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First published online 1 February 2006
doi: 10.1242/dev.02254
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Department of Chemical Engineering and the Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94720-1462, USA.
* Author for correspondence (e-mail: schaffer{at}cchem.berkeley.edu)
Accepted 5 December 2005
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SUMMARY |
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 TOP SUMMARY INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key words: Morphogen, Sonic hedgehog, Diffusion, Transport, Modeling
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INTRODUCTION |
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TOPSUMMARYINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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; Turing,
1952). The hypothesis states that chemical signals, termed
`morphogens', are secreted from signaling centers, and that the resulting
static extracellular morphogen concentration gradient emanating from the
center spatially organizes and patterns tissue architecture. That is, rapid
morphogen transport creates a concentration gradient invariant over the time
window of tissue patterning (i.e. at steady state). Sonic hedgehog (Shh),
which forms a concentration gradient to pattern the limb bud
(Riddle et al., 1993),
midbrain (Britto et al., 2002),
forebrain (Ericson et al.,
1995) and spinal cord (Roelink
et al., 1995) during vertebrate development, is ostensibly a
canonical example of the morphogen hypothesis. However, very recent studies
suggest that Shh concentration gradient dynamics play a crucial role in tissue
patterning. Both the time of exposure of a cell to a given Shh concentration
(Ahn and Joyner, 2004;
Harfe et al., 2004;
Kohtz et al., 1998;
Park et al., 2004;
Wolff et al., 2003;
Yang et al., 1997) and the
timing of Shh source secretion (Ericson et
al., 1996) are crucial determinants of Shh tissue patterning. The
classical morphogen hypothesis does not account for such dynamics in gradient
formation and cellular response.
Beyond passive diffusion, morphogen systems can have a number of
`accessory' mechanisms that modulate ligand transport. Specifically, each
transport mechanism potentially modifies not only the steady state
concentration gradient, but also the rate of morphogen transport at various
times in the patterning process. For example, studies in Drosophila
have identified numerous genes essential for actively transporting morphogens
upon their release from secreting cells, and mutating such transporters
disrupts tissue patterning (Chen et al.,
2004; Han et al.,
2004; Takei et al.,
2004). Also, high affinity interactions of morphogens with cell
surface (Chuang and McMahon,
1999) and extracellular matrix (ECM) components
(The et al., 1999) serve the
putative roles of depleting or immobilizing extracellular-diffusing morphogens
to limit long-range signaling. Any of these mechanisms can affect the temporal
evolution of concentration gradients in developing tissue, which is overlooked
by the focus of the morphogen hypothesis on the steady state concentration
gradient.
To investigate temporal effects of transport and signaling, we model Shh
regulation of dorsoventral spinal cord patterning in chick embryonic
development stages 10-26 [
33-116 hours after egg laying
(Ricklefs and Starck, 1998)].
Shh, secreted from the floorplate, diffuses into the neural tube
(Roelink et al., 1995), and,
as its concentration decreases within the tissue from approximately 15 nM at
the floorplate to 0.5 nM at dorsal edge of the neural tube, target cells
switch at threshold values from mature ventral to dorsal phenotypes [e.g. from
V3
MNV2V1 in Fig.
1A, as has been previously reviewed
(Persson et al., 2002)]. Our
model begins after the neural fold appears and essentially as the neural tube
closes at stage 10, when Shh is first secreted from the floorplate. We
subsequently track the cell fate switch between V3 interneurons (V3) and
motoneurons (MN) that occurs through stage 26.
The structure of Shh, as well as its various interacting proteins, has
complicated a simple understanding of how its transport establishes a gradient
during this process. Shh is covalently modified by hydrophobic moieties,
including a C-terminal cholesterol and a N-terminal palmitic acid
(Pepinsky et al., 1998;
Porter et al., 1996), which
may anchor the ligand to cell membranes and thereby significantly reduce its
diffusivity. However, Shh is still capable of signaling at a large distance,
up to 20 cell diameters, away from its source. In addition, the Shh receptor
Patched (Ptc) is upregulated by Shh signaling, and its subsequent binding and
receptor-mediated internalization of Shh depletes the ligand from the
extracellular space (Chen and Struhl,
1996; Marigo and Tabin,
1996). Furthermore, Shh and its Drosophila homolog
Hedgehog can form multimers, and the transmembrane protein Dispatched (Dis) is
likely to be involved in regulating their assembly and intercellular transport
(Kawakami et al., 2002).
Moreover, a membrane glycoprotein, Hedgehog-interacting protein (Hip), binds
Shh with high affinity to modulate its signaling activity
(Chuang and McMahon, 1999).
