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

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

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

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,

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

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

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-

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

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

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-

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

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

< 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

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

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

, 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

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
¨
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

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)

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

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.

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

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].
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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