Ernesto M. Nicola

Polarization of PAR proteins by advective triggering of a pattern-forming system.

Patterning of Caenorhabditis elegans zygotes involves passive as well as active mechanisms. In the Caenorhabditis elegans zygote, a conserved network of partitioning-defective (PAR) polarity proteins segregates into an anterior and a posterior domain, facilitated by flows of the cortical actomyosin meshwork. The physical mechanisms by which stable asymmetric PAR distributions arise from transient cortical flows remain unclear. We present evidence that PAR polarity arises from coupling of advective transport by the flowing cell cortex to a multistable PAR reaction-diffusion system. By inducing transient PAR segregation, advection serves as a mechanical trigger for the formation of a PAR pattern within an otherwise stably unpolarized system. We suggest that passive advective transport in an active and flowing material may be a general mechanism for mechanochemical pattern formation in developmental systems.

Parameter-space topology of models for cell polarity

Reaction–diffusion systems have been widely successful in the theoretical description of biological patterning phenomena, giving rise to numerous models based on differing mechanisms, mathematical implementations and parameter choices. However, even for models with common design features, the diversity of mathematical realizations may hinder the identification of common behavior. Here, we analyze three different reaction–diffusion models for cell polarity that feature conservation of mass, rapid cytoplasmic diffusion and bistability via a cusp bifurcation of uniform states. In all three models, the nonuniform polar states are front solutions, and growth of domains ceases through stalling of a propagating front. For these three models we find a characteristic parameter space topology, comprising a region of linear instability that loops around the cusp point and that is enclosed by a ‘comet-shaped’ region of nonuniform domain states. We propose a minimal model based on the cusp bifurcation normal form that includes essential characteristics of all cell polarity models considered. For this minimal model, we provide a complete analytical description of the parameter space topology, and find that the instability loop appears as a generic property of the cusp bifurcation. This topological analysis provides a unifying understanding of earlier mathematically distinct models and is suitable to classify future models.

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 Hydras 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 Hydras osmoregulation.

Mobility induces global synchronization of oscillators in periodic extended systems

We study the synchronization of locally coupled noisy phase oscillators that move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits wave- like states displaying local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical mobility above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by a shift in the relative size of attractor basins associated with wave- like states. Mobility disrupts these states and paves the way for the system to attain global synchronization.

Breaking chirality in nonequilibrium systems on the lattice

We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in the continuum and using symmetry arguments, we derive a simple dynamical system that captures the dynamics of fronts in the lattice. We can expect our approach to be extended to other pattern-forming problems on lattices.