Species-specific differences in follicular antral sizes result from diffusion-based limitations on the thickness of the granulosa cell layer

The size of mature oocytes is similar across mammalian species, yet the size of ovarian follicles increases with species size, with some ovarian follicles reaching diameters more than 1000-fold the size of the enclosed oocyte. Here we show that the different follicular sizes can be explained with diffusion-based limitations on the thickness of the hormone-secreting granulosa layer. By analysing published data on human follicular growth and granulosa cell expansion during follicular maturation we find that the 4-fold increase of the antral follicle diameter is entirely driven by an increase in the follicular fluid volume, while the thickness of the surrounding granulosa layer remains constant at about 45+/-10 mkm. Based on the measured kinetic constants, the model reveals that the observed fall in the gonadotropin concentration from peripheral blood circulation to the follicular antrum is a result of sequestration in the granulosa. The model further shows that as a result of sequestration, an increased granulosa thickness cannot substantially increase estradiol production but rather deprives the oocyte from gonadotropins. Larger animals (with a larger blood volume) require more estradiol as produced by the ovaries to downregulate FSH-secretion in the pituitary. Larger follicle diameters result in larger follicle surface areas for constant granulosa layer thickness. The reported increase in follicular surface area in larger species indeed correlates linearly both with species mass and with the predicted increase in estradiol output. In summary, we propose a structural role for the antrum in that it determines the volume of the granulosa layer and thus the level of estrogen production.Comment: Mol Hum Repr 201

Species-specific differences in follicular antral sizes result from diffusion-based limitations on the thickness of the granulosa cell layer

The size of mature oocytes is similar across mammalian species, yet the size of ovarian follicles increases with species size, with some ovarian follicles reaching diameters >1000-fold the size of the enclosed oocyte. Here we show that the different follicular sizes can be explained with diffusion-based limitations on the thickness of the hormone-secreting granulosa layer. By analysing published data on human follicular growth and granulosa cell expansion during follicular maturation we find that the 4-fold increase of the antral follicle diameter is entirely driven by an increase in the follicular fluid volume, while the thickness of the surrounding granulosa layer remains constant at ∼45 ± 10 µm. Based on the measured kinetic constants, the model reveals that the observed fall in the gonadotrophin concentration from peripheral blood circulation to the follicular antrum is a result of sequestration in the granulosa. The model further shows that as a result of sequestration, an increased granulosa thickness cannot substantially increase estradiol production but rather deprives the oocyte from gonadotrophins. Larger animals (with a larger blood volume) require more estradiol as produced by the ovaries to down-regulate follicle-stimulating hormone-secretion in the pituitary. Larger follicle diameters result in larger follicle surface areas for constant granulosa layer thickness. The reported increase in the follicular surface area in larger species indeed correlates linearly both with species mass and with the predicted increase in estradiol output. In summary, we propose a structural role for the antrum in that it determines the volume of the granulosa layer and thus the level of estrogen productio

Dynamic Image-Based Modelling of Kidney Branching Morphogenesis

Kidney branching morphogenesis has been studied extensively, but the mechanism that defines the branch points is still elusive. Here we obtained a 2D movie of kidney branching morphogenesis in culture to test different models of branching morphogenesis with physiological growth dynamics. We carried out image segmentation and calculated the displacement fields between the frames. The models were subsequently solved on the 2D domain, that was extracted from the movie. We find that Turing patterns are sensitive to the initial conditions when solved on the epithelial shapes. A previously proposed diffusion-dependent geometry effect allowed us to reproduce the growth fields reasonably well, both for an inhibitor of branching that was produced in the epithelium, and for an inducer of branching that was produced in the mesenchyme. The latter could be represented by Glial-derived neurotrophic factor (GDNF), which is expressed in the mesenchyme and induces outgrowth of ureteric branches. Considering that the Turing model represents the interaction between the GDNF and its receptor RET very well and that the model reproduces the relevant expression patterns in developing wildtype and mutant kidneys, it is well possible that a combination of the Turing mechanism and the geometry effect control branching morphogenesis

