Abstract
Understanding how complex organ systems are assembled from simple embryonic tissues is a major challenge. Across the animal kingdom a great diversity of visual organs are initiated by a ‘master control gene’ called Pax6, which is both necessary and sufficient for eye development1–6. Yet precisely how Pax6 achieves this deeply homologous function is poorly understood. Here we show that vertebrate Pax6 interacts with a pair of morphogen-coding genes, Tgfb2 and Fst, to form a putative Turing network7, which we have computationally modelled. Computer simulations suggest that this gene network is sufficient to spontaneously polarise the developing retina, establishing the eye’s first organisational axis and prefiguring its further development. Our findings reveal how retinal self-organisation may be initiated independent of the highly ordered tissue interactions that help to assemble the eye in vivo. These results help to explain how stem cell aggregates spontaneously self-organise into functional eye-cups in vitro8. We anticipate these findings will help to underpin retinal organoid technology, which holds much promise as a platform for disease modelling, drug development and regenerative therapies.
Introduction
Positional cues that govern cell fate decisions in the embryo may arise at multiple organisational levels: cell-intrinsically (e.g. asymmetric cell divisions), tissue-intrinsically (e.g. reaction-diffusion mechanisms), tissue-extrinsically (e.g. inductive tissue interactions) or some combination of these. Historically, the early patterning of cell fates within the vertebrate eye has emphasised inductive interactions, stemming from Spemann’s seminal work on lens induction9. These inductive interactions coordinate self-assembly of the various tissues that comprise the vertebrate camera eye including the optic vesicle of the forebrain, which generates the retina, and the overlying presumptive lens tissue. In the embryo, interactions with neighboring tissues help to remodel the hemi-spherical optic vesicle into a bi-layered optic cup. Yet this vesicle-to-cup transformation is spontaneously recapitulated by stem cell-derived retinal organoids in vitro8, revealing that a hitherto unsuspected tissue-intrinsic mechanism suffices to self-organise the primary retinal axis. Here we provide evidence for a self-organising mechanism centered on the transcription factor-coding gene Paired box 6 (Pax6).
Pax6 has been called an eye master control gene10 and is necessary for eye development across much of the animal kingdom, from flies to humans1–3, 11. Mis-expression of mammalian or cephalopod Pax6 genes triggers the spontaneous development of ectopic compound eyes in arthropods4, 5, as well as supernumerary camera eyes in vertebrates6. This deeply homologous function, whereby a shared Pax6 genetic apparatus builds eye structures that are morphologically and phylogenetically distinct12, is poorly understood. Here we describe a putative self-organising Turing network7 comprising Pax6 and a pair of morphogen-coding genes Transforming Growth Factor-beta 2 (Tgfb2) and Follistatin (Fst). Using reaction-diffusion modelling we show how this gene network may spontaneously polarise the optic vesicle to trigger self-organisation of the vertebrate retina.
Results
Optic vesicle polarisation is apparent from Hamburger & Hamilton13 stage HH10 in the chick, evidenced by differential gene expression along a proximal-distal axis: Pax6 and Visual system homeobox 2 (Vsx2; formerly Chx10) are expressed distally (Fig.1a, b), whereas Microphthalmia associated transcription factor (Mitf) and Wnt family member 2b (Wnt2b; formerly Wnt13) are expressed proximally (Fig.1c, d). We additionally report that two further genes, Transforming Growth Factor-beta 2 (Tgfb2) and Follistatin (Fst) are co-expressed with Pax6 in the distal optic vesicle (Fig.1e, f).
