Anteroposterior patterning of the zebrafish ear through Fgf- and Hh-dependent regulation of hmx3a expression

In the zebrafish, Fgf and Hh signalling assign anterior and posterior identity, respectively, to the poles of the developing ear. Mis-expression of fgf3 or inhibition of Hh signalling results in double-anterior ears, including ectopic expression of hmx3a. To understand how this double-anterior pattern is established, we characterised transcriptional responses in Fgf gain-of-signalling or Hh loss-of-signalling backgrounds. Mis-expression of fgf3 resulted in rapid expansion of anterior otic markers, refining over time to give the duplicated pattern. Response to Hh inhibition was very different: initial anteroposterior asymmetry was retained, with de novo duplicate expression domains appearing later. We show that Hmx3a is required for normal anterior otic patterning, and that otic patterning defects in hmx3a-/- mutants are a close phenocopy to those seen in fgf3-/- mutants. However, neither loss nor gain of hmx3a function was sufficient to generate full ear duplications. Using our data to infer a transcriptional regulatory network required for acquisition of otic anterior identity, we can recapitulate both the wild-type and the double-anterior pattern in a mathematical model.


Abstract 23
In the zebrafish, Fgf and Hh signalling assign anterior and posterior identity, 24 respectively, to the poles of the developing ear. Mis-expression of fgf3 or inhibition of 25 Hh signalling results in double-anterior ears, including ectopic expression of hmx3a. 26 To understand how this double-anterior pattern is established, we characterised 27 transcriptional responses in Fgf gain-of-signalling or Hh loss-of-signalling 28 backgrounds. Mis-expression of fgf3 resulted in rapid expansion of anterior otic 29 markers, refining over time to give the duplicated pattern. Response to Hh inhibition 30 was very different: initial anteroposterior asymmetry was retained, with de novo 31 duplicate expression domains appearing later. We show that Hmx3a is required for 32 normal anterior otic patterning, but neither loss nor gain of hmx3a function was 33 sufficient to generate ear duplications. Using our data to infer a transcriptional 34 regulatory network required for acquisition of otic anterior identity, we can 35 recapitulate both the wild-type and the double-anterior pattern in a mathematical 36 model. 37

