Tài liệu Báo cáo khoa học: Effects of sequestration on signal transduction cascades docx

Effects of sequestration on signal transduction cascades
Nils Blu
¨
thgen
1,
* Frank J. Bruggeman
2
, Stefan Legewie
1
, Hanspeter Herzel
1
, Hans V. Westerhoff
2,3
and Boris N. Kholodenko
4
1 Institute for Theoretical Biology, Humboldt University Berlin, Germany
2 Department of Molecular Cell Physiology, Institute of Molecular Cell Biology, Faculty of Earth and Life Sciences, Vrije Universiteit,
Amsterdam, the Netherlands
3 Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, School of Chemistry, University of
Manchester, UK
4 Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Philadelphia, USA
In most biological organisms intracellular signal pro-
cessing is carried out by networks composed of
enzymes that activate and inactivate each other by co-
valent modification. Signals received at the cell mem-
brane ripple through signalling networks via covalent
modification events to reach various locations in the
cell and ultimately cause cellular responses. The bio-
chemical building blocks of these networks are fre-
quently enzyme pairs, such as a kinase and a
phosphatase, that form covalent modification cycles in

which the target enzyme is covalently modified at sin-
gle or multiple sites in a reversible manner.
In some experiments, the stimulus–response curves
display strong sigmoidal dependencies in vivo, for
example, in the activation of the mitogen-activated
protein kinase (MAPK) cascade [2] and Sic1 [3], and
in vitro, for example, in the phosphorylation of
isocitrate dehydrogenase [4], muscle glycolysis [5] and
in postsynaptic calcium signalling [6]. Sigmoidal
stimulus–response curves imply that the responses are
highly sensitive to changes in signals around the
threshold level. Thus it is more sensitive than a typical
Michaelis–Menten-like response, a property that has
been termed ultrasensitivity [1].
Keywords
MAPK; phosphorylation; sequestration;
signal transduction; zero-order ultrasensitivity
Correspondence
N. Blu
¨
thgen, Institute for Theoretical
Biology, Humboldt University Berlin,
Invalidenstr. 43, 10115 Berlin, Germany
Fax: +49 30 838 56943
Tel: +49 30 838 56971
E-mail:
*Present address
Molecular Neurobiology, Institute of Biology,
Free University of Berlin, Germany.
Note

Nils Blu
¨
thgen and Frank J. Bruggerman
contributed equally to this study.
(Received 21 November 2005, accepted
15 December 2005)
doi:10.1111/j.1742-4658.2006.05105.x
The building blocks of most signal transduction pathways are pairs of
enzymes, such as kinases and phosphatases, that control the activity of pro-
tein targets by covalent modification. It has previously been shown [Gold-
beter A & Koshland DE (1981) Proc Natl Acad Sci USA 78, 6840–6844]
that these systems can be highly sensitive to changes in stimuli if their cata-
lysing enzymes are saturated with their target protein substrates. This
mechanism, termed zero-order ultrasensitivity, may set thresholds that filter
out subthreshold stimuli. Experimental data on protein abundance suggest
that the enzymes and their target proteins are present in comparable con-
centrations. Under these conditions a large fraction of the target protein
may be sequestrated by the enzymes. This causes a reduction in ultrasensi-
tivity so that the proposed mechanism is unlikely to account for ultrasensi-
tivity under the conditions present in most in vivo signalling cascades.
Furthermore, we show that sequestration changes the dynamics of a cova-
lent modification cycle and may account for signal termination and a sign-
sensitive delay. Finally, we analyse the effect of sequestration on the
dynamics of a complex signal transduction cascade: the mitogen-activated
protein kinase (MAPK) cascade with negative feedback. We show that
sequestration limits ultrasensitivity in this cascade and may thereby abolish
the potential for oscillations induced by negative feedback.
Abbreviations
JAK, janus kinase; MAPK, mitogen-activated protein kinase; MAPKK, mitogen-activated protein kinase kinase; MCA, metabolic control analysis.
FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS 895

Sigmoid responses can be used to generate binary-like
decisions [7] and to filter out noise or delay responses
[8]. Moreover, ultrasensitive signal transduction cas-
cades can display oscillations in combination with a neg-
ative feedback loop [9] and bistability (hysteresis) in
combination with positive feedback [10,11]. Surpris-
ingly, ultrasensitivity coupled with negative feedback
also yields highly linear responses and signal fidelity in
the presence of high load [12].
Several mechanisms account for ultrasensitive stimu-
lus–response curves, including cooperativity, multisite
phosphorylation, feed-forward loops and enzymes
operating under saturation. The latter mechanism
has been termed zero-order ultrasensitivity because a
necessary condition is that the modifying and de-modi-
fying enzyme of a covalent modification cycle display
zero-order kinetics. This mechanism was explored for
the steady-states of cycles composed of enzymes with
irreversible product-insensitive kinetics in pioneering
work by Goldbeter & Koshland [1]. Zero-order sensi-
tivity is appealing because of its simplicity: all it needs
is one modification site on a protein that acts as a sub-
strate (e.g. a phosphorylation site) and, for example, a
kinase and a phosphatase in which at least one of the
enzymes has a K
M
value for their substrate that is low
compared with the total concentration of the protein
substrate. This mechanism might provide cells with
simple ultrasensitive signalling units that can be inter-