As the optic vesicles evaginate between stages HH8 and HH10, they encounter Bone morphogenetic protein (Bmp) family growth factors from the overlying surface ectoderm (e.g. Bmp4; Fig. 1g). Bmps are implicated in establishing both distal and proximal cell identities within the optic vesicle; Bmp alone promotes distal character14, whereas combined with canonical Wnt signalling it was proposed to induce proximal character15. Consistently, we found that exposing HH10 optic vesicle explants to Bmp4 ligand for 16 hours in vitro led to an up-regulation of distal Pax6 (2.35 ± 0.19 fold, mean ± standard deviation; P < 0.01; n = 4) as measured by RT-QPCR (Fig. 1h). The remaining distal (Vsx2) and proximal (Wnt2b, Mitf) markers were not significantly affected (Fig. 1h). Following combined exposure to both Bmp4 and the Wnt agonist BIO (6-bromoindirubin-3’-oxime; GSK3 inhibitor)16, Pax6 (1.88 ± 0.38 fold; P < 0.05; n = 5) was similarly affected (Fig. 1i), while the proximal marker Wnt2b was additionally up-regulated (9.28 ± 7.89 fold; P < 0.05; n = 5), suggesting that Wnt2b may auto-regulate. Wnt activation alone induced proximal Wnt2b (3.69 ± 1.43 fold; P < 0.01; n = 4) without significantly affecting distal markers (Fig. 1j), while exposure to DMSO (carrier for BIO) had no impact (Fig. 1k). These data do not support a direct synergism between Bmp and Wnt signalling in establishing proximal-distal polarity, as their combined action is merely additive.
To validate the interaction between Bmp signalling and Pax6 expression in vivo, we performed electroporation-mediated gene transfer to mis-express the cell-autonomous Bmp inhibitor Smad6 in single optic vesicles, while un-electroporated contralateral vesicles served as internal negative controls (Fig. 2a). In comparison to mis-expression of a benign Enhanced Green Fluorescent Protein (GFP; 1.13 ± 0.37 fold; n = 7; Fig. 2b, c, d), Smad6 caused a asymmetric reduction in the area of Pax6 expression between transfected and contralateral control vesicles (0.56 ± 0.31 fold; P < 0.05; n = 13; Fig. 2b, e, f). This confirms that distal Pax6 expression in vivo requires upstream Bmp.
Auto-regulation of Pax6 has been reported in a number of tissues including the lens17. To test for Pax6 auto-regulation in the optic vesicle, a C-terminally truncated dominant negative Pax6 gene (dnPax6)18 was mis-expressed unilaterally, while a C-terminal riboprobe was used to selectively detect endogenous Pax6 expression. dnPax6 did not disrupt endogenous Pax6 expression (0.75 ± 0.36 fold; P > 0.05; n = 9; Fig. 2b, g, h) compared with the GFP control, yet nor could we distinguish a difference between dnPax6 and Smad6 mis-expression (Fig. 2b; P> 0.05). Thus, while distal Pax6 expression in the optic vesicle requires Bmp signalling in vivo, we cannot exclude the possibility that upstream Bmp action may mask subsequent Pax6 auto-regulation.
Migratory neural crest cells reach the optic vesicle at stage HH10 and are thought to induce proximal and suppress distal gene expression via Tgfb subfamily signalling19, 20. Exogenously supplied Tgfb subfamily ligand (Activin A) was reported to induce proximal (Wnt2b, Mitf) and inhibit distal (Pax6, Vsx2) gene expression in explant cultures19. In contrast to this tissue-extrinsic induction mechanism, stem cell-derived retinal organoids are reported to polarise tissue-autonomously, exemplified by the spontaneous acquisition of proximal Wnt activity21. This raises the possibility of a redundant tissue-intrinsic polarising activity. Given that distal Tgfb2 expression correlates with Pax6 (Fig. 1a & e) we asked whether Pax6 might induce Tgfb2 to activate proximal target genes tissue-autonomously. In comparison with GFP controls (1.06 ± 0.17 fold; n = 8; Fig. 3a, b, c), mis-expression of dnPax6 in single optic vesicles diminished Tgfb2 expression relative to contralateral control vesicles (0.79 ± 0.54 fold; P < 0.05; n = 15; Fig. 3a, d, e). Thus, the Pax6 master controller is required for Tgfb2 expression in the distal vesicle, consistent with a report of Pax6 binding sites located within the Tgfb2 promoter22.