ECM proteins also regulate Shh transport, as high-affinity binding of Shh to
vitronectin in the neural tube has been suggested to aid in the proper
presentation of Shh to differentiating motoneurons
(Pons and Marti, 2000).
Finally, the effective transport of Drosophila Hedgehog depends upon
the activity of heparan sulfate proteoglycans (HSPG)
(Bornemann et al., 2004;
Takei et al., 2004;
The et al., 1999), and Shh has
also been shown to bind HSPG (Rubin et
al., 2002). The individual and synergistic contributions of each
of these highly complex elements to the ability of Shh to pattern tissue are
unclear. Shh transport via diffusion was previously modeled in the vertebrate
limb bud, using a simple signal transduction mechanism without consideration
of these accessory transport mechanisms
(Dillon et al., 2003).
Therefore, to complement, synthesize, and guide experimental work, we have
applied a systems biology analysis to explore the effects of diffusion,
receptor-ligand dynamics and gene regulation dynamics on Shh gradient
formation and tissue patterning.
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) to analyze
Shh patterning of the developing spinal cord and find that the concentration
gradient initially established by diffusion can be modified by several long
timescale mechanisms, including morphogen binding to ECM and gene expression.
Modeling results are able to reproduce the experimental profiles and clarify
the potential roles of six modular mechanisms involved in Shh gradient
formation and cellular signaling (Fig.
1B). This investigation suggests that different components can be
assembled in a modular fashion to dynamically pattern a morphogen gradient
according to the needs of specific tissues. |
MATERIALS AND METHODS |
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TOPSUMMARYINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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). The
diffusion coefficient was modified to account for tortuosity
(Lander et al., 2002). A Shh
molecule moving through the continuous extracellular space of the mesh
(Fig. 1A) can smoothly diffuse
through the extracellular regions in cubes A, B and then C. By contrast, all
cell surface and intracellular species (e.g. receptors and receptor-ligand
complexes) are completely restricted within their cellular volume compartment,
which is surrounded by a small 10 nm plasma membrane element/barrier.
Developmental time window
At the ventral-most region of the chick neural tube, high level Shh
expression is initiated exclusively in the floorplate
(Fig. 1A) during stages 10-12
(34 hours after egg laying). At this time (t=0), all cells in
the tube have the same initial gene expression profile. As time progresses,
Shh diffuses dorsally from its floorplate source through the mesh and binds to
receptors or other components, and high Shh signal levels induce a cell
phenotype switch (Lai et al.,
2004). The position of the mature phenotypes seen in wild-type
embryos after stages 26 (>80 hours after laying) is shown
(Fig. 1A). Recent work in mouse
embryos indicates that early Shh secretion from the notochord may diffuse far
into the neural tube to affect MN commitment
(Jeong and McMahon, 2005), and
such scenarios in chick embryos could readily be incorporated by adding extra
elements for the notochord cells (at x<0), with appropriate Shh
secretion dynamics.
Mathematical formulation of Shh transport by diffusion and receptor kinetics
The Shh signaling network is represented as a set of differential equations
that track the rates of change in the concentrations of network constituents,
and whose individual terms represent rates of diffusion, protein synthesis and
degradation (Fig. 1B, Fig. 2A). At the single cell
level, we build upon the Shh signaling network derived by previously
(Lai et al., 2004) to include
cellular internalization effects (see Figs S3, S4 in the supplementary
material). As Shh is increased above a threshold concentration, it stimulates
Gli production to the point where Gli positively feeds back upon its own
expression and rapidly switches the state of the network to `on'
(Fig. 2B). The activities of
Gli2, which overlap with those of both Gli1 and Gli3, are highly context
dependent, and its molecular interactions in the neural tube progenitor cells
require further characterization (Bai et
al., 2004; Ruiz i Altaba,
1999). As a result, we have effectively parsed the effects of Gli2
into two types: either a pure transcriptional activator, the `Gli1' type, or a
transcription factor of both repressor and activator functions, the `Gli3'
type. Thus, in the model, the effects of Gli2 are effectively lumped into a
Gli1 term and a Gli3 term. We report the Gli1 concentration as the important
system output, as the on/off gli1 expression interface demarcates the
V3/MN boundary.
Parameters and computational techniques
Kinetic, diffusive and binding parameter values were either directly taken
from the literature or estimated based upon analogous biological systems
(Fig. 2 legend, see also Table
S1 in the supplementary material). Parameter estimates were chosen to meet the
three following experimental observations: switching `on' of homeodomain
nkx2.2 (which serves as the gli1 domain marker in the case
of the model) expression at a 3 nM Shh threshold at steady state
(Ericson et al., 1995;
Ericson et al., 1997b);
50-hour kinetic timescale of Shh secretion from the floorplate [based
upon timescales for MN specification from figure 3D in Ericson et al.
