ABSTRACT

During embryonic development, the telecephalon undergoes extensive growth and cleaves into right and left cerebral hemispheres. Although molecular signals have been implicated in this process and linked to congenital abnormalities, few studies have examined the role of mechanical forces. In this study, we quantified morphology, cell proliferation and tissue growth in the forebrain of chicken embryos during Hamburger-Hamilton stages 17-21. By altering embryonic cerebrospinal fluid pressure during development, we found that neuroepithelial growth depends on not only chemical morphogen gradients but also mechanical feedback. Using these data, as well as published information on morphogen activity, we developed a chemomechanical growth law to mathematically describe growth of the neuroepithelium. Finally, we constructed a three-dimensional computational model based on these laws, with all parameters based on experimental data. The resulting model predicts forebrain shapes consistent with observations in normal embryos, as well as observations under chemical or mechanical perturbation. These results suggest that molecular and mechanical signals play important roles in early forebrain morphogenesis and may contribute to the development of congenital malformations.

INTRODUCTION

Cerebral hemispheres account for the majority of brain volume in adult humans, and abnormalities during early development can result in dramatic downstream effects. Incomplete hemisphere division, or holoprosencephaly, represents the most common, and often lethal, brain malformation (1 in 250 human pregnancies; 1 in 10,000 live births) (Matsunaga and Shiota, 1977; Leoncini et al., 2008). Abnormally small (microcephalic) or large (megalencephalic) cerebral hemispheres have been associated with disorders including epilepsy, cerebral palsy and autism (Barkovich et al., 2012). To understand how these congenital malformations develop, more work is needed to translate known genetic and teratogenic factors into mechanical and structural changes.

After neurulation, local constrictions along the length (rostral-caudal axis) of the neural tube produce distinct primary brain vesicles: the forebrain, midbrain and hindbrain (Filas et al., 2012; Garcia et al., 2017). As described extensively by Puelles et al. (2012), the forebrain can be further segmented along its length into the secondary prosencephalon (SP, rostral tip) and diencephalon (between the SP and midbrain) (Fig. 1A). Once the neural tube seals, embryonic cerebrospinal fluid (eCSF) is secreted into the lumen of the brain, and all vesicles undergo dramatic, pressure-driven expansion (Lowery and Sive, 2009; Garcia et al., 2017) (Fig. 1B). During this period, the SP consists of one large, eCSF-filled vesicle (telencephalon and hypothalamus) and two optic vesicles (prospective eyes) connected via narrow optic stalks. Left and right cerebral hemispheres grow rapidly from the telencephalon (dorsal portion), whereas the hypothalamus (ventral portion) remains relatively small and conical (Fig. 1A′,B′).

Fig. 1.

Normal development of the telencephalic hemispheres in the chicken embryo. (A,B) Brightfield images of whole embryo at HH17 and HH21. Constrictions visibly separate the SP (denoted with white dotted line), diencephalon (d), midbrain (m) and hindbrain (h). Black arrows point from the ventral to dorsal aspect of the SP and denote location of cross-sections shown in A′,B′. (A′,B′) Cross-sectional OCT images containing telencephalon (tel) and hypothalamus (hy). The space between surface ectoderm (white line) and neuroepithelial wall (multicolored line) is filled with loose mesenchymal tissue (mes) and prospective eyes (e). (C) Schematic of HH21 brain geometry, regions, and key signaling centers. Prospective eyes connect to the hypothalamus via narrow optic stalks (os). (D) Three-dimensional reconstruction of the SP from OCT image stack at HH21, illustrating prominent molecular signals in hemisphere morphogenesis. BMP4 produced at the roof plate (RP, teal) inhibits FGF8 production, and vice versa. SHH produced at the floor plate (FP, orange) promotes FGF8, which is also produced at the ANR (red). Asterisks in B′ denote telencephalic hemispheres. Scale bars: 500 μm.

Fig. 1.

Normal development of the telencephalic hemispheres in the chicken embryo. (A,B) Brightfield images of whole embryo at HH17 and HH21. Constrictions visibly separate the SP (denoted with white dotted line), diencephalon (d), midbrain (m) and hindbrain (h). Black arrows point from the ventral to dorsal aspect of the SP and denote location of cross-sections shown in A′,B′. (A′,B′) Cross-sectional OCT images containing telencephalon (tel) and hypothalamus (hy). The space between surface ectoderm (white line) and neuroepithelial wall (multicolored line) is filled with loose mesenchymal tissue (mes) and prospective eyes (e). (C) Schematic of HH21 brain geometry, regions, and key signaling centers. Prospective eyes connect to the hypothalamus via narrow optic stalks (os). (D) Three-dimensional reconstruction of the SP from OCT image stack at HH21, illustrating prominent molecular signals in hemisphere morphogenesis. BMP4 produced at the roof plate (RP, teal) inhibits FGF8 production, and vice versa. SHH produced at the floor plate (FP, orange) promotes FGF8, which is also produced at the ANR (red). Asterisks in B′ denote telencephalic hemispheres. Scale bars: 500 μm.

Chemical morphogens are known to play a crucial role in hemisphere morphogenesis. Sonic hedgehog proteins (SHH) secreted by the ventral floor plate form a positive-feedback loop with fibroblast growth factors (e.g. FGF8) secreted by the anterior neural ridge (ANR) to promote proliferation and cell survival of the neuroepithelium (Monuki, 2007; Toyoda et al., 2010) (Fig. 1C,D). By contrast, bone morphogenetic proteins (e.g. BMP4) secreted by the dorsal roof plate reduce proliferation and form a negative-feedback loop with FGF8 (Ohkubo et al., 2002). In avian and rodent models, reducing SHH, reducing FGF8, or increasing BMP4 results in underdeveloped ventral and lateral structures, similar to classic holoprosencephaly in human (Fernandes et al., 2007; Furuta et al., 1997; Storm et al., 2006; Ohkubo et al., 2002; Huang et al., 2007b). By contrast, midline interhemispheric holoprosencephaly, a phenotype in which the dorsal midline fails to develop, can be induced by decreasing BMP4 or increasing SHH (Fernandes et al., 2007; Huang et al., 2007a).

Although these findings suggest a morphogen-dependent gradient of growth, no studies have analyzed whether the resulting growth pattern is physically sufficient to shape the cerebral hemispheres and hypothalamus. Furthermore, the role of mechanical feedback has been generally overlooked in studies of hemisphere division and holoprosencephaly. After the brain tube seals, eCSF exerts mechanical pressure on the walls of the early brain tube, stretching the neuroepithelium and stimulating growth (Jelinek and Pexieder, 1968; Desmond et al., 2005). During these stages, Desmond et al. (2014) detected upregulation and activation of focal adhesion kinase (FAK; also known as PTK2) due to eCSF pressure, suggesting a mechanotransduction pathway similar to other epithelial systems (Lehoux et al., 2005; Chaturvedi et al., 2007).

Here, we hypothesize that hemisphere morphogenesis depends on both morphogen concentration and mechanical feedback. By quantifying cell proliferation and tissue growth during normal hemisphere division in chicken embryos (Gallus gallus), we confirm regional differences consistent with known morphogen gradients. By subjecting embryos to different mechanical loads during development, we also confirm a role for mechanical feedback. Finally, a three-dimensional computational model shows that the proposed combination of mechanisms (morphogen gradients, external loads, and mechanical feedback) is sufficient to explain observed hemisphere morphologies as well as previously reported malformations. By elucidating the interplay of mechanical forces and chemomechanical signals in forebrain morphogenesis, our results offer new insights into congenital abnormalities, such as microcephaly, megalencephaly and holoprosencephaly.

RESULTS

To understand the mechanics of initial hemisphere cleavage and growth, we focused on forebrain development from 2.5 to 3.5 days incubation in the chicken embryo. All embryos were staged according to the Hamburger and Hamilton (HH) staging system (Hamburger and Hamilton, 1951), such that HH17 (2.5 days) and HH21 (3.5 days) correspond to stages before and after hemisphere formation, respectively.

