QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online 1 February 2006
doi: 10.1242/dev.02254

This Article Summary Full Text Full Text (PDF) Supplementary Material A corrigendum has been published Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Saha, K. Articles by Schaffer, D. V. Search for Related Content PubMed PubMed Citation Articles by Saha, K. Articles by Schaffer, D. V. Social Bookmarking                         What's this?

Signal dynamics in Sonic hedgehog tissue patterning

Department of Chemical Engineering and the Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94720-1462, USA.

View larger version (67K): [in a new window]   Fig. 1. Finite element model (FEM) of the vertebrate developing neural tube. (A) One-dimensional projection of neural tube tissue. A transverse cross section of a stage 16 chick embryo depicts expression of shh (green) and pax6 (red) [adapted, with permission, from Ericson et al. (Ericson et al., 1997b)]. White labels indicate subsequent mature stage 26 cell fates. MN, motoneurons; V1-3, distinct populations of ventral interneurons. On the right, cells A-C are depicted with a surface membrane (orange), nuclei (dashed ovals), and extracellular space (light gray). In the FEM mesh, each black circle represents a mesh boundary, and each gray `x' represents a node where concentrations are defined in the mesh. (B) The Shh core signaling network (red dashed line with internalization labeled as I) and hypothesized accessory mechanisms (labeled II-VI) are shown around a representative cell. Arrows between proteins represent binding or dissociation, arrows from genes to proteins represent expression, and arrows from proteins to genes indicate activation or repression. Vit, vitronectin; Smo, Smoothened. At the cellular level, Shh induces cell fate switching by interacting with its transmembrane receptor, Patched (Ptc). In absence of Shh, Ptc represses the signaling activity of the transmembrane protein Smo and therefore acts as a repressor of Shh signaling as described previously (Lai et al., 2004). gli upregulation represents positive feedback, whereas ptc upregulation yields negative feedback.

View larger version (39K): [in a new window]   Fig. 2. Spatial and temporal evolution of the Shh signal. (A) Reaction-diffusion equations for the core Shh signaling network. `Promoter' and `basal' terms have been previously defined (Lai et al., 2004). (B) Three classes of steady-state behavior in the core single cell Shh model as described previously (Lai et al., 2004). Two time-invariant levels of concentrations (steady states) corresponding to a gli1 `on' and a gli1 `off' state can exist, as we have previously described (Lai et al., 2004). There are three distinct regimes controlled by extracellular Shh concentration: only the `off' state is stable, only the `on' state is stable, and an intermediate bistable regime where either state is stable. (C) Sensitivity analysis of parameters in the single cell Shh network. To determine which parameters most strongly control the response of single cells to Shh, we performed a sensitivity analysis, i.e. we varied each parameter while holding others constant and observed changes in the on/off switch. This graph shows the changes in steady-state behavior as particular parameters are varied 100-fold above and below the best available literature value. Ranges of parameter values at which single cell behavior falls into the three classes schematically represented and shaded in B are shown. kperturb, value of parameter for which the behavior of the model is plotted; klit, value of parameter in literature. Notice that several parameters need to be controlled within a narrow range of values (e.g. kGmax) and several can vary over a wide range (e.g. kPout). (D) The time for a single cell to switch from a V3 to a MN fate (i.e. to achieve a greater than 7-fold increase in Gli1 concentration) at various constant extracellular Shh concentrations. (E-H) The spatiotemporal evolution of various Shh network constituents in a wild-type embryo is shown: (E) Shh extracellular concentration; (F) Ptc intracellular concentration; (G) Ptc-Shh complex intracellular concentration; and (H) Gli1 intracellular concentration. Bolded lines in each figure correspond to concentration profiles at the end of the V3/MN developmental time window (t=83 hours). Simulation initial conditions were: [Shh]=0; [PtcShhin]=0; [PtcShhout]=0; [Ptcout]=2.0 nM; [Ptcin]=0.33 nM; [Gli1]=1.63 nM; [Gli3]=5.81 nM; and [Gli3R]=61.2 nM. Parameters for core pathway: DShh=1.0x10-7 cm2/s; koff=0.10 min-1; kon=120,000,000 M-1 min-1; kCin=0.2 min-1; kCout=0.00181 min-1; kCdeg=0.00198 min-1; kPmax=2.25x10-9 M min-1; kPbas=1.73x10-11 M min-1; kPin=0.03 min-1; kPout=0.00036 min-1; kPdeg=0.09 min-1; kGmax=2.74x10-10 M min-1; kGbas=2.11x10-12 M min-1; kdeg=0.009 min-1; rg3b=3.1x10-19 M2 min-1; kg3r=0.0117 min-1; Kg3rc=0.12; Kptc=3.32x10-11 M; and KGli3=8.3x10-10 M (see Table S1 in the supplementary material for parameter descriptions and sources). Boundary conditions for all species were impermeable at the source (/x=0 at x=0 µm) and zero at large distances (concentration=0 at x=300 µm).

