Rapid changes in tissue mechanics regulate cell behaviour in the developing embryonic brain

1During embryonic development, many biological processes are regulated by tissue mechanics, including cell migration, neuronal growth, and large-scale tissue remodelling. Recent measurements at specific time points suggested that tissue mechanics change during developmental and pathological processes, which might significantly impact cell function. Furthermore, several approaches have recently been developed to measure in vivo tissue stiffness, including atomic force microscopy, magnetic resonance elastography, Brillouin microscopy, and magnetically responsive ferrofluid microdroplets. However, the precise spatiotemporal dynamics of tissue mechanics remains poorly understood, and how cells respond to changes in local tissue stiffness in vivo is largely unknown.

2To enable time-resolved measurements of developmental tissue mechanics, we here developed time-lapse in vivo atomic force microscopy (tiv-AFM), a method that combines sensitive upright epifluorescence imaging of opaque samples, such as frog embryos, with iterated AFM indentation measurements of in vivo tissue at cellular resolution and at a time scale of tens of minutes (Figure 1). A fluorescence zoom stereomicroscope equipped with an sCMOS camera (quantum yield 82%) was custom-fitted above a bio-AFM set-up (Figure 1—figure supplement 1), which had a transparent pathway along the area of the cantilever. To cope with the long working distance required for imaging through the AFM head, the microscope was fitted with a 0.125 NA/114 mm WD objective. The AFM was set up on an automated motorised stage containing a temperature-controlled sample holder to maintain live specimens at optimal conditions during the experimental time course. (Figure 1a,b) (see Materials and methods for details).

3We tested tiv-AFM using the developing Xenopus embryo brain during outgrowth of the optic tract (OT) as a model (Figure 1c). In the OT, retinal ganglion cell (RGC) axons grow in a bundle across the brain surface, making a stereotypical turn in the caudal direction en route that directs them to their target, the optic tectum. We previously demonstrated that by later stages of OT outgrowth (i.e. when axons had reached their target), a local stiffness gradient lies orthogonal to the path of OT axons, with the stiffer region rostral to the OT and softer region caudal to it. This gradient strongly correlated with axon turning, with the OT routinely turning caudally towards softer tissue. We therefore wanted to determine when this stiffness gradient first developed, whether its emergence preceded OT axon turning, and what the origin of the stiffness gradient was.

4To answer these questions, we performed iterated tiv-AFM measurements of the embryonic brain in vivo at early-intermediate stages, that is, just before and during turn initiation by the first ‘pioneer’ OT axons. The apparent elastic modulus K, which is a measure of the tissue’s elastic stiffness, was assessed in an ~150 by 250 µm raster at 20 µm resolution every ~35 min, producing a sequence of ‘stiffness maps’ of the area (Figure 2—figure supplement 1). The applied force (F = 10 nN) and cantilever probe (r = 18.64 µm) were chosen to measure the stiffness mainly of the top ~20–30 µm of the tissue, within which RGC axons grow. To reduce noise, raw AFM data were interpolated and smoothed in x-, y-, and time dimensions using an algorithm based on the discrete cosine transform (Figure 2a,b, see Materials and methods for details). Simultaneously, we recorded optical time-lapse images of fluorescently labelled RGC axons growing through the region of interest (Figure 2a, Figure 2—figure supplement 1).

5To assess whether repeated AFM measurements of the Xenopus brain affect RGC axon growth, we first conducted time-lapse AFM measurements on one group of embryos while we exposed another group to the same conditions without making force measurements. At the end of the experiments (i.e., at stage 37/38), OTs were labelled with DiI, and their elongation and turning angles measured. We did not find any significant differences between the groups (Figure 2—figure supplement 2), suggesting that repeated AFM measurements do not affect axon growth.

6We then performed tiv-AFM measurements of developing Xenopus brains. Early in the time-lapse sequence (i.e. prior to axon turning), the stiffness of the brain was similar on both sides of the OT. However, over the time course of the measurements a stiffness gradient arose, mostly due to rising stiffness of tissue rostral to the OT (Figure 2a,b). Visual inspection of the fold-change in tissue stiffness from one time point to the next indicated that significant changes in tissue mechanics were already occurring approximately 40–80 min after the onset of measurements (Figure 2b), that is before axons started turning caudally, suggesting that the tissue stiffness gradient was established prior to axon turning.

