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Fig. S1. Extracellular matrix component, vitronectin, function effectively to modulate Shh diffusivity. Vitronectin reversibly binds Shh in the extracellular space (Martinez-Morales et al., 1997; Pons and Marti, 2000), and is selectively expressed in the notochord and ventral regions of the neural tube (Martinez-Morales et al., 1997). We again propose that modulating diffusion, this time via vitronectin concentration, can change neural tube patterning, as changing the initial vitronectin concentration yields the same biphasic response as with HSPG (see Fig. 7A). (A) Gli1 intracellular concentration at t=83 hours is shown at various maximal rates of vitronectin secretion by gli1 upregulation (kVmax). (B) gli1 expression interface position at t=83 hours are shown at various kVmax Simulation initial conditions and parameters same as those listed in Fig. 2, except vitronectin mechanism parameters and equations were added (see Fig. S4 in the supplementary material). At long times (>80 hours), vitronectin upregulation creates a more homogeneous, flat gli1 on state (compare A with upregulation with Fig. 7A without upregulation). Note that modulating vitronectin expression does not create a biphasic response and that high expression rates are (kVmax>108 M/minute) needed to influence the pattern. Upregulation of vitronectin occurs on a slower time scale than does Shh diffusion. Therefore, B is not biphasic, as upregulating vitronectin occurs too late to build up signal near the floorplate. The initial concentration and maximal rate of synthesis of Vitronectin are both robust, tunable parameters, as Shh binds to three different fragments of vitronectin with varying affinities (Martinez-Morales et al., 1997). Although both of these parameters act to increase extracellular vitronectin concentration, the contrast between Fig. 7B and B highlight the importance of considering dynamics. Experiments with constitutively on vitronectin cells in the neural tube would function to increase initial vitronectin concentration and thus modulate dynamics further than experiments that just overexpress vitronectin as a Shh transcriptional target.
References
Martinez-Morales, J. R., Barbas, J. A., Marti, E., Bovolenta, P., Edgar, D. and Rodriguez-Tebar, A. (1997). Vitronectin is expressed in the ventral region of the neural tube and promotes the differentiation of motor neurons. Development 124, 5139-5147.
Pons, S. and Marti, E. (2000). Sonic hedgehog synergizes with the extracellular matrix protein vitronectin to induce spinal motor neuron differentiation. Development 127, 333-342.
Fig. S2. Autocrine Shh signaling shifts patterning dorsally. Multiple genes and regulatory sequences are involved in activating shh transcription along the length of the anteroposterior axis of the mouse embryo (Epstein et al., 2000). Specifically, hnf3b is a Shh transcriptional target, and there are multiple hnf3b enhancer elements in the Shh promoter. Although Shh autocrine signaling has not been seen to extend beyond the floorplate, we investigated the hypothetical effects of an autocrine loop in the neural tube (see Fig. 1B, VI). (A,B) Shh extracellular concentration (A) and Gli1 intracellular concentration (B) are shown at t=83 hours at various maximal rates of Shh secretion by gli1 upregulation (kShhmax). (C) gli1 expression interface position at t=83 hours is shown at various levels of kShhmax. Simulation initial conditions and parameters same as those listed in Fig. 2, except autocrine mechanism parameters and equations were added (see Fig. S4 in the supplementary material). There needs to be high shh expression or Shh secretion (>1010 M/minute) to influence the interface position. The rate of autocrine upregulation, kShhmax, is a sensitive factor that can be tuned easily by evolution to move the interface dorsally.
Reference
Epstein, D. J., Martinu, L., Michaud, J. L., Losos, K. M., Fan, C.-M. and Joyner, A. L. (2000). Members of the bHLH-PAS family regulate Shh transcription in forebrain regions of the mouse CNS. Development 127, 4701-4709.
Fig. S3. Non-dimensional equations for core Shh signaling network. Parameter and variable descriptions are listed in Table S1 in the supplementary material. Schematic for core Shh signaling network is shown in Fig. 1B within dashed lines.
Fig. S4. Non-dimensional equations for accessory mechanisms. Parameter and variable descriptions are listed in Table S1 in the supplementary material. Schematic of accessory mechanisms are shown in Fig. 1B.
Fig. S5. Comparison of Patched assays in chicken and mouse with model predictions. Snapshots of either Patched1 expression or protein levels at various times during mouse and chicken neural tube development. For comparison to modeling results, all Patched1 species have been lumped together ([All Ptc species]=[PtcShhin]+[PtcShhout]+[Ptcout]+[Ptcin]) in a plot in the upper left-hand corner, and snapshots of that profile are shown to the right. An inset in the bottom left-hand corner indicates snapshots of Shh secretion at early time points to determine that floorplate Shh secretion starts between 10 and 13 somites for mice.