(Ericson et al., 1997b)]; and
a Nkx2.2 protein fluorescence intensity spatial profile in a wild-type chick
embryo [see figure 3B in Ericson et al.
(Ericson et al., 1997b)]. To
satisfy the last criterion, because the Shh secretion rate from the floorplate
has not been quantitatively determined, we chose it such that our pattern
matched the Nkx2.2 switching interface seen at 70 µm from the floorplate
(Ericson et al., 1997b). For
the ventral-most cells (close to x=0), floorplate induction, marked
by an increase in hnf3ß, occurs above a 10 nM Shh concentration
(Briscoe et al., 2000). Such
floorplate induction, probably due to additional downstream targets of
gli1 or other signals not included in this model, accounts for the
decrease in nkx2.2 expression seen experimentally in and near the
floorplate (Fig. 3B). For each
parameter in the core-signaling pathway, we conducted sensitivity analysis for
parameter values over four orders of magnitude to observe whether the single
cell response to Shh varied (Fig.
2C). Model behavior was investigated for parameter values that
changed the 3 nM Shh switching threshold at steady state from 1 to 10 nM and
pattern evolution time from 30 to 150 hours Shh secretion, and all conclusions
and trends discussed below remained qualitatively the same.
The set of equations in Fig. 2A are presented in dimensional form. However, relationships between groups of variables can be intuitively easier to interpret than individual parameters. In addition, grouping variables reduces the number of independent parameters that are necessary to describe the model. As a result, the following types of variables were non-dimensionalized by the corresponding parameters: concentrations by KGli3, space by 1 cm, and time by 1/kdeg. The corresponding non-dimensional equations are shown in Figs S3, S4 (in the supplementary material) and were coded into the FEMLAB software.
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RESULTS |
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TOPSUMMARYINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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;
Jessell, 2000), among the
earliest of which are the markers Nkx2.2 in the V3 region and Pax6 in the
remainder of the tube. In this work, we focus on the ventral-most binary cell
fate switch delineating the V3/MN boundary, which results in the Nkx2.2/Pax6
histological demarcation. Homeodomain protein expression patterns are also
regulated by BMP, FGF and retinoid signals (reviewed by
Jessell, 2000), events that
can be incorporated into the model in future work to evolve the model behavior
from a binary switch into a ladder of cell fates. Given that the V3 domain and
Nkx2.2 expression are entirely lost in mutants with compromised Shh signaling
[e.g. Shh-/- (Litingtung and
Chiang, 2000), Smo-/-
(Wijgerde et al., 2002),
Shh-/-/Gli3-/- (Bai
et al., 2004; Litingtung and
Chiang, 2000), Gli3-/-/Smo-/-
(Wijgerde et al., 2002), and
Gli1-/-/Gli2-/-
(Park et al., 2000) mice], we
use Nkx2.2 purely as a robust marker of cells where Shh signaling is active,
and where Gli is presumably expressed. Also, because Nkx2.2 is rapidly
upregulated following Shh signaling, we assume that it can be used as a marker
of Shh signaling activity, without requiring knowledge of the mechanistic and
molecular interactions that connect Gli to Nkx2.2.
|
). However,
we found that the Shh signaling network also undergoes robust switching
behavior before reaching steady state, particularly within the 3-day time
window for V3/MN pattern completion in chick embryos
(Fig. 2D). In contrast to the
canonical morphogen hypothesis, the tissue may not need to wait for the
morphogen concentration to reach a steady state in order to undergo
patterning. That is, as soon as morphogen signaling increases the expression
of a target transcription factor above a key threshold value, it can induce a
cell phenotype switch. Quantitative results from other systems indicate that
as little as a twofold increase in the concentration of a transcription factor
can switch cell fate (Niwa et al.,
2000; Shimizu and Gurdon,
1999), indicating that it is possible or even likely that cells
begin to interpret the Shh gradient information before the gradient reaches
steady state. In support of this hypothesis, numerous recent studies have
shown that not just the level but also the duration of Shh exposure is an
important determinant of cell response (Ahn
and Joyner, 2004; Harfe et
al., 2004; Kohtz et al.,
1998; Park et al.,
2004; Wolff et al.,
2003; Yang et al.,
1997). The model supports these studies. If we conservatively
assume that a cell can switch phenotype once it achieves a sevenfold increase
in Gli1 concentration from its initial basal concentration, the model predicts
that a cell exposed to different Shh concentrations will switch fate after
different durations (Fig. 2D,
results were qualitatively similar for other threshold increases such as
threefold to tenfold, data not shown). In reality, as the gradient evolves,
cells in the neural tube will be exposed to a complex sequence of Shh
concentrations that will drive cell fate changes (i.e. the V3/MN boundary) at
different times after exposure, and probably before Shh reaches a steady state
gradient. For all subsequent analysis, we analyze the Shh gradient at 83 hours, the time at which the neural tube has been experimentally shown to have a mature V3/MN demarcation, but before the morphogen gradient has achieved steady state. Note that a higher Shh concentration threshold must be present to switch cell fate within early time windows than if the tissue were allowed to proceed to steady state (5.7 nM for a switch at 43 hours, 4.5 nM for 83 hours, and 3.5 nM for steady state, respectively, in Fig. 2D). Accessory transport mechanisms will modulate cell phenotype patterning by dynamically varying the Shh concentration a cell is exposed to during this developmental time window.