Hemisphere division coincides with decreased proliferation at the roof plate

We first quantified proliferation patterns before and after hemisphere division, labeling cells undergoing DNA synthesis with 5-ethynyl-2′-deoxyuridine (EdU) (Warren et al., 2009) at HH17 and HH21. Before hemisphere division (HH17), proliferation was visible throughout the SP. After hemisphere division (HH21), proliferation was absent at the roof plate (Fig. 2A,B). For quantitative analysis, proliferation fraction was defined as the number of EdU-labeled nuclei divided by the total number of nuclei. No regional differences were detected at HH17, but roof plate proliferation was significantly lower at HH21 (Fig. 2C, n=5 per group). The latter result is consistent with previous reports of reduced proliferation at the hemisphere midline (Furuta et al., 1997; Gupta and Sen, 2015). Furthermore, the dynamic shift in proliferation is consistent with stage-dependent gene expression in chicken, where the territory of Bmp4 expression remains fairly small until HH18 (Crossley et al., 2001).

Fig. 2.

Cell proliferation in the SP. (A,B) Cross-sections through the SP showing EdU-labeled nuclei (magenta) and all nuclei (blue). At HH17, proliferating cells (magenta nuclei) are visible throughout the neuroepithelial wall (outer surface denoted with white dotted line). At HH21, proliferation appears to be reduced in the roof plate (RP, white arrowheads). e, prospective eye; FP, floor plate. (C) Proliferation fraction is significantly decreased in the RP of HH21 embryos relative to the RP at HH17 and hemispheres (Hem) at either stage (n=5 in each group, **P<0.01, two-way ANOVA). Error bars represent s.d. Asterisks in B denote right and left hemispheres. Scale bars: 250 μm.

Fig. 2.

Cell proliferation in the SP. (A,B) Cross-sections through the SP showing EdU-labeled nuclei (magenta) and all nuclei (blue). At HH17, proliferating cells (magenta nuclei) are visible throughout the neuroepithelial wall (outer surface denoted with white dotted line). At HH21, proliferation appears to be reduced in the roof plate (RP, white arrowheads). e, prospective eye; FP, floor plate. (C) Proliferation fraction is significantly decreased in the RP of HH21 embryos relative to the RP at HH17 and hemispheres (Hem) at either stage (n=5 in each group, **P<0.01, two-way ANOVA). Error bars represent s.d. Asterisks in B denote right and left hemispheres. Scale bars: 250 μm.

A subset of embryos were also cryosectioned and analyzed at four levels in the forebrain: rostral SP, middle SP, caudal SP and diencephalon (Fig. S1). Proliferation appeared uniform throughout the forebrain at HH17 (n=3). By contrast, the proliferation fraction dropped sharply to zero at the SP roof plate of HH21 embryos (n=2), but not at the diencephalon roof plate, consistent with reported patterns of BMP4 expression (Shimogori et al., 2004; Furuta et al., 1997).

Taken together, these results confirm that proliferation is inhibited at the telencephalic roof plate during hemisphere formation but not during earlier stages or in more caudal regions (i.e. diencephalon) where cleavage is not occurring.

Hemisphere size and division depend on eCSF pressure

Numerous studies have noted an effect of eCSF pressure on brain tissue volume (Jelinek and Pexieder, 1968; Desmond and Jacobson, 1977; Alonso et al., 1998) and cell proliferation (Desmond et al., 2005, 2014; Desmond and Jacobson, 1977), but none has quantified these effects in the telencephalic hemispheres. To address this issue, we quantified geometric changes under decreased and increased eCSF pressure using live optical coherence tomography (OCT) during the period of telencephalic hemisphere division (Fig. 3). To reduce pressure in HH17 embryos, an open glass tube was inserted into the midbrain (Desmond and Jacobson, 1977) to alleviate eCSF pressure and prevent recovery of pressure over a 24 h culture period (Fig. 3A,A′). To control for wounding effects (Jelinek and Pexieder, 1968; Desmond and Jacobson, 1977), closed glass tubes were also inserted into the midbrain of sham embryos (Fig. 3B,B′). This procedure caused an initial deflation followed by re-inflation (Fig. S2), producing a final morphology similar to the control group (Fig. 3C,C′). Lastly, to determine the effect of increased pressure on hemisphere size, eCSF pressure was osmotically increased during culture with β-D-xyloside (BDX; Fig. 3D,D′) (Alonso et al., 1998; Desmond et al., 2014).

Fig. 3.

Altering eCSF pressure in the embryonic brain. (A-D) Brightfield images of HH21 embryos cultured for 24 h from HH17 under one of four conditions: (A) intubated (n=15, black arrowhead denotes open glass tube inserted into the midbrain), (B) sham (n=10, white arrowhead denotes closed glass rod inserted into the midbrain), (C) control media (n=13), and (D) BDX media (n=14). (A′-D′) Representative OCT cross-sections through telencephalon (white lines in A-D). Colored lines represent hemisphere arc, traced on right hemisphere and flipped to left for visualization. (E) Percentage increase in hemisphere arc length, defined as change in hemisphere arc length (final-initial) divided by initial hemisphere arc length. Dots represent individual data points, violin plots represent probability density, and letters a-c denote statistically different groups (one-way ANOVA). (F) Direct measurement of eCSF pressure after 24 h culture with BDX (n=5) or control media (n=6). *P<0.05 (two-sample t-test). Error bars represent s.d. Scale bars: 500 μm.

Fig. 3.

Altering eCSF pressure in the embryonic brain. (A-D) Brightfield images of HH21 embryos cultured for 24 h from HH17 under one of four conditions: (A) intubated (n=15, black arrowhead denotes open glass tube inserted into the midbrain), (B) sham (n=10, white arrowhead denotes closed glass rod inserted into the midbrain), (C) control media (n=13), and (D) BDX media (n=14). (A′-D′) Representative OCT cross-sections through telencephalon (white lines in A-D). Colored lines represent hemisphere arc, traced on right hemisphere and flipped to left for visualization. (E) Percentage increase in hemisphere arc length, defined as change in hemisphere arc length (final-initial) divided by initial hemisphere arc length. Dots represent individual data points, violin plots represent probability density, and letters a-c denote statistically different groups (one-way ANOVA). (F) Direct measurement of eCSF pressure after 24 h culture with BDX (n=5) or control media (n=6). *P<0.05 (two-sample t-test). Error bars represent s.d. Scale bars: 500 μm.

To assess differences between each experimental case, increase in hemisphere arc length from HH17 to HH21 was measured for each embryo (Fig. 3E). Embryos subjected to higher eCSF pressure had significantly longer hemisphere arc lengths compared with controls (P<0.01; BDX n=9; control n=13), and embryos cultured under zero eCSF pressure had significantly smaller hemisphere arc lengths compared with sham and control embryos (P<0.001; intubated n=13, sham n=10). As no significant differences were detected between sham and control embryos, these results are grouped as ‘normal pressure’ in subsequent analysis. Fig. 3A′-D′ shows representative OCT cross-sections of the telencephalic hemispheres under each experimental case. Notably, hemispheres failed to divide in intubated embryos (n=13) despite similar reductions in roof plate proliferation (n=4, Fig. S1E,F).

Previous measurements of normal eCSF pressure in chicken embryos have spanned several orders of magnitude: 25±9 Pa (Jelinek and Pexieder, 1968), 350±40 Pa (Desmond et al., 2005) and 3700±150 Pa (Alonso et al., 1998). Therefore, this study sought to obtain reasonably accurate values of eCSF pressure in control and BDX-treated embryos (Fig. 3F). In embryos extracted at HH17 and HH21, we found average eCSF pressures of 15.4±3.8 Pa (n=7; mean±s.d.) and 15.4±2.5 Pa (n=5), respectively. These values fall within the range reported by Jelinek and Pexieder (1968), and the observed consistency over time matches reports by Jelinek and Pexieder (1968) and Desmond et al. (2005). Measuring eCSF pressure in BDX-treated embryos (21.0±2.0 Pa, n=5) revealed a significant increase (P=0.018) relative to controls (16.1±3.2 Pa, n=6) after 24 h (HH21) (Fig. 3F). This increase is consistent with the relative increase reported by Alonso et al. (1998).

Collectively, these results suggest that eCSF pressure remains low and constant during the period of hemisphere division, but the magnitude of eCSF pressure serves as a key regulator of cerebral hemisphere size.

Mechanical feedback modulates in-plane neuroepithelial growth

Most studies involving eCSF pressure have not translated changes in brain tissue volume (Jelinek and Pexieder, 1968; Desmond and Jacobson, 1977; Alonso et al., 1998) or cell proliferation (Desmond et al., 2005; Desmond and Jacobson, 1977) to tangential (in-plane) and radial (thickening) growth components, which may represent distinct biological mechanisms (Fish et al., 2008). However, Desmond et al. (2014) proposed a twofold role for FAK as a mechanotransducer to both (1) upregulate proliferation and (2) loosen the extracellular matrix to facilitate in-plane intercalation of newly formed daughter cells. Therefore, we hypothesized that eCSF pressure preferentially increases tangential (in-plane), rather than radial, growth.