7To test this hypothesis, we quantified the temporal evolution of the stiffness gradient in a small region immediately in front of the advancing OT (Figure 2—figure supplement 1a). At the beginning of each time point in the sequence of tiv-AFM maps, we calculated the angle through which axons turned (‘OT turn angle’). For each animal, minimum and maximum absolute values were rescaled to 0 and 1, respectively (Figure 2c). The projected appearance of the stiffness gradient preceded the projected onset of axon turning on average by 18 min (Figure 2d,e), indicating that axons indeed turned after the stiffness gradient was established, which is consistent with a role for mechanical gradients in helping to guide OT axons caudally. Based on the first time point at which we detected axon turning in each animal, our data suggested that a stiffness gradient of at least (0.9 ± 0.4) Pa/µm (mean ± SEM) was required for axons to change their growth direction. In line with this idea, RGC axons from heterochronic eye primordia transplants growing through Xenopus brains at stages before the stiffness gradient is established grow rather straight and do not turn caudally in the mid-diencephalon.

8We have previously shown that tissue stiffness scales with local cell body density, and that in Xenopus embryo brains local stiffness gradients at later developmental stages (39-40) correlate with a gradient in cell density. To determine if changes in cell densities are driving changes in tissue stiffness, and thus parallel the evolution of the stiffness gradient at earlier stages, we assayed cell densities using DAPI labelling of nuclei in whole-mounted brains with fluorescently labelled OTs, beginning at the morphological stage corresponding to the start of tiv-AFM measurements (33/34) and repeated for the two subsequent stages encompassing OT turning (35/36 and 37/38).

9While at the first stage cell densities on both sides of the OT were similar, a clear difference in nuclear densities rostral and caudal to the OT developed at later stages (Figure 3a). Cell densities at the two later stages were significantly higher in the region rostral to the OT (i.e. where tissue was stiffer) than caudal to it, and the overall magnitude of the cell density gradient significantly rose over time (Figure 3b). Plotting the stage-specific gradient in cell body densities against the stiffness gradient revealed a strong linear correlation between them (Pearson’s correlation coefficient ρ=0.97) (Figure 3c).

10To test if local cell densities drive the evolution of the stiffness gradient during OT turning, we repeated both nuclear staining and tiv-AFM measurements on embryos treated with the mitotic blocker BI2536, which inhibits Polo-like kinase 1 and has previously been used to inhibit in vivo cell proliferation in the embryonic retina. BI2536 also triggered mitotic arrest in brains of developing Xenopus embryos, as the number of phosphorylated histone H3 (pH3)-positive cells was significantly higher in treated compared to control brains, and the cross-sectional area of treated brains was significantly decreased at later stages, indicating a decrease in total cell number (Figure 4a–c). Inspection of the stage-dependent distribution of cells in the developing Xenopus brain suggested that in BI2536-treated brains, the nuclear density was decreased particularly rostral to the OT (Figure 4d, Figure 4—figure supplement 1). In tiv-AFM experiments, blocking cell proliferation significantly attenuated the increase of both the stiffness gradient and the OT turn angle over the time course of the experiment (Figure 4e,f), suggesting that the gradient in cell densities strongly contributed to the stiffness gradient, which in turn helps instruct axon growth.

11The absence of an increase in tissue stiffness near the advancing OT in BI2536-treated brains was furthermore accompanied by a decrease in OT elongation (Figure 4g). Similarly, OT elongation decreased when brains were softened by manipulating the extracellular matrix, confirming that tissue stiffness is involved in regulating axon growth in vivo.

12We obtained similar results using a different mitotic blocker, hydroxyurea/aphidicolin (HUA), which inhibits DNA replication and has previously been used to block cell division in Xenopus embryos. HUA also decreased the gradient in nuclear densities (mainly by reducing nuclear densities rostral to the OT), decreased brain stiffness, and generated defects in OT outgrowth (Figure 4—figure supplement 2).

