other complexes containing Hsp90. Even under
normal cellular conditions, a small proportion of protein
becomes denatured and is constantly being reformed with
the aid of chaperones. So we assume that there is enough free
Hsp90 within the cell to form complexes with this low levelcontribute to the overall decline in chaperone capacity with
age. According to the hypothesis of So˝ti et al. (2003) this
will lead to an increase in cellular senescence, apoptosis
or necrosis, depending on the degree of damage and the
balance between damaged protein and available free func-
tional chaperones.
3. Elements of the model
We have developed a model of protein turnover and the
role of Hsp90 in guarding protein homeostasis. The main
components of the model are described below.
3.1. Hsp90 and heat shock factor-1 (HSF1)
Hsp90 is a 90 kDa molecular chaperone and is one of the
most abundant cytosolic proteins in eukaryotes, constituting
about 1–2% of total protein (Jakob and Buchner, 1994).
Hsp90 is a phosphorylated dimer containing 2–3 covalently
bound phosphates per monomer. It forms multichaperone
complexes that bind to so-called client proteins such as
steroid receptors and protein kinases, under nonstress
conditions. Clients are inherently unstable multidomain
proteins with hydrophobic interaction surfaces. In these
interactions, Hsp90 stabilises the clients in a partially folded,
functional state in an ATP-dependent active process, to
prevent their collapse and degradation. Hsp90 also interacts
with actin and tubulin, constituents of the cytoskeleton,
and stabilizes the integrity of the cellular network (Sreedhar
et al., 2003). However, during stress, it works in an
ATP-independent passive mode sequestering damaged
proteins for future refolding or proteasome-mediated
degradation.
Hsp90 is not able to refold denatured proteins by itself but
requires other chaperones to complete the task, in particular
Hsp70 (Csermely et al., 1998). In our current model, we
assume that there is always sufficient Hsp70 in the cell for
refolding to take place and do not include Hsp70 as a
separate element. The reason for this assumption is to keep
the model as simple as possible, but we have built the model
in such a way that it will be relatively straightforward to add
Hsp70 (and other chaperones) to the model at a future date.
Although the cellular concentration of Hsp90 is high, most
of this protein is bound to other proteins or complexes and so
there is a need for an increase in Hsp90 levels when there is a
rise in denatured proteins in the cell. Denatured proteins
C.J. Proctor et al. / Mechanisms of Agof denatured protein.Heat shock factor-1 (HSF1) contains a DNA-binding
motif in the amino terminus and adjacent hydrophobic
heptad repeats which mediates subunit trimerisation.
Hsp90 forms complexes with HSF1 in unstressed cells
(Nadeau et al., 1993). During stress, e.g. elevated
temperatures, the level of denatured proteins rises and
then competes for Hsp90, causing Hsp90 to dissociate from
HSF1. HSF1 then forms trimers, a reaction which is
favoured at increased temperature (Zou et al., 1998) and
becomes transcriptionally active. Trimerisation is a
reversible reaction in vivo but not in vitro (Zou et al.,
1998). Trimers bind to DNA at the HSE which results in
the transcription of heat shock proteins. For example,
at elevated temperatures, the concentration of Hsp90
increases several folds. These findings suggest that Hsp90
is a repressor of HSF1 activation under normal conditions
(Zou et al., 1998).
3.2. Protein
Proteins are continually being turned over in a cell:
degraded if they are damaged or when no longer needed by
the cell; and newly synthesized as required. Newly
synthesized proteins have to fold into their correct three-
dimensional conformation. Many proteins are able to fold
without any assistance but about 10–20% of newly-
synthesized proteins are found to be associated with
chaperones.
The protein that we initially chose for our model
was citrate synthase (CS), an enzyme composed of two
identical 48 kDa subunits, which catalyses the reaction of
oxaloacetic acid and acetyl-CoA to form citric acid
and CoA. It is a fairly stable protein having a half-life of
about 6–7 days in skeletal muscle (Booth and Holloszy,
1977). It is inactivated and aggregates rapidly upon
incubation at 43 8C (Jakob et al., 1995). Jakob et al.
(1995) showed that Hsp90 binds transiently to unfolding
intermediates of thermal unfolding CS and that these
intermediates are able to rapidly refold to their native state
upon release from Hsp90.
We chose a protein which is fairly stable, but we can also
use our model to examine how protein stability affects
protein homeostasis. If we know the half-life of the protein
then we can adjust the parameters that affect protein
turnover. This will be further explained in the next section.