This presents a paradox however; Tgfb2 expression (Fig. 1e) negatively correlates with its positive targets Wnt2b and Mitf (Fig. 1c, d), yet positively correlates with its negative targets Pax6 and Vsx2 (Fig. 1a, b)19. How might Tgfb pathway activation become inverted relative to Tgfb2 gene expression? We considered whether Pax6 might also activate Fst (Fig. 1f), a Tgfb antagonist, to grant distal immunity from Tgfb signalling. Compared with GFP controls (1.31 ± 0.63 fold; n = 6; Fig. 3f, g, h), mis-expression of dnPax6 in a single optic vesicle significantly reduced Fst expression (0.69 ± 0.34 fold; P < 0.05; n = 8; Fig. 3f, i, j). Thus, Pax6 function is additionally required for Fst expression in the distal vesicle.
The paradoxical out-of-phase expression of distal Tgfb2 and its proximal (positive) targets might then be explained by differential diffusion of Tgfb2 and Fst gene products resulting in: i) Tgfb2 being locally sequestered by slow-diffusing Fst within the distal vesicle, thereby preserving distal character; ii) fast-diffusing Tgfb2 dispersing proximally away from Fst, to induce proximal character within the neighboring proximal vesicle.
To test if this hypothesis is plausible, we examined a reaction-diffusion model of the interactions summarised in Fig. 4a (Model A; see Supplementary Information) and performed numerical simulations with a variety of diffusion ratios for Tgfb2 dimers and Fst monomers versus Fst:Tgfb2 complexes (e.g. Fig. 4b, c; Supplementary Movie 1). Simulations demonstrated that local inhibition and lateral-activation of Tgfb signalling may occur if the diffusion rate of Fst:Tgfb2 complexes exceed that of Fst monomers. Although initially counter-intuitive, there is precedent for ligand:antagonist complexes that disperse faster than their individual constituents23 and our subsequent simulations assume this condition is satisfied.
Given that Tgfb signalling is known to disrupt Pax6 protein function18, such local inhibition and lateral-activation of Tgfb signalling equates to local positive feedback and lateral-inhibition of the Pax6 master control gene, respectively (Fig. 4d). This is functionally equivalent to a simple Activator-Inhibitor24 type Turing network7, which can serve as a spontaneous pattern generator; Pax6 and Fst comprising a short-range auto-regulating Activator, and Tgfb2 as the long-range Inhibitor. To explore whether the network of Fig. 4d possesses spontaneous polarising activity, we simply extended Model A to include inhibition of Pax6 function by Tgfb signalling (Model B; see Supplementary Information). Simulations showed that an initially homogenous but noisy Pax6 distribution is readily converted into a polarised pattern, wherein Pax6 expression becomes regionally restricted (Fig. 4e) and out-of-phase with Tgfb receptor activation (Fig. 4f; Supplementary Movie 2). Additionally, simulating larger tissue sizes results not in a larger Pax6-expressing distal pole, but in a greater number of Pax6-expressing distal poles of approximately equal size (Fig. 4g, h). This hallmark feature of Turing networks is remarkably consistent with observations of retinal organoid cultures in which stem cell aggregates yielded between one and four retinas each8.
It follows that reducing tissue size should limit the number of Pax6-expressing distal poles until polarisation is no longer possible. When cultured as isolated explants in the absence of serum, polarised HH10 optic vesicles (e.g. Fig. 4i) collapse into compact spheroids (Fig. 4j) reducing this tissue’s longest dimension to ≤0.5 fold. Continuing the Model B simulation of Fig. 4e & f after reducing the length of this polarised tissue predicts that proximal-distal polarity should be lost in this case (Fig. 4k, l). To test this, we compared proximal and distal gene expression before and after vesicle collapse under neutral culture conditions. In agreement with the simulation, the four distal markers Pax6 (0.40 ± 0.08 fold; P < 0.001; n = 4), Fst (0.12 ± 0.04 fold; P < 0.001; n = 4), Tgfb2 (0.65 ± 0.17 fold; P < 0.05; n = 4) and Vsx2 (0.66 ± 0.25 fold; P < 0.05; n = 4) are all reduced following vesicle collapse (Fig. 4m).
