Otdfbt

Membrane localization does not significantly enhance
diffusion-limited signal transfer

It has earlier been suggested that localization of signaling proteins close
to the cell membrane causes an increase in the first-encounter rate
(Adam and Delbruck, 1968); the
solutes do not `get lost' by wondering off into the bulk phase
(Axelrod and Wang, 1994;
Berg and Purcell, 1977).
However, such an increase appears to be too small to account for significantly
enhanced signal transduction (Kholodenko
et al., 2000b). The diffusion-limited rates in the membrane and in
the cytosol can be compared in terms of the ratio (h) of the
corresponding association rate constants in two dimensions and in three
dimensions. For diffusion-limited association of two proteins located in the
plasma membrane of a spherical cell or delocalized over the cytosol volume,
the ratio h was estimated to be
(0.02–0.05)×(D_membr/D_cyt)×(r_cell/r_prot)
(Kholodenko et al., 2000b).
For instance, if the cell radius (r_cell) is 10 μm and
the sum (r_prot) of typical protein radii is approximately
10^-2 μm, then
h≈(20–50)×D_membr/D_cyt.
Because the diffusion coefficients of proteins in the membrane
(D_membr) are about two orders of magnitude lower than in
the cytosol (D_cyt)
(Cherry, 1979;
Kusumi et al., 1993), we
conclude that the function of the membrane recruitment is unlikely to be an
enhancement of the encounter rates. In fact, it has already been suggested
that the fastest route to diffuse is through the cytosol, not through the
membrane, because of two orders of magnitude difference in the diffusion
coefficients (Bray, 1998).

Gain in the number of signaling complexes is more critical than an
increase in the association rate

In the reaction-limited extreme, the first-encounter rate is much faster
than the signal transduction rate, which can be estimated as the fraction of
molecules in the associated state (as if this step were at equilibrium)
multiplied by the reaction rate constant. An increase in the effective local
concentration of a cytosolic protein due to membrane relocation brings about
an increase in the apparent affinity to a binding partner in the membrane
(Ferrell, 1998). Haugh and
Lauffenburger (1997) estimated
that an increase in the reaction-limited protein association rate could be as
high as 10²–10³. In the general case, however, the
rate enhancement depends on many kinetic and molecular details including the
probability of success per diffusion encounter, the concentration depletion
zones near the targets, the reversibility of the binding and other factors
(Axelrod and Wang, 1994). The
binding reversibility suggests that the dissociation rate constant, in
addition to the association rate, may change upon the membrane relocation, as
in fact was observed for affinity enhancement due to `macromolecular crowding'
(Rohwer et al., 1998).
Therefore, although the speed of signal transduction increases by the
translocation of signaling proteins, it should not be assumed that any such
enhancement is due to an increase in the rate of formation of protein
complexes. Instead, the underlying mechanism can be an increase in the number
(or average lifetime) of signaling complexes, which act as catalysts
activating downstream processes. We submit that membrane localization serves
to enhance the extent of complex formation of signal-transduction proteins,
and hence increase the intensity of the signal that is being transduced.

Receptor-mediated membrane recruitment significantly increases the
number of complexes formed by a cytoplasmic protein and a membrane-anchored
protein

A gain in the number of signaling complexes involving a cytosolic protein X
and a membrane-bound protein Y can be brought about by a two-step, `piggyback'
mechanism. The first step is binding of X to an activated membrane receptor R
(`piggy'), which confines X to a membrane shell, where Y is located. The
second step is a `piggyback riding' of X until it meets membrane-anchored Y. X
then forms a complex with Y, while continuing to ride piggyback on R. The
quantitative analysis shows that this piggyback riding leads to a strong
reduction of the apparent dissociation constant, K_d,app,
which can be expressed through the equilibrium dissociation constant
K_d of cytosolic X and membrane-bound Y, as follows
(Kholodenko et al., 2000b):
1
V_c is the cytosol volume and V_m is the
volume of a water layer adjacent to the membrane where protein Y is confined.
The value of the dimensionless factor k is determined by the ratio of the
dissociation constant K_d,R for the binding of cytosolic X
to the activated receptor R and the concentration of the latter
(C_R). Experimental data show that the
K_d,R values appear to be in the range of 1–100 nmol
l^-1, whereas the total RTK concentrations (based on the whole
cytoplasmic volume) are in the range of 100–1000 nmol l^-1 and
approximately 20–50% of the total amount is activated by the stimuli
(see Kholodenko et al., 1999;
Moehren et al., 2002, and the
references therein). Therefore, for membrane recruitment by RTKs, the value of
k does not exceed 1. We conclude that when the activated receptor is present
in excess of cytosolic X, the apparent dissociation constant decreases by a
factor as high as V_m/V_c, i.e. by 2 or
3 orders of magnitude in comparison with the actual K_d of
binding X and Y.