To test this hypothesis, we first considered geometric changes at the diencephalon-midbrain boundary (DMB) as a representative region for the entire brain tube (Fig. 4B,C). This landmark is easily distinguished across all stages considered and is free of large structures (i.e. prospective eyes) that can partially obscure the SP and diencephalon in OCT images (Fig. 1B′). The roughly cylindrical geometry of the DMB also facilitates derivation of closed-form mathematical solutions, which become useful in determining growth parameters for a mechanical feedback law. Approximating the DMB as a circular cross-section, we separated growth and deformation into circumferential (tangential) and radial components.

Fig. 4.

Effects of eCSF pressure on growth and deformation. (A) Expansion of the embryonic brain depends on elastic inflation due to eCSF pressure (λ*=R′/R at HH17, λ*=r′/r at HH21) and tissue growth. Circumferential and radial growth were estimated from deflated brain geometries (G=r/R and GR=h/H, respectively). (B) Measurements were made at the DMB (white line on brightfield image). (C) OCT cross-section of DMB before deflation (top) and after deflation (bottom). White dotted lines denote inner (apical) and outer (basal) surfaces. (D) Deflated radius and thickness at HH17 (R, H) and HH21 (r, h) after culture under zero, normal and high pressure (p). Left to right: n=19,15,17,14; statistically different groups denoted by a-d (one-way ANOVA). (E) Circumferential and radial growth from theoretical model (black lines) and experimental measures (green bars). Error bars represent s.d. Scale bars: 500 μm.

Fig. 4.

Effects of eCSF pressure on growth and deformation. (A) Expansion of the embryonic brain depends on elastic inflation due to eCSF pressure (λ*=R′/R at HH17, λ*=r′/r at HH21) and tissue growth. Circumferential and radial growth were estimated from deflated brain geometries (G=r/R and GR=h/H, respectively). (B) Measurements were made at the DMB (white line on brightfield image). (C) OCT cross-section of DMB before deflation (top) and after deflation (bottom). White dotted lines denote inner (apical) and outer (basal) surfaces. (D) Deflated radius and thickness at HH17 (R, H) and HH21 (r, h) after culture under zero, normal and high pressure (p). Left to right: n=19,15,17,14; statistically different groups denoted by a-d (one-way ANOVA). (E) Circumferential and radial growth from theoretical model (black lines) and experimental measures (green bars). Error bars represent s.d. Scale bars: 500 μm.

Observed changes in brain tube size, as reported in Fig. 3E, involve a combination of both tissue growth (increase in unloaded tissue volume) and elastic deformation (tissue stretch due to pressure). Therefore, to quantify tissue growth under normal- and high-pressure conditions, we cannot simply consider the initial and final pressurized geometries. To separate elastic deformation due to eCSF pressure, we estimated tissue growth as the difference between initial and final deflated geometries (Fig. 4A), for embryos cultured under no pressure, normal pressure and high-pressure conditions.

Mathematically, the total circumferential stretch ratio at time t can be decomposed as λ(t)=λ*(t)G(t), where λ*(t) represents the elastic stretch ratio and G(t) represents the growth ratio. Over the time period considered here (HH17 to HH21, or t=1 day), total circumferential stretch can be defined by the ratio λ(1)=r′/R′, where R′ and r′ are the inflated radii at initial (HH17) and final (HH21) time points, respectively (Fig. 4A). Circumferential growth over t=1 day can be approximated from the deflated radii (R at HH17 and r at HH21) such that G(1)=r/R, where G(0)=1 and G>1 indicates positive growth (Taber, 2009). Elastic stretch due to inflation is defined instantaneously, such that λ*(0)=R′/R at HH17 and λ*(1)=r′/r at HH21.

Measurements in deflated brains (Fig. 4D) revealed a significant increase in deflated radius between HH17 (R) and HH21 (r). Furthermore, the deflated radius r was significantly larger in embryos cultured with high eCSF pressure (n=14) and smaller in embryos cultured with no eCSF pressure (n=15) compared with controls (n=17). Wall thickness increased between HH17 (H) and HH21 (h) but was not significantly affected by pressure. Note that R and H represent measures from intubated and sham embryos only (n=19), because only these experimental groups underwent initial deflation. As no significant differences existed in inflated geometries at HH17 (R′ and H′), we assume the same R and H across all groups for calculations of circumferential growth, G=r/R, and radial growth, GR=h/H, over t=1 day (Fig. 4E). Elastic stretch due to inflation was relatively small at both HH17 [λ*(0)=1.13±0.05, n=19] and HH21 [λ*(1)=1.09±0.08, n=15 under normal pressure; λ*(1)=1.14±0.09, n=10 under high pressure], with no significant differences detected between groups.

As a fraction of total DMB expansion, the contribution of elastic stretch (approximately 10%) was considerably smaller than the contribution of growth (50-100%), in agreement with studies at earlier stages (Garcia et al., 2017). Importantly, our results indicate that circumferential growth depends on eCSF pressure but radial growth does not (Fig. 4E). This finding supports the idea that neuroepithelial expansion and thickening represent different biological mechanisms (Fish et al., 2008), and is consistent with our hypothesis that eCSF pressure primarily influences in-plane growth.

A chemomechanical feedback law describes growth in the embryonic brain

Using the results described above, we developed a mathematical growth law for the developing brain that depends on both chemical morphogen concentrations and mechanical feedback. As in previous studies (Garcia et al., 2017), we assume growth is transversely isotropic such that the tangential growth ratio, G, is equal in the circumferential and longitudinal directions (GGΘ=GΦ). This assumption is based on the observation that, in simple epithelial monolayers, large strains (≥30%) were required to bias cell divisions in the direction of maximum stretch (Wyatt et al., 2015).

We consider a growth law that includes mechanical feedback in the form
formula
(1)
where and R represent the rates of tangential growth and radial growth (thickening) with respect to time. For stress-dependent growth, mechanical feedback is incorporated via the nondimensionalized average wall stress at each point,
formula
(2)
where µ is the shear modulus of the neuroepithelium, σΘ is the circumferential stress, and σΦ is the longitudinal stress. For comparison, growth that depends directly on the uniform cavity pressure can also be considered by assigning a constant, uniform value for σ̄ throughout the wall. The constants g0 and g0r represent baseline growth rates in the absence of mechanical feedback (σ̄ =0), and β and gσ are non-negative, morphogen-dependent growth coefficients.
To account for chemical morphogen influences on growth, we define gradients of BMP4 and FGF8 with normalized concentrations CBMP and CFGF, respectively, such that 0≤CBMP,CFGF≤1. Consistent with evidence that high concentrations of BMP4 inhibit growth (Ohkubo et al., 2002), we let
formula
(3)
such that =R=0 (no growth) at maximum BMP4 concentration (CBMP=1). To model growth-promoting effects of FGF8 (Monuki, 2007; Toyoda et al., 2010), we let
formula
(4)
where a describes stress-dependent growth at minimum FGF8 concentration (CFGF=0) and a+b describes stress-dependent growth at maximum FGF8 concentration (CFGF=1). Toyoda et al. (2010) quantified the intensity of FGF8 immunofluorescence throughout the embryonic forebrain, finding a fivefold increase at the rostral tip (ANR) compared with the caudal end of the SP (Puelles et al., 2012; Puelles and Rubenstein, 2015). Based on this gradient, we let b=5, such that gσ=6a at the ANR (CFGF=1) and gσ=a at the DMB (CFGF=0). Notably, this form assumes that mechanical stress is a prerequisite for growth factor-dependent effects, as described for other systems of FAK-dependent cell proliferation (Walker et al., 2005).

Assuming a circular cross-section and CFGF=CBMP=0, a closed-form solution for growth can be obtained at the DMB based on the proposed growth law (see Materials and Methods for details). This allowed us to determine the remaining growth constants (g0, g0r and a) using data in Fig. 4. From intubated and normal-pressure data, we obtained: g0=0.39 d−1, g0r=0.32 d−1 and a=2.1 d−1. To check the predictive ability of the proposed growth law, we simulated BDX experiments by increasing pressure without changing these parameters. For a 40% increase in pressure during culture with BDX (Fig. 3F) (Alonso et al., 1998), Eqn 10 yields G=2.09, in close agreement with experimentally measured values for BDX-treated brains (G=2.07±0.10; Fig. 4E).