3.3. Reactive oxygen species
Reactive oxygen species (ROS) are produced by
mitochondria as a by-product of normal metabolism. Levels
of ROS within the cell are normally kept at low levels by the
action of antioxidants. However, if a cell is stressed the
levels of ROS can increase considerably. There is also a
gradual increase in ROS levels during ageing. For example,
the number of damaged mitochondria may increase with age
nd Development 126 (2005) 119–131 121and so more ROS are produced, or there may be a decrease in

protein (5% of total protein). Initially the majority of HSF1
ing ais bound to Hsp90 and the concentration of HSF1 is too low
to form trimers. This low level prevents further transcription
of the chaperone. Any misfolded protein may be either
refolded (with the help of a chaperone), degraded (by the
ubiquitin–proteasome system) or form aggregates (AggP).
Both refolding and degradation require ATP. There are two
ways in which a misfolded protein can form an aggregate:
either two misfolded proteins bind together or a misfolded
protein binds to a previously formed aggregate. An increase
in the number of misfolded proteins leads to Hsp90
disassociating from HSF1 and binding to MisP. HSF1 is
then free to form dimers (DiH), and then trimers (TriH), with
both reactions being reversible. A trimer can bind to HSE to
form a complex (HSETriH) which then activates the
transcription of Hsp90 leading to an increase in the level
of Hsp90 in the cell. This increases the chance of any
misfolded protein being correctly refolded.
We build our model by constructing a set of biochemical
reactions to describe the processes outlined above. The
reactions are described below in Section 4.1. The networkthe efficiency of anti-oxidant systems. High levels of ROS
cause damage to DNA, protein and lipids. In particular, there
may be an increase in protein misfolding.
3.4. ATP
Hsp90 has an ATP/ADP binding site in its N terminal
domain. The passive, stress-induced chaperone activity of
Hsp90 does not require ATP. The stabilisation of client
proteins by Hsp90 is ATP-dependent but we do not include
this process in our model. The process of refolding damaged
proteins requires ATP (in fact, it is Hsp70 which uses ATP
for the refolding of damaged proteins but for simplicity we
omit Hsp70 from the refolding step in our model at the
present time). Degradation of proteins by the ubiquitin
system also requires ATP. If the level of damaged proteins
within a cell reaches a critical threshold, the cell may
become senescent, undergo apoptosis or undergo necrosis.
The fate of the cell is partly determined by the ATP level.
4. Description of the model
New proteins need to be synthesized in order to replace
the damaged proteins which are degraded. The rate of
synthesis depends on the half-life of the protein. Once
synthesized, they have to be folded into their native state. For
simplicity we model this as one reaction. In this model we
assume that proteins are either in their native form, i.e.
correctly folded (NatP) or are misfolded (MisP).
We assume that Hsp90 is present in its active dimeric
state. Although Hsp90 is very abundant in the cell, we only
consider the pool of Hsp90 which is available for binding
with HSF1 and for binding to a low level of misfolded
C.J. Proctor et al. / Mechanisms of Age122diagram of reactions is shown in Fig. 1. We use mass-actionkinetics for all the reactions, i.e. we assume that the
instantaneous rate of a reaction is directly proportional
to the concentration or each reactant raised to the power of
its stoichiometry. We also assume that all the reactions
take place within one compartment, namely the cell, and do
not consider subcellular localization in this model.
However, it is intended that we will modify the model in
the future to include different compartments within the
cell such as the nucleus, the cytosol, and the mitochondria.
We would then need to add further reactions to represent
translocation from one compartment to another. For
example, in our model we would add a reaction to
represent the translocation of HSF1-trimers from the
cytosol to the nucleus.
The model is encoded using the systems biology markup
language (SBML) (Hucka et al., 2003). SBML is a
computer-readable format for representing models of
biochemical reaction networks. Once a model has been
encoded, it can then be simulated using one of a number of
software tools. Our BASIS system provides one such tool,
where models can be simulated, results plotted and
parameters can be changed (www.basis.ncl.ac.uk).
The model described here is too complex to reason about
directly and so it is necessary to carry out simulations to see
how the system changes with time. We used stochastic
modelling rather than a deterministic analysis, since it is
important to include the inherently stochastic behaviour of
the intra-cellular processes. Also some of the species in the
model are present in small numbers, and so it would be
incorrect to use a deterministic approach.