An alternative mechanism of an enhancement in signal transfer rate may be
an increase in the efficiency of the reaction between cytosolic X and
membrane-bound Y due to a conformational change of X upon binding to a
membrane anchor, such as receptor R. However, for SOS-Ras interactions,
structural and kinetic data on the catalytic mechanism and activity rule out
this possibility (Buday and Downward,
1993; Corbalan-Garcia et al.,
1998; Lenzen et al.,
1998).

Recruitment to a scaffold

Our results apply not only to the case of membrane translocation, but to
translocation into any subcellular compartment. Scaffolds of various sorts
should be mentioned here. They act as templates, bringing together signaling
proteins, organizing and coordinating the function of entire signaling
cascades (Bray, 1998).
Importantly, our results suggest that the number of signaling complexes will
increase only if these complexes do not dissociate from a scaffold. Even if
the interacting proteins were brought to close vicinity on a scaffold, the
dissociation of the protein complex from the scaffold will result in further
dissociation of the complex, which will be in thermodynamic equilibrium with
its components.

Specifics of SOS-Ras and GAP-Ras interactions

The calculations demonstrate that activation of Ras by SOS from the cytosol
is two or three orders of magnitude less effective than the catalysis,
mediated by the RTK-bound SOS, for instance, mediated by the EGFR-Grb2-SOS and
EGFR-Shc-Grb2-SOS complexes (Haugh and
Lauffenburger, 1997). After the dissociation of phosphorylated Src
homology and collagen domain protein (Shc) from EGFR, the Shc-Grb-SOS
complexes may bring about an additional route for Ras activation. However,
quasi-equilibrium association of these complexes with Ras may be insignificant
compared to receptor-mediated association unless the Shc-Grb-SOS complexes are
also targeted to the plasma membrane through specific domains, such as
phosphotyrosine-binding and pleckstrin homology domains
(Drugan et al., 2000;
Ugi et al., 2002).
Quantification of relative contributions of SOS complexes with the receptor
and with phosphorylated Shc to Ras activation is awaiting experimental
verification.

Signaling of activated Ras is turned off by the activation of
GTPase-activating proteins (GAPs) (Bollag
and McCormick, 1992). Similar to SOS, p120 GAP is a cytoplasmic
protein. As in the case of SOS signals, the membrane recruitment of GAP is
necessary for an appreciable increase in the rate of GTP hydrolysis on
Ras.

A variation on the topic of Ras activation by RTKs has been described for
fibroblast growth factor receptors (FGFRs)
(Kouhara et al., 1997).
Stimulation of FGFRs induces cell proliferation, differentiation and migration
by activation of the Ras/MAPK signaling pathway. However, unlike other RTKs,
activated FGFR cannot bind Grb2 directly. Recently, a novel membrane-anchored
protein, phosphorylated by activated FGFR, has been discovered and is known as
FRS2 (FGFR substrate 2) (Kouhara et al.,
1997). Tyrosine-phosphorylated FRS2 is able to bind Grb2 and,
therefore, the Grb2-SOS complex. In a familiar twist, the juxtaposition of the
FRS2-Grb2-Sos complex on the membrane may facilitate the Ras activation by
SOS, providing a feasible mechanism for linking FGFRs to the Grb2/SOS/Ras/MAPK
pathway.