connected to form networks that can display a great
variety of responses [13].
However, cells also use more complicated mecha-
nisms that activate proteins by multiple modification
events to bring about ultrasensitivity. Examples of such
protein targets are Sic1 which has at least six phos-
phorylation sites [3]. Nuclear factor of activated T-cells
(NFAT) has even more phosphorylation sites [14], and
the MAPK cascades containing MAPK kinase
(MAPKK) and MAPK both become fully activated by
double phosphorylation. It remains a puzzle, why other,
more complicated means like multisite phosphorylation
need to be applied to get high sensitivity when there is a
simple mechanism like zero-order ultrasensitivity.
Goldbeter & Koshland discussed briefly that product
sensitivity and a large amount of enzyme–substrate
complex compared with the total concentration of the
interconvertible enzyme may reduce the sensitivity of
the cycle. They did not analyse any of the general con-
sequences of sequestration, however, and the severe
consequences of sequestration for ultrasensitivity there-
fore remain unclear. The effect of product sensitivity
has been quantified in more detail by Ortega et al.
[15], who showed that ultrasensitivity disappears if the
enzymes are product sensitive. Data about protein
abundance in signal transduction cascades are now in
hand, showing that members of the cascades are pre-
sent in concentrations of the same order of magnitude
[16] (see Table 1 for examples). Therefore, we decided
to investigate the effect of high enzyme concentration

on the sensitivity of signal transduction cascades in
more detail. Without loss of generality we assume that
the modification is phosphorylation and the enzymes
are kinases and phosphatases. First, we investigate the
amount of sequestered substrate in a simple covalent
modification cycle (Fig. 1). We then show that seques-
tration reduces zero-order ultrasensitivity dramatically.
Subsequently, we illustrate the consequences of seques-
tration on zero-order ultrasensitivity by numerical
simulations and confirm the predictions.
We show that sequestration also has dramatic effects
on signalling dynamics. Sequestration can account for
the transient transduction of a permanent signal.
Multisite phosphorylation and kinase sequestration
can work as a sign-sensitive delay element [17], in
which the rise in the signal is delayed but the dropping
signal is transduced immediately.
Finally, we analyse the effect of sequestration on a
complex signal transduction cascade, the MAPK cas-
cade. Computational studies by Kholodenko [9] have
shown that oscillation can arise in this system from a
combination of ultrasensitivity and negative feedback.
We show that sequestration abolishes those oscillations
by reducing zero-order ultrasensitivity.
Results
Sequestration in covalent modification cycles
Unlike metabolic systems, the modification cycles in-
volved in signal transduction cascades often exhibit
comparable amounts of protein substrates and enzymes
[16]. For example, the individual concentrations of

Table 1. Concentrations of members of the MAPK cascade
(MAPKKK, MAPKK, MAPK) in different organisms and cell types as
found in the literature. In many of these, the concentrations are of
the same order of magnitude. RU, relative units.
Cell type MAPKKK MAPKK MAPK Ref.
Budding yeast < 35 n
M 100 nM [7]
Chinese hamster
ovary cells
1300 n
M 2800 nM [7]
Xenopus oocytes 3 n
M 1200 nM 330 nM [7]
HeLa cells 30 l
M 30 lM [40]
Rat 1 1 RU 1.6 RU 2.4 RU [41]
NIH 3T3 1 RU 1.4 RU 3.5 RU [41]
208F 1 RU 2.9 RU 5.9 RU [41]
COS-1 1 RU 0.7 RU 9 RU [41]
Effects of sequestration N. Blu
¨
thgen et al.
896 FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS
the three kinases of the well-characterized MAPK cas-
cade are similar in a variety of cell types and organ-
isms (Table 1). Each of these kinases modifies its
target protein and is itself a target for the upstream
kinase. Because the concentration of kinases and their
target proteins are comparable, the kinase can seques-
ter a significant amount of target by binding to it,

provided that the kinase shows high affinity towards
the substrate. This sequestered fraction of the target is
no longer accessible to other kinases and phosphatases.
Available data about phosphatase concentrations sug-
gest that they are also likely to be of the same order of
magnitude as or even exceed their substrate concentra-
tions [18,19].
The concentration of the kinase–substrate complex
[TK] in the steady-state can be calculated using the
Michaelis–Menten formula:
½TK¼
½T½K
T