13In order to test if the mitotic blocker BI2536 perturbs neuronal mechanosensing, we cultured eye primordia on laminin-coated polyacrylamide substrates of different stiffnesses, exposed the outgrowing RGC axons to the drug, and quantified axon growth as a function of substrate stiffness. While RGC axon growth on stiff substrates with a shear modulus G’~5,500 Pa was not altered by the presence of BI2536 if compared to control conditions (Figure 4—figure supplement 3e), axons grew longer on soft substrates of G’~200 Pa when they were exposed to 50 nM BI2536 but not when they were exposed to 500 nM (Figure 4—figure supplement 3f), suggesting that the drug might partially impact axon growth on very soft substrates (although no significant differences were observed when axons were grown on slightly stiffer substrates of G’~300 Pa, Figure 4—figure supplement 3d). However, similar to control conditions, axons exposed to different concentrations of BI2536 grew significantly longer on stiff substrates compared to softer substrates. Hence, RGC axons responded to substrate stiffness despite the presence of the mitotic blocker (Figure 4—figure supplement 3g).

14Our data show that, during early embryonic development, local tissue stiffness may change significantly within only tens of minutes (Figure 2), leading to heterogeneous stiffness distributions which, in the developing Xenopus brain, impact RGC axon growth. These stiffness heterogeneities were largely governed by differential cell proliferation (Figures 3 and 4), which is in agreement with previously published correlations between cell body densities and tissue stiffness. Mitotic blockers almost completely abolished the rise of the stiffness gradient (Figure 4), which was accompanied by a decrease in turning angle of the OT, emphasizing the importance of the control of local cell proliferation for mechanosensitive cellular processes in vivo.

15As changes in substrate stiffness have been shown to promote cell proliferation in vitro, an increase in cell density might lead to a mechanical positive feedback loop, facilitating further cell proliferation. Perturbing cell division, on the other hand, might alter not only local tissue stiffness but also topological cues in the tissue, which may also provide important signals regulating axon growth. Having fewer cell bodies rostral to the OT might decrease the amount of steric hindrance and provide more space for axons to grow into, contributing to the reduction in OT turning angle (Figure 4e).

16Our analysis of the correlation between local cell body density gradients and stiffness gradients suggests that other structures may contribute to the stiffness gradient as well (Figure 3c), although perhaps to a smaller degree. Potential candidates include radial glial cells as well as components of the extracellular matrix.

17Tiv-AFM allows simultaneous time-lapse measurements of tissue mechanics in vivo and optical monitoring of fluorescently labelled structures at the surface of otherwise optically opaque samples, at length and time scales that are relevant for developmental processes. It enabled us for the first time to trace the in vivo mechanical properties of the embryonic Xenopus brain as the embryo developed, and to relate changes in tissue mechanics to a key event in axon pathfinding. As in all other AFM applications, in tiv-AFM forces are applied to sample surfaces, restricting it to biological processes that occur within tens of micrometers away from the surface, such as OT elongation in developing Xenopus embryos. Mapping of the whole Xenopus brain at cellular resolution takes about half an hour, which defines the maximum temporal resolution that can currently be achieved. Future developments of alternative approaches may enable measurements within tissues at even higher rates. However, tiv-AFM in its current form revealed that significant changes in tissue stiffness occur in vivo within tens of minutes, and that these changes have significant implications for a biological process, the outgrowth of RGC axons along the developing embryonic brain.

18More broadly, tiv-AFM can also be easily adapted for in vivo applications in other small organisms, or alternatively in tissues ex vivo. It can be used to study cellular responses to a range of mechanical stimuli via the AFM in vivo, such as sustained compression, or to track the temporal mechanical response of tissues or organs to different pharmacological treatments (such as the mitotic inhibitor used here). Additionally, the setup is very versatile and can be further expanded, for example, by combining it with calcium imaging to investigate how cellular activity is regulated by changes in tissue stiffness during development and pathology. Tiv-AFM will greatly expand the range of bio-AFM experiments possible, allowing for more scope both for a detailed characterisation of in vivo tissue mechanics during development and disease progression, and for testing how mechanics shapes cell behaviour and function.