A three-dimensional feedback model produces normal hemisphere morphogenesis

To determine whether our assumptions are sufficient to shape the hemispheres, we created a three-dimensional computational model of the SP including realistic morphogen gradients and mechanical loads. Because previous studies have found that actomyosin contraction has little effect on brain shape during the stages considered in this paper (Garcia et al., 2017), growth is the primary morphogenetic mechanism in the model. All model parameters were measured experimentally or approximated from previously reported studies, as summarized in Table 1.

Table 1.

Model parameters

Model parameters
Model parameters

As shown in Fig. 5A, the initial, unloaded geometry is based on dimensions of the deflated SP at HH17, and a constant eCSF pressure is applied along the inner wall. Because the hypothalamus is surrounded by external tissues (prospective eyes and mesenchyme) that may reinforce or constrain this region, a relatively soft elastic foundation (denoted by springs) is attached to the outer conical surface. Normalized morphogen gradients were generated on the initial geometry such that BMP4 concentration (CBMP) is highest at the roof plate, FGF8 concentration (CFGF) is highest at the ANR, and stress-dependent growth at all points is governed by Eqns 1-4. (See Materials and Methods for material properties and additional details.) Fig. 5B illustrates the shape of the SP after 24 h (HH21) and compares two different forms of mechanical feedback: (1) stress-based feedback, which can vary at each point across the neuroepithelium, and (2) pressure-based feedback, which is uniform across the neuroepithelium. Both models result in two distinct hemispheres. However, only the stress-dependent growth model (Fig. 5B, right; see also Fig. 7A,B) captures realistic expansion of the hemispheres relative to the hypothalamus (Fig. 5C).

Fig. 5.

Computational model for hemisphere division. (A) Initial geometry (HH17) and initial conditions for the SP including telencephalon (tel) and hypothalamus (hy). eCSF pressure is specified along the inner wall (teal arrows), and ventral reinforcement from surrounding tissue is represented by an elastic foundation (orange springs). Normalized morphogen gradients (CBMP and CFGF) approximate BMP4 and FGF8 diffusion from the roof plate (RP) and ANR, respectively. (B) Over 24 h (HH17 to HH21), the model grows and develops left and right hemispheres (rostral view), based on morphogen gradients and mechanical feedback. Left: model with pressure-based mechanical feedback (constant, uniform σ̄). Right: model with stress-based mechanical feedback (σ̄ defined at each point by spatially and temporally varying wall stresses). Color represents tangential growth, G. (C) Modified drawing from Bardet et al. (2010) illustrates qualitative comparison between our stress-based model and commonly observed morphology. Thin lines divide functional areas of the SP, following contours similar to those of the deformed mesh (representing initial dorsal-ventral and medial-lateral directions). All model images are shown to scale.

Fig. 5.

Computational model for hemisphere division. (A) Initial geometry (HH17) and initial conditions for the SP including telencephalon (tel) and hypothalamus (hy). eCSF pressure is specified along the inner wall (teal arrows), and ventral reinforcement from surrounding tissue is represented by an elastic foundation (orange springs). Normalized morphogen gradients (CBMP and CFGF) approximate BMP4 and FGF8 diffusion from the roof plate (RP) and ANR, respectively. (B) Over 24 h (HH17 to HH21), the model grows and develops left and right hemispheres (rostral view), based on morphogen gradients and mechanical feedback. Left: model with pressure-based mechanical feedback (constant, uniform σ̄). Right: model with stress-based mechanical feedback (σ̄ defined at each point by spatially and temporally varying wall stresses). Color represents tangential growth, G. (C) Modified drawing from Bardet et al. (2010) illustrates qualitative comparison between our stress-based model and commonly observed morphology. Thin lines divide functional areas of the SP, following contours similar to those of the deformed mesh (representing initial dorsal-ventral and medial-lateral directions). All model images are shown to scale.

This model also yields relatively low stress in regions of stress-dependent growth (Fig. 6A). Similarly, Wyatt et al. (2015) found that cell divisions can reduce tension and encourage isotropic cell shapes in epithelia. By contrast, areas in which stress-dependent growth is inhibited (high BMP4 in the roof plate, as defined in Fig. 5A) are subject to high stress and anisotropic stretch (Fig. 6B). Consistent with these patterns, F-actin staining at HH21 reveals transversely isotropic (circular) apical cell shapes in the regions of low stress, as well as drastically stretched cells in the nonproliferative roof plate (Fig. 6C), with the direction of maximum stretch matching model results (Fig. 6B). During initial inflation, we also note that tension was highest along the inner surface for spherical and cylindrical regions, as expected for a pressurized vessel. This pattern of stress is consistent with the observations of Desmond et al. (2014), who reported increased FAK activation along the luminal surface due to osmotically increased eCSF pressure.

Fig. 6.

Comparison of model and experimentally observed apical stress. (A) HH21 model reveals high in-plane tension, σ̄ =(σΘΦ)/(2 µ), along the apical (inner) roof plate (RP), where stress-dependent growth is inhibited. (B) Magnified view of the white box region in A, where lines represent the direction of maximum stress and color represents magnitude. (C) Staining for F-actin in the same region reveals RP cells that are dramatically stretched in the direction of maximum stress (n=5, red arrows). Conversely, regions of stress-dependent growth (hemispheres, shown on right and left edges) maintain relatively small, round cells (n=5 for hemisphere and hypothalamus regions). In B,C, black dashed lines enclose RP, white dashed line denotes midline. Scale bar: 40 μm.

Fig. 6.

Comparison of model and experimentally observed apical stress. (A) HH21 model reveals high in-plane tension, σ̄ =(σΘΦ)/(2 µ), along the apical (inner) roof plate (RP), where stress-dependent growth is inhibited. (B) Magnified view of the white box region in A, where lines represent the direction of maximum stress and color represents magnitude. (C) Staining for F-actin in the same region reveals RP cells that are dramatically stretched in the direction of maximum stress (n=5, red arrows). Conversely, regions of stress-dependent growth (hemispheres, shown on right and left edges) maintain relatively small, round cells (n=5 for hemisphere and hypothalamus regions). In B,C, black dashed lines enclose RP, white dashed line denotes midline. Scale bar: 40 μm.

To test our model further, cell proliferation fraction was calculated along the circumference of the SP wall in EdU-stained cross-sections (Fig. 2B) and in equivalent model cross-sections (see Fig. 7B). Total circumference was normalized so that x=0 at the roof plate and x=±1 at the floor plate (x>0 for right hemisphere, x<0 for left hemisphere). As shown in Fig. 7C, measured proliferation drops sharply to zero at the roof plate of HH21 embryos (n=2), and a subtle decline is visible from the hemispheres (0.1<|x|<0.5) to the hypothalamus (|x|>0.5). The spatial trends in relative growth rate given by the full model (black line) are similar to experimentally measured distributions in proliferation, with a sharp drop near the roof plate as CBMP→1 and a decrease near the hypothalamus. Importantly, our model predicts the latter due to reduced mechanical stress (reinforcement from external tissues; Figs 1B′ and 5A), rather than a chemical morphogen gradient.

Fig. 7.

Comparison of model and experimental growth gradients. (A) Lateral view of isolated SP (outlined with white dotted line) at HH21 appears qualitatively similar to the full model after 24 h (B, left). (B) Lateral and rostral views of full model (left and right, respectively) with black line denoting location of SP cross-section (center) used to compare model growth with measured proliferation patterns. (C) Comparison of model-predicted growth fraction (black line, ΔGGmax) and measured cell proliferation fraction (dots) along the neuroepithelial wall. Each dot represents the average for a 60 µm-long region of wall at HH21 (n=2 samples, denoted by filled and unfilled dots; gray dots correspond to adjacent section denoted by dashed white line in A). Location along the wall (x) is normalized so that x=0 at the roof plate (RP), x=±1 at the floor plate (FP). (D) Model-predicted proliferation fraction in the absence of key factors: mechanical feedback (a=0; teal short-dashed line), external tissues (µext=0; orange dotted line), FGF8 (CFGF=0; red dash-dot line), or BMP4 (CBMP=0; blue long-dashed line). (E) Model shapes for the cases shown in D. Note: owing to the dramatic increase in growth in the absence of BMP4, the ‘no BMP4 gradient’ model is compared after 18 h (75% of the growth period). All models are shown to scale.