½TþK
M
ð1Þ
where [T] and [K
T
] are the free target concentration
and total kinase concentration, respectively, and K
M
is
the Michaelis–Menten constant of the kinase. The con-
centration of the complex [TK] approaches the total
concentration of the kinase as [T]>K
M
. The phos-
phatase–substrate concentration can be calculated
accordingly. To illustrate this effect for a covalent

modification cycle, we investigate a special case, i.e.
when both kinase and phosphatase have the same kin-
etic constants and the same concentrations. Conse-
quently, the two substrates are in equal steady-state
concentrations ([T] ¼ [T*]) and the two complex con-
centrations are equal ([TK] ¼ [T*P]). Therefore, the
total target concentration can be expressed as: T
T
¼
2[T]+2[TK]. After substitution of the resulting expres-
sion for [TK] into the Michaelis–Menten formula, we
obtain:
2
½K
T
½T
K
M
þ½T
¼ T
T
À 2½Tð2Þ
From this, the amount of free substrate in the cycle, i.e.
[T]+[T*] ¼ 2[T] can be calculated from the total con-
centrations of kinase and target. Importantly, the con-
centrations of the free substrate forms [T] and [T*]
decrease below K
M
if [K
T

]>[T
T
] ) 2K
M
(see Supple-
mentary material for mathematical details). If the cata-
lytic activity of the phosphatase exceeds the activity of
the kinase, the free substrates can be higher. In this case,
[T] and [T*] will still fall below K
M
if the kinase and
phosphatase concentrations together exceed twice the
target concentration, i.e. [K
T
]+[P
T
]>2[T
T
] ) 4K
M
.
Thus, in a signalling cycle, sequestration reduces the
free target concentrations such that the concentration
of the free target is below the K
M
value of the
enzymes, provided that the enzymes are available in a
concentration as high as their total protein substrate
concentration.
The effect of sequestration on zero-order

ultrasensitivity
The sensitivity of simple modification cycles was
explored in pioneering work by Goldbeter & Koshland
[1] using methods from nonlinear dynamics. Later, it
was formulated in terms of metabolic control analysis
(MCA) by Small & Fell [20]. Small & Fell expressed
the response of the active fraction to a change of the
kinase concentration as a function of the concentra-
tions of the two forms ([T] and [T*]) and the elastici-
ties of the enzymes by the following simple relation:
R
T
Ã
K
T
¼
½T
e
t
2
T
Ã
½Tþe
t
1
T
½T
Ã

ð3Þ

As discussed in the Methods, this response coefficient
expresses the fractional change of the active form
T
T
T
T
1a
2b
1b
2a
K
K
P
P
*
*
Fig. 1. Schematic representation of the simplest covalent modifica-
tion cycle. The target protein T can be covalently modified. The
unmodified protein T binds to the kinase K in the first reaction (1a) to
form the complex TK. The second reaction (1b) is the catalytic modifi-
cation step yielding K and the covalently modified target protein T*.
In the third reaction (2a), the phosphatase P binds T* to form the
complex T*P. In the fourth reaction (2b) the cycle is closed by the
recycling of T via catalytic demodification and the release of P. Reac-
tions 1b and 2b are assumed to be irreversible for simplicity.
N. Blu
¨
thgen et al. Effects of sequestration
FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS 897
[T*] upon a fractional change of the kinase concen-

tration. If the enzymes are unsaturated, their elastici-
ties are e
m
2
TÃ
% 1 and e
m
1
T
% 1, and the response
coefficient is R
T
Ã
K
T
< 1, corresponding to a sublinear
response. In this case, no ultrasensitivity is observed.
In contrast, saturation of the enzymes leads to elasti-
cities closer to 0, hence R
T
Ã
K
T
can exceed 1 and give
rise to an ultrasensitive response. In the derivation of
Eqn (3), Small & Fell [20] assumed that the concen-
tration of the substrate bound to the enzyme is negli-
gible. But as discussed above, this assumption does
not hold where the concentrations of enzymes and
substrate are similar, as observed in signal transduc-

tion cascades if the enzymes are saturated. Therefore,
the assumptions made to derive Eqn (3) may not
necessarily hold.
If the effect of sequestration is taken into account
the response coefficient modifies to:
R
T
Ã
K
T
¼
½T
e
t
2
T
Ã
½Tþe
t
1
T
½T
Ã
þe
t
2
T
Ã
e
t

1
T
½TKþ½T
Ã
P
ð4Þ
A detailed mathematical derivation of Eqn (4) can be
found in the Supplementary material. Comparison of
Eqn (4) with Eqn (3) reveals the effect of sequestration
on zero-order ultrasensitivity as an additional term in
the denominator which increases with the extent of
sequestration, i.e. ([TK]+[T*P]). Therefore, at con-
stant elasticities, sensitivity should decrease with
sequestration. Another effect is hidden in the equa-
tions: an increase in sequestration also increases the
elasticities e
t
2
T
Ã
and e
t
1
T
, because the available substrate
decreases. This eventually causes an additional
decrease in the sensitivity R
T
Ã
K