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Introduction 40 The otic placode-precursor of the vertebrate inner ear-has the remarkable ability 41 to generate a mirror-image organ with duplicate structures under some experimental 42 conditions in fish and amphibians, as originally described by R. G. Harrison over 43 eighty years ago (reviewed in (Whitfield and Hammond, 2007)). Understanding the 44 generation of such duplicated structures can give us fundamental insights into 45 mechanisms of organ patterning, tissue polarity and symmetry-breaking during 46 embryogenesis. During normal development in the zebrafish, anteroposterior 47 asymmetries in otic gene expression are evident as early as the 4-somite stage (11.5 48 hours post fertilisation (hpf)), when expression of the transcription factor gene hmx3a 49 appears at the anterior of the otic placode (Feng and Xu, 2010). Additional genes 50 with predominantly anterior patterns of expression in the otic placode or vesicle begin 51 to be expressed over the next 10 hours, including the transcription factor genes hmx2 52 and pax5 (Feng and Xu, 2010;Kwak et al., 2006), together with the fibroblast growth 53 factor (Fgf) family genes fgf3, fgf8a and fgf10a (Léger and Brand, 2002;McCarroll 54 and Nechiporuk, 2013). Later, at otic vesicle stages (24 hpf onwards), the size and 55 position of the otoliths, together with the position, shape and planar polarity patterns 56 of the sensory maculae, provide landmarks for distinguishing anterior and posterior 57 structures in the ear (Hammond and Whitfield, 2011) (Fig. 1). In addition, a few 58 markers begin to be expressed specifically in posterior otic tissue (pou3f3b, bmp7a 59 and fsta) at otic vesicle stages (Kwak et al., 2006;Mowbray et al., 2001;Schmid et 60 al., 2000), but these are not reliable posterior markers at earlier otic placode stages. 61 62 Concomitant with the appearance of anteroposterior asymmetry in the zebrafish otic 63 domain, other early patterning events occur that are symmetrical about the 64 anteroposterior axis. Of relevance for our study, a single sensory-competent domain, 65 marked by the expression of atoh1b, splits into two domains, one at each pole of the 66 ear, by 12 hpf. This process is dependent on Notch signalling and atoh1b function, 67 and defines differences between the poles of the otic placode and a central zone 68 (Millimaki et al., 2007). The two poles express various markers symmetrically, 69 including atoh1a and deltaD, between 14-18 hpf (Millimaki et al., 2007), presaging 70 the appearance of pairs of myo7aa-positive sensory hair cells (tether cells) at each 71 pole by 18-24 hpf (Ernest et al., 2000). Thus, by the completion of otic induction at 72 14 hpf (10 somites), the otic domain has two clear poles defined by the symmetric 73 expression of atoh1a and deltaD, with the anterior pole distinguished from the 74 posterior by the asymmetric expression of hmx3a. 75 Although anteroposterior asymmetries in otic gene expression are already apparent 77 by 12 hpf in the zebrafish, these can be disrupted by interfering with extrinsic 78 signalling pathway activity after this time. For example, manipulations of either 79 Fibroblast growth factor (Fgf) or Hedgehog (Hh) signalling between 14-19 hpf can 80 result in striking double-anterior or double-posterior mirror-image ears. Fgf signalling 81 is both required and sufficient to act as an anteriorising cue, whereas Hh signalling is 82 both required and sufficient for the acquisition of posterior otic identity (Hammond et 83 al., 2003;Hammond et al., 2010;Hammond and Whitfield, 2011). In these studies, 84 we showed that transient In this study, we have compared the dynamics of the transcriptional responses that 94 precede the acquisition of a duplicated anterior otic fate in an Fgf gain-of-signalling or 95 a Hh loss-of-signalling context. Although the final duplicated ear structures appear 96 similar after each manipulation, the early transcriptional responses differ for each 97 signalling pathway, progressing in distinct ways to give rise to the double-anterior 98 pattern at larval stages. One gene that shows an early transcriptional response in 99 the