Denis Menshykau

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 modes.

The control of branching morphogenesis

Many organs of higher organisms are heavily branched structures and arise by an apparently similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in these organs. It is an open question whether the regulatory processes work according to a common principle and how far physical and geometrical constraints determine the branching process. Here, we review the known regulatory factors and physical constraints in lung, kidney, pancreas, prostate, mammary gland and salivary gland branching morphogenesis, and describe the models that have been formulated to analyse their impacts.

Digit patterning during limb development as a result of the BMP-receptor interaction

Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of receptor-ligand interaction can give rise to Schnakenberg-type Turing patterns, which reproduce patterning during lung and kidney branching morphogenesis. Recent knockout experiments have identified Smad4 as a key protein in digit patterning. We show here that the BMP-receptor interaction meets the conditions for a Schnakenberg-type Turing pattern, and that the resulting model reproduces available wildtype and mutant data on the expression patterns of BMP, its receptor, and Fgfs in the apical ectodermal ridge (AER) when solved on a realistic 2D domain that we extracted from limb bud images of E11.5 mouse embryos. We propose that receptor-ligand-based mechanisms serve as a molecular basis for the emergence of Turing patterns in many developing tissues.

Kidney branching morphogenesis under the control of a ligand–receptor-based Turing mechanism

The main signalling proteins that control early kidney branching have been defined. Yet the underlying mechanism is still elusive. We have previously shown that a Schnakenberg-type Turing mechanism can recapitulate the branching and protein expression patterns in wild-type and mutant lungs, but it is unclear whether this mechanism would extend to other branched organs that are regulated by other proteins. Here, we show that the glial cell line-derived neurotrophic factor-RET regulatory interaction gives rise to a Schnakenberg-type Turing model that reproduces the observed budding of the ureteric bud from the Wolffian duct, its invasion into the mesenchyme and the observed branching pattern. The model also recapitulates all relevant protein expression patterns in wild-type and mutant mice. The lung and kidney models are both based on a particular receptor-ligand interaction and require (1) cooperative binding of ligand and receptor, (2) a lower diffusion coefficient for the receptor than for the ligand and (3) an increase in the receptor concentration in response to receptor-ligand binding (by enhanced transcription, more recycling or similar). These conditions are met also by other receptor-ligand systems. We propose that ligand-receptor-based Turing patterns represent a general mechanism to control branching morphogenesis and other developmental processes.

An interplay of geometry and signaling enables robust lung branching morphogenesis

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.

SrGAP2-Dependent Integration of Membrane Geometry and Slit-Robo-Repulsive Cues Regulates Fibroblast Contact Inhibition of Locomotion

Migrating fibroblasts undergo contact inhibition of locomotion (CIL), a process that was discovered five decades ago and still is not fully understood at the molecular level. We identify the Slit2-Robo4-srGAP2 signaling network as a key regulator of CIL in fibroblasts. CIL involves highly dynamic contact protrusions with a specialized actin cytoskeleton that stochastically explore cell-cell overlaps between colliding fibroblasts. A membrane curvature-sensing F-BAR domain pre-localizes srGAP2 to protruding edges and terminates their extension phase in response to cell collision. A FRET-based biosensor reveals that Rac1 activity is focused in a band at the tip of contact protrusions, in contrast to the broad activation gradient in contact-free protrusions. SrGAP2 specifically controls the duration of Rac1 activity in contact protrusions, but not in contact-free protrusions. We propose that srGAP2 integrates cell edge curvature and Slit-Robo-mediated repulsive cues to fine-tune Rac1 activation dynamics in contact protrusions to spatiotemporally coordinate CIL.

Simulations demonstrate a simple network to be sufficient to control branch point selection, smooth muscle and vasculature formation during lung branching morphogenesis.

Summary Proper lung functioning requires not only a correct structure of the conducting airway tree, but also the simultaneous development of smooth muscles and vasculature. Lung branching morphogenesis is strongly stereotyped and involves the recursive use of only three modes of branching. We have previously shown that the experimentally described interactions between Fibroblast growth factor (FGF)10, Sonic hedgehog (SHH) and Patched (Ptc) can give rise to a Turing mechanism that not only reproduces the experimentally observed wildtype branching pattern but also, in part counterintuitive, patterns in mutant mice. Here we show that, even though many proteins affect smooth muscle formation and the expression of Vegfa, an inducer of blood vessel formation, it is sufficient to add FGF9 to the FGF10/SHH/Ptc module to successfully predict simultaneously the emergence of smooth muscles in the clefts between growing lung buds, and Vegfa expression in the distal sub-epithelial mesenchyme. Our model reproduces the phenotype of both wildtype and relevant mutant mice, as well as the results of most culture conditions described in the literature.

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.

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 production.

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models.

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.