MAPK activation by RTKs and GPCRs

MAPK cascades are widely involved in eukaryotic signal transduction, and
these pathways are evolutionarily conserved in cells from yeast to mammals
(reviewed in Chang and Karin,
2001; Lewis et al.,
1998). Mammalian cells express at least four different MAPK
families, including the ERK, the c-Jun N-terminal kinase (JNK) and p38 MAPK
cascades. A three-tiered cascade comprises MAPK, MAPK kinase (MKK) and MKK
kinase (MKKK). A kinase at the first cascade level, MKKK, is activated at the
cell membrane. A kinase at the bottom level, MAPK, is activated in the cytosol
and phosphorylates target proteins both in the cytosol and nucleus. Mitogenic
signaling by RTKs and GPCRs is associated with Ras-dependent stimulation of
the ERK cascade. The classical paradigm for GPCR signaling involves the
agonist-dependent interaction of GPCRs with heterotrimeric G proteins that
stimulates the exchange of bound GDP for GTP, resulting in dissociation of G
proteins into α and βγ subunits. Subsequent interaction ofα
and βγ subunits with effector enzymes or ion channels
regulates the generation of soluble second messengers or ionic conductance
changes. However, this paradigm should be extended to include the
proliferative and differentiative effects of GPCRs. It is presently known that
in a multitude of cell types, GPCRs stimulate the MAPK cascades, such as the
ERK, JNK and p38 MAPK cascades (Garrington
and Johnson, 1999; Gutkind,
1998; van Biesen et al.,
1996). Interestingly, the pathways of GPCR and RTK-mediated MAPK
activation often converge. Recently, evidence has emerged that the overlap of
GPCR and RTK signaling pathways is accounted for in part by GPCR-mediated
`transactivation' of RTKs, such as EGFR
(Fig.1), platelet-derived
growth factor receptor and insulin-like growth factor-1 receptor. For
instance, EGFR activation by GPCR was shown to be mediated by signaling
pathways involving non-receptor tyrosine kinases, Src and Pyk2, and through
activation of the metalloprotease leading to the release of heparin binding
EGF (Pierce et al., 2001;
Prenzel et al., 1999). It is,
however, important to realize that although RTK transactivation is now a
recognized mechanism for GPCR-induced activation of the ERK cascade, other
signaling pathways can also contribute to this link
(Andreev et al., 2001;
Miller and Lefkowitz,
2001).

Heterogeneous spatial distribution of activated components in MAPK
cascades

Multiple cellular proteins are phosphorylated and dephosphorylated at
distinct cellular locations. In the Ras-ERK pathway, inactive Raf-1 (MKKK)
resides in the cytosol. Upon stimulation of cell-surface receptors, Raf-1 is
translocated from the cytosol to the plasma membrane by a high-affinity
binding to GTP-loaded Ras. At the membrane, Raf-1 undergoes a series of
activation steps involving interaction with 14-3-3 proteins and
phosphorylation on specific tyrosine and serine residues
(Mason et al., 1999). Although
the mechanism of activation is not yet completely understood, the association
of Raf-1 with membranes appears to be essential for its activation. The Raf-1
kinase phosphorylates the cytosolic kinase MEK (MKK) at the plasma membrane,
whereas soluble serine/threonine phosphatases dephosphorylate the activated
MEK in the bulk phase (Kyriakis et al.,
1992; Strack et al.,
1997). In the cytosol, active MEK kinase phosphorylates ERK (MAPK)
and specific ERK phosphatases are localized to the cytosol and nucleus.
Spatial separation of protein kinases and phosphatases suggests that there may
be cellular gradients of phosphorylated (active) forms of MEK and ERK, with
high concentrations in the periplasmic region near the phosphorylation
location and low concentrations at a distance from the plasma membrane. Since
activated ERK phosphorylates multiple cytoplasmic and nuclear targets, large
spatial gradients of this kinase may have very important implications for cell
signaling.