19All chemicals and reagents were obtained from Sigma-Aldrich unless otherwise noted.

20All animal experiments were approved by the Ethical Review Committee of the University of Cambridge and complied with guidelines set by the UK Home Office. Single-cell-stage, wild-type Xenopus laevis embryos of both sexes were obtained via in vitro fertilisation. Embryos were reared in 0.1× Modified Barth’s Saline (MBS) at 14–18°C to reach the desired developmental stage, as described by. All embryos used in this study were below stage 45.

21To visualise the developing OT during time-lapse AFM experiments, an ath5::GAP-eGFP construct (pCS2+ vector) was injected (100 pg/5 nL) into one dorsal blastomere of embryos at the 4 cell stage. The construct consisted of a membrane-tagged GFP fusion under control of the retinal ganglion cell (RGC)-specific atonal homolog 5 promoter. This selectively labelled RGCs in a single retina, the axons of which grew across the optic chiasm and into the unlabelled brain hemisphere.

22Stage 33/34 embryos were anaesthetised, the eye primordium was removed and the underlying brain hemisphere exposed as described. Briefly, embryos were transferred to 1.3 × MBS solution (composition: 1.3 × MBS with 0.04% (w/v) MS222 anaesthetic (3-aminobenzoic acid ethyl ester methanesulfonate) and 1 × penicillin/streptomycin/Fungizone (P/S/F; Lonza), pH 7.4). The higher osmolarity retards skin regrowth, allowing for experiments spanning several hours. Embryos were immobilised on low Petri dishes (TPP, Switzerland) coated with Sylgard 184 using bent 0.2 mm minutien pins, with one side of the body facing up. The eye, epidermis, and dura were removed with 0.1 or 0.15 mm minutien pins and fine forceps to expose one brain hemisphere from the dorsal to ventral midline and from the hindbrain to the telencephalon. Embryos were then immediately used for time-lapse in vivo AFM (tiv-AFM) measurements or, alternatively, transferred to a 4-well plate containing either 1.3× MBS solution+50 µM BI2536 (MedChem Express) (control, 1.3× MBS solution + 0.5% v/v DMSO) or 1.3× MBS solution + 20 mM hydroxyurea and 150 µM aphidicolin (control, 1.3× MBS solution + 1.5% v/v DMSO) and allowed to develop at ~25°C until the desired developmental stage. Embryo viability throughout all in vivo experiments was assessed by the presence of a visible heartbeat (which begins at st. 33/34).

23BI2536 inhibitor or mock-treated embryos were fixed at the requisite stages in 4% PFA overnight at 4°C, washed thrice in phosphate-buffered saline (PBS) for 10 min, and kept in 30% sucrose for 1 hr at 4°C. The embryos were embedded in optimum cutting temperature compound (OCT, VWR). 12µm-thick coronal sections were made and collected on Superfrost plus slides (ThermoScientific).

24Polyacrylamide hydrogels were prepared as previously described. Briefly, 19 mm ‘bottom’ coverslips were coated with 1N NaOH using a cotton bud and allowed to air dry. Coverslips were treated with (3-aminopropyl)trimethoxysilane (APTMS) for 3 min, washed thoroughly, treated with 0.5% glutaraldehyde solution for 30 min, and then washed and allowed to air-dry. 18 mm ‘top’ coverslips were treated with Rain-X (Shell Car Care International Ltd, UK) for 10 min and then dried.

25Gel pre-mixes were prepared using 40% (w/v) acrylamide (AA) solution and 2% bis-acrylamide (Bis-AA) solution (Fisher Scientific, UK, or SIGMA) diluted in PBS. Concentration titration measurements used a premix composition previously determined to give a shear modulus G (a measure of stiffness) of ~300 Pa (5% AA, 0.07% Bis-AA in PBS). For gels used for stiffness sensing experiments, the precise stiffness was measured using AFM. Stiff gels were comprised of 7.5% AA/0.2% Bis-AA in PBS, resulting in a shear modulus of G ~5,500 Pa; soft gels were comprised of 5% AA/0.04% Bis-AA in PBS, resulting in G ~200 Pa.