Spatiotemporal evolution of the Shh signal
To gain comprehensive spatial as well as temporal insights into how the Shh
signal propagates in the neural tube, we dynamically tracked the
concentrations of Shh network constituents in a multicellular, spatial model.
For the core Shh signaling pathway, which includes intracellular signal
transduction and ligand internalization (within the dashed line in
Fig. 1B), the simulation
correctly reproduced a wild-type tissue pattern with distinct regions of
gli1 `on' and `off' cells (Fig.
2; see also Movies 1-8 in the supplementary material).
During this patterning process, extracellular Shh rapidly built to a high
concentration within 5 hours, but then fell to approach steady state levels at
60-80 hours (Fig. 2E). Note
that Shh rapidly (t<5 hours) rose well above the static levels
found to induce a MN to V3 phenotype switch [3 nM
(Ericson et al., 1997b)].
Because protein expression from Shh target genes does not build appreciably
within this relatively short timescale, receptor-ligand internalization and
passive diffusion alone governed the early evolution of the Shh concentration
profile. Shh levels then more rapidly declined as Ptc, a direct Shh
transcriptional target, increased in the ventral-most portions of the embryo
and began to mediate Shh degradation via receptor-mediated endocytosis
(Fig. 2F). In contrast to the
more continuous Shh profile that is smoothened by transport, Ptc profiles
exhibited discrete on/off regions due to induced ptc expression above
the Shh switching threshold (Fig.
2D,E). Near the floorplate, free Ptc initially decreased as
extracellular Shh levels rapidly elevated and bound free Ptc. The resulting
Ptc-Shh complexes were rapidly internalized but degraded more slowly, so that
the predominant form of Ptc was an internal, complexed form
(Fig. 2G), consistent with
previous observations (Incardona et al.,
2002; Incardona et al.,
2000). After 20 hours, ptc was highly upregulated due to
high Shh signaling near the floorplate.
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). In this study, embryos at stages 10-12 were
transfected on one side of the neural tube and then imaged at stages 20-24
(t=39-63 hours). To simulate the transfection in
Fig. 3A, cells between 40-60
µm and 80-110 µm were supplied with a signaling-defective Ptc by making
Smo activity insensitive to Ptc in the differential equations governing
intracellular signaling [i.e. by setting the ratio
(KGli3/Kptc)
in Fig. S2A in the
supplementary material]. Briscoe et al. found that transfected cells (green in
Fig. 3A) lacked nkx2.2
expression (Briscoe et al.,
2001), whereas the contralateral, untransfected side exhibited the
previously described wild-type pattern
(Ericson et al., 1997b). The
model captured the effects of the mutant Ptc on pattern formation, as the Shh
signaling range increased in both the experimental and modeling results for
the transfected side (transfected range 90 µm>70 µm for
wild type in Fig. 3B). The
transfected cells cannot sense Shh signal, and therefore do not upregulate
ptc, which on the untransfected side serves as a barrier to Shh
transport.
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Internalization via Hedgehog interacting protein causes ventral patterning shifts
Hip is a transmembrane glycoprotein that functions as an inducible
antagonist of Shh signaling, because it is a non-signaling transcriptional
target of Shh signaling that binds and sequesters Shh
(Chuang and McMahon, 1999;
Jeong and McMahon, 2005). We
simulated Gli upregulation of Hip and allowed it to bind Shh reversibly, as
well as to undergo internalization to accelerate Shh degradation
(Fig. 1B, II). Ventral shifts
in the wild-type pattern occur when Hip is added to the model
(Fig. 4). By sequestering
extracellular Shh, Hip acts as a `shunt' to remove free Shh from the tissue.
Therefore, as the initial (t=0) Hip concentration
(Fig. 4A) or the maximal Hip
synthesis rate (Fig. 4B) was
increased, the extracellular Shh concentration progressively decreased and
shifted the interface ventrally, consistent with recent experimental results
(Stamataki et al., 2005).