T
.
To elucidate this further, we examined the special case
when both kinase and phosphatase have the same kin-
etic constants. In this case, we expect, on the basis of
symmetry, that the highest response coefficient occurs
when there are equal amounts of phosphorylated
and unphosphorylated target. We can then express
all concentrations and elasticities in terms of [T], the
Michaelis–Menten constant, K
M
, of kinase and phos-
phatase. In this case Eqn (4) reads:
R
T
Ã
K
T
¼
1 þ
½T
K
M
21þ
K
M
½K
T

ðK

M
þ½TÞ
2

ð5Þ
R
T
Ã
K
T
increases with [T] and decreases with [K
T
]. This
shows that the response coefficient gets smaller as the
amount of free substrate [T] decreases due to seques-
tration. As discussed previously, similar concentra-
tions of the enzymes and target imply that the free
target falls below the K
M
value. The response is then
sublinear, i.e. R
T
Ã
K
T
< 1, because
2K
M
½TþK
M

% 1. Also, if
K
M
is very small, most of the substrate is sequestered,
leading to essentially zero concentrations of T and
T*.
Goldbeter & Koshland [1] discussed the possibility
that ultrasensitivity might be preserved if the phospha-
tase–target complex T*P is assumed to be active. How-
ever, as calculated in the Supplementary material, the
combined response of T and T*P, R
T
Ã
þT
Ã
P
K
T
is always
< R
T
Ã
K
T
. Thus, the attenuation of sensitivity by seques-
tration cannot be restored by an active phosphatase–
target complex.
The consequences of sequestration for
ultrasensitivity: numerical investigations
To further investigate the consequences of sequestra-

tion on ultrasensitivity, the steady-state of the cycle
depicted in Fig. 1 was calculated numerically. The
K
M
value was chosen to be much smaller than the
total concentration (K
M
¼ 0.02[T
T
]) for both the kin-
ase and the phosphatase. The phosphatase concentra-
tion [P
T
] was increased from 0 to 2[T
T
], to vary the
amount of sequestration. Figure 2B shows that this
increase is accompanied by an increase in the seques-
tered fraction ([TK] + [T*P]) ⁄ [T
T
]. The response of
the cycle [T*] to the input [K
T
] decreases if the total
levels of the phosphatase approach half of the total
target concentration [T
T
] (Fig. 2A). Taken together
these two plots illustrate our argument: when the kin-
ase and phosphatase concentrations become compar-

able with the total concentration of the target
protein, the sequestered fraction increases, which cau-
ses the sensitivity to decrease. In Fig. 2C the activated
fraction of the target T* is plotted, illustrating that
the fraction of activated target decreases dramatically
as the phosphatase concentration exceeds [T
T
] ⁄ 2.
These results are in good agreement with the esti-
mates made above. This suggests that in vivo, where
in many cases the concentrations of the kinase, the
phosphatase and the target protein are comparable,
the sensitivity of covalent-modification cycles is likely
to be achieved by mechanisms other than zero-order
ultrasensitivity. Simulations for different catalytic
activities of kinases and phosphatases are shown in
Fig. 2D–I. If the phosphatase is catalytically 10-fold
more active than the kinase, the region of enhanced
sensitivity is broadened slightly (Fig. 2D–F). In con-
trast, if the kinase is more active than the phos-
phatase, the region if ultrasensitivity is drastically
reduced (Fig. 2G–I). It seems that in case of mamma-
lian MAPK cascades high concentrations of the phos-
Effects of sequestration N. Blu
¨
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898 FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS
phatases yield high sequestration which do not allow
for zero-order ultrasensitivity.
The consequences of sequestration for signalling

dynamics
Receptor desensitization is a relatively slow process
and downstream signal transduction cascades are often
in a quasi-steady-state with the receptor activity. How-
ever, some downstream parameters adapt very quickly
(e.g. insulin receptor substrate phosphorylation after
insulin and Erk after epidermal growth factor), sug-
gesting that downstream pathways are capable of
adaptation. Figure 3A shows the dynamics of the co-
valent modification cycle for a fast kinase with low
affinity and a slow phosphatase with high affinity. If a
permanent stimulus is given, the target displays only
transient activation. Thus a covalent modification cycle
is capable of terminating prolonged signals. The fast
kinase phosphorylates the available target, but the
1
0
2
1
2
1
2
1
2
[K ]
T
T
[P ]
1
2

0.1
0.2
[K ]
T
T
[P ]
[K ]
T
T
[P ]
Legend A,D,G
0
20
[P ]
T
[P ]
T
1
2
[P ]
T
1
2
0
1
2
1
2
1
2

Response
Coefficient
Sequestered
Target
Activated
Fraction
K =0.1
1b,f
K=1
1b,f
K =0.01
1b,f
1
0
2
0.1
0.2
10
0
20
0
1
0
2
0.1
0.2
10
0
20
0