The model was simulated using the STOCKS simulator,
developed by Andrzej Kierzek and colleagues (Puchalka and
Kierzek, 2004), which combines the Gibson and Bruck
(2000) algorithm with the t-leap method of Gillespie
(Gillespie, 2001).
4.1. Reactions in the model
The following set of reactions are shown in Fig. 1a.
New proteins are synthesized and fold into their native
state at rate k1: !
k1 NatP:
Normal proteins (NatP) become misfolded, depending on
the level of ROS in the cell, at a rate k2: NatP þ ROS
!k2 MisPþ ROS. This also includes nascent proteins which
do not fold correctly.
Misfolded proteins (MisP) are bound by Hsp90 at rate
k3, competing with HSF1: MisPþ Hsp90!
k3 MCom; where
MCom represents the complex of misfolded protein with
Hsp90.
Misfolded proteins bound to Hsp90 dissociate at rate
k4: MCom!
k4 MisPþ Hsp90:This represents unsuccessful
refolding.
The misfolded protein which is bound to Hsp90 (MCom) is
refolded to form NatP and released at rate k5: MComþ
nd Development 126 (2005) 119–131ATP!k5 NatPþ Hsp90þ ADP: This reaction requires ATP.

eing aC.J. Proctor et al. / Mechanisms of AgIf refolding is unsuccessful, misfolded proteins are
degraded at rate k6: MisPþ ATP!
k6 ADP: This reaction
requires ATP.
Misfolded proteins which are neither refolded nor
degraded form aggregates (AggP) at rate k7:
2MisP!k7 AggP:
The next set of reactions are shown in Fig. 1b.
Hsp90 binds to HSF1 to form a complex at rate k8:
Hsp90 þ HSF1!k8 HCom; where HCom represents the
complex of Hsp90 and HSF1.
Hsp90–HSF1 complexes dissociate at rate k9:
HCom!k9 HSF1 þ Hsp90:
HSF1 forms dimers at rate k10 : 2HSF1!
k10 DiH: HSF1
reacts with dimers to form trimers at rate k11: HSF1 þ
DiHrrow
k11 TriH: These reactions are reversible with the
reverse reactions proceeding at rate k12 and k13, respectively.
The trimer (TriH) binds to HSE at rate k14: TriH þ
HSE w
k14HSETriH; and dissociates at rate k15.
Fig. 1. Network diagram of the model. (a) Protend Development 126 (2005) 119–131 123Bound HSE activates transcription of Hsp90 at rate k16:
HSETriH!k16 HSETriHþ Hsp90:
Hsp90 degrades at rate k17: Hsp90þ ATP!
k17 ADP; a
reaction which requires ATP.
The following set of reactions are not shown in Fig. 1.
ATP is generated by the mitochondria in the cell
from ADP at rate k18: ADP!
k18 ATP:
Other cellular processes, apart from refolding, consume
ATP to form ADP at rate k19: ATP!
k19 ADP:
Reactive oxygen species (ROS) are produced by the
mitochondria at rate k20: !
k20 ROS:
ROS is scavenged by antioxidants at rate k21: ROS!
k21 ? :
4.2. Setting the parameter values and initial conditions
Table 1 lists the species and initial conditions. We
assume that there are 6  106 molecules of native protein
initially. Since we assume that under normal conditions, 5%
in turnover. (b) Autoregulation of Hsp90.

of native protein is misfolded and complexed to Hsp90,
we set the initial level of Hsp90 to 300,000. We assume
that there are 6000 molecules of HSF1 but that the majority
of it is initially complexed to Hsp90. The levels of ROS, ATP
and ADP are initially set at 100, 100,000 and 1000,
respectively.
Table 2 lists the default parameter values and also
some of the assumptions made in estimating the values. It
is not always possible to obtain exact parameter values
as experimental data are often qualitative rather than
quantitative. For example, it is known that Hsp90 has a
strong binding affinity for HSF1, as it is a client protein, and
a much weaker affinity for a misfolded protein. Therefore,
we set the values of k3 and k8, the rates for binding of Hsp90
to misfolded protein and HSF1, respectively, so that k8 is 10
times greater than k3.