Fig. 7.

Comparison of model and experimental growth gradients. (A) Lateral view of isolated SP (outlined with white dotted line) at HH21 appears qualitatively similar to the full model after 24 h (B, left). (B) Lateral and rostral views of full model (left and right, respectively) with black line denoting location of SP cross-section (center) used to compare model growth with measured proliferation patterns. (C) Comparison of model-predicted growth fraction (black line, ΔGGmax) and measured cell proliferation fraction (dots) along the neuroepithelial wall. Each dot represents the average for a 60 µm-long region of wall at HH21 (n=2 samples, denoted by filled and unfilled dots; gray dots correspond to adjacent section denoted by dashed white line in A). Location along the wall (x) is normalized so that x=0 at the roof plate (RP), x=±1 at the floor plate (FP). (D) Model-predicted proliferation fraction in the absence of key factors: mechanical feedback (a=0; teal short-dashed line), external tissues (µext=0; orange dotted line), FGF8 (CFGF=0; red dash-dot line), or BMP4 (CBMP=0; blue long-dashed line). (E) Model shapes for the cases shown in D. Note: owing to the dramatic increase in growth in the absence of BMP4, the ‘no BMP4 gradient’ model is compared after 18 h (75% of the growth period). All models are shown to scale.

Collectively, these results support a model of normal hemisphere morphogenesis regulated by (1) chemical morphogen gradients, (2) mechanical loads including eCSF pressure and external tissues, and (3) growth gradients based on both chemical morphogen and mechanical tension gradients.

Model predicts abnormal hemisphere morphogenesis under perturbed conditions

To test the predictive capability of our model, we also compared model and experimental results for embryos subjected to chemical and mechanical perturbations.

As shown in Fig. 7D,E, removing external mechanical loads representing the prospective eyes and surrounding mesenchyme (the elastic foundation) predicts elevated growth and overexpansion of the hypothalamus. To test this prediction, we removed prospective eyes and adjacent mesenchyme prior to HH17 and cultured embryos to HH21. For these cases, the hypothalamus was significantly wider at HH21 compared with controls (n=5 per group; Fig. S3), supporting a role for ventral tissues in constraining hypothalamic growth.

Fig. 7D,E also illustrates the effect of removing chemical morphogen gradients. Removing the caudal-to-rostral increase in FGF8 (CFGF=0 everywhere) dramatically reduces growth throughout our model and prevents clear hemisphere evagination. The resulting microcephalic, holoprosencephalic morphology agrees with experiments that reduced FGF8 directly (Storm et al., 2006) or indirectly via SHH downregulation (Huang et al., 2007b). According to our model, global overexpression of BMP4 (CBMP=1 everywhere) inhibits both tangential and radial growth (G=GR=1 everywhere), similar to experimental observations under ectopic BMP4 application (Furuta et al., 1997). Conversely, global underexpression of BMP4 (CBMP=0 everywhere) results in maximal growth at the roof plate, producing one large lobe instead of two distinct hemispheres. This predicted morphology is similar to midline interhemispheric holoprosencephaly, as reported in experiments that reduced BMP4 directly (Fernandes et al., 2007) or indirectly via SHH upregulation (Huang et al., 2007a).

In Fig. 8 we examined the effects of altered eCSF pressure within the brain lumen for three cases: no pressure (intubated, p=0 Pa), normal pressure (sham and control, p=15 Pa) and high pressure (BDX, p=21 Pa). Hemisphere growth, G, was estimated from OCT images as described in Figs 3 and 4. For each case, we also measured relative roof plate invagination depth, defined as the vertical distance from hemisphere peak to roof plate valley (Fig. 8B), normalized by total hemisphere arc length (Fig. 3A′-D′).

Fig. 8.

Comparison of model and experimental results under perturbed eCSF pressure. (A) Comparable HH21 cross-sections for full model (left) and representative embryos (right, OCT images) after 24 h culture under zero, normal and high pressure. For evolution of full 3D geometry under each loading condition, see Movies 1-3. (B) Growth of the telencephalic hemispheres (green arc length) was estimated as described in Fig. 4. Hemisphere division is quantified by depth of the RP relative to maximum hemisphere height (orange arrow). To normalize with respect to size, the depth was divided by the final, inflated hemisphere arc length. Bars represent experimentally measured hemisphere growth (green) and RP depth (orange). Black lines represent predictions for full model, where growth is regulated by wall stress due to pressure. Left to right: n=10,15,7 for G; n=13,23,9 for relative RP depth; statistically different groups denoted by a-c (one-way ANOVA). Error bars represent s.d. Scale bars: 500 μm.

Fig. 8.

Comparison of model and experimental results under perturbed eCSF pressure. (A) Comparable HH21 cross-sections for full model (left) and representative embryos (right, OCT images) after 24 h culture under zero, normal and high pressure. For evolution of full 3D geometry under each loading condition, see Movies 1-3. (B) Growth of the telencephalic hemispheres (green arc length) was estimated as described in Fig. 4. Hemisphere division is quantified by depth of the RP relative to maximum hemisphere height (orange arrow). To normalize with respect to size, the depth was divided by the final, inflated hemisphere arc length. Bars represent experimentally measured hemisphere growth (green) and RP depth (orange). Black lines represent predictions for full model, where growth is regulated by wall stress due to pressure. Left to right: n=10,15,7 for G; n=13,23,9 for relative RP depth; statistically different groups denoted by a-c (one-way ANOVA). Error bars represent s.d. Scale bars: 500 μm.

Hemisphere growth was significantly different between each pressure case (P<0.0001, n=10 zero pressure, n=15 normal pressure, n=7 high pressure), an effect accurately predicted by our model. Under no eCSF pressure (Fig. 8A, left), hemispheres grew less than controls and failed to separate, as illustrated by a significant reduction in relative roof plate depth (P<0.0001, Fig. 8B). This microcephalic, holoprosencephalic morphology (classic holoprosencephaly) has been previously reported in embryos subjected to reduced FGF8 (gσa) (Storm et al., 2006; Ohkubo et al., 2002; Huang et al., 2007b) or increased BMP4 (β→1) (Fernandes et al., 2007; Furuta et al., 1997), but no previous studies have reported holoprosencephaly as the result of eCSF pressure reduction (σ̄→0). For p=0 Pa, our model accurately predicts quantitative reductions in both hemisphere growth and roof plate depth.

Under high pressure, experimentally measured hemisphere growth increased significantly relative to controls (Fig. 8A, right), corresponding to a megalencephalic (abnormally large) hemisphere morphology. Given that eCSF pressure tends to push the roof plate outward elastically and wall stresses generally increase with tangential growth (see Eqn 7), one might also expect a subtle holoprosencephalic morphology under increased pressure. However, no decreases in roof plate depth were observed experimentally or in our model (Fig. 8B). Instead, full inhibition of growth at the roof plate combined with increased growth of the hemispheres serves to increase differential growth, the driving force for hemisphere division. In this way, mechanical feedback counteracts the outward push of higher pressures to maintain relatively normal roof plate depth and hemisphere separation. This effect requires sufficiently large value for gσ (promoting invagination) relative to p (impeding invagination), stressing the importance of accurate pressure and material property measurements when determining stress-dependent growth parameters.

Taken together, our results support the hypothesis that molecular and mechanical signals act synergistically to shape the SP by influencing hemisphere size, hemisphere separation and hypothalamus constraint.

DISCUSSION

In this study, we hypothesized that early cerebral morphogenesis is driven by both molecular and mechanical signals, which together control differential growth of the secondary prosencephalon. To test this hypothesis, we first quantified cell proliferation, morphology, and tissue growth under normal and altered loading conditions. Next, we proposed a chemomechanical growth law to reconcile the effects of morphogens and mechanical stress on growth, with a mathematical form and parameter values based on experimentally determined measures. Three-dimensional modeling based on these laws confirmed that differential growth is sufficient to induce hemisphere division and highlighted the role of mechanical feedback in shaping the embryonic forebrain. By considering mechanical forces, this study demonstrates how a range of abnormal hemisphere morphologies can be produced by perturbations beyond molecular signals.