zebrafish otic placode to disruption of either Fgf or Hh signalling is the Hmx family 100 homeobox gene hmx3a. We have examined the effects of both loss-of-function and 101 gain-of-function of hmx3a on inner ear patterning. Our data suggest that hmx3a is a 102 key early target for the otic anteriorising activity of Fgf signalling, and that the function 103 of hmx3a is required for the anterior-specific otic expression of fgf3 and pax5, 104 together with correct positioning and development of the sensory maculae. However, 105 unlike high Fgf levels or low Hh pathway activity, mis-expression of hmx3a was 106 unable to generate full duplications of anterior character at the posterior of the ear. A 107 mathematical model based on our experimental findings can recapitulate both the 108 wild-type and duplicated anterior pattern, allowing us to explore the dynamical 109 principles underlying the generation of a mirror-image duplicated organ system. To optimise our protocols for generating double-anterior duplicated ears through 154 inhibition of Hh signalling, we first examined the ear phenotype in smo hi1640Tg/hi1640Tg 155 mutants. The hi1640Tg allele (a transgenic insertion in the smoothened gene, and a 156 likely null (Chen et al., 2001)) is thought to result in a stronger reduction in Hh 157 signalling than the point mutation alleles smo b641 and smo b577 , both of which predict 158 single amino acid substitutions (Varga et al., 2001), and which we used in previous 159 studies (Hammond et al., 2003;Hammond and Whitfield, 2011). The the small molecule cyclopamine, can also produce double-anterior ear duplications 171 (Hammond et al., 2010;Sapède and Pujades, 2010). This approach enables a 172 conditional inhibition of Hh signalling over a defined time window. For the 173 experiments described here, we treated wild-type embryos with 100 µM cyclopamine 174 from 14-22.5 hpf. To examine later stages, we washed out the cyclopamine at 22.5 175 hpf and allowed embryos to develop further until 3 dpf (72 hpf), when they were fixed 176 for staining and imaging. Stage-matched sibling embryos-either untreated, or 177 treated with vehicle (ethanol) only-served as controls. This cyclopamine treatment 178 regime was sufficient to generate the double-anterior ear phenotype, characterised 179 by two ventrally-positioned, small (utricular-like) otoliths, loss of the posterior 180 (saccular) macula, and a clear duplication of the anterior (utricular) macula ( Fig.  181 1E,J). Ears in 4/8 treated embryos had four cristae (Fig. 1J'); the remaining 4/8 had 182 the normal complement of three cristae. The size and shape of the ear were less 183 affected than in the smo hi1640Tg/hi1640Tg mutant embryos, presumably due to the 184 transient nature of the cyclopamine treatment. Taken together, these data show that 185 either genetic or pharmacological inhibition of Hh signalling in wild-type zebrafish 186 embryos between 14-22.5 hpf results in a robust and reproducible double-anterior 187 ear phenotype at 3 dpf. 188 189 Following early fgf3 mis-expression, otic expression of anterior markers is 190 initially broad, with pax5 resolving into two discrete domains 191 One of the most striking transcriptional changes in response to fgf3 mis-expression is 192 the expansion or duplication of the expression of the anterior otic markers hmx2 and 193 pax5 by 24 hpf (Hammond and Whitfield, 2011). To examine the temporal dynamics 194 of this transcriptional response, we assayed for expression of these and additional 195 anterior otic marker genes following our optimised 'early' heat-shock regime (14 hpf, 196 30 min, 39°C) at three different time points: 16 hpf (2 hours post heat shock, to 197 examine any rapid response), 22.5 hpf (8.5 hours post heat shock, when anterior otic 198 expression of hmx2 and pax5 is strongly established in wild-type embryos) and 36 199 hpf (22 hours post heat shock, to examine whether any disruption to the expression 200 pattern resolves or changes over time). For hmx2 and pax5, which showed dynamic 201 expression changes, we subsequently included two additional time points (25.5 hpf 202 and 30 hpf) to capture these changes in more detail. 203