Model B (Fig. 4d) further predicts that interference with Fst gene expression should derepress Tgfb signalling and inhibit Pax6 protein function in the distal vesicle, via the direct Tgfb-dependent interaction of Smad3 with Pax618. Moreover, if Pax6 auto-regulates in the distal vesicle, this should manifest as a Tgfb-mediated reduction in Pax6 gene expression. To test this prediction, we employed morpholino oligonucleotides to suppress Fst translation within single optic vesicles and compared Pax6 expression between these and unperturbed contralateral vesicles. Fst morpholino (FstMO) was first shown by Western Blotting to suppress endogenous Fst protein expression in cultured chick embryonic cells, as compared to a standard control morpholino (StdMO) that does not target Fst (Fig. 5a). In vivo, StdMO controls had no impact on Pax6 expression in transfected optic vesicles (1.05 ± 0.31 fold; n = 20; Fig. 6b, c, d). In comparison, FstMO reduced Pax6 expression in transfected vesicles (0.76 ± 0.50 fold; P < 0.01; n = 18; Fig. 5b, e, f), as predicted by Model B. We were able to rescue this loss of Pax6 expression by co-transfecting FstMO together with an exogenous Fst transgene that evades FstMO (0.98 ± 0.35 fold; P > 0.05; n = 25; Fig. 5b, g, h), confirming that loss of Pax6 was not due to a morpholino off-target effect. Thus, Fst is required for distal Pax6 expression in the optic vesicle. This is consistent with earlier reports that neural induction by way of Fst overexpression induces Pax6 in Xenopus animal cap explants25.
To verify that loss of Pax6 expression is indeed due to the predicted de-repression of Tgfb signalling, we attempted an alternate rescue by co-transfecting FstMO together with a cell-autonomous Tgfb pathway inhibitor, Smad7. As can be seen (Fig. 5b, i, j), no significant loss of Pax6 expression was observed (0.91 ± 0.31 fold; P > 0.05; n = 13) when Fst translation and Tgfb signalling were simultaneously suppressed.
In addition to inducing Pax625, overexpression of Fst in Xenopus animal cap explants was reported to induce expression of the retinal photoreceptor marker Opsin26. We therefore investigated whether Vsx2, a distally expressed neural retinal marker27 (Fig. 1b), is similarly affected upon disruption of the Pax6/Fst/Tgfb2 gene network. In comparison to StdMO controls (1.51 ± 1.05 fold; n = 7; Fig. 5k, l, m), FstMO significantly reduced distal Vsx2 expression in transfected optic vesicles (0.69 ± 0.33 fold; P < 0.05; n = 9; Fig. 5k, n, o). Thus, de-repression of endogenous Tgfb signalling in the distal vesicle is detrimental for correct proximal-distal patterning, including specification of the neural retina. These results are consistent with Model B (Fig. 4d) and support the idea that Fst and Tgfb2 morphogens positively and negatively regulate Pax6 function, respectively, in order to polarise the optic vesicle.
Discussion
The question of Pax6’s master control mechanism has been unresolved for a quarter of a century28. Here we have shown that the vertebrate Pax6 directs expression of a pair of morphogen coding genes, Fst and Tgfb2, which modulate Pax6 function via positive and negative feedbacks. Our reaction-diffusion simulations showed that the Pax6/Fst/Tgfb2 gene network may act as a self-organising Turing network, providing certain assumptions are satisfied. For instance, we have assumed that larger Fst:Tgfb2 complexes diffuse more quickly than smaller Fst monomers. This is counter-intuitive since pure diffusion rate is a function of molecular mass, yet there is precedent for this phenomenon; e.g. Sfrp:Wnt complexes have been observed to diffuse further than Wnt alone23. We postulate that Fst monomers disperse sub-diffusively due to binding interactions with extra-cellular matrix components and/or cell surface factors, e.g. heparin sulfate proteoglycans29. In the context of Fst:Tgfb2 complexes, interaction surfaces may be shielded enabling the larger complex to disperse further and faster than its constituents.