Mechanical feedback as a key regulator of morphogenesis

For decades, researchers have known that eCSF influences growth in the early brain tube (Desmond and Jacobson, 1977; Alonso et al., 1998; Desmond et al., 2005), and mechanical tension has been hypothesized as a driver of early cerebral growth (Van Essen et al., 1997). However, the mechanisms by which eCSF pressure affects morphogenesis are not fully understood, particularly in the context of the cerebral hemispheres.

In this study, we found that tangential growth, but not radial growth, varied with pressure (Fig. 4), supporting the notion that in-plane growth and wall thickening result from different biological processes (Fish et al., 2008). At early stages of development, the wall of the brain is a pseudostratified monolayer, and tangential growth may represent symmetric cell divisions. During neural development, symmetric divisions increase the pool of neural progenitor cells that continue to proliferate, ultimately determining brain size (Fish et al., 2008; Konno et al., 2008). Conversely, asymmetric cell divisions are linked to differentiation and thickening of the neuroepithelium, which may depend on other factors (Fish et al., 2008).

We considered several observations from other epithelial monolayers in determining our proposed stress-dependent growth law. Namely, symmetric cell divisions have been shown to increase with planar stretch (Wyatt et al., 2015; Streichan et al., 2014) and depend on mechanical feedback between G1 and S phases of the cell cycle, with no memory of stretch from past phases (Streichan et al., 2014). For this reason, our growth law is based on the current stress, rather than a time-averaged stress defined by the cell cycle. We also assume transversely isotropic growth, based on the additional observation that in-plane stretch direction did not bias the direction of cell division at low levels (<30% strain) (Streichan et al., 2014).

Desmond et al. (2014) have proposed FAK as a key mechanotransducer in the embryonic brain, finding upregulation of both expression and activity in the presence of pressure. FAK is present throughout the early brain tube (Hens and DeSimone, 1995; Desmond et al., 2014) and has been implicated in stretch-induced cell proliferation in other systems (Chaturvedi et al., 2007; Lehoux et al., 2005; Walker et al., 2005). Therefore, they hypothesize that FAK relocalization induces mitosis via an intracellular cascade of FAK, Src and Erk, and possibly loosens the extracellular matrix to facilitate intercalation of newly formed daughter cells. These ideas are supported by our observation of mechanically induced tangential growth.

Synergistic roles for molecular and mechanical signals

Despite extensive knowledge on the chemical morphogens involved in hemisphere morphogenesis (Monuki, 2007; Toyoda et al., 2010; Ohkubo et al., 2002; Fernandes et al., 2007), no previous studies have attempted a rigorous, quantitative approach to testing proposed physical mechanisms of hemisphere formation. Here, we find that a computational model coupling morphogen gradients and mechanical feedback can explain most experimental observations.

The results of the present study show that wall stresses influence both the size and shape of the forebrain in the early chick embryo. Compared with controls, hemispheres grew more under osmotically increased pressure and less under mechanically reduced pressure (Figs 3 and 8). These trends are consistent with growth modulation throughout the forebrain during earlier stages (Garcia et al., 2017), and similar effects have been reported in terms of total brain tissue volume (Alonso et al., 1998; Desmond and Jacobson, 1977) as well as proliferation rate in the midbrain (Desmond et al., 2005, 2014). However, by assessing two regions of the forebrain, the SP (near the source of FGF8) and the DMB (far from the source of FGF8), we find different stress-dependent growth rates. Therefore, we propose a synergistic (multiplicative) relationship between FGF8-induced and tension-induced growth. This form produces realistic SP shapes in our model, and a biological basis for this type of relationship has been explored in other systems (Walker et al., 2005).

The coupled effects of molecular and mechanical signals also help us understand morphological differences along the dorsal-ventral extent of the SP. Our experimental observations suggest that growth is higher in the dorsal hemispheres than the ventral hypothalamus (Fig. 7C), a gradient that is not predicted by BMP4, FGF8 and SHH morphogen gradients alone (Fig. 1D). However, this gradient may be explained by mechanical interaction with surrounding ventral tissues that constrain the hypothalamus and reduce tension (Fig. S3). The resulting growth differential may set the stage for later development, culminating in adult cerebral hemispheres much larger than the hypothalmus (Matsunaga and Shiota, 1977).

The present study provides evidence supporting mechanical tension as a prerequisite for the mitogenic effects of FGF8. Conversely, effects attributed to BMP4 (full inhibition of roof plate proliferation) appear to be independent of mechanical tension (Fig. S1E). In this region of no proliferation, the model yields relatively high stresses and elongated cell morphology (Fig. 6), illustrating the need for stress-regulated growth to keep tissue stress low (Wyatt et al., 2015). These insights with respect to integration of molecular and mechanical signals may not be obvious without a fully 3D chemomechanical growth model.

Clinical relevance: holoprosencephaly, microcephaly and megalencephaly

The results in this study point to a novel mechanism – dysregulation of eCSF pressure – that could account for abnormal cerebral hemisphere morphologies. Holoprosencephaly represents a diverse group of conditions, ranging in severity and etiology (Fernandes et al., 2007). Although some cases have been directly linked to genetic markers, external factors including alcohol, retinoic acid and maternal diabetes have also been implicated in animal models (Petryk et al., 2015).

We found that decreasing eCSF pressure produces hemispheres that are both holoprosencephalic and microcephalic (classic holoprosencephaly). Though microcephaly had been reported for chicken embryos intubated at earlier stages (Desmond and Jacobson, 1977; Garcia et al., 2017), as well as in chicken and rat embryos cultured under osmotically decreased eCSF pressure (Ramasubramanian et al., 2013; Morriss-Kay et al., 1986; Alonso et al., 2000), the report of holoprosencephaly is novel to this paper. Furthermore, here we found that increasing pressure produced megalencephaly (Fig. 8B), a condition linked to neurodevelopmental delays, epilepsy and corticospinal dysfunction (Barkovich et al., 2012).

Because regulation of eCSF pressure represents a complex process, pressure perturbations could occur during natural development. In zebrafish, genetic mutations related to eCSF secretion have been shown to induce pressure dysregulation (Lowery and Sive, 2005; Doǧanlı et al., 2013). In chicken embryos, pressure can be altered by overproduction or breakdown of osmotically active components (e.g. chondroitin sulfate) (Alonso et al., 1998; Ramasubramanian et al., 2013; Morriss-Kay et al., 1986; Alonso et al., 2000) or an increase in external osmolarity (Chen et al., 2014). In mammalian systems, hyperglycemia, a condition with osmotic effects, has been proposed as a cause of holoprosencephaly in maternal diabetes (Petryk et al., 2015).

Limitations and future work

Using assumptions and initial conditions based on experimental evidence, our model accurately predicts many aspects of normal and abnormal morphogenesis. However, it is worth mentioning several limitations and avenues for future research:

In this study, we approximated morphogen gradients based on available data from literature, reporting the territories of and cross-regulation between BMP4, SHH and FGF8 in the early SP (Furuta et al., 1997; Monuki, 2007; Bardet et al., 2010; Toyoda et al., 2010). For simplicity, our model consolidated these positive- and negative-feedback effects (Fig. 1D) into one BMP4 gradient and one FGF8 gradient defined to approximate the steady-state diffusion solution at t=0 (Fig. 5A). Furthermore, our model did not consider new morphogen gradients that begin to emerge after HH17, such as FGF8 along the dorsomedial diencephalon and expanded SHH at the zona limitans interthalamica of the ventral diencephalon (Crossley et al., 2001), nor did we consider gradients in morphogen signal receptors that may influence tissue response to morphogen concentration. Future models may consider true, dynamic signal diffusion and morphogen interactions, although additional experimental work is needed to quantify reaction-diffusion parameters in this context. Additionally, future models may incorporate parameters related to cell differentiation and tissue-type specification, which can also influence morphogenesis.

Through our model we show that the eCSF plays an important mechanical role by inflating the early brain. However, this fluid may also contain important signals that are lost via intubation or modified by BDX (Lowery and Sive, 2009), which are not considered in this study. Our model predicts reasonable increases in growth from BDX experiments, providing some confidence that growth depends primarily on mechanical pressure, not chemical signals within the eCSF. Furthermore, related studies that use other means to alter eCSF pressure report similar effects on cell proliferation and size in the developing brain (Ramasubramanian et al., 2013; Morriss-Kay et al., 1986; Alonso et al., 2000; Desmond et al., 2005; 2014). Although these results support a driving role for mechanical stimuli, future exploration of the interplay between osmolarity, eCSF components, and growth is warranted.