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Shh aggregation via Dispatched effectively modifies Shh signal diffusivity
The transmembrane protein Dis interacts with cholesterol-modified Hh
(Kawakami et al., 2002) and
has been hypothesized to be involved in packaging lipid-modified Shh into
clusters (Zeng et al., 2001).
Dis is incorporated in our model as a catalyst for complexing membrane-bound
Shh into freely diffusing aggregates [six Shh units large
(Zeng et al., 2001)], which
can then more readily diffuse dorsally and induce signaling
(Fig. 1B, III). To mimic
membrane-bound Shh, we reduced the diffusivity of monomeric Shh to
10-10 cm2/s and observed the effects of Dis
concentration and aggregate diffusivity on patterning. Similar to the Shh
diffusivity results, varying both of these parameters yielded a biphasic
response (Fig. 6A,B). At low
Dis concentration (10-4-10-1 nM), a sufficient aggregate
of high diffusivity was formed to signal deeper into the tube. However, at
high Dis concentration (>101 nM), most Shh was absorbed into the
hexameric form. The resulting net decrease in the number of signaling
molecules therefore counteracted the benefits of the enhanced diffusion of
these aggregates and shifted the interface ventrally. In addition, the
biphasic response to Dis concentration
(Fig. 6A) and aggregate
diffusivity (Fig. 6B) occurs
for the same reasons as for monomeric Shh diffusivity
(Fig. 5).
Extracellular matrix effectively modifies Shh signal diffusivity
As Shh diffuses, it can encounter various components of the ECM. Because
such interactions have been proposed to modify the neural tube pattern, we
analyzed the effects of reversible Shh binding to one constitutively expressed
ECM component, HSPG [mechanism IV in Fig.
1B (Gould et al.,
1995)]. A biphasic response was observed as a function of HSPG
extracellular concentration (Fig.
7A,B). High HSPG concentrations act as a high-capacity morphogen
`sponge' that prevents free Shh from building up to levels sufficiently high
to effectively signal. By contrast, at very low HSPG concentrations, Shh
diffusion is unhindered, and the morphogen rapidly spreads to large distances,
leading to a dilution of the factor to levels too low to effectively signal
(as in Fig. 5). However, at
intermediate ranges of HSPG, this ECM component can concentrate Shh within a
relatively broad region near its source, leading to a dorsal shift in the
interface. Adding immobilized HSPG to the system [5-30 µM] therefore
functions analogously to reduce Shh diffusivity and, paradoxically, increases
the range of effective Shh signaling by hindering its transport. However, for
an estimated Shh affinity for HSPG of 350 nM
(Loo et al., 2001), relatively
high levels of HSPG are required to modify the pattern.
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DISCUSSION |
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TOPSUMMARYINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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3-day developmental window (stages 10-26)
(Ericson et al., 1996;
Ericson et al., 1997b;
Roelink et al., 1995).
With the core-signaling pathway (dashed circle in
Fig. 1B), the simulation
predicts a highly dynamic profile for both intracellular and extracellular Shh
network constituents. Full knowledge of such profiles can help to both
interpret and guide experimentation. Initially, Shh levels rapidly escalate
and extend deep into the tissue for t<20 hours, followed by
substantial reductions at longer times
(Fig. 2E). Therefore,
experimental analysis of the Shh concentration profile only at later times
could miss the early Shh build-up and thereby misinterpret the ligand
signaling range. The steady state Shh profile (approximately shown in
Fig. 2E for t>60
hrs) has a rapid decay close to the morphogen source and a slow decay further
away from the source, consistent with previous theoretical studies of steady
state morphogen profiles (Eldar et al.,
2003). Note that early in our patterning results (0-24 hours),
there is a smooth Gli1, Ptc, Gli3R and Gli3A gradient
(Fig. 2H,F, and Movies 1-8 in
the supplementary material), but this profile begins to sharpen into a
discrete interface at 72 hours (stage 16-26). Quantitative assays of the
expression of Gli1, Gli3 or Ptc at a broad range of times from stage 12
through 26 can further test directly whether our framework accurately predicts
their expression patterns, and many experimental stains for Gli or Ptc
expression at times before steady-state are consistent with smooth
concentration gradients in the MN domain
(Lei et al., 2004;
Stamataki et al., 2005). In
particular, snapshots of the Ptc profile in the neural tube indicate a highly
dynamic, initially graded profile consistent with our results (see Fig. S5 in
the supplementary material), and at later times processes not included in the
model (e.g. Shh-independent signals influencing the relatively uncharacterized
Ptc promoter) are likely to modulate ptc expression, especially in
the more dorsal sections. Recent work supports a role for a graded Gli3
profile in early patterning (Stamataki et
al., 2005), although several experimental details preclude a
direct, quantitative comparison between these results and our simulations. In
particular, endogenous Gli1, Gli2 or Gli3 expression is not directly measured,
and exogenously introduced Gli3 is expressed at levels that vary over time.