26Premix polymerization was initiated by adding 5 µL ammonium persulfate followed by 1.5 µL of N,N,N’,N’-tetramethylethylenediamine (TEMED, ThermoFisher). 25 µL of premix was pipetted onto the bottom coverslip and the top coverslip placed on top. Once the gel had polymerized, the top coverslip was removed and gels were treated with hydrazine hydrate for 3.5–4 hr, and then with 5% acetic acid (ACROS Organics) for 1 hr. Gels were then washed, sterilized by 30 min UV treatment, and functionalized with 10 µg/mL Poly-D-lysine (MW 70,000–150,000) overnight followed by 5 µg/mL laminin for 2 hr immediately prior to plating cells.

27For eye primordia culture experiments, stage 33/34 or 35/36 embryos were placed in a Petri dish coated with Sylgard 184 (Dow Corning) and anaesthetized with 0.04% (w/v) MS222 solution (dissolved in 1 × MBS + 1% v/v PSF, adjusted to pH 7.6–7.8, and filter-sterilized). Whole eye primordia were dissected out using insect pins, and placed onto hydrogels with the lens facing up. BI2536 or control solution (DMSO) was added 2 hr after explants were plated. Dishes were cultured at 20°C for 22–24 hr in Xenopus cell culture medium (60% L15 medium + 1× PSF, adjusted to pH 7.6–7.8, and filter sterilized). In all experiments, DMSO controls utilized the amount of DMSO equivalent to that in the most concentrated BI 2536 condition (0.1% v/v for concentration titration, 0.01% v/v for stiffness sensing experiments). Explants were imaged on a Leica DMi8 inverted microscope with a 10× NA = 0.4 phase contrast objective.

28Eye primordia explant morphology was analyzed using the Sholl Analysis plugin in Fiji. An ellipse was fitted to the explant, and the innermost (starting) radius set to R, with A being the ellipse area. Images were filtered with an FFT bandpass filter to correct uneven background illumination and manually thresholded. The outer radius was set to a point beyond the reach of the longest axon. Spacing between consecutive measurements was set to 5 µm. ‘Median sholl radius’ was calculated as the median outgrowth radius reached by axons of a particular explant.

29Where required, to visualise the OT and nuclei for cell body density measurements, embryos at the desired developmental stage were fixed in 4% paraformaldehyde for 1.5–2 hr at room temperature or overnight at 4°C. OTs were either labelled with ath5::GAP-eGFP or by injecting a solution of DiI crystals diluted in ethanol at the boundary between lens and the retina (as previously described ). Fixed brains were then dissected out and stained with 4,6-diamidino-2-phenylindole (DAPI; 1 µg/ml). Stained specimens were mounted in either Fluoromount-G (eBioscience, UK; ath5::GAP-eGFP-labelled OTs) or 1 × PBS (DiI-labelled OTs) and the lateral brain surface, including the OT, was imaged using an SP-8 confocal microscope (SP8, Leica Microsystems, UK; 20× air, NA = 0.75; z-step size = 1 μm).

30Sectioned tissues on slides were washed thrice in PBS, followed by three 10 min washes in PBS with 0.1% TritonX. The sections were blocked in 5% goat serum in PBS with 0.1% TritonX for 30–45 min and incubated with Rabbit polyclonal anti-phospho-Histone H3 (Ser10) (EMD Millipore, 06–570, dilution = 1:1000 in blocking solution) overnight at 4°C or for 2 hr at room temperature. This was followed by three 10 min washes in PBS and secondary antibody incubation with goat anti-rabbit Alexa Fluor 594 (Abcam, ab150084, dilution = 1:500 in blocking solution) for 45–60 min. The slides were washed twice for 10 min with PBS and nuclei were labeled using 4,6-diamidino-2-phenylindole (DAPI, 1 μg/ml). Sections were mounted with Fluoromount-G (eBioscience) and imaged with a confocal microscope (SP8, Leica Microsystems, UK; 20×/0.75 air and 63×/1.4 oil). Z-stacks were taken across 8 µm of tissue (z-step size = 1 µm). Only slices with eye tissue present were selected, to reliably ensure that the brain sections imaged and analysed were indeed exposed to the treatment solutions. This also allowed us to easily ascertain the intact- versus exposed- brain side in each section.