A
D
G
B
E
H
C
F
I
>3
<3
<2
< 1.5
< 1.25
<1
< 0.75
< 0.5
> 0.9
< 0.9
< 0.5
< 0.15
< 0.1
< 0.05
< 0.02
< 0.01
> 0.9
< 0.9
< 0.8
< 0.7
< 0.6

< 0.5
< 0.4
< 0.3
< 0.2
< 0.1
10
Legend B,E,H Legend C,F,I
Fig. 2. Steady-state signalling characteristics of a covalent-modification cycle for equal catalytic activity of kinase and phosphatase (A–C), for
10-fold higher catalytic activity of the kinase (D–F), for 10-fold reduced catalytic activity of the kinase (G–I). (A) Contour plot of the response
coefficient R
T Ã
K
T
as function of the total concentration of the phosphatase and the kinase (normalized to the phosphatase concentration). (B)
Sequestered fraction of the target protein. (C) Fraction of the activated target protein. Parameter values: T
T
¼ 1, k
1a,f
¼ 10, k
1a,r
¼ 0.1,
k
1b,r
¼ 0, k
2a,f
¼ 10, k
2b,f
¼ 0.1 and k
2b,r
¼ 0 varied to simulate different catalytic activity of the kinase: (A–C) k

1b,f
¼ 0.1, (D–F) k
1b,f
¼ 1,
(G–I) k
1b,f
¼ 0.01. K
T
and P
T
refer to the total kinase and phosphatase concentration, respectively.
N. Blu
¨
thgen et al. Effects of sequestration
FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS 899
phosphorylated target is subsequently sequestered by
the low-activity high-affinity phosphatase. At steady-
states most of the target substrate is sequestered by the
phosphatase. Thus substrate sequestration by a phos-
phatase might be a means to achieve signal termin-
ation and desensitization downstream of receptors
without involving a negative feedback loop.
For many signals, their duration determines the bio-
logical response [21]. We have pointed out that seques-
tration might cause short, transient signals. However,
interpretation of the signal by the signal transduction
network requires circuits that respond only to pro-
longed activation. As pointed out by Deshaies &
Ferrell [22], such signal duration decoding requires a
threshold time. Also, deactivation must be fast in com-

parison with activation as removal of the signal has
to be translated into an immediate response. Such
properties have been described for coherent feed-for-
ward loops, which display sign-sensitive delay [17].
Figure 3B shows that competition for the enzyme by
two phosphorylation sites may also account for such a
sign-sensitive delay and dramatically improves dur-
ation decoding. The solid line shows the dynamics of
double-phosphorylation in which both phosphoryla-
tion sites compete for the kinase, the dotted line shows
the dynamics of the corresponding system in case there
is no competition (details in the Supplementary mater-
ial). If the stimulus increases it must be of a certain
length to be transduced if the sites compete for the
kinase. However, if the stimulus falls, the change is
transduced immediately. Thus, sequestration and
multisite phosphorylation might be a mechanism for
sign-sensitive delays, similar to coherent feed-forward
loops in transcriptional networks [17].
Changes in the steady-state stimulus–response curve
might also have a large impact on the dynamics
because the onset of oscillations in a signal transduc-
tion cascade harbouring a negative feedback is deter-
mined by the sensitivity of the stimulus–response curve
in the steady-state. We investigated the effects of
sequestration in a complex signal transduction cascade
with negative feedback as described below.
The effect of sequestration in MAPK signal
transduction cascade
The MAPK cascade consists of three kinases that

activate their downstream kinases by phosphorylation
(Fig. 4). It has the potential to be ultrasensitive
because of the combination of multisite phosphoryla-
tion, zero-order kinetics [23] and cascade amplification
effects [24]. According to Kholodenko [9] a negative
feedback that is wrapped around this ultrasensitive
cascade can bring about sustained oscillations over a
wide range of stimuli if sequestration is neglected
(Fig. 6A).
As the kinases are present at similar concentrations,
we investigated whether sequestration affects ultrasen-
sitivity and oscillatory behaviour. We modelled the
cascade such that sequestration was taken into account
(similar to Huang & Ferrell [23], with parameters
adopted to reflect the catalytic and Michaelis–Menten
constants from Kholodenko [9], see Supplementary
material for details). We chose concentrations of the
phosphatases for MAPK and MAPKK that were as
high as that of their substrate (300 nm). First, we ana-
lysed the cascade without feedback. Figure 5 compares
02040
time
0
25
50
A
[T*]
x0.1
B
0 5 50 55

time
0
20
40
60
80
100
[T**]
Fig. 3. (A) The dynamics of free phosphorylated target protein in
case of more active kinase than phosphatases k
1a,f
¼ 0.005,
k
1a,r
¼ 0.4,k
1b,f
¼ 0.1, k
2a,f
¼ 0.0005, k
2a,r
¼ 0.004, k
2b,f
¼ 0.001
T
T
¼ 100 K
T
¼ 300 P
T
¼ (300). At zero time-point, the system is at