Indeed, the quantitative analysis demonstrates that the spatial separation
of kinases and phosphatases potentially results in precipitous gradients of
phospho-proteins, given measured values of protein diffusion coefficients and
phosphatase and kinase activities (Brown
and Kholodenko, 1999;
Kholodenko et al., 2000a). We
illustrate this analysis by calculating the spatial gradients for a single
level cascade, in which the kinase is located on the plasma membrane and the
phosphatase is distributed homogeneously in the cytoplasm (These calculations
and Fig. 2, which illustrates
them, are reproduced from Kholodenko,
2002, with permission from Elsevier Science.) For a spherical
cell, the following equation describes radial diffusion of the phospho-protein
(p) from the cell membrane, where p is produced at the rate,
v_kin, to the cell interior, where p is
dephosphorylated at the rate, v_p,
2
Here p is the phospho-protein concentration, D is the
protein diffusion coefficient in the cytosol (assumed to be equal for the
phosphorylated and unphosphorylated forms), x is a dimensionless
coordinate, equal to the distance from the cell center divided by the cell
radius, L [the distance d from the cell membrane is
expressed in terms of x as
d=(1–x)L], v_kin and
v_p are the rates of the kinase and phosphatase,
respectively. If we assume that the phosphatase is not saturated by a target
phospho-protein (a reasonable assumption for most cytosolic phosphatases), the
phosphatase rate v_p can be described as
v_p=K_p×p, where
K_p is the observed first-order rate constant (equal to the
ratio of the maximal activity to the Michaelis constant,
K_p=V_max,p/K_m,p).
Then, the steady-state solution to Equation 1 can be found readily
(Kholodenko et al., 2000a),
and the ratio of the phospho-protein concentrations at the distance x
from the cell center and at the plasma membrane,
p(x)/p(1), is given by:
3
Therefore, the phospho-protein concentration decreases toward the cell
interior approximately exponentially, as illustrated in
Fig.2. The phospho-protein
concentration profile, p(x)/p(1), depends on the
dimensionless parameter α (recognizable as the square root of the
Damkohler number), which compares the phosphatase and the diffusive time
scales. Therefore, all we need to know are the observed first-order rate
constant of the phosphatase reaction K_p, the diffusion
coefficient D and the cell radius. A typical value for a hepatocyte
radius is 10 μm, D is estimated to be of the order of
10^-8 cm² s^-1
(Arrio-Dupont et al., 2000;
Dayel et al., 1999;
Gershon et al., 1985;
Jacobson and Wojcieszyn,
1984), and values for K_p were found to range
from roughly 0.1 to 10 s^-1 (see
Haugh and Lauffenburger, 1998;
Kholodenko et al., 2000a;
Zhao and Zhang, 2001, and
references therein). With K_p values of 0.25 or 1
s^-1, the distance from the plasma membrane, at which the
phosphorylation signal is attenuated by a factor of 10, is equal to 6.8 or 2.6μ
m, respectively. Importantly, the exponential character of the rapid
decrease in the phosphorylation signal with the distance from the cell
membrane, d=L(1–x), does not depend on the
specific activity and kinetics of the membrane kinase, provided that the
phosphatase is far from saturation.

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Fig.2.

Decline in the phospho-protein concentration with distance from the cell
membrane at different values of the parameter α. The parameter α
is determined by the ratio of the characteristic times of diffusion and the
phosphatase reaction
(α²=K_p×L²/D,
where L is the cell radius,
K_p=V_max,p/K_m,p is
the observed first-order rate constant of the phosphatase and D is
the protein diffusion coefficient). The decline,
p(x)/p(1), is calculated as the ratio of the
concentrations of the phosphorylated form at distance xL from the
cell center and at the plasma membrane, where x=1. Reproduced with
permission from Kholodenko
(2002).

This analysis suggests that unless there is an additional mechanism
(besides slow protein diffusion) for signal propagation through the MAPK
cascade, the levels of activated MEK and ERK will drop precipitously in the
cell interior. At distances larger than several μm from the plasma
membrane, the phosphorylation signal should decrease to subthreshold levels,
provided that the cytosolic phosphatase activity is sufficiently high. Since
eukaryotic cell radii vary from 5 to 50 μm, we conclude that propagating a
message from the plasma membrane to the nucleus can require an additional
vehicle besides diffusion in the cytoplasm.