However, this important work provides strong evidence for the role of gene
expression dynamics in tissue patterning.
The mechanism by which a single cell interprets a morphogen gradient can
occur at the transcription factor level
(Niwa et al., 2000;
Shimizu and Gurdon, 1999).
Quantitative differences in Gli have not been experimentally tested for V3/MN
patterning in the vertebrate neural tube; however, given the Shh threshold and
kinetic data from chick V3/MN patterning used for our parameter estimates (see
Materials and methods), the model predicts that V3 cell fate specification
could be established at a sevenfold increase in Gli1 from its initial basal
concentration [i.e. a Gli1 concentration at the time of V3 specification of
>11 nM (or 7xGli1 concentration at t=0)]. We tested model
behavior for V3 cell fate specification occurring at a range of thresholds
from three- to tenfold Gli (4.9-16.3 nM) increases, and all of our conclusions
remain qualitatively the same (data not shown). The sevenfold increase above
basal/initial Gli expression levels corresponds to a two- to threefold Gli1
difference across the V3/MN interface position at approximately t=50
hours (Fig. 2H). Therefore, the
model behavior is consistent with the twofold increase in Oct3/Oct4 expression
in embryonic stem cells (Niwa et al.,
2000) and the threefold increase in SMAD complexes in a
Xenopus blastula cell (Shimizu
and Gurdon, 1999) that have been found to trigger cell fate
switching. It is notable that certain borderline cells
(Fig. 2H) experience transient
two- or threefold increases in Gli1, and a deeper investigation of the
induction kinetics for the next generations of transcription factors
downstream of Gli may reveal whether these cells transiently express MN
markers (Ericson et al., 1996)
or permanently commit to an MN fate. As we have previously discussed in a
single cell model, stochastic effects, which can in the future be incorporated
into this spatial model, may account for the transient co-expression of
markers of different cell fates (Lai et
al., 2004). Finally, future incorporation of more detailed
mechanisms of interaction between the transcription factors Gli1-Gli3, Nkx2.2,
Pax6 and others, as these interactions are further elucidated, would help
update the model to match or predict future patterning results.
Intracellular degradation can shunt the Shh signal
Vertebrate Shh patterning can be further complicated by the fact that Ptc
is not the only receptor that mediates ligand degradation. Like Ptc, Hip also
binds Shh with high affinity and is a Shh transcriptional target, yet Hip
mediates Shh endocytosis and degradation without transducing a signal. A shunt
in an electrical circuit is an alternate pathway that diverts current away
from the remainder of the circuit, analogous to the receptor-mediated
endocytosis and ensuing degradation that divert a morphogen from signaling.
Intracellular shunting by Ptc and Hip, as seen in the modeling results
(Fig. 4A,B), attenuates Shh
signaling, consistent with several studies in various organisms
(Chuang and McMahon, 1999;
Jeong and McMahon, 2005).
Negative-feedback loops, which establish shunts via molecules like Hip, limit
Shh penetration and can `stabilize' patterning, a mechanism previously
proposed for morphogen gradients (Eldar et
al., 2003).
Although Hip expression has been detected near all Shh signaling centers,
its basal concentration and extent of upregulation upon Shh signaling are both
parameters that vertebrates may use to regulate Hedgehog signaling with great
spatial precision (Chiang et al.,
1999; Chuang et al.,
2003; Tojo et al.,
2002). For example, Hip prevents the spread of excess Shh ligand
beyond odontogenic mesenchyme in tooth development, thus restricting the Shh
signaling to specific regions of the oral axis
(Coulombe et al., 2004). Other
than basal concentration and extent of Hip upregulation, other rates in the
Hip pathway may be modulated in different organisms, as in the mouse neural
tube where Hip-Shh complex internalization appears to be slow
(Chuang and McMahon, 1999;
Jeong and McMahon, 2005). The
ventralization of the tube observed when Hip is overexpressed
(Fig. 4), and the
non-cell-autonomous nature of this expansion, is very consistent with recent
experimental work (Stamataki et al.,
2005). Interestingly, soluble, diffusible forms of Hip have
recently been found in the mature brain
(Coulombe et al., 2004). Our
modeling results suggest that this new mechanism may potentially extend the
Shh signaling range by protecting Shh from binding to the cell surface Hip
variant, Ptc, or even HSPG (data not shown).