View larger version (35K): [in a new window]   Fig. 3. Model predicts experimental patterning results. (A) A cross section of a stage 20-24 chick embryo indicates expression of nkx2.2 (red) and cells transfected with a signaling-defective Ptc (green) [adapted, with permission, from Briscoe et al. (Briscoe et al., 2001)]. (B) Modeling results of the Gli1 concentration in both the wild-type and transfected sides of the embryo after 63 hours of Shh secretion match experimental profiles. The dashed line indicates the experimentally measured Nkx2.2 profile at stage 18, t=50 hours (Ericson et al., 1997b). See text for relationship between Nkx2.2 and Gli1. Simulation initial conditions and parameters are the same as those listed in Fig. 2, except within the transfected regions where (Kptc KGli3)106. See text for details.

View larger version (32K): [in a new window]   Fig. 4. Shh binding to Hedgehog-interacting-protein (Hip) shifts pattern ventrally. The Gli1 protein interface position at t=83 hours is shown at various levels of (A) initial Hip surface concentration and (B) maximal Gli1-induced rate of Hip synthesis, kHipmax. Simulation initial conditions and parameters are the same as those listed in Fig. 2; however, Hip mechanism equations and parameters were added (see Fig. S4 in the supplementary material).

View larger version (33K): [in a new window]   Fig. 5. Restricted diffusion of Shh can propagate a morphogen signal. (A) Extracellular Shh concentration and (B) intracellular Gli1 concentration are shown at t=83 hours at various Shh diffusivities. (C) The Gli1 protein interface position is shown at various diffusivities at t=83 hours. Simulation initial conditions and parameters are the same as those listed in Fig. 2, except DShh was varied.

View larger version (43K): [in a new window]   Fig. 6. Shh aggregation by Dispatched can overcome diffusion limitations. The Gli1 protein interface position at t=83 hours is shown at various levels of (A) initial Dispatched intracellular concentration and (B) diffusivity of a Shh aggregate. Simulation initial conditions and parameters are the same as those listed in Fig. 2; however, Dispatched mechanism parameters and equations were added (see Fig. S4 in the supplementary material).

View larger version (32K): [in a new window]   Fig. 7. Extracellular matrix components function effectively to modulate Shh diffusivity. (A) Gli1 intracellular concentration at t=83 hours is shown at various levels of initial HSPG extracellular concentration. (B) The Gli1 protein interface position at t=83 hours is shown at various levels of HSPG extracellular concentration. Simulation initial conditions and parameters are the same as those listed in Fig. 2; however, HSPG mechanism equations and parameters were added (see Fig. S4 in the supplementary material).

View larger version (51K): [in a new window]   Fig. 8. Three classes of mechanisms modify the Shh extracellular gradient. An intermediate snapshot (30 hours after secretion) of the concentration versus distance profile is shown for cells that have mechanisms of the wild-type chick embryo: a signal accumulation regime, a signal dispersal regime, or a shunting mechanism. Mechanisms that promote the signal accumulation regime hinder Shh transport, thereby causing high accumulation of Shh near the source. By contrast, mechanisms that induce signal dispersal promote Shh transport along the axis, thereby creating a shallow Shh gradient over the entire tissue. Shunting mechanisms degrade Shh over the entire tissue, thereby decreasing extracellular Shh. V3 specification occurs above the 2.5 nM Shh signaling threshold and can be tuned to a particular distance from the source depending on which mechanisms are active.

CiteULike

Complore

Connotea

Del.icio.us

Digg

Reddit

Technorati

Twitter