A novel role of endocytosis in activation of MAPK signaling

Upon ligand binding and activation, many GPCRs and RTKs internalize
via clathrin-coated pits. For instance, in hepatocytes over 50% of
phosphorylated EGFR is transferred to early endosomes during the first 10 min
after EGF stimulation (Di Guglielmo et
al., 1994). Internalization takes receptor–ligand complexes
and other signaling proteins from the plasma membrane and brings them inside
the cell. Molecules that were not recycled back to the cell membrane are
degraded in lysosomes. Although internalized GPCRs continuously recycle back
to the cell surface after dephosphorylation in endosomes, a significant
proportion of receptors are located internally
(Koenig and Edwardson, 1997).
Therefore, traditionally, clathrin-mediated endocytosis has been implicated in
downregulation of signaling by plasma membrane receptors. A novel role of
endocytosis in `turning on' activation of the ERK cascade by cell surface
receptors was first reported for the EGF receptor
(Vieira et al., 1996). A
conditional defect in endocytosis can be imposed by the regulated expression
of a mutant form of dynamin (Dyn1-K44A), a GTPase that is required for
clathrin-coated vesicle formation. In HeLa cells, this expression led to a
marked decrease in EGF-induced ERK activation, whereas Shc phosphorylation was
enhanced in endocytosis-defective cells. Subsequent studies have demonstrated
that both GPCR- and EGFR-mediated activation of ERK is sensitive to various
distinct inhibitors of clathrin-mediated endocytosis, including
monodansylcadaverine, depletion of intracellular K⁺ or cholesterol,
cytochalasin D and a mutant dynamin
(Ceresa et al., 1998;
Daaka et al., 1998;
Kranenburg et al., 1999;
Maudsley et al., 2000;
Rizzo et al., 2001;
Vieira et al., 1996).
Therefore, a possible mechanism of control over signal transduction may engage
receptor endocytosis (Clague and Urbe,
2001; Di Fiore and De Camilli,
2001; Haugh et al.,
1999). However, whereas experimental evidence points to an
essential role of receptor endocytosis in the activation of MAPK cascades, the
reason for the involvement of the endocytic machinery remains poorly
understood (Ceresa and Schmid,
2000; Kranenburg et al.,
1999; Pierce et al.,
2000). Interestingly, in some cellular systems endocytosis was not
required to activate ERK (for a review, see
Leof, 2000).

The relationship between receptor internalization and ERK activation allows
us to suggest that trafficking of signaling intermediates within endocytic
vesicles may be an efficient way of propagating the signal
(Kholodenko, 2002). Indeed, it
was reported that the engagement of the endocytic machinery is essential for
ERK activation by MEK, but not for activation of Ras
(Kranenburg et al., 1999).
Interestingly, the data on the subcellular distribution of activated MEK
demonstrated that biphosphorylated MEK is detectable only at the plasma
membrane and in intracellular vesicles, whereas the total MEK pool is
cytosolic (Kranenburg et al.,
1999). Endocytic trafficking of active MEK can help to avoid the
formation of steep spatial gradients of phosphorylated MEK and ERK, since this
mechanism overcomes the spatial separation of kinases and phosphatases within
the MAPK cascade. Therefore, the endocytosis of phosphorylated MEK (or a
protein complex containing activated MEK) rather than of activated receptors
appears to be critical for ERK activation.

Scaffolding, cytoplasmic streaming and active transport as mechanisms
facilitating signal propagation

Other mechanisms besides endocytosis can help to spread the phosphorylation
signals from the plasma membrane further into the cell by preventing the
formation of steep spatial gradients of phosphorylated ERK. For instance,
cytoplasmic streaming, i.e. solvent fluxes brought about by the movement of
cytoplasmic organelles along actin cables, can contribute to intracellular
transport of activated MAPK kinases
(Agutter et al., 1995). Recent
evidence indicates that the MAPK cascade components can bind to scaffolding
proteins, e.g. MP1 and JIP-1 in mammalian cells (for a review, see
Garrington and Johnson, 1999).
Dephosphorylation of the MAP kinases in scaffold complexes may be decreased or
even precluded because of sterical obstructions, as was suggested by Levchenko
et al. (2000).