steady-state for zero stimulus (initial conditions: [T](0) ¼ T
T
,
[T*](0) ¼ [TK](0) ¼ [T*P](0) ¼ 0). (B) The dynamics of double-phos-
phorylation in case the kinase shows higher affinity towards the un-
phosphorylated target. Solid line: the case of kinase sequestration,
dotted line: no kinase sequestration. Grey lines indicate the stimu-
lus (i.e. kinase concentration), scaled by 0.1 in (A).
Effects of sequestration N. Blu
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900 FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS
a model neglecting sequestration (Fig. 5A–C) and one
including the effect of sequestration (Fig. 5D,E).
Whereas the response of the first molecule
(MAPKKK) is relatively unchanged because its kinase
and phosphatase are present only at low concentra-
tions, the response of the second and third molecules
(MAPKK and MAPK) is changed dramatically. There
are two main effects of sequestration visible in the
response of MAPKK and MAPK: the ultrasensitivity
of the stimulus response curves is reduced and the
amount of maximally activated kinases in this cascade
is decreased.
If we add a negative feedback loop to this model,
similar to the model by Kholodenko [9], no oscillations
arise (Fig. 6B). The effect of lower activation of
MAPK can be compensated for by a stronger feedback
(lower values of k
loop

, see Supplementary material).
However, lowering of k
loop
does not restore oscilla-
tions (Fig. 6B). This leads us to conclude that the
reduction in ultrasensitivity due to sequestration is
responsible for the diminishing of oscillations.
We observed in the analysis of simple, isolated cova-
lent modification cycles that an increase in the total
target concentration will limit the sequestered fraction
of the target and restore ultrasensitivity. However, in
cascades such as the MAPK cascade the kinases are
both enzymes for the modification of the downstream
kinase and substrate for the upstream kinase. Hence,
the complex of, for example, MAPK and MAPKK
reduces the free concentration of both MAPK and
MAPKK. Therefore, an increase of the MAPK con-
centration in this cascade gives rise to more sequestra-
tion of MAPKK by MAPK. Consequently, it is not
surprising that we found that an increase in MAPK of
one order of magnitude cannot restore the oscillations.
In addition, we investigated the effects of sequestra-
tion by phosphatases. We found that oscillations can
be restored if the phosphatase concentrations of
MAPK- and MAPKK-phosphatase are lowered to one
fifth of the kinase concentrations (while increasing
their catalytic activity by factor five to keep the V
max
value constant). However, in contrast to the model
that neglects sequestration, the stimulus needs to be

rather low (Fig. 6C). In this case, sequestration due to
the phosphatase is reduced and the upstream kinases
of MAPK and MAPKK are only slightly activated
and can sequester only limited fractions of MAPK and
MAPKK.
Discussion
The function of the signal transduction network is to
sense changes in the environment of the organism in the
form of signals of physicochemical origin, e.g. concen-
trations of molecules or mechanical stress, and to integ-
rate these with the current cellular status to ‘compute’
an adaptive response [12]. Such adaptive responses
involve covalent modification of enzymes, changes in
gene expression, and cell-fate decisions that occur on
different time scales. Many signal transduction networks
have common building blocks: enzyme couples that acti-
vate and inactive their protein targets via covalent modi-
fication. It is reasonable to expect that network
responses can be highly sensitive to changes in the sig-
nals. Ultrasensitivity can be used generate thresholds,
oscillations and linear responses [12]. Therefore, it may
not be surprising that ultrasensitivity has been docu-
mented experimentally for some signalling systems [10].
Theoretical studies by Goldbeter & Koshland [1]
unveiled a potential mechanism responsible for ultra-
sensitivity: the kinase and phosphatase have to be sat-
urated with their target protein. This case has been
referred to as zero-order ultrasensitivity. Since then,
many groups have analysed zero-order ultrasensitivity
[15,25,26,27]. Although the effect of complex forma-

tion in a substrate cycle has been addressed previously
[28], the impact of sequestration on zero-order ultra-
sensitivity has not.
P
P
P
MAPKK
P
MAPKK
P
MAPKK
P
MAPKKK MAPKKK
P
MAPK MAPK MAPK
MAPKKKK
Fig. 4. Sketch of the MAPK cascade. A MAPKKKK stimulates the
phosphorylation of MAPKKK, which after phosphorylation phos-
phorylates MAPKK at two sites. The double-phosphorylated
MAPKK phosphorylates MAPK also at two sites. The double-phos-
phorylated MAPK in turn inhibits the activity of MAPKKKK.
N. Blu
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thgen et al. Effects of sequestration
FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS 901
Experimental data (Table 1) indicate that the concen-
trations of enzymes and target proteins in signal trans-
duction cascades are similar. When the affinity of
enzymes for their target is sufficiently high, it implies
that a high fraction of the target concentration is bound