In some cases we have quantitative data, for example the
half-life of a protein, but it is not always possible to use the
values directly. It would seem straightforward to calculate
the degradation rates and synthesis rates of protein from the
C.J. Proctor et al. / Mechanisms of Ageing and Development 126 (2005) 119–131124
Table 1
Initial conditions for the model
Species Initial value (number of molecules) Comments
Native protein 6000000 Only one type of protein is considered
Hsp90–HSF1 complex 5900 The majority of HSF1 is bound to Hsp90
Hsp90 300000 Assume that there is sufficient free Hsp90 to bind to 5% of native protein
HSF1 100 Assume ratio of bound to free HSF1 is 59:1 initially
ROS 100 This value can be varied during the simulation
ATP 10000 Assume only a small proportion of cellular ATP is available for the refolding reaction
ADP 1000 Ratio of ATP:ADP is 10:1 under normal cellular conditions
HSE 1 One inducible gene on chromosome 14 (Csermely et al., 1998)
All species not shown in Table 1 have their initial amount set to zero.
Table 2
Default parameter values of the model
Reaction Parameter Default value Units Assumptions made
Protein synthesis k1 10.0 mol s
1 Half-life of 6–7days (Kawanaka et al., 1997)
Misfolding k2 0.00002 mol
1 s1 Ratio of native:misfolded proteins is 19:1 under
normal conditions (Lodish et al., 2000)
Binding of misfolded k3 50.0 mol
1 s1 The binding affinity of misfolded protein to Hsp90 is
protein by Hsp90
Dissociation of misfolded
protein complex
k4 0.00001
Re-folding k5 4.0  106
Protein degradation k6 6.0  107
Protein aggregation k7 1.0  107
Binding of HSF1 and Hsp90 k8 500.0
Dissociation of HSF1 complex k9 1.0
Dimerisation of HSF1 k10 0.01Trimerisation of HSF1 k11 100.0
Dissociation of HSF1-trimers k12 0.5
Dissociation of HSF1-dimers k13 0.5
Binding of HSE and
HSF1-trimers
k14 0.05
Dissociation of HSE and
HSF1-trimers
k15 0.08
Hsp90 transcription k16 1000.0
Hsp90 degradation k17 8.02  109
ATP formation k18 12.0
ADP formation k19 0.02
ROS production k20 0.1
ROS removal k21 0.001
mol: number of molecules.less than that of HSF1
s1 The rate of unsuccessful refolding is low compared to
refolding under normal conditions
mol1 s1 Rapid reaction when bound to Hsp90
(Jakob et al., 1995) if ATP levels are high
mol1 s1 Half-life of 6–7days (Kawanaka et al., 1997)
mol1 s1 This is a slow reaction unless high levels of
misfolded protein
mol1 s1 The affinity of HSF1for Hsp90 is 10 times
stronger than that of misfolded proteins
s1 Under normal conditions most of HSF1 is
complexed to Hsp90
mol1 s1 This reaction is rapid only when levels ofunbound HSF1 are high
mol1 s1 This is a fast reaction once dimers are formed
s1 This is a slow reaction
s1 This is a slow reaction
mol1s1 This reaction only proceeds when trimers are available
s1 If all HSF1 forms trimers, the ratio of the forward
to reverse reaction is about 1000:1
s1 This is fast when HSE is bound
s1 Half-life of 1 day
s1 Assume that ratio of ATP:ADP is 10:1 under
normal conditions
s1
mol s1 Assume constant production level of ROS
s1 Rate of removal depends on level of ROS

C.J. Proctor et al. / Mechanisms of Ageing and Development 126 (2005) 119–131 125
Fig. 2. Simulation results for a normal unstressed cell. (a) Levels of native protein (NatP), misfolded protein (MisP), misfolded protein complexed with Hsp90,
aggregated protein (AggP) and unbound Hsp90. (b) Levels of ATP, ADP and ROS (ROS was scaled 20 for clearer visualisation). Initial conditions and
parameters as in Tables 1 and 2, respectively.

C.J. Proctor et al. / Mechanisms of Ageing and Development 126 (2005) 119–131126
Fig. 3. Simulation results for cell undergoing period of stress. In this simulation the level of ROS was increased two-fold for 10 min. (a) Levels of native protein
(NatP), misfolded protein (MisP), misfolded protein complexed with Hsp90, aggregated protein (AggP) and unbound Hsp90. (b) Levels of ATP, ADP and ROS
(ROS was scaled 20 for clearer visualisation). Initial conditions and parameters as in Tables 1 and 2, respectively.