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We first tested expression of three genes coding for transcription factors (hmx3a, 205 hmx2 and pax5; Fig. 2). At the earliest time point (16 hpf, two hours after heat 206 shock), hmx3a showed the strongest response: expression had already expanded to 207 cover the entire anteroposterior extent of the otic placode ( Fig. 2A,B). The anterior 208 markers hmx2 and pax5, not normally expressed at this stage in wild-type embryos, 209 were expressed at very low levels in the anterior of the otic placode of heat-shocked 210 embryos ( Fig. 2C-F). We were also able to detect widespread and robust up-211 regulation of the Fgf target gene etv4 (formerly pea3) in transgenic embryos at this 212 time point (Fig. 2-Supplemental file 1). By 22.5 hpf, all three transcription factor 213 genes were strongly expressed in a broad zone across the entire anteroposterior axis 214 of the otic vesicle in heat-shocked embryos, on the medial side, as can be seen in a 215 dorsal view (Fig. 2G-L). Note that the overall size and shape of these otic vesicles 216 were relatively normal. Although there was some variability (including between both 217 ears of the same fish), the vesicles were oval in shape, indicating that otic induction 218 had not been compromised (compare with the small, rounded vesicles of fgf8a ti282/ti282 219 mutants, in which otic induction is disrupted (Léger and Brand, 2002)). By 36 hpf, 220 wild-type otic expression of hmx genes was more complex, but a clear difference To test whether the milder ear phenotype caused by a later heat shock reflects a 231 failure to establish the early transcriptional responses described above, we also 232 examined expression of anterior markers in Tg(hsp70:fgf3) embryos after heat shock 233 at 18 hpf (30 min, 39°C). Unexpectedly, we found that the otic expression of hmx3a 234 and pax5 was very similar to that following an early (14 hpf To compare the transcriptional response after fgf3 mis-expression at 14 hpf with that 244 following conditional Hh pathway inhibition from the same time point, we examined 245 otic expression of anterior marker genes after treatment of wild-type embryos with 246 cyclopamine (100 µM, 14-22.5 hpf; Fig. 3). To confirm the efficacy of cyclopamine 247 treatment, we also examined the expression of ptch2, a known target of Hh 248 signalling. Expression of ptch2 was down-regulated throughout the embryo at 22.5 249 hpf, but not abolished ( Fig. 3-Supplemental file 1). (By contrast, ptch2 expression 250 is almost entirely lost at 24 hpf in smo hi1640Tg/hi1640Tg mutants (Chen et al., 2001)). We 251 also checked expression of etv4 following cyclopamine treatment, but found no major 252 changes in expression at 22.5 hpf ( Expression of fgf3 is itself a marker of anterior otic epithelium from 21 hpf (Millimaki 300 et al., 2007), and so can also be used to indicate the presence of a duplicated 301 anterior otic pattern. We therefore examined the expression of fgf genes to provide 302 additional confirmation of anterior character in the duplicated ears. To distinguish 303 between expression of the fgf3 transgene and endogenous fgf3 expression, we used 304 a probe generated from the fgf3 3' UTR, which is not included in the transgenic 305 construct. In Tg(hsp70:fgf3) embryos after early (14 hpf Given the early anterior-specific otic expression of hmx3a (Feng and Xu, 2010), the 337 dependence of this expression on Fgf signalling (Adamska et al., 2000;Hammond 338 and Whitfield, 2011;Kwak et al., 2002), and the rapid change in otic hmx3a 339 expression after mis-expression of fgf3 or Hh inhibition (this work), we hypothesised 340 that hmx3a is required for normal otic anterior development. A previous study using 341 morpholino-mediated knockdown suggested a requirement for both hmx3a and hmx2 342 in acquisition of anterior otic identity and expression of pax5 (Feng and Xu, 2010). 343 However, the effects of individual gene knockdown or mutation were not reported. 344 To test the individual requirement for hmx3a function in the acquisition of otic anterior 345 identity, we examined the ear phenotype in homozygous mutants for a recessive 346 truncating allele lacking the homeodomain, hmx3a SU3 , which we generated using 347 CRISPR/Cas9 technology ( Fig. 5A; Materials and Methods). In homozygous 348 hmx3a SU3/SU3 mutants, the otoliths were positioned close together at 33 hpf, were side 349 by side at 48 hpf, had started to fuse at 66 hpf and had fully fused by 4 dpf (Fig. 5B,C 350 and data not shown). This phenotype appeared to be fully penetrant (38/143 351 embryos from a cross between heterozygous parents; 26.6%). Semicircular canal 352 pillars and the dorsolateral septum were present in the ears of mutant embryos, 353 although formation of the ventral pillar was delayed. Overall, the ear shape appeared 354 more symmetrical than in wild-type siblings (Fig. 5B,C). We imaged ears from three 355 mutant embryos at 3 dpf to analyse sensory patch formation ( To check that the hmx3a transgene was functional, we sequenced it from genomic 433 DNA of transgenic embryos, which indicated that the open reading frame was intact 434 (data not shown). We also examined the phenotype of transgenic embryos after an 435 even earlier heat shock, during otic placode induction (8-9 hpf and 10-11 hpf). 436 Here, we saw a range of otic abnormalities in 80% of transgenic embryos (n=106), 437 including missing otoliths, but some embryos also had small heads and eyes (Fig. 438 6-Supplemental file 1). Ear patterning appeared normal in about 20% of transgenic 439 embryos heat-shocked at these earlier stages. Longer (1-or 2-hour) heat shocks at 440 14-15 hpf also resulted in normal otic patterning (n=49; Fig. 6-Supplemental file 1). 441 We conclude that the hmx3a transgene is likely to be functional, but that its mis- attenuation is unlikely to be at the level of an immediate target of Fgf signalling such 478 as etv4, as Hh inhibition did not result in major changes to etv4 expression ((Hammond and Whitfield, 2011); this work). One possibility is that it could reflect 480 integration of activity of the two signalling pathways at the level of binding sites in the 481 promoters of the otic anterior genes. In addition, we propose that Hmx3a, together 482 with Fgf and Hh, regulates its own expression and that of other genes in the network. 483 Currently, our data do not distinguish whether these regulatory relationships are 484 direct or indirect. 485