to the enzymes, and thereby sequestered. This, in
turn, decreases the amount of target accessible to the
enzymes, and reduces ultrasensitivity. Moreover, the
amount of activated target decreases dramatically. Con-
sequently, the concentrations of the complexes can no
longer be neglected in the analysis of ultrasensitivity,
as long as the concentrations of players in the signal
transduction cascades are comparable.
We investigated the consequences of sequestration
on zero-order ultrasensitivity using the analytical
approach of MCA and numerical simulations. In terms
of MCA, ultrasensitivity is equivalent to a response
coefficient higher than 1 [15]. We derived an analytical
expression for the response coefficient (Eqn 4) that
accounts for the effect of sequestration. Comparison
with a response coefficient that neglects sequestration
(Eqn 3) suggests that sequestration may significantly
reduce and even eliminate ultrasensitivity. Eqn (5) cor-
roborates this for a simple example in which the kin-
etic parameters of both enzymes are equal. It shows
that the response coefficient decreases below 0.5:
hence, ultrasensitivity is absent. The results of numer-
ical simulations illustrated that if the total concentra-
tions of both enzymes are increased simultaneously,
ultrasensitivity decreases and ultimately vanishes when
these concentrations exceed 70% of the total target
concentration. This correlated with high sequestration
of the target protein by the enzymes, which illustrates
that sequestration reduces ultrasensitivity.
Another problem of zero-order ultrasensitivity arises

due to the sequestration of the enzyme by the sub-
strate: The saturated enzyme may then not be available
for other reactions. This is of special importance if the
enzyme itself is the substrate of a modification cycle
like MAPKK, which is itself controlled by phosphory-
lation and is the enzyme that phosphorylates MAPK.
Here sequestration reduces the zero-order ultrasensitiv-
ity in both cycles: the cycle in which the enzyme drives
the modification and that in which the enzyme is
subject to modification. In such signalling cascades
sequestration can be significant even if the kinase
concentrations increase along the cascades due to the
sequestration of the enzymes. The extent of ultrasensi-
tivity that can be generated by signal transduction cas-
cades is thereby limited by sequestration. This effect
0
50
100
0
100
200
300
0 0.05 0.10 0.05 0.1
0
100
200
300
MAPKKK-PMAPK-PPMAPK-PP
no sequestration
activated kinase (nM)

sequestration
stimulus (MAPKKKK in nM)
A
B
C
D
E
F
Fig. 5. Stimulus–response curves for the
three layers of the MAPK cascade in the
model considered by Kholodenko [9] (A–C),
which neglects sequestration and the cor-
responding model that takes the effects of
sequestration into account (D–F).
Effects of sequestration N. Blu
¨
thgen et al.
902 FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS
might be responsible for the fact that sustained
oscillations have not yet been documented in the
MAPK cascade as opposed to the NF-jB cascade [29].
Because each enzyme usually targets more than one
reaction, as, for example, most phosphatases, modifica-
tion cycles compete for the enzymes. After a pathway
is activated it recruits its phosphatases, which are no
longer accessible to others. We show that sequestration
of the kinase in a double-phosphorylation cycle may
account for a sign-sensitive delay element, such that
the activation of a target enzyme upon a signal is
delayed, but it is in-activated immediately after

removal of the signal. Such a delay element provides
cells with units that neglect short fluctuations in sig-
nals, but transduce long signals.
In addition, sequestration might mediate cross-talk
between pathways if an enzyme is shared. This has
been observed in the JAK⁄ STAT pathway, in which
the receptors share the janus kinase (JAK) and mul-
tiple receptors compete for it. Upregulation of one
receptor downregulates the response of the other by
sequestration of JAK [30].
Our results suggest that to generate ultrasensitivity,
cells need to exploit mechanisms that do not require
enzyme saturation. Such mechanisms include multisite
phosphorylation, which generates ultrasensitivity with-
out the need for sequestration. Moreover, not only
ultrasensitivity, but also bistability and hysteresis arise
from multisite covalent modification in signalling cas-
cades [31]. Ultrasensitivity and bistability induced by
multisite phosphorylation may be a widespread mech-
anism for the control of protein activity in signalling
networks, whereas zero-order ultrasensitivity is unli-
kely to be the major means of generating switch-like
behaviour in such systems.
One thing is clear, the covalent cycle is extremely
versatile for eliciting different kinds of behaviour
[12,32]. This great versatility may partly explain why
signalling pathways, in both prokaryotic and eukaryot-
ic systems, employ this motif in so many instances.
0123
MAPKKKK (n