The assumed rapid dispersal of Fst:Tgfb2 complexes is only required if Tgfb2 sequestration by Fst is reversible, which is currently unknown. Low affinity Fst:Bmp interactions are known to be reversible whereas high affinity Fst:Activin interactions are effectively irreversible30. If Fst:Tgfb2 associate irreversibly then spontaneous pattern formation is still possible, but it changes assumptions regarding effective diffusion rates: Fst:Tgfb2 diffusion would then become irrelevant and instead, Tgfb2 dimers must diffuse faster than Fst monomers31.
By demonstrating how Pax6 may drive self-organisation of the primary retinal axis, our findings offer the first mechanistic explanation of Pax6‘s long-known but poorly understood master control function. In the embryo, we propose that this putative Turing network acts to self-organise the optic vesicle’s proximal-distal axis (as summarised in Fig. 6a & b) and that previously identified inductive interactions serve to trigger and/or synchronise this tissue-autonomous activity with neighboring tissues. For instance, Bmp signals from the overlying head ectoderm may bias proximal-distal polarity to align the distal pole with the prospective lens. BMP inhibition14 (or an absence of lens ectoderm) may then prevent the reported Pax6/Fst/Tgfb2 network from being activated, or else permit supplementary Tgfbs from the surrounding neural crest mesenchyme19, 20 to overwhelm this tissue-intrinsic polarising activity. In turn, it has not escaped our attention that distal Fst may mediate classical lens induction9 by opposing these same lens-inhibitory Tgfb signals20; indeed, Fst overexpression induces lens crystallin expression in Xenopus animal cap explants25.
We did not investigate the role of Wnt in establishing proximal identity within the optic vesicle, except to test for direct synergism between Wnt and Bmp as previously proposed15. In the absence of such synergism, we suggest that Wnt acts downstream of the Pax6/Fst/Tgfb2 gene network, since i) Wnt2b is a Tgfb target gene19 restricted to the proximal optic vesicle (Fig. 1c), and ii) expression of Wnt2b is absent from the peri-ocular surface ectoderm until HH1120 prior to which, polarised Wnt2b expression is already established within the optic vesicle itself (Fig. 1c).
During retinal organoid development in vitro8, we propose that the Pax6/Fst/Tgfb2 network may suffice to self-organise the retina’s primary axis in the absence of well-ordered tissue interactions characteristic of embryonic eye development. The comparatively chaotic nature of organoids makes them an ideal counterpart to embryonic models of development as they can unmask cryptic self-organising mechanisms and test them to breaking point; contrast the straightforward elaboration of an existing pre-pattern (Fig. 4b, c; analogous to localised Pax6 induction by neighboring Bmps in vivo) with the more turbulent emergence of order from disorder (Fig. 4e, f; analogous to spontaneous Pax6 activation in retinal organoids). Further exploration of the Pax6/Fst/Tgfb2 network may drive future developments in retinal organoid technology and help underpin applications in disease modelling, drug discovery and regenerative therapies. Given the deeply homologous nature of Pax6’s master control function, we would predict that Pax6 orthologues participate in functionally homologous Turing networks in non-vertebrates, which may comprise the same or different morphogens.
Materials & Methods
Chick embryos
Fertile brown hen’s eggs (Henry Stewart) were incubated at 38 °C in a humidified incubator until the required stage of development: HH8 for in ovo electroporation experiments; HH10 for in vitro explant experiments.