Restricting diffusion can propagate a morphogen signal
Although receptor binding can restrict the morphogen signaling range, other
mechanisms may unexpectedly enhance it. Two ostensibly opposing experimental
observations have been difficult to reconcile: the long-range signaling
ability of Shh and membrane anchorage of the ligand by hydrophobic
modification. Shh associates with the membrane through the addition of two
lipid tethers during its synthesis, a N-terminal palmitic acid
(Pepinsky et al., 1998) and a
C-terminal cholesterol (Porter et al.,
1996). Despite the reduced diffusivity accompanying membrane
association, many studies have demonstrated the long range signaling ability
of Shh in the neural tube over 20 cell diameters (>200 µm)
(Briscoe et al., 2001;
Ericson et al., 1997a;
Gritli-Linde et al.,
2001).
The simulation counterintuitively predicts that lower diffusion constants
can actually concentrate the signal in the ventral neural tube and thereby
extend its signaling range (Fig.
5A). Specifically, a typical 20 kDa protein in solution has a
diffusivity of order 1x10-7 cm2/s, and
hydrophobic modification is likely to decrease the diffusivity to a range
between 10-8 and 10-10 cm2/s
(Creighton, 1992). This
reduction may actually help Shh to extend its signaling range two additional
cell layers further from the floorplate
(Fig. 5C). In one study in the
vertebrate limb, Shh was detected 200 µm from the source, whereas
knock-in of a non-lipid modified Shh led to ligand detection only at lower
levels and much closer to the source (see
Lewis et al., 2001). The
interpretation was that lipid modification was necessary for long-range
transport. By contrast, our results indicate that the rapidly diffusing,
non-lipid-modified form may be rapidly diluted within the tissue to fall below
the experimental threshold of detection, whereas the lipid modification
concentrates the ligand.
Mechanisms modulating ligand diffusion
Via independent mechanisms, both Dis and ECM can also extend the signaling
range of Shh. First, although experiments have yet to quantify a spatial
profile for Shh aggregates in the neural tube, our modeling results show that
Dis-catalyzed aggregation of highly diffusible Shh aggregates can propagate a
Shh signal (Fig. 6A,B).
Analogous to the monomeric Shh results
(Fig. 5), there is a biphasic
response in the V3/MN pattern to both the diffusivity of the aggregate and the
Dis-catalyzed rate of aggregate generation. In the neural tube of dis
mutant mice, ventral fates are not properly specified, and Shh
immunoreactivity is detected only in Shh-producing cells in the ventral neural
tube, somite and limb (Kawakami et al.,
2002), indicating that this mechanism exerts significant control
over the range of signaling. Although Dis may have additional functions in the
Hedgehog pathway, Dis-catalyzed Shh aggregation may be a general transport
modulating mechanism operating in Drosophila
(Burke et al., 1999) and
zebrafish (Nakano et al.,
2004).
Distinguishing among the potential roles of ECM in ligand presentation,
stabilization and accumulation has been difficult
(Bornemann et al., 2004;
Giráldez et al., 2002;
Pons and Marti, 2000;
Rubin et al., 2002;
The et al., 1999). Our results
indicate that a very simple mechanism, the reversible binding of Shh to HSPG,
can either lengthen or restrict the signaling range depending on the HSPG
concentration (Fig. 7A). Both
HSPGs and the EXT genes involved in their synthesis are abundantly expressed
in a developmentally regulated manner in the mammalian central nervous system,
suggesting their functional roles in neural tube patterning
(Gould et al., 1995;
Inatani et al., 2003;
Yamaguchi, 2001). As HSPG is
actively remodeled by proteases in many tissues, and the ligand affinity for
HSPG can be correspondingly modulated, HSPG concentration and affinity can
serve as robust, tunable parameters to modulate ligand signaling in particular
tissues. Our results also indicate that vitronectin, a direct Shh
transcriptional target, can also modulate ligand transport (see Fig. S2 in the
supplementary material).
|
This analysis has led to the identification of three major regimes in which accessory Shh transport mechanisms modulate patterning (Fig. 8). Signal accumulation mechanisms limit Shh diffusion by restricting morphogen accumulation to near the source. By contrast, signal dispersal mechanisms promote high Shh diffusion to provide a shallow signal gradient over the developing field, such that the concentration is sufficiently high to change cell fate only near the source. Signaling range is maximized between these two extremes. Furthermore, shunting mechanisms promote intracellular degradation of the Shh signal across the entire profile to decrease the spatial Shh concentration profile. Finally, caution should be taken in interpreting experimental results, as the intersecting profiles indicate that experimental interpretations are highly dependent on assay sensitivity. For example, immunostaining for Shh with a 2.5 nM sensitivity would indicate that signal accumulation mechanisms result in the deepest Shh transport, whereas an assay with a 0.5 nM sensitivity would indicate that signal dispersal mechanisms give rise to the farthest transport.