486
The dynamic behaviour of the model is presented in Figure 8 (for full details, see The zebrafish otic placode is a convenient system in which to understand the gene 512 network dynamics that lead to asymmetries along the axis of a developing organ. 513 Asymmetries in gene expression are evident from early (otic placode) stages, but the 514 system is clearly equipotential, since either a gain of Fgf signalling or a loss of Hh 515 pathway activity at otic placode stages can produce remarkably similar double- Our data and mathematical model suggest that the Fgf/Hh system is sufficient to 534 pattern the anteroposterior axis of the ear. In our scheme, there is only one input 535 (extrinsic Fgf activity) that has a graded distribution across the otic anteroposterior 536 axis. Notably, there is no need to infer an opposing graded input of extrinsic 537 signalling activity that is high at the posterior of the ear. Although Retinoic Acid (RA) 538 is thought to form such a gradient, and contributes to anteroposterior patterning in 539 both the chick and zebrafish ear (Bok et al., 2011;Radosevic et al., 2011), its activity 540 can clearly be over-ridden by manipulations of Fgf or Hh signalling in generating 541 either double-anterior or double-posterior zebrafish ears. Our model therefore differs 542 from other models of axial patterning, for example in generation of dorsoventral 543 pattern in the vertebrate neural tube. Here, information from two anti-parallel noisy 544 gradients is integrated and refined by cross-repressing interactions between target 545 genes, providing precise positional information along the axis (Briscoe and Small, 546 2015;Zagorski et al., 2017). However, the sufficiency of our network and model 547 does not necessarily rule out a contribution from the RA gradient in generating 548 correct anteroposterior patterning in the wild-type ear. 549 550 At present, we do not have a full mechanistic explanation for the differences in 551 response dynamics after manipulations of the Fgf and Hh signalling pathways. 552 Although hmx3a responds rapidly to manipulation of Fgf signalling, its regulation may 553 well be indirect; a recent study identified only one gene, Etv5, as a direct up-554 Anterior-specific otic expression of Hmx3 and Hmx2, including their temporal order of 663 expression onset in the ear, is conserved between zebrafish, mouse and chick (Feng 664 and Xu, 2010;Herbrand et al., 1998;Rinkwitz-Brandt et al., 1995;Wang et al., 1998). these mutants, all three semicircular canal ducts were present, but the lateral 672 (horizontal) ampulla and crista were missing. The utricular and saccular maculae 673 were juxtaposed in a common utriculosaccular chamber (Wang et al., 2004;Wang et 674 al., 1998), as we found in the zebrafish hmx3a SU3/SU3 mutant. A notable difference 675 between the mouse and zebrafish mutants is the presence of all three cristae, 676 including the lateral crista, in the zebrafish hmx3a SU3/SU3 mutants. Formation of the 677 ventral pillar for the lateral canal was also present, although delayed. It will be 678 interesting to see whether mutations in hmx2 (not currently available) affect 679 morphogenesis of the zebrafish semicircular canal system; in the mouse, targeted 680 disruption of Hmx2 results in a loss of all three semicircular canal ducts, with partial 681 or complete loss of some ampullae and cristae, in addition to a fused utriculosaccular 682 chamber (Wang et al., 2001). In humans, HMX3 and HMX2 are located together, 683 close to FGFR4, on chromosome 10; hemizygous microdeletions that remove all 684 three genes are thought to be causative for syndromes characterised by inner ear 685 morphological anomalies, vestibular dysfunction and sensorineural hearing loss 686 (Miller et al., 2009;Sangu et al., 2016). 687