Explant Assays
HH10 embryos were incubated with 0.25 % Trypsin-EDTA at 38 °C for 7 minutes. Trypsin was then de-activated by transferring into 20 % chick serum on ice for 5 minutes. Embryos were then washed with Tyrodes solution and pinned onto Sylgard-coated dissection dishes. Head surface ectoderm and peri-ocular mesenchyme were carefully removed using 30 gauge syringe needles from both dorsal and ventral sides. Once cleaned, both optic vesicles were removed and held in Tyrodes solution on ice. Left and right optic vesicles were separately pooled from at least five embryos, yielding two match-paired pools for use as treated and control samples. Pooled vesicles were cultured in polyHEMA (Sigma) coated culture wells to prevent adhesion, with DMEM-F12 media (Invitrogen) supplemented with 1X N2 (Invitrogen), 1X L-Glutamate and 1X Penicillin/Streptomycin at 37 °C and 5% CO2 for 16 hrs. Culture media for treated samples was supplemented with the following factors as required: 35 ng/ml Bmp4 (R&D Systems), 0.5 μM BIO (Sigma) with 0.1 % DMSO (Sigma), or 0.1 % DMSO only.
Quantitative RT-PCR
Explant samples were lysed in 1 ml Trizol (Ambion) and processed for total RNA extraction. RNA samples were digested with DNase I (Ambion) and re-extracted by acidic Phenol/Chloroform. RNA concentrations were determined by NanoDrop ND-1000 Spectrophotometer. For each experiment, equal quantities of treated and control sample RNA (typically between 0.1 – 0.6 μg) were used as template for first strand cDNA synthesis using Superscript II reverse transcriptase (Invitrogen) and random hexamers. cDNAs were diluted 1:20 before relative quantitation of transcript levels by real-time PCR using SYBR Green master mix (Applied Biosystems) and target-specific primers (Supplementary Table 1). Relative transcript quantification was via the standard curve method, and target gene expression was normalised to the reference gene β-Actin. Fold changes were calculated for each matched-pair (treated/control) then log-transformed to ensure normal distribution. These were plotted as mean +/-standard deviation. Student’s paired t-test was used to calculate the probability of the observed (or more extreme) differences between match-paired (treated and control) sample means assuming that the null hypothesis is true.
Morpholino Knockdown Validation
Fst-expressing somite tissue from wild-type chick embryos were dissected and cultured in Dulbecco’s Modified Eagle Medium, 10% foetal bovine serum, 1% penicillin/streptomycin for 4 h before transfecting with 1 mM translation-blocking FstMO (Gene Tools; sequence 5’-GATCCTCTGATTTAACATCCTCAGC-3’) or 1mM StdMO negative control (Gene Tools; sequence 5’-CCTCTTACCTCAGTTACAATTTATA-3’) using Endoporter PEG (Gene Tools). Protein was extracted after 48 h. Protein lysate (30 μg) was run on pre-cast 4-15% polyacrylamide gels (Bio-Rad) and blotted onto polyvinylidene fluoride membrane (Bio-Rad). Primary antibody against Fst (Abcam ab47941; 1:2,000) was applied at 4°C overnight and secondary polyclonal goat anti-rabbit-HRP (Cell Signaling Technology #7074; 1:2,000) was applied for 1 h at room temperature. Primary antibody against HSC70 (Santa Cruz sc-7298; 1:2,500) was applied at 4°C overnight and secondary polyclonal goat anti-mouse-HRP (Agilent P0447; 1:1,000) was applied for 1 h at room temperature. The blots were treated with an ECL substrate kit and imaged.
In Ovo Embryo Electroporation
Plasmid DNA (2 – 5 μg/ul) or plasmid DNA and FITC-labelled Morpholino oligonucleotides (2 μg/ul and 0.5 mM, respectively), were injected into the open neural tube of stage HH8 chick embryos in ovo (Fig. 2a). A pair of platinum electrodes connected to an Ovodyne electroporator and current amplifier (Intracel) were then used to electroporate the DNA or DNA + Morpholino into either left or right side of the anterior neural tube via 4 pulses of 22 volts with 50 ms duration and at 1 second intervals. Once electroporated, embryos were sealed with adhesive tape and incubated for 10 – 12 hours at 38 °C until embryos had reached stage HH10.