References
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Goodrich, L. V., Johnson, R. L., Milenkovic, L., McMahon, J. A. and Scott, M. P. (1996). Conservation of the hedgehog/patched signaling pathway from flies to mice: induction of a mouse patched gene by Hedgehog. Genes Dev. 10, 301-312.
Goodrich, L. V., Jung, D., Higgins, K. M. and Scott, M. P. (1999). Overexpression of ptc1 inhibits induction of Shh target genes and prevents normal patterning in the neural tube. Dev. Biol. 211, 323-334.
Jeong, J. and McMahon, A. P. (2005). Growth and pattern of the mammalian neural tube are governed by partially overlapping feedback activities of the hedgehog antagonists patched 1 and Hhip1. Development 132, 143-154.
Litingtung, Y. and Chiang, C. (2000). Specification of ventral neuron types is mediated by an antagonistic interaction between shh and gli3. Nat. Neurosci. 3, 979-985.
Marigo, V. and Tabin, C. J. (1996). Regulation of patched by sonic hedgehog in the developing neural tube. Proc. Natl. Acad. Sci. USA 93, 9346-9351.
Motoyama, J., Milenkovic, L., Iwama, M., Shikata, Y., Scott, M. P. and Hui, C. C. (2003). Differential requirement for Gli2 and Gli3 in ventral neural cell fate specification. Dev. Biol. 259, 150-161.
Persson, M., Stamataki, D., te Welscher, P., Andersson, E., Bose, J., Ruther, U., Ericson, J. and Briscoe, J. (2002). Dorsal-ventral patterning of the spinal cord requires Gli3 transcriptional repressor activity. Genes Dev. 16, 2865-2878.
Ricklefs, R. E. and Starck, J. M. (1998). Series of Embryonic Chicken Growth. In Avian Growth and Development. Evolution within the altricial precocial spectrum (ed. R. E. Ricklefs and J. M. Starck). New York: Oxford University Press.
Theiler, K. (1989). The House Mouse: Atlas of Embryonic Development. New York: Springer-Verlag.
Wijgerde, M., McMahon, J. A., Rule, M. and McMahon, A. P. (2002). A direct requirement for Hedgehog signaling for normal specification of all ventral progenitor domains in the presumptive mammalian spinal cord. Genes Dev. 16, 2849-2864.
Zhu, A. J. and Scott, M. P. (2004). Incredible journey: how do developmental signals travel through tissue? Genes Dev. 18, 2985-2997.
Movie 1. Spatial evolution of extracellular Shh along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters, while the ordinate is the non-dimensional Shh concentration (mol extracellular Shh)/(L of extracellular liquid volume)/(Kgli3)/(vff). See Table S1 in the supplementary material for parameter descriptions.
Movie 2. concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional intracellular Gli1 concentration (mol intracellular Gli1)/(L of intracellular liquid volume)/(Kgli3). See Table S1 in the supplementary material for parameter descriptions.
Movie 3. Spatial evolution of intracellular Ptc-Shh complex concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional intracellular Ptc-Shh complex concentration (mol intracellular Ptc-Shh complex)/(L of intracellular liquid volume)/(Kgli3). See Table S1 in the supplementary material for parameter descriptions.
Movie 4. Spatial evolution of extracellular Ptc concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional extracellular free Ptc concentration (mol membranic free Ptc)/(L of extracellular liquid volume)/(Kgli3)/(vff). See Table S1 in the supplementary material for parameter descriptions.
Movie 5. Spatial evolution of intracellular Gli3 concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the nondimensional intracellular Gli3 concentration (mol intracellular Gli3)/(L of intracellular liquid volume)/(Kgli3). See Table S1 in the supplementary material for parameter descriptions.
Movie 6. Spatial evolution of intracellular Gli3 repressor concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional intracellular Gli3 repressor concentration (mol intracellular Gli3 repressor)/(L of intracellular liquid volume)/(Kgli3). See Table S1 in the supplementary material for parameter descriptions.
Movie 7. Spatial evolution of membranic Ptc-Shh complex concentration along the wild-type neural tube. The total duration is 49 seconds, representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional membranic Ptc-Shh complex concentration (mol membranic Ptc-Shh complex)/(L of extracellular liquid volume)/(Kgli3)/(vff). See Table S1 in the supplementary material for parameter descriptions.
Movie 8. Spatial evolution of intracellular Ptc concentration along the wild-type neural tube. The total duration is 49 seconds representing 83 hours of development after floorplate Shh secretion (sped up 6097×). The abscissa represents the distance from the floorplate in centimeters (see Fig. 1A), while the ordinate is the non-dimensional intracellular free Ptc concentration (mol intracellular free Ptc)/(L of intracellular liquid volume)/(Kgli3). See Table S1 in the supplementary material for parameter descriptions.
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