688
In conclusion, our study demonstrates that although Fgf gain-of-signalling and Hh 689 loss-of-signalling produce similar morphological duplications of the zebrafish ear, 690 they do so via distinct dynamical patterns of gene expression, providing valuable 691 insights into normal anterior otic development. In addition, we determine that hmx3a, 692 a gene expressed as an early transcriptional response to both Fgf and Hh manipulation, has a conserved role in correct separation of the sensory maculae 694 within the otic vesicle, and is required-but not sufficient-for normal anterior otic 695 development. We have also shown that our proposed genetic network for zebrafish 696 otic anterior development can be recapitulated with a mathematical model that 697 assumes interactions between a graded extrinsic source of Fgf, a uniform inhibitory 698 influence of Hh, and equipotential competence to adopt an anterior identity at the otic 699 poles. Interactions between these inputs and their downstream targets within the otic 700 tissue (hmx3a, hmx2, pax5 and fgf genes) lead to correct anteroposterior patterning 701 in the developing zebrafish ear. The model will be a useful framework for further 702 elucidation and functional validation of the proposed gene regulatory network 703 required for the acquisition of anterior otic identity in the zebrafish.

Heat shock 717
Embryos were cultured in E3 at 28.5°C prior to heat shock. For heat shock, embryos 718 from either a cross between two hemizygous transgenic carriers, or an outcross 719 between a transgenic carrier and a wild-type, were transferred to 25 ml of preheated 720 E3 in a Falcon tube and incubated at 39°C for 30 minutes, unless otherwise 721 indicated. Embryos were then returned to their original plates of E3, which had been 722 preheated to 33°C during the heat shock, and incubated for a further 30 minutes at 723 33°C. Plates were then returned to 28.5°C and incubated until embryos reached the 724 desired stage for fixation. In heat-shock experiments with mixed batches of 725 transgenic and non-transgenic embryos, a transgenic genotype was confirmed by 726 expression of tdTomato in Tg(hsp70:hmx3a) embryos or abnormal shape of the yolk 727 extension in Tg(hsp70:fgf3) embryos, in addition to analysis of the phenotypes 728 described in the text. 729

Cyclopamine treatment 730
Embryos were treated in 12-well plates (3 ml total volume; £30 embryos per well) at 731 28.5°C with InSolution Cyclopamine, V. californicum (Calbiochem). Chorions were 732 punctured with a sterile hypodermic needle prior to treatment to improve compound 733 penetration. After treatment, embryos were washed twice in E3 before either being 734 fixed or incubated in E3 before fixation later. Vehicle-only controls consisted of a 735 volume of the solvent (ethanol) equivalent to that used in the highest experimental 736 treatment concentration. Embryos from the same batch (siblings) were randomly 737 allocated into control and treatment groups.

In situ hybridisation 739
Embryos were dechorionated and fixed in 4% paraformaldehyde overnight at 4°C. In 740 situ hybridisation was carried out as described (Thisse and Thisse, 2008). For most 741 experiments, at least 25 embryos (biological replicates) were stained in any given 742 batch. Where relevant, numbers of embryos with the phenotype of interest and total 743 number in the batch (e.g. 29/30) are shown directly on the figure panels (see figure  744 legends for details). Analysis of gene expression via in situ hybridisation is not 745 quantitative, but we have chosen markers that give a clear and robust qualitative 746 response to changes in signalling pathway activity. We have used information from 747 these spatial expression patterns to infer parameters for the mathematical model 748 (see below). Where appropriate, we have measured the spatial extent of expression 749 along the medial side of the otic vesicle in a dorsal view using ImageJ. 750 751

Generation of a template for the fgf3 3' UTR-specific in situ hybridisation probe 752
The 3' UTR of fgf3 was amplified from wild-type (AB strain) genomic DNA in a nested 753 PCR, incorporating the T7 promoter, using the following primers:  Details of the mathematical model

Representation of otic tissue
For the purposes of modelling gene expression in the developing otic tissue between 14 and 36 hours post fertilisation (hpf), we represent the medial side of the otic tissue as a one-dimensional array of cells. Distance along this array-represented by the variable x-is measured in percentage length along the anterior-posterior (AP) axis. At the stages studied, the length of the medial side is approximately 100µm.

Competence to express fgf
Our data suggest that competence to express fgf in the otic tissue (fgf i ) begins at around 14 hpf (see Fig. 7B) and is strongest at the poles. We therefore assume that this competence can be represented by a function of the form where 0 ≤ x ≤ 100 is percentage length along the AP axis, x c is a measure of the extent of the polar competence regions, and m is a measure of the sharpness of the boundaries between regions of high and low competence. In our model simulations, we assume x c = 20% AP length and m = 5, giving the competence profile shown in Fig. S1A.