In terms of external forces, the current 3D model approximates mechanical interaction with external tissues using an elastic foundation. This approximation was used to reduce computational time, as incorporation of all tissues would require contact between separate structures representing mesenchyme, prospective eyes, and surface ectoderm. Although our approach does not capture the details of these structures, we find it sufficient to capture basic effects on our structure of interest: constrained growth of the ventral hypothalamus.

At later stages of hemisphere morphogenesis, mesenchyme between the cortical hemispheres has been proposed as a crucial factor in roof plate signaling and hemisphere maintenance (Choe et al., 2014), potentially exerting force to assist roof plate invagination (Gupta and Sen, 2015). Notably, our model did not require downward force from the dorsal mesenchyme to initiate hemisphere division (Fig. 5). However, we did observe dramatic stretch of the thinning roof plate region (Fig. S3), which forms delicate choroid plexus projections at later stages (Choe et al., 2014). Like ventral tissues that reinforce the hypothalamus, it is possible that mesenchyme serves to reinforce the roof plate at later stages. Studies of later development should consider the role of mesenchyme in choroid plexus morphogenesis.

In conclusion, both chemical and mechanical factors likely play important roles in clinically observed congenital malformations. Future studies are warranted to elucidate the relative contributions of these factors in brain development.

MATERIALS AND METHODS

Embryo culture, perturbation, and imaging

Fertilized white Leghorn chicken eggs (Gallus gallus) were incubated at 38°C (90% humidity), and embryos were extracted at 48 or 60 h (HH13 or HH17, respectively) using a filter paper carrier (Chapman et al., 2001). Embryos were cultured on 0.3% agar-albumen gels in 35 mm culture dishes (Chapman et al., 2001), with a 200 µl layer of culture media on top. Unless otherwise stated, culture media contained Dulbecco's Modified Eagle's Medium (Sigma-Aldrich) with 10% chick serum (Sigma-Aldrich) and 1% penicillin/streptomycin/neomycin (Invitrogen). To ensure adequate oxygen delivery during culture under media, embryos were superfused with a mixture of 95% oxygen and 5% carbon dioxide (Voronov and Taber, 2002).

To increase eCSF pressure during development, 100 µl of media was replaced with media containing 4 mM β-D-xyloside (BDX, Sigma-Aldrich), which increases osmolarity of the eCSF, thereby increasing the pressure required for osmotic-pressure equilibrium (Alonso et al., 1998; Desmond et al., 2014). To reduce eCSF pressure during development, an open glass capillary tube (inner diameter=150 µm) was inserted into the midbrain. The relatively large tube allows fluid to flow out of the brain with little resistance, negating any potential build-up in eCSF pressure caused by increases in eCSF secretion during the culture period. Only embryos in which the tube remained intact for the full 24 h culture were used for subsequent analysis. For sham embryos, a closed glass rod was used instead. To measure deflated final geometries, a small incision was made in the midbrain. To reduce the influence of external tissues, prospective eyes and lateral mesenchyme were dissected from the HH13 forebrain, and embryos were cultured for 48 h to HH21 (allowing an additional 12 h for healing and slower culture in vitro).

All embryos were examined over the course of development using OCT (Thorlabs) and a Leica MZ8 microscope. To measure changes due to growth, geometries were recorded with OCT before and after culture. To measure geometric changes due to inflation, geometries were also recorded immediately before and after deflation where applicable.

Fluorescent labeling and quantification

To quantify cell proliferation, EdU was incorporated into cells undergoing DNA synthesis using the Click-iT EdU assay (Invitrogen). Based on previous optimization for chicken embryos (Warren et al., 2009), 400 µl of 1 mM EdU was pipetted directly on top of embryos (HH17 or HH21), which were then cultured for 4 h and immediately fixed in 3.7% formaldehyde. Embryos were manually cut through the SP (n=2 HH17, n=3 HH21) or cryosectioned (n=3 HH17, n=2 HH21) before permeabilizing for 1 h in 1% bovine serum albumin (Sigma-Aldrich) and 0.1% Triton X-100 (Sigma-Aldrich). The Click-iT EdU reaction was applied according to the manufacturer's protocol. To protect the integrity of cryosectioned tissues, embryos were soaked in 30% sucrose prior to freezing. To label all nuclei, samples were then incubated 30 min in 5 µg/ml Hoechst 33342 (DNA stain). To visualize apical F-actin on the inner surface of the brain, additional embryos were fixed with 3.7% formaldehyde, manually cut through the SP (HH17 or HH21), permeabilized, and stained with phalloidin as described by Garcia et al. (2017).

Fixed fluorescent samples were imaged using a Zeiss LSM 710 confocal microscope at 20× magnification. For large sections, Fiji/ImageJ (Schneider et al., 2012) was used to stitch multiple 20× z-stacks (Preibisch et al., 2009), then z-stacks were transformed to maximum intensity z-projections (see Fig. 2A,B). To minimize bias when determining proliferation fraction, nuclei were semi-automatically counted as follows. First, EdU maximum intensity projections were run through a 3D Gaussian blur filter of 0.5 µm×0.5 µm×0.5 µm, followed by a CLAHE (contrast-limited adaptive histogram equalization) algorithm to optimize local contrast for each channel. For continuous quantification along the wall of the brain tube (Fig. 7, Fig. S1), the neuroepithelium was traced and straightened (Kocsis et al., 1991) such that the x-dimension represented distance from the roof plate. Finally, local maxima (representing EdU-labeled or Hoechst 33342-labeled nuclei) were counted, using a 1-pixel (36 µm2) Gaussian filter to avoid labeling noise as nuclei. Images were checked manually to ensure accurate capture of nuclei. Owing to variability in image quality, some images required an additional round of Gaussian blur (1 pixel≈36 µm2) after z-projection and CLAHE. For a given region, proliferation fraction was calculated as the number of EdU-labeled nuclei (undergoing S phase during the 4-h labeling window) divided by the total number of Hoechst 33342-labeled nuclei. For Fig. 7C and Fig. S1, each data point represents a 60 µm-long segment along the circumference of the wall.

Measuring growth and deformation

OCT image stacks were reoriented in ImageJ/Fiji (Schneider et al., 2012) to yield cross-sections through the DMB or SP as shown in Figs 4B and 1A′,B′, respectively. For measures at the DMB, the wall perimeter, δ, was traced for each cross-section, and average radius was computed as δ/(2π). For intubated and sham embryos, initial radius (HH17) was recorded before deflation (R′) and after deflation (R), whereas only the initial inflated radius (R′) could be recorded for control and BDX cases (Fig. 3). For all cases, final radius (HH21) was recorded before deflation (r′) and after deflation (r). Elastic circumferential stretch, λ*, was calculated as the ratio of inflated to deflated radius at each stage as described in Fig. 4. Using the average value of to represent all experimental groups before perturbation, circumferential growth was estimated as . (Overbar denotes group average.)

Deflated wall thickness (H at HH17, h at HH21) was also measured in the lateral DMB (top of OCT image in Fig. 4C), where image quality was maintained at late stages. Because elastic deformation was too small to be detected in the thickness direction, average radial growth was estimated as .

To estimate hemisphere growth, the same techniques were applied, replacing DMB radius with equivalent hemisphere radius, calculated from arc lengths shown in Fig. 3.

Pressure measurement

Lumen pressure was measured with a micropipette connected to a pressure transducer, as adapted from Jelinek and Pexieder (1968). Briefly, borosilicate glass micropipettes were pulled to an internal diameter greater than 80 µm with a 30° beveled tip and connected via polyethylene tubing (BD; 427440) to a differential pressure transducer (Honeywell; CPCL04DFC). A signal conditioner (Omega; DMD4059-DC) was used to amplify the transducer signal, and a data acquisition module (National Instruments; USB-6009), and custom LabVIEW program were used to record voltage over time. The transducer was calibrated using a water manometer, and all data were processed in MATLAB.

At HH17 or HH21, chicken embryos were extracted and transferred to a PBS-filled Petri dish. Micropipettes and tubing were backfilled with PBS to match the osmolality of chick cerebrospinal fluid (Alonso et al., 1998). A baseline voltage was recorded for at least 5 min and then the micropipette was inserted into the hindbrain, where the roof plate neuroepithelium is thinner, to prevent clogging. As the brain tube is a continuous fluid-filled cavity with negligible flow, equivalent pressures are expected in more rostral brain vesicles at the stages considered here (Desmond et al., 2005). Data was recorded for at least 5 min before being removed, and pressure values were calculated as the mean pressure over at least the first 3 min after insertion.

