Morphogenesis by coupled regulatory networks: reliable control of positional information and proportion regulation

Master stability functions for metacommunities with two types of habitats

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the master stability function formalism to inhomogeneous biregular networks having two types of spatial nodes. Notably, this class of systems also allows the investigation of certain types of dynamics on higher-order networks. Combined with the generalized modeling approach to study the linear stability of steady states, this is a powerful tool to numerically asses the stability of large ensembles of systems. We analyze the stability of ecological metacommunities with two distinct types of habitats analytically and numerically in order to identify several sets of conditions under which the dynamics can become stabilized by dispersal. Our analytical approach allows general insights into stabilizing and destabilizing effects in metapopulations. Specifically, we identify self-regulation and negative feedback loops between source and sink populations as stabilizing mechanisms and we show that maladaptive dispersal may be stable under certain conditions.

Patterning the insect eye: From stochastic to deterministic mechanisms

While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity. In human and Drosophila eyes, photoreceptors sensitive to different wavelengths of light are distributed in stochastic patterns, and one such patterning system has been analyzed in detail in the Drosophila retina. Interestingly, some species in the dipteran family Dolichopodidae (the “long legged” flies, or “Doli”) instead exhibit highly orderly deterministic eye patterns. In these species, alternating columns of ommatidia (unit eyes) produce corneal lenses of different colors. Occasional perturbations in some individuals disrupt the regular columns in a way that suggests that patterning occurs via a posterior-to-anterior signaling relay during development, and that specification follows a local, cellular-automaton-like rule. We hypothesize that the regulatory mechanisms that pattern the eye are largely conserved among flies and that the difference between unordered Drosophila and ordered dolichopodid eyes can be explained in terms of relative strengths of signaling interactions rather than a rewiring of the regulatory network itself. We present a simple stochastic model that is capable of explaining both the stochastic Drosophila eye and the striped pattern of Dolichopodidae eyes and thereby characterize the least number of underlying developmental rules necessary to produce both stochastic and deterministic patterns. We show that only small changes to model parameters are needed to also reproduce intermediate, semi-random patterns observed in another Doli species, and quantification of ommatidial distributions in these eyes suggests that their patterning follows similar rules.

A simple model is able to account for a diversity of photoreceptor patterns in different fly species, ranging from highly deterministic to fully random.

Cell-cell interaction and diversity of emergent behaviours

Despite myriads of possible gene expression profiles, cells tend to be found in a confined number of expression patterns. The dynamics of Boolean models of gene regulatory networks has proven to be a likely candidate for the description of such self-organisation phenomena. Because cells do not live in isolation, but they constantly shape their functions to adapt to signals from other cells, this raises the question of whether the cooperation among cells entails an expansion or a reduction of their possible steady states. Multi random Boolean networks are introduced here as a model for interaction among cells that might be suitable for the investigation of some generic properties regarding the influence of communication on the diversity of cell behaviours. In spite of its simplicity, the model exhibits a non-obvious phenomenon according to which a moderate exchange of products among adjacent cells fosters the variety of their possible behaviours, which on the other hand are more similar to one another. On the contrary, a more invasive coupling would lead cells towards homogeneity.

Receptor cross-talk in angiogenesis: mapping environmental cues to cell phenotype using a stochastic, Boolean signaling network model

Cancer invasion and metastasis depend on tumor-induced angiogenesis, the means by which cancer cells attract and maintain a blood supply. During angiogenesis, cellular processes are tightly coordinated by signaling molecules and their receptors. Understanding how endothelial cells synthesize multiple biochemical signals can catalyze the development of novel therapeutic strategies to combat cancer. This study is the first to propose a signal transduction model highlighting the cross-talk between key receptors involved in angiogenesis, namely the VEGF, integrin, and cadherin receptors. From experimental data, we construct a network model of receptor cross-talk and analyze its dynamics. We identify relationships between receptor activation combinations and cellular function, and show that cross-talk is crucial to phenotype determination. The network converges to a unique set of output states that correspond to known cell phenotypes: migratory, proliferating, quiescent, apoptotic, and it predicts one phenotype that challenges the "go or grow" hypothesis. Finally, we use the model to study protein inhibition and to suggest molecular targets for anti-angiogenic therapies.

Neutrality and robustness in evo-devo: emergence of lateral inhibition

Embryonic development is defined by the hierarchical dynamical process that translates genetic information (genotype) into a spatial gene expression pattern (phenotype) providing the positional information for the correct unfolding of the organism. The nature and evolutionary implications of genotype-phenotype mapping still remain key topics in evolutionary developmental biology (evo-devo). We have explored here issues of neutrality, robustness, and diversity in evo-devo by means of a simple model of gene regulatory networks. The small size of the system allowed an exhaustive analysis of the entire fitness landscape and the extent of its neutrality. This analysis shows that evolution leads to a class of robust genetic networks with an expression pattern characteristic of lateral inhibition. This class is a repertoire of distinct implementations of this key developmental process, the diversity of which provides valuable clues about its underlying causal principles.

An osmoregulatory basis for shape oscillations in regenerating hydra

The freshwater polyp Hydra has considerable regeneration capabilities. A small fragment of tissue excised from an adult animal is sufficient to regenerate an entire Hydra in the course of a few days. During the initial stages of the regeneration process, the tissue forms a hollow sphere. Then the sphere exhibits shape oscillations in the form of repeated cycles of swelling and collapse. We propose a biophysical model for the swelling mechanism. Our model takes the osmotic pressure difference between Hydra's inner and outer media and the elastic forces of the Hydra shell into account. We validate the model by a comprehensive experimental study including variations in initial medium concentrations, Hydra sphere sizes and temperatures. Numerical simulations of the model provide values for the swelling rates that are in agreement with the ones measured experimentally. Based on our results we argue that the shape oscillations are a consequence of Hydra's osmoregulation.