Dynamic information through modeling
Correlating patterning with morphogen gradients only at steady state can
overlook many of the processes that contribute to tissue patterning, a
hypothesis that emerging evidence in a variety of morphogen systems supports.
First, in the vertebrate limb, sensitivity to the time a cell is exposed to a
given Shh concentration (Ahn and Joyner,
2004; Harfe et al.,
2004; Kohtz et al.,
1998; Park et al.,
2004; Wolff et al.,
2003; Yang et al.,
1997) indicates that specification clearly does not only occur at
or after steady state but throughout the entire morphogen transport process.
Second, waves of Shh source secretion in the neural tube
(Ericson et al., 1996) were
crucial determinants of MN specification, suggesting that the sequence of Shh
concentration levels may be important for specification. Third, morphogen
degradation during transport can determine its signaling range, as the
stability and therefore the signaling range of Nodal are regulated by its
hydrophobic modifications, which are intriguingly similar to those of Shh
(Le Good et al., 2005).
Lastly, because cellular competence to a morphogen, a phenomenon not yet
considered in our model, can be transient and regulated by several signals,
steady state morphogen gradients established after a cell loses competence are
irrelevant to tissue patterning. For all of these reasons, accurate monitoring
of cell fate as a function of time is important in studying tissue pattering
by morphogens.
Mechanistic models serve several roles in developmental biology: they test
which experimental results can be accounted for with all that is currently
known about a system, they can guide/suggest future experimentation, and they
can test whether several hypothesized mechanisms can account for a novel
phenotype. For example, high throughput siRNA approaches have recently
identified novel components of the Hh pathway
(Lum et al., 2003), and
modeling can be used to test their potential mechanisms of action. Other
molecules can also be included, such as Ptc2, Megalin, and the You class of
proteins, whose precise mechanism in the Hedgehog pathway is not yet known
(Carpenter et al., 1998;
Ding et al., 1998). For
example, our preliminary modeling work does not support a function of Megalin
as an active Shh transporter through the cytoplasm
(McCarthy et al., 2002), as
long-range signaling is not observed, even with extremely fast intracellular
transport rates of Shh-Megalin complexes (data not shown). Furthermore, a
unique advantage of this finite element numerical approach is that it can
incorporate the effects of cell division and death during patterning. Future
work can expand the current static model geometry to a `living mesh', so that
elements are added (or subtracted) as they arise (or die) in irregular
geometries and at various times. Finally, the simulation indicates that the
rate of Shh secretion from the floorplate, which feeds the patterning process
through the activity of a highly complex promoter not yet modeled
(Epstein et al., 1999), is a
highly important parameter that should be experimentally measured.
The model guides and predicts numerous additional experiments to analyze
Shh patterning in the neural tube, and potentially other tissues where Shh
transport is involved. First, knock-in of various forms of Shh with varying
extents of lipid modification (Feng et
al., 2004) is predicted to pattern to differing depths, as a
function of Shh diffusivity (Fig.
5). Likewise, Shh diffusivity can be tuned by injecting soluble
HSPG. Similar to experiments in the brain where the spread of molecules with
an HSPG interaction domain have been increased
(Nguyen et al., 2001), high
levels of soluble HSPG would induce Shh signal dispersal
(Fig. 8). Second, the secretion
rate of Shh can be varied in the floorplate through the use of a regulable
promoter, and the model can be used to predict the precise position of the
V3/MN interface as more MN are produced at the expense of V3 neurons with
increasing secretion. Finally, neural tube explants can be incubated in
blocking antibodies against Hip, Dis, HSPG or vitronectin. The concentration
of such antibodies would tune the levels of active Hip, Dis, HSPG and
vitronectin to the levels shown in Figs
4,
6 and
7, and Fig. S1 (in the
supplementary material), respectively, to test the predicted biphasic
responses.
In conclusion, we have analyzed how complex mechanisms acting at various times regulate morphogen transport and modulate tissue patterning. The results guide and suggest further experiments on how these mechanisms work in concert to provide robust Shh neural tube patterning. Future modeling work can explore the effects of numerous modular mechanisms in the Hedgehog pathway, and may intriguingly suggest further experiments on how these modules have been evolutionary `plugged' into particular tissues to restrict or propagate the Hedgehog signal when required.
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ACKNOWLEDGMENTS |
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|
Footnotes |
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Supplementary material for this article is available at http://dev.biologists.org/cgi/content/full/133/5/889/DC1
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REFERENCES |
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