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio

Shape Self-Regulation in Early Lung Morphogenesis

The arborescent architecture of mammalian conductive airways results from the repeated branching of lung endoderm into surrounding mesoderm. Subsequent lung’s striking geometrical features have long raised the question of developmental mechanisms involved in morphogenesis. Many molecular actors have been identified, and several studies demonstrated the central role of Fgf10 and Shh in growth and branching. However, the actual branching mechanism and the way branching events are organized at the organ scale to achieve a self-avoiding tree remain to be understood through a model compatible with evidenced signaling. In this paper we show that the mere diffusion of FGF10 from distal mesenchyme involves differential epithelial proliferation that spontaneously leads to branching. Modeling FGF10 diffusion from sub-mesothelial mesenchyme where Fgf10 is known to be expressed and computing epithelial and mesenchymal growth in a coupled manner, we found that the resulting laplacian dynamics precisely accounts for the patterning of FGF10-induced genes, and that it spontaneously involves differential proliferation leading to a self-avoiding and space-filling tree, through mechanisms that we detail. The tree’s fine morphological features depend on the epithelial growth response to FGF10, underlain by the lung’s complex regulatory network. Notably, our results suggest that no branching information has to be encoded and that no master routine is required to organize branching events at the organ scale. Despite its simplicity, this model identifies key mechanisms of lung development, from branching to organ-scale organization, and could prove relevant to the development of other branched organs relying on similar pathways

The Influence of Electrode Porosity on Diffusional Cyclic Voltammetry

A simple generic model to predict the influence of electrode porosity on the cyclic voltammetric response of an electrode is presented. The conditions under which deviation from the behavior of a perfectly flat, planar electrode can be expected are predicted. The scope for misinterpretation when conventional flat electrode theory is applied to porous electrodes is highlighted, especially in respect to the extraction of electrode kinetic parameters and the influence of 'electrocatalysis'. © 2008 Wiley-VCH Verlag GmbH and Co. KGaA

Electrodes modified with electroinactive layers: distinguishing through-film transport from pinhole (pore) diffusion.

Electrodes modified with layers, for example, of polymers or self-assembled monolayers, are of great importance from both the fundamental and applied points of view. Two different models of electrodes covered with electroinactive layers can be proposed. First, the electrode is covered with a uniform layer into which the electroactive species dissolves and then diffuses through, or second, the layer contains pinholes that are exclusively responsible for diffusional transport to the electrode. Both models are simulated and then compared to identify conditions under which they can be distinguished. The models are studied for a broad range of parameters reflecting experimentally viable values. Different types of cyclic voltammograms can be observed in the studied models corresponding to classical Randles-Sevcik, thin layer, and steady-state behaviors. We show that the models can be distinguished experimentally through recording cyclic voltammograms over a sufficiently broad range of voltage scan rates

Influence of Electrode Roughness on Stripping Voltammetry: Mathematical Modeling and Numerical Simulation

Electrodes with rough surfaces inevitably have practical importance from both applied and fundamental points of view including electroanalysis where stripping voltammetry is a popular technique due to its simplicity and high sensitivity. The diffusional domain approach is used to model stripping voltammetry at rough electrodes: two models of the electrode surface, "rough" and "scratched", are considered. Electron transfer is described by three models which correspond to cases of stripping of a monolayer, a thin layer, and a bulk layer. The shape of the votammograms strongly depends on the model of the electron transfer but is not always sensitive to the precise model of the electrode surface; the conditions under which this is the case are identified, and generic roughness effects on stripping voltammetry are quantified. We conclude that electrode roughness can have a significant effect on the stripping of the metals from the solid electrode especially in respect of the voltammetric waveshape. © 2009 American Chemical Society

Influence of electrode roughness on cyclic voltammetry

Electrodes with rough surfaces are of great practical importance from both applied and fundamental points of view. The diffusion domain approach is used to model cyclic voltammetry at such electrodes. Electrode roughness only has a significant effect on the shape of cyclic voltammograms and peak currents at relatively high values of electrode roughness. To verify the theory two experimental systems were used: TMPD in acetonitrile and Ru(NH3) 6Cl3 in aqueous solution. In both cases cyclic voltammograms on the flat and roughened glassy carbon electrodes were in agreement with theory. Even significant surface roughness produced by deliberate polishing or scratching is not sufficient to be distinguished in cyclic voltammetry experiments conducted under the usual conditions. © 2008 American Chemical Society