Wholemount In Situ Hybridization and Immunofluorescence
Embryos were fixed in 4% PFA overnight at 4 °C, then dehydrated by methanol series and stored at −20 °C. Following rehydration, embryos were processed for wholemount in situ hybridization using 1 μg/ml DIG-labelled antisense probes for Pax6, Vsx2, Mitf, Fst (see Supplementary Table 2 for PCR primers), Tgfb2 (EST clone ChEST262a17)32, Wnt2b (a gift from Susan Chapman) and Bmp4 (a gift from Elisa Martí). Probes were hybridized at 65 °C for up to 72 hrs. After incubation with 1:5,000 anti-DIG antibody (Roche) and washing, 4.5 μl nitroblue tetrazolium (50 mg/ml) and 3.5 μl 5-bromo-4-chloro-3-indolyl phosphate (50 mg/ml) per 1.5 ml developing solution were used for color development. Embryos were embedded in 7.5 % gelatin, 15 % sucrose and cryo-sectioned at 15 μm thickness. Following de-gelatinisation, sections were blocked in PBTS buffer (PBS with 2 % BSA, 0.1 % Triton X-100 and 10 % goat serum) for 1 hr at room temperature. EGFP transgene expression was then detected using rabbit anti-GFP primary antibody (Abcam; 1:500 dilution) and Alexa568 goat anti-rabbit secondary antibody (Invitrogen; 1:1000 dilution). Morpholino FITC fluorescence was observed directly. Labelled sections were imaged using a 20X objective on an Axioplan widefield fluorescence microscope with Axiocam HRc camera and Axiovision software (Carl Zeiss).
Relative Quantification of In Situ Hybridization Staining
Assuming that average cell size is invariant between left and right optic vesicles of the same embryo, then the relative area of staining is proportional to the relative number of cells exceeding a common detection threshold. To quantify this, brightfield micrographs were converted to greyscale, inverted then thresholded and the area of optic vesicle staining measured in FIJI33. Transfected and contralateral controls from the same embryo were processed simultaneously to ensure identical treatment. Staining area in transfected vesicles was then normalised to internal contralateral controls, yielding fold change in gene expression area. Fold changes were log-transformed to ensure normal distribution prior to plotting and null hypothesis significance testing. Box plots showing mean Log10(fold change) +/-standard deviation were generated in R with the package ‘Beeswarm’. Welch’s two-sample t-test (for pairwise comparisons) or one-way ANOVA with Tukey’s post hoc test (for groupwise comparisons) were used to calculate the probability of the observed (or more extreme) differences between sample means assuming that the null hypothesis is true.
Reaction-Diffusion Simulations
Partial differential equations were coded in R using the function tran.1d() from package ‘ReacTran’ to handle diffusion terms. 1-D numerical simulations used the function ode.1d() from package ‘deSolve’ and the default integrator. Parameter sweeps were performed to identify suitable diffusion rates (see Supplementary Movies 1 & 2). Simulations were run with both periodic and zero-flux boundary conditions, with comparable results. See Supplementary Information for model code and narrative text. The model code is explained in Supplementary Information, is available via our GitHub repository (https://github.com/GrocottLab/) and is accessible as an interactive Jupyter Notebook (https://mybinder.org/v2/gh/GrocottLab/Pax6-Fst-Tgfb2_Reaction_Diffusion_Models/master).
Author Contributions
T.G. conceived the project, designed/performed the experiments and computational modelling, analysed the data and prepared the figures. T.G. and A.E.M. interpreted the data and wrote the manuscript. G.F.M. and E.L.-V. performed morpholino knockdown validation.
Acknowledgements
This work was supported by a Fight for Sight UK Early Career Investigator Award to T.G. (1365/66), a BBSRC Project Grant (BB/N007034/1) to A.E.M. and a H2020 Marie Sklodowska-Curie Actions Individual Fellowship (705089) to E.L.-V. We thank Paul Thomas of the Henry Wellcome Laboratory for Cell Imaging for assistance with microscopy and colleagues in the laboratories of Grant Wheeler and Andrea Münsterberg for valuable discussions. We thank Elisa Martí and Susan Chapman for sharing plasmids.