Scaffolding may also help to deliver an entire signaling complex containing
the MAP kinases to endocytic vesicles. Novel mechanisms have been discovered
that link GPCRs to MAPK activation through use of β-arrestin as a
scaffold for the ERK and JNK cascades
(Miller and Lefkowitz, 2001;
Pierce et al., 2001). Besides
its role in GPCR desensitization, β-arrestin has been shown to promote
the targeting of the receptor to clathrin-coated pits. As β-arrestins can
also recruit and activate Src, it is likely that the entire ERK and JNK
cascades can be activated and recruited for clathrin-mediated
internalization.

Recent data suggest that molecular motors can be involved in transport of
signaling complexes. In fact, in nerve cells, a cargo for the molecular motor
kinesin has been identified as scaffolding proteins for the JNK pathway, known
as JIPs (Verhey and Rapoport,
2001). Endocytic vesicles and signaling complexes, loaded on
molecular motors, can be transported along microtubules to remote cellular
locations.

Retrograde transport of signaling complexes

One of the most interesting puzzles facing neurobiologists is concerned
with unraveling the molecular mechanisms used by neurons to transfer signals
over long distances. The survival and function of developing neurons depends
on growth factors, the neurotrophins, such as nerve growth factor (NGF) and
its receptor, TrkA. NGF, which is made by peripheral tissues, binds to TrkA
receptors on distal axons, located up to 1 m away from the neuronal soma. How
does the survival signal propagate over a remarkably long distance to the cell
body in a physiologically relevant span of time? Diffusion is ruled out as a
mechanism of the retrograde signaling, since it would be prohibitively slow.
Indeed, we have seen above that diffusion may be insufficient even for
spreading the phosphorylation signals within the cell body from the plasma
membrane to the nucleus.

Several models were suggested to explain the retrograde transduction of
neuronal survival signals (for a review, see
Ginty and Segal, 2002).
According to a widely accepted model, shortly after NGF binding to TrkA at
nerve terminals, the NGF-TrkA complexes are internalized into endosomes by
means of clathrin-mediated endocytosis. Signaling endosomes containing
activated TrkA with associated ligand are retrogradely transported to the cell
bodies. Data on blocking the NGF-TrkA transport by the dynein ATPase inhibitor
(EHNA) suggest that vesicular transport can be carried out by molecular motors
(Reynolds et al., 1998). In
fact, Trk neurotrophin receptors were found to bind directly to a dynein light
chain (Yano et al., 2001). The
retrograde axonal transport was also shown to be inhibited by the
phosphatidylinositol 3-kinase (PI3K) inhibitor wortmannin, by cytochalasin D,
a disruptor of actin filaments, and by the microtubule inhibitor colchicine
(Reynolds et al., 1998). Taken
together, these studies support a model where the retrograde transport of the
NGF-TrkA complexes along axon structural elements (e.g. microtubules) can
provide survival signals to neurons.

Ligand-independent waves of receptor activation

Cells have developed multiple mechanisms to overcome the problem of
long-distance signaling. It was recently discovered that survival signals
might not depend on retrograde transport of NGF
(MacInnis and Campenot, 2002).
Application of NGF, which was covalently cross-linked to beads to prevent
internalization, showed that survival signals were able to reach the cell
bodies unaccompanied by the ligand that initiated TrkA activation. One
possibility is that activated TrkA can be internalized and retrogradely
transported without NGF, implying that the active state of TrkA can be
maintained in the absence of the ligand. Another possibility is that
downstream TrkA targets, such as PI3K or Akt, can mediate the retrograde
signal. An intriguing possibility is that activation of TrkA receptors in
nerve terminals brings about an NGF-independent wave of TrkA activation, which
rapidly propagates through the neuronal axon
(Ginty and Segal, 2002).
Indeed, ligand-independent waves of receptor (EGFR) activation, emanated from
a point EGF source, were recently reported
(Verveer et al., 2000).

How can waves of receptor activation emerge? A possible scenario is that an
activated receptor, monomer or dimer, is capable of transphosphorylating and
activating an inactive receptor molecule upon diffusive encounter, potentially
resulting in lateral spread of receptor activation. In fact, spontaneous
activation and signaling by overexpressed EGFR has been reported recently
(Thomas et al., 2003). Let us
sketch the functional implications of this local amplification assumption for
the dynamics of the receptor system on the cell surface. For simplicity, a
one-dimensional diffusion is analyzed, and only monomer or dimer forms of the
receptor are taken into account (the model can be generalized to include
monomer-dimer association/dissociation).