M)
0
100
200
300
activated MAPK (nM)
0123
MAPKKKK (n
M)
0
25
50
A
C
B
0 0.01 0.02 0.03 0.04
MAPKKKK (n
M)
0
30
60
sustained
oscillations
no sustained oscillations
Phophatase concentrations
Fig. 6. Bifurcation diagrams for the models
that neglect (A) and include (B,C) the effects
of sequestration. Solid lines show stable
steady-states, dotted lines indicate unstable
steady-states. The dashed lines mark the

amplitude of the oscillations observed in the
model that neglects sequestration. The four
lines in (B) show situations for different
feedback parameters (from top to bottom:
k
loop
¼ 9, 1, 0.1, 0.01 nM). (C) Two-dimen-
sional bifurcation diagram for the model that
includes the effect of sequestration. Con-
centrations of the MAPK- and MAPKK-phos-
phatases (vertical axis) and the stimulus
(horizontal axis) are changed. The dashed
area shows the region where sustained
oscillations occur. Insets show qualitatively
the dynamics in the corresponding areas.
N. Blu
¨
thgen et al. Effects of sequestration
FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS 903
Unfortunately, the lack of any clear guidance from
experimental data means we are unable to determine
exactly the true functional role played by these motifs.
Although many signalling networks have been mapped
in great detail we still have very little understanding of
their actual dynamical behaviour. Until experimental-
ists embrace a systems approach we will remain in the
dark regarding this question.
Methods
The model files used to perform numerical simulations are
available from the authors upon request.

Metabolic control analysis
To analyse ultrasensitivity, we adopt some methods and
terms from MCA [33–35], for application to conserved moi-
eties, see Hofmeyr et al. [27]. MCA has been successfully
applied to intracellular signal transduction systems in the
past [36–38]. MCA links ‘global’ control properties of a
network to ‘local’ properties (e.g. mechanistic details of
enzyme-catalysed reactions). The local properties are called
elasticity coefficients and are defined by e
v
j
x
i
¼
x
i
v
j
@v
j
@½x
i

. Elasti-
cities evaluate the relative change in a reaction rate as a
result of an infinitesimal relative change in one of its sub-
strate, product, or effector concentrations (e.g. [x
i
]). The
elasticities of an enzyme e

j
following irreversible Michaelis–
Menten kinetics with the Michaelis–Menten constant K
M
are e
v
j
e
j
¼ 1 with respect to the enzyme concentration and
e
v
j
S
¼
K
M
½SþK
M
for the substrate S.
Global properties are called response coefficients and
describe the response of the entire system to small perturba-
tions in parameters, R
S
i
p
j
¼
p
j

½S
i

d½S
i

dp
j
. Here, R
S
i
p
j
accounts for a
relative change in steady-state metabolite concentration
[S
i
] upon infinitesimal relative change in the value of the
parameter p
j
.
Model of a simple interconversion cycle
In the first part of this paper we analyse a simple covalent
modification cycle that consists of two enzymes K and P
that phosphorylate and dephosphorylate a target protein T,
respectively (Fig. 1). T can be in a modified and unmodified
form, denoted by T and T, respectively. To investigate the
effect of sequestration, we model the reactions catalysed by
the two enzymes K and P. We explicitly take the enzyme–
target complex into account. In the case of reversibility and

product sensitivity, this system has been shown not to be
ultrasensitive, and therefore such effects are not considered
here [15]. However, Ortega et al. [15] did not consider
sequestration. The total concentrations of the three
enzymes involved are denoted by [T
T
], [K
T
] and [P
T
]. The
enzyme–substrate complexes are called TK and T*P.We
describe the dynamics of this kinetic scheme depicted in
Fig. 1 by a system of three ordinary differential equations
using mass-action kinetics.
Models of the MAPK cascade
We shall also analyse the effect of sequestration in a more
complicated system, the MAPK cascade. We construct two
models: One according to Kholodenko [9], which neglects
sequestration, and a second one similar to Huang & Ferrell
[23], which takes enzyme–substrate complexes into account. In
the second model, the parameters are adopted such that they
reflect the catalytic constants and K
M
values of the model by
Kholodenko [9]. The details of the kinetic model can be found
in the appendix. The numerical analysis of the equations was
carried out using mathematica and xpp-auto [39].
Acknowledgements
We would also like to thank Herbert M. Sauro for

critically reading the manuscript and for assisting NB
in the development of some of the theory outlined here
during NB’s stay at Sauro’s Laboratory in Los Ange-
les. NB acknowledges support from DFG (SFB 618).
FB was supported by the European Union through the
Network of Excellence BioSim, Contract No. LSHB-
CT-2004-005137. Cooperation between NB and FB
was supported by the DFG Graduate Program GK268
‘Dynamics and Evolution of Cellular and Macromole-
cular Processes’. BNK acknowledges support from the
National Institute of Health Grant GM59570. HMS
acknowledges support from the National Science
Foundation Grant CCF-0432190.
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Supplementary material
The following supplementary material is available
online:
Doc S1A. Control coefficient for sequestration in a
simple covalent modification cycle.
Doc S1B. Amount of sequestration in covalent modifi-
cation cycles.
Doc S1C. Models of double-phosphorylation and

sequestration.
Doc S1D. Model of MAPK cascade with sequestration
and negative feedback.
This material is available as part of the online article
from
Effects of sequestration N. Blu
¨
thgen et al.
906 FEBS Journal 273 (2006) 895–906 ª 2006 The Authors Journal compilation ª 2006 FEBS