Determining growth constants from measurements at the DMB

To determine values for the parameters in the proposed growth law (Eqn 1), we considered the following approximations and experimental data at the DMB.

Because the DMB is far from territories of high BMP4 (roof plate of the SP) and FGF8 (anterior neural ridge, as well as the midbrain-hindbrain boundary) (Crossley et al., 2001; Toyoda et al., 2010), we set CFGF=CBMP=0, such that Eqn 1 became
formula
(5)
To compute σ̄, the DMB region was approximated as a cylindrical tube with an internal pressure p. According to Laplace's Law, the average circumferential and longitudinal wall stresses are σΘ=pr′i/h′ and σΦ=pr′i/2h′, where r′i=r′h′/2 and h′ are the elastically deformed inner radius and wall thickness, respectively. At the initial time (t=0), substituting these relations into Eqn 2 yields
formula
(6)
where R′i and H′i are the elastically deformed inner radius and wall thickness, respectively, at HH17. For the relatively small elastic deformation given by our measurements, geometric changes to the unloaded geometry are assumed to be caused mostly by growth such that ri=GRi and hi=GRHi. Approximating r′=r, h′=h, R′=R, and H′=H, we obtain
formula
(7)
Inserting this relation into Eqn 5 gives the nonlinear differential equation
formula
(8)
In solving Eqns 5 and 8 for GR(t) and G(t), we use the initial conditions GR(0)=G(0)=1. In the absence of mechanical feedback (a=0 or σ̄ = 0), the solution simplifies to
formula
(9)
which represents typical exponential growth. When mechanical feedback is included (a≠0 and σ̄ ≠ 0), the radial growth does not change. With GR(t) from Eqn 9, Eqn 8 can be solved in closed-form to obtain the tangential growth
formula
(10)
Growth parameters g0, g0r and a were calculated as follows.
  1. With the measured values G=1.48±0.17 and GR=1.38±0.22 at HH21 (t=1 d) under zero pressure (Fig. 4), Eqn 9 gives g0=0.39 d−1 and g0r=0.32 d−1. These values characterize baseline growth, in the absence of eCSF pressure, FGF8 and BMP4.

  2. For normal pressure of p=15 Pa, shear modulus μ=300 Pa (Xu et al., 2010), initial radius R′i=222±24 μm (n=19), and initial wall thickness H′=87±7 μm (n=12) (Fig. 4D), Eqn 6 gives σ̄0 = 0.095. Given G=1.87±0.08 over t=1 d in control brains (Fig. 4), Eqn 10 yields a=2.1 d−1.

See Fig. S5 for the effects of these parameters on the model.

Computational methods

Finite element models were created in ABAQUS Standard (v6.10, SIMULIA) using C3D20R elements (20-node quadratic brick elements with reduced integration). For models of hemisphere division, the initial, unloaded geometry was based on OCT images of the deflated SP at HH17. As shown in Fig. 5A, this consists of a spherical telencephalon of inner radius RT=3H, a conical hypothalamus defined such that the total dorsal-ventral length L=4RT, and a caudal portion extending straight (D=3H  long) to represent the boundary connecting SP to diencephalon. To reduce computational time, only the left half of the brain was simulated, with symmetry conditions applied at the midline. The caudal end was constrained with a roller boundary condition. For H=88 μm, this leads to a model domain of size of approximately 1.06 mm×0.62 mm×0.35 mm. The full model contained four elements across the thickness, for a total of 12,448 elements.

A normal (measured) eCSF pressure of p=15 Pa was applied along the inner wall. BDX cases were modeled by applying a 40% increase in pressure (p=21 Pa) according to Alonso et al. (1998) and measurements reported in this study. Intubated cases were modeled without pressure (p=0 Pa). The conical hypothalamus and its caudal extension were constrained by an external elastic foundation, assuming a spring stiffness per unit area of k/A=1.0 Pa/μm (for a 600 µm-thick layer of external tissue, the shear modulus is μext≈0.35 μ). This value is reasonable if we consider surrounding tissues as a composite, with prospective eye neuroepithelium (µ similar to that of the brain tube; Oltean et al., 2016) filling approximately one-third of the space (Fig. 1B′) and mesenchyme (extremely low µ) filling the rest. Shear moduli of other tissues, such as the myocardium and cardiac jelly of the developing heart, have been reported as low as 0.34 µ and 0.07 µ, respectively (Zamir et al., 2003).

To simulate growth in ABAQUS, we implemented a custom user subroutine based on the UMAT generator developed by Young et al. (2010). Based on the nonlinear theory for volumetric growth (Rodriguez et al., 1994), we decompose the 3D deformation gradient tensor as F = F*·G, where G is the growth tensor and F* is the elastic deformation gradient tensor. We assume transversely isotropic growth such that
formula
(11)
where ei terms represent unit base vectors of the local curvilinear coordinate system in the initial configuration (Fig. 5A). The Cauchy stress tensor, σ, depends on F* according to
formula
(12)
where J* = det F* is the elastic volume ratio and T denotes the transpose. Morphogen- and stress-dependent growth is defined according to Eqn 1.

We also considered the possibility that mechanical feedback depends directly on pressure, rather than wall stress (Fig. 5B, left). As pressure is approximately constant (Jelinek and Pexieder, 1968; Desmond et al., 2005) and uniform throughout the brain tube (a continuous, fluid-filled cavity with negligible flow) at these stages, we assigned σ̄ to a constant, uniform value. To obtain similar levels of overall growth for the pressure-dependent growth case, we set σ̄ = 0.125.

Based on past measurements in the chick brain tube, the neuroepithelial wall is treated as a nearly incompressible, pseudoelastic material with shear modulus μ=300 Pa and bulk modulus κ=100 μ (Xu et al., 2010). Following Xu et al. (2010), we use a modified neo-Hookean strain energy density of the form
formula
(13)
where Ī1*=J*−2/3 tr(F*T · F*) is the first strain invariant. To approximate observed constriction between the SP and diencephalon and improve model convergence, the caudal end was stiffened such that μ=1.8 kPa. Because inertia effects can be ignored during relatively slow morphogenetic processes, a quasi-static analysis was used to solve the problem.

Morphogen gradients were defined in the initial configuration, approximating the solution for steady-state diffusion from a source. To obtain an approximately linear gradient that is differentiable near the source and sink, we considered the general form C=[1+ec(X/d−1)]−1, where C is the morphogen concentration, X is the initial distance from the source (C=1), and c and d control the slope and positioning of the gradient (Tallinen et al., 2016). As shown in Fig. 5A, the FGF8 gradient is relatively diffuse (Toyoda et al., 2010), with a characteristic length of 0.55 mm. By contrast, we define a relatively sharp BMP4 gradient, with a characteristic length of 0.03 mm. Illustrations and effects of characteristic length on model predictions are available in supplementary materials (Fig. S4).

Statistics

Analysis of variance (ANOVA) with post-hoc Tukey test was used to compare data between more than two groups, and Student's t-test was used to compare data between two groups. Ratio data were log-transformed to produce normal distributions. For all tests, P<0.05 was considered significant. All error bars denote standard deviation.

Acknowledgements

We gratefully acknowledge Haley Nichols, who assisted with preliminary experiments and analysis that helped guide this study.

Footnotes

Author contributions

Conceptualization: K.E.G., J.P.G., L.A.T.; Methodology: K.E.G., W.G.S., M.G.E., L.A.T.; Formal analysis: K.E.G., W.G.S., M.G.E.; Investigation: K.E.G., L.A.T.; Resources: W.G.S., M.G.E., L.A.T.; Writing - original draft: K.E.G.; Writing - review & editing: K.E.G., W.G.S., M.G.E., J.P.G., L.A.T.; Visualization: K.E.G.; Supervision: J.P.G., L.A.T.; Project administration: L.A.T.; Funding acquisition: J.P.G., L.A.T.

Funding

This work was supported by National Institutes of Health grants (R01 NS070918 to L.A.T.; T32 EB018266 to K.E.G.; R01 HL133163 to J.P.G.; R21 ES027962 to J.P.G.); a National Science Foundation grant (1537256 to J.P.G.); and the Washington University Chancellor's Graduate Fellowship Program (M.G.E.). Deposited in PMC for release after 12 months.

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Competing interests

The authors declare no competing or financial interests.

Supplementary information