31Tipless silicon cantilevers (Arrow-TL1, NanoWorld) were calibrated using the thermal noise method to determine the spring constant k, and those with k between 0.02–0.04 N/m were selected. Monodisperse spherical polystyrene beads (diameter 37.28 ± 0.34 µm; microParticles GmbH) were glued to the cantilever ends as probes. Cantilevers were mounted on a CellHesion-200 AFM head (JPK Instruments), which was set up on an x/y motorised stage (JPK Instruments) controlled by custom-written Python scripts. Indentation measurements (maximum indentation force: 10 nN, approach speed: 5 µm/s, data rate: 1,000 Hz) were performed automatically in a user-defined rectangular grid to create a 2-D ‘stiffness map’ of the area. After each measurement, the cantilever was retracted by 100 µm, and the stage moved by a set distance (20–25 µm) to the next position.

32To allow simultaneous time-lapse imaging of the growing OT and in vivo stiffness measurements of live Xenopus brains, which are optically opaque, an upright epifluorescence set-up was custom-fit above the AFM head, which was based on a Zeiss AxioZoom V16 fluorescence stereomicroscope (without eyepieces). The microscope was mounted on a custom-designed horizontal sliding stand (parts obtained from ThorLabs) via a custom-made adaptor (K-Tec Microscope Services) bolted to the side of the microscope (Figure 1—figure supplement 1). A long working distance objective with automatic zoom and high NA (PlanApo Z 0.5×/0.125, working distance 114 mm, Zeiss) allowed in vivo fluorescence imaging of RGC axons through the transparent AFM head, which was re-fitted with optical elements optimised for fluorescence imaging. The sample was illuminated through the AFM head using a metal halide lamp, and bright-field as well as epifluorescence images of the brain collected with an sCMOS camera (Andor Zyla 4.2; quantum efficiency 82%) (Figure 1a,b).

33Stage 33/34 embryos with ath5::GAP-eGFP-labelled OTs were prepared with one brain hemisphere exposed as described above, and those in which the OT was clearly visible (but had not yet formed the mid-OT bend) were selected. Embryos were mounted on the AFM motorised stage and a measurement region of approximately 150 × 250 µm defined to include both the growing OT and the region of the mid-diencephalic turn. Images of the upper right and lower left corners of the selected region (with cantilever approached) were collected to identify the precise area mapped by the AFM. A stiffness map of the area was collected and the map iterated over the same area every ~35 min. At the end of every line in the measurement grid, the stage was moved back to a pre-defined location and a fluorescence image of the optic tract automatically collected. Temperature was maintained at 25°C for the duration of the measurement by a PetriDish Heater (JPK Instruments).

34Force-distance curves obtained from stiffness measurements were analysed with a custom-written MATLAB script to obtain the reduced apparent elastic modulus K. Raw AFM data were fitted to the Hertz model,where F is the applied force, K the reduced apparent elastic modulus E/(1-ν2) (with Poisson ratio ν), R the radius of the indenter, and is sample indentation. Force-distance curves were analysed at the maximum applied force F = 10 nN. Points where the AFM data were not analysable were excluded; criteria for excluding individual force-distance curves were (1) inability to apply linear fits through the baseline region, for example due to noise, and (2) inability to apply good-quality Hertzian fits to the indentation region, that is, the fit did not align with the raw data.

35To minimise noise for region-of-interest analysis of small areas, previously sorted, gridded AFM data were smoothed in x-, y-, and time dimensions using an algorithm based on the discrete cosine transform by Garcia et al. Briefly, an iteratively weighted version of the penalized least squares approach was used to smooth the data and interpolate missing values where the force-distance curves were not analysable. Stiffness data from each experiment were arranged into a 3D array (x*y*frame number) and used as an argument for the smoothn.m MATLAB implementation of the algorithm. This algorithm has the advantage of using the entire data set to interpolate missing values, as opposed to only the nearest neighbouring data (as, for example, in other smoothing methods such as a simple spline interpolation).