Extrinsic Fgf expression
We assume that rhombomere 4 of the hindbrain acts as the main source of extrinsic Fgf signalling; both fgf3 and fgf8a are expressed here at the time of initial otic anteroposterior patterning (Maves et al., 2002). Further support is provided by analysis of mutants for mafba (Kwak et al., 2002) and hnf1ba (Lecaudey et al., 2007). These two genes code for transcription factors expressed in the hindbrain and are required for restriction of fgf3 expression to rhombomere 4. In the mafba −/− and hnf1ba −/− mutants, posterior expansions of fgf3 expression in the hindbrain correlate with expansions or duplications of otic anterior markers similar to those we see in Tg(hsp70:fgf3) embryos after heat shock.
We assume that the extrinsic Fgf3 protein spreads away from the cells in which it is produced, resulting in a graded expression profile in the neighbouring otic tissue. In support of this, we show in Fig. 7 -Supplemental File 1 that a reporter of Fgf signalling activity is expressed in a decreasing gradient in the otic region, with highest activity in the tissue neighbouring rhombomere 4. Up to time t = 18 hpf, we assume that the distribution of rhombomeric Fgf protein in the otic tissue is given by  (2)). F 0 = 18.5, x 0 = 30% AP axis, λ f = 15% AP axis.
where F r (x) is the Fgf protein concentration (in arbitrary units) in the otic tissue at AP position x, 0 ≤ x ≤ x 0 is the region of overlap between rhombomere 4 and the otic tissue, F 0 is the maximum protein concentration, and λ f is the effective "diffusion wavelength" of Fgf. The resulting concentration profile is shown in Fig. S1B for F 0 = 18.5, x 0 = 30% AP axis, and λ f = 15% AP axis (approximately 15 µm at the stages studied). fgf expression in rhombomere 4 decreases significantly at around 18 hpf (Maves et al., 2002). Up until this time, the Fgf concentration profile in the otic tissue is given by Eq.
(2). At times later than 18 hpf, we assume linear degradation of the Fgf protein. The Fgf concentration at time t is therefore given by where τ e is the half-life (in hours) of the Fgf protein.

Regulated gene expression in the otic tissue
Fgf protein originating from rhombomere 4 initiates a temporal sequence of spatially patterned gene expression in the otic tissue. Based on the inferred interactions summarised in Fig. 7A, we represent transcription and translation using a system of coupled differential equations as follows: where represents the total amount of Fgf protein in the otic tissue and the transcription regulation functions are given by increasing sigmoid (Hill) functions of the general form: In these functions, the parameter θ represents the activation threshold -the concentration of activator required to achieve a half-maximal rate of transcription. The effect of Hh attenuation is to increase the threshold in Eq. (14) by an amount ρR, where R is a measure of the amount of Hh signalling in the otic tissue, and ρ is the relative attenuation strength for each gene. Hh attenuation thus reduces the rate of transcription resulting from a given concentration of Fgf.
The meaning of all model variables and parameters is summarised in Tables S1-S3.
In the model, expression of all genes is activated by the total amount of Fgf protein (both extrinsic and that produced within the otic tissue) and attenuated by Hh protein.
Expression of hmx3a, pax5, fgf3, fgf8a and fgf10a is additionally activated by Hmx3a protein.   Tables S2  and S3 on a discrete spatial domain comprising 100 spatial cells (with the diffusion terms in Eqs. (10)-(12) represented by a simple finite difference scheme), with zero-flux boundary conditions at the anterior and posterior poles of the otic vesicle. Simulations covered the time period 10-36 hpf, with initial values of all intrinsic mRNA and protein variables set to zero. The resulting spatiotemporal mRNA expression patterns are shown in Fig. 8, for three conditions: wild type (1st column), heat shock induction of fgf3 (2nd column), and inhibition of Hh signalling by cyclopamine treatment (3rd column). The simulation protocols for the latter two conditions are described below. Fig. S2 shows the spatial profiles of mRNA and total Fgf protein expression for the three conditions at 22.5 hpf and 36 hpf.
Transcription and translation rates for all endogenous genes and proteins have been set to 1, so all expression levels are expressed in arbitrary units. Half-lives of mRNA and protein have been set to reflect the observed dynamics of expression patterns. For example, the pax5 mRNA half life is set to be low (0.5 hrs) to reflect the fact that pax5 mRNA expression induced in the middle part of the otic vesicle by heat shock Fgf3 protein is lost by 36 hpf. The hmx3a mRNA half life is also set to be low (0.5 hrs) to reflect the early onset of hmx3a expression. In contrast, the fgf mRNA half lives are set to be higher to reflect the later onset of their expression. The Fgf protein diffusion coefficient is set to be low in order to avoid Fgf protein produced in the anterior and posterior poles "flooding" the otic vesicle. The short half lives of the Fgf proteins also contribute to the restriction of Fgf proteins to the poles. Indeed, Fgf protein diffusion can be omitted from the model without affecting the dynamics of the mRNA expression patterns.
The transcription regulation parameters, which reflect the level of expression at which regulating proteins effect regulation of their targets, were chosen with reference to the expression levels achieved by each protein in the model (shown in Fig. S3). For example, the threshold for regulation of hmx3a expression by Fgf protein (θ 1 ) is the primary determinant of the extent of the anterior expression domain of hmx3a mRNA.