C.J. Proctor et al. / Mechanisms of Ageing and Development 126 (2005) 119–131 127
Fig. 4. Simulation results for a cell experiencing increased levels of ROS with time. (a) Levels of native protein (NatP), misfolded protein (MisP), misfolded
protein complexed with Hsp90, aggregated protein (AggP) and unbound Hsp90. Total Hsp90 increases in step with misfolded protein complexed to Hsp90,
native protein corresponding decreases, all other species are close to zero. (b) Levels of ATP, ADP and ROS. Initial conditions as in Table 1. k21 = 0.00001, all
other parameters as in Table 2.

half-life. Using this procedure we obtained a value of
7
The levels of ROS, ATP and ADP remain fairly constant
throughout the simulation with values 100, 10000, and 1000,
respectively (see Fig. 2b).
5.2. Cell exposed to transient stress
We next examined the effect of increasing the ROS level
two-fold for 10 min, after the simulation had been running
for about 8 min. Fig. 3 shows the results of a simulation run
for 2000 s. We can see a sudden decrease in native protein as
it denatures and rapidly forms complexes with Hsp90. There
is also an increase in aggregated protein. When the ROS
level returns to normal, some of the denatured protein is
ing and Development 126 (2005) 119–131k6 = 6.0  10 .
In order to calculate the synthesis rate k1, we assume that
the level of protein remains constant. We set the initial value
of native protein as 6,000,000 molecules so at steady state
k1 = 6  106  1.34  106 = 8.04. We can also calculate
the misfolding rate k2, using the observation that 95% of
protein is in its native form under normal conditions (Lodish
et al., 2000).
We set the parameter describing the binding affinity of
Hsp90 to HSF1 (k6), so that it is ten times greater than the
binding affinity of Hsp90 to misfolded protein (k3). In
reality, the ratio of these parameters should be in the region
of 100–1000. The reason for this discrepancy is that we have
only included a subset of protein in our model. If we had
included total cellular protein, then there would be a larger
amount of misfolded protein competing with HSF1 for
Hsp90.
The key benefit of a mathematical model is that it allows
us to explore the effects of varying any of the default
parameter values. For example, we varied the rate of ROS
removal k21, so that the level of ROS increased with time
(see Section 5.3).
5. Results
5.1. Unstressed cell
Using the initial conditions and parameter values listed in
Tables 1 and 2, we carried out a simulation for 10,000 s.
(Note: time here and in subsequent results refers to
simulation time within the biological context of the model,
not the actual run-time of the simulation on the computer.)
Fig. 2 shows a typical simulation. If we repeated the
simulations many times and averaged the results we would
obtain smoother curves. However, even from a single
simulation we can see that the species quickly reach a steady
state. About 95% of the total protein is in its native form with
the remaining 5% being misfolded and complexed to Hsp90.given half-life, if we assume that the protein level remains
constant. However, we have more than one step to
degradation which means that further information is needed.
In our model we have chosen a protein with a half-life of 6
days. Using the formula l = ln(0.5)/t1/2, where l is the
degradation rate, gives l = 1.34  106 s1. Since the
native protein has to be misfolded before it can be degraded,
k6 needs to be higher than this value. If all misfolded protein
was degraded then we could simply set k6 = l  19 (since
the ratio of native to misfolded protein is 19:1). However,
misfolded protein can also be refolded or form aggregates.
So to find the value of k6 which results in the half-life
of native proteins being equal to 6 days, we set the
synthesis rate to zero and ran the simulation for various
values of k6 until we found a value which gave the correct
C.J. Proctor et al. / Mechanisms of Age128There is no aggregated protein present.refolded. However, the aggregated protein persists because
we have assumed that it cannot be degraded and that
aggregation is not reversible. This results in the level of
native protein being lower than its initial level. The level of
Hsp90 remains at a higher level as it is a relatively stable
protein but we would expect it to return slowly to normal
levels.
5.3. Increase in ROS with time
In this simulation we decreased the rate of ROS removal
by changing the parameter k21 from 0.001to 0.00001. This
causes a gradual increase in ROS over time. As shown by
Fig. 4, the model predicts that the level of native protein
rapidly declines and there is a corresponding increase in the
denatured protein which forms complexes with Hsp90.