Given that the total receptor concentration (or surface density) is
c and the concentration of activated receptors at a distance
x from a ligand source is a(x), the amount of newly
activated receptors per unit time and volume/area will be
k×a(x)×[c–a(x)],
where the constant k is proportional to the probability of
phosphorylation per diffusive encounter. Active receptors are dephosphorylated
by the phosphatases at the rate v_p(a). Under
these assumptions, the spatial propagation of activated receptor (from a
source at x=0) is described by the following equation:
4
where D is the diffusion coefficient. When the phosphatase activity
is low, Equation 4 reduces to the Fisher-like equation, the first partial
differential equation known to generate traveling waves
(Murray, 1993). A traveling
wave propagates without change of shape, i.e. the shape and speed of
propagation of the front is constant over time. From Equation 4, it follows
that an increase in total receptor amount (c) and a decrease in the
phosphatase activity (v_p) may trigger global RTK
activation. The situation in which a cell can be `switched on' by a localized
stimulus is in contrast to the current paradigm of `restricted' signaling by
RTKs activated by local growth factor stimulation reported recently for EGF
signaling in COS cells (Sawano et al.,
2002). Remarkably, overexpression of EGF receptors in these same
cells resulted in global EGFR activation over the entire cell surface
following a localized stimulation with EGF
(Sawano et al., 2002). We
conclude that an initial localized stimulation can be responsible for
triggering global RTK activation in cells. Such a mechanism may have
implications for the pathogenesis of cancer, where RTKs are overexpressed due
to mutations (Thomas et al.,
2003). Studies of the dependence of traveling wave solutions on
molecular mechanisms of RTK activation and kinetic parameters may help
facilitate our understanding of crucial control points in tumor
development.

Traveling waves of activated protein kinases

Another possible scenario of how a survival signal can spread over the axon
includes traveling waves that may arise in a bistable protein kinase cascade.
Bistability is a common theme in cell signaling cascades that contain a
positive feedback loop, or a double-negative feedback loop
(Bhalla and Iyengar, 1999;
Ferrell and Machleder, 1998;
Gardner et al., 2000; Thron,
1997,
1999;
Tyson and Novak, 2001). A
bistable protein kinase cascade can switch between two different stable
states, one corresponding to a low and another to a high activity, but cannot
exist in an intermediate unstable state. When the signal strength is below a
given threshold, a kinase cascade, such as the Mos-MEK-p42 MAPK cascade and
the JNK cascade in Xenopus oocytes
(Bagowski and Ferrell, 2001;
Ferrell, 1999), and the ERK
cascade in mouse NIH-3T3 cells (Bhalla et
al., 2002), remains in a low activity state. An increase in the
signal above the threshold switches the cascade to a high activity state.
Importantly, the cascade will remain in this high activity state even when the
initial signal decreases to subthreshold values.

It was proposed that cells utilize bistable signaling circuits that would
enable them to be capable of `all-or-none' switching and to `remember' a
transient differentiation stimulus long after the stimulus was removed
(Ferrell, 2002). Here we
suggest that yet another role for bistable protein kinase cascades may be to
support traveling waves of activated phospho-proteins, propagating signals to
remote cellular locations. Bistability produces local amplification of the
spreading signal, and the combination of local amplification and diffusion may
generate traveling waves. In fact, traveling waves in bistable systems have
been extensively studied in physics, chemistry and biology
(Castiglione et al., 2002;
Christoph et al., 1999;
Keener and Sneyd, 1998;
Shvartsman et al., 2002;
Zhabotinsky and Zaikin, 1973).
MAPK cascades and the PI3K/PDK1/Akt cascade coupled with the PIP3 synthesis
pathway might be candidates for bistable protein kinase cascades that are
capable of propagating traveling waves.

Importantly, all of the models of long-range signaling considered are not
mutually exclusive. We hypothesize that multiple mechanisms of information
transfer have evolved in neurons to transmit signals over long distances.
Future experimental work will show if waves of activated kinases emerge in
cells.