36For visual presentation of interpolated stiffness data, additional arrays of robustly smoothed K values were generated using the separate ‘robust’ option available in smoothn.m. This automatically reduces the weight assigned to high-leverage points and outliers, which optimises visualisation of overall changes in stiffness. To generate time-lapse montages of both raw and robustly smoothed AFM data, values of K were converted to 8-bit scale, colour-coded maps using the desired MATLAB colourmap pre-set. The resulting stiffness maps were then mapped onto images of the brain and OT using custom-written MATLAB scripts.

37Another MATLAB script was used to calculate local tissue stiffness gradients in the area just ahead of the advancing OT. Mean values of K were calculated for a 50 × 50 µm2 region of interest (ROI) on the rostral (KR) and caudal sides (KC) of the OT, and the gradient calculated by:

38For each frame in a given time-lapse series, ROIs were defined three times and the mean of the three measurements for each ROI was used for further analysis. Where direct comparison between the dynamics of stiffness gradients and OT turning was required across different animals, values for both parameters were rescaled. The minimum value obtained for each embryo measured was set to 0 and the maximum set to 1, using the following formula:

39When linear fits to AFM data and OT turning angles were required, the built-in MATLAB first degree polynomial fit was used in all cases.

40For each embryo, in vivo time-lapse movies of the growing OT were created by collating fluorescence images taken at the beginning of every successive AFM stiffness map. The magnitude of the OT turn was calculated from each frame of these movies using the FIJI Angle tool. Three points were defined manually (chiasm, mid-diencephalic turn, and end of OT) such that the two lines drawn through these points ran through the centre of the OT. Each measurement was repeated three times, averaged, and subtracted from 180° to give the angle through which the OT had turned; a positive value denotes turning in the caudal direction.

41Maximum projections were made across 10 µm confocal image stacks of wholemount brains with DiI-labelled OTs. The OTs were manually outlined in Adobe Illustrator. Elongation of the OT was calculated by the major-to-minor axis ratio using a previously described automated algorithm in Matlab. In short, axes were determined by fitting ellipses, with the same normalized second central moment as the OT area, around the OTs.

42Confocal image stacks of fixed brains (with fluorescently-labelled OT and nuclei) were imported into FIJI. For each brain, the image where the leading axons were in focus was selected. A maximum intensity projection was generated of this image and one image above and below it in the stack. Two 50 μm × 50 μm regions of interest (matching the size of regions of interest used in stiffness gradient analysis) were selected, rostral (DR) and caudal (DC) to the region corresponding to the OT caudal bend. Noise was removed with a Gaussian blur filter (sigma = 2.0). The resulting image was thresholded, with the threshold manually adjusted to capture all nuclei as accurately as possible. The image was binarised and the FIJI built-in function ‘Analyse Particle’ (size: 1–∞; circularity: 0.2–1.00) was used to determine the area in each region covered by nuclei. Relative cell body density was calculated by dividing the area occupied by nuclei by the total region area. Where required, gradients in relative cell body density were obtained using:

43Confocal images taken with the 20 × air objective were imported into FIJI. Maximum projections were made of the stacks (z-stack height = 8 µm). The brain was identified in each section and both intact and exposed hemispheres were outlined. The area occupied by nuclei in each brain hemisphere was measured using the ‘Analyse > Measure’ tool. Normalised brain areas were obtained by calculating the ratio of exposed brain area to intact brain area.

44Confocal images taken with the 20 × air objective were imported into FIJI. Maximum projections were made of the stacks (z-stack height = 8 µm) and pH3+ cells were counted and normalized to the total measured brain area in each section. The data is presented as the number of pH3+ cells per 10,000 µm2 of brain tissue.

45Data were collected from at least three independent experiments (N ≥ 3). The order of data collection was randomized with no blinding and no data were excluded from the analysis. Non-parametric tests as well as linear regression analysis were used for statistical analyses of the data as described in the figure captions. R2 values provide an estimate of the quality of the fits used in the plots. Pearson’s correlation coefficient, on the other hand, provides a measure of the magnitude of correlation between the cell body density gradient and the stiffness gradient.