There is a corresponding decrease in the level of ATP as ATP
is needed for both the refolding and degradation of
misfolded protein. However, note that the linear increase
in ROS leads to a non-linear decrease in ATP. This is due to
the initial steep decrease in the level of native protein, which
is then followed by a more gradual decline. The level of
Hsp90 increases and is able to deal with the increase in
denatured protein so that the level of aggregated protein
remains close to zero. The decline in ATP results in the
misfolded protein remaining in complex with Hsp90 as both
the capacity for refolding and degradation is reduced. Note
that we have so far assumed that there is no decline in the
Fig. 5. Extending the model. Hsp90 becomes misfolded and then either is
degraded or forms aggregates.

C.J. Proctor et al. / Mechanisms of Ageing and Development 126 (2005) 119–131 129
Fig. 6. Simulation results for the extended model with increasing levels of ROS. (a) Levels of native protein (NatP), misfolded protein (MisP), misfolded protein
complexed with Hsp90, aggregated protein (AggP) and unbound Hsp90. (b) Levels of ATP, ADP and ROS. Initial conditions as in Table 1. k17 = 1.52  107,
k21 = 0.00001, k22 = 10
6, k23 = 10
7, all other parameters as in Table 2.

Fig. 6 with Fig. 4.
relatively short, for example, Fig. 3 was generated in under
homeostasis hypothesis’’ (So˝ti et al., 2003). The outcome
ing a6. Discussion
We have developed a mathematical model of the
chaperone system, with particular focus on the role of
Hsp90 in guarding protein homeostasis. Our model shows
that when the level of denatured protein rises as a result of
increased stress, Hsp90 is upregulated and can prevent the
formation of aggregated protein, provided that the stress is
not too severe or long-lasting. As levels of oxidative stress
increase with age, we see that eventually there comes a point
when the levels of Hsp90 cannot increase enough to form
complexes with the increasing numbers of denatured
proteins, and as a consequence, aggregated protein begins
to form. If the chaperones themselves also become damaged
and the degradation machinery becomes less efficient with
time, then the formation of aggregates is further increased.
Since ATP is required for both refolding and degradation, a
decline in ATP with age makes the situation worse.
The models described here are available on our web-site
(www.basis.ncl.ac.uk) and we encourage the reader to carry
out their own simulations and to change parameter values of
interest. The levels of native protein, misfolded protein and
aggregated protein can then be compared with Fig. 2.
It is also possible to change the initial number of each
species in the model, for example the initial amount of native
protein. However, when changing initial levels of species itcapacity of Hsp90. In the next section we modify this
assumption.
5.4. Extensions to the model
One of the advantages of building our models using the
network approach is that it is straightforward to extend the
model as more information becomes available or new
hypotheses are formed. For example, in our basic model we
modelled the degradation of Hsp90 by one reaction (see Fig.
1b). The rate of this reaction depended on the level of Hsp90
and ATP. However, Hsp90 is also subject to damage and as it
has many hydrophobic regions, it will also form aggregates
when it is not in its correct conformation. So we modified the
model so that Hsp90 can become misfolded, and that once
misfolded, it can either be degraded or form aggregates. Fig.
5 shows the additional reactions. For simplicity the figure
shows the reaction of aggregation of misfolded Hsp90 by a
single arrow. However, we actually model this as three
different reactions, either two misfolded Hsp90 molecules
can aggregate, a misfolded Hsp90 can aggregate with a
misfolded protein other than Hsp90, or a misfolded Hsp90
can bind to previously formed aggregated protein. The result
of adding this detail to the model, is that the level of
aggregated proteins begins to rise with time due to the
decline in functional Hsp90 as can be seen by comparing
C.J. Proctor et al. / Mechanisms of Age130may also be necessary to change parameter values that affectwill depend on the levels of denatured protein, aggregated
protein, Hsp90 and ATP. We will then be able to obtain the
distribution of cells in each state at different time points and
will also be able to compare the distributions obtained for
different sets of parameter values.
We set the levels of ROS, ATP and ADP in this model and
put in reactions to represent ROS production and scavenging
and general reactions of ATP/ADP. However, we are also
currently developing models of the mitochondria where the
ROS and ATP are produced. Future developments will link
the chaperone model to the mitochondria model by taking
out the general reactions of ROS and ATP and replacing the
initial levels of these species with the levels output from the
mitochondria model.
The model that we have described can be extended in
many ways. For example, we could include the function of
other chaperones such as the role of Hsp100 in dissolving
protein aggregates. Further detail could also be added to
many of the reactions described such as protein synthesis,
Hsp90 synthesis and the degradation steps.
Acknowledgements
This work was funded by BBSRC, MRC, DTI and
Unilever plc. We thank an anonymous referee for helpful
comments.
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