The diverse effects of mechanical loading on active hair bundles.

Hair cells in the auditory, vestibular, and lateral-line systems of vertebrates receive inputs through a remarkable variety of accessory structures that impose complex mechanical loads on the mechanoreceptive hair bundles. Although the physiological and morphological properties of the hair bundles in each organ are specialized for detecting the relevant inputs, we propose that the mechanical load on the bundles also adjusts their responsiveness to external signals. We use a parsimonious description of active hair-bundle motility to show how the mechanical environment can regulate a bundle's innate behavior and response to input. We find that an unloaded hair bundle can behave very differently from one subjected to a mechanical load. Depending on how it is loaded, a hair bundle can function as a switch, active oscillator, quiescent resonator, or low-pass filter. Moreover, a bundle displays a sharply tuned, nonlinear, and sensitive response for some loading conditions and an untuned or weakly tuned, linear, and insensitive response under other circumstances. Our simple characterization of active hair-bundle motility explains qualitatively most of the observed features of bundle motion from different organs and organisms. The predictions stemming from this description provide insight into the operation of hair bundles in a variety of contexts.

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

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.

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system.

BACKGROUND: A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze. RESULTS: Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations. CONCLUSIONS: This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.

Inward rotating spiral waves in glycolysis.

We report on the first observation of inward rotating spiral waves (antispirals) in a biochemical reaction-diffusion system. Experiments are performed with extracts from yeast cells in an open spatial reactor. By increasing the protein concentration of the extract we observe a transition from outward to inward propagating waves of glycolytic activity. Numerical simulations with an allosteric model for the phosphofructokinase can reproduce these inward propagating waves over a wide range of parameters if the octameric structure of yeast phosphofructokinase is taken into account.

Critical asymmetry for giant diffusion of active Brownian particles.

We study the effect of an asymmetry on the transport properties of an active Brownian particle. We demonstrate the existence of a critical force or, more generally, of a critical asymmetry that separates parameter regimes of giant diffusion from those with reliable directed transport. We derive a condition for the critical asymmetry by means of an exact expression for the diffusion coefficient and by a simplified discrete picture. A critical asymmetry, as predicted by the simple model, is also found in a detailed model of coupled molecular motors displaying bidirectional motion.

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.

Wave instability induced by nonlocal spatial coupling in a model of the light-sensitive Belousov-Zhabotinsky reaction.

We study spatiotemporal patterns resulting from instabilities induced by nonlocal spatial coupling in the Oregonator model of the light-sensitive Belousov-Zhabotinsky reaction. In this system, nonlocal coupling can be externally imposed by means of an optical feedback loop which links the intensity of locally applied illumination with the activity in a certain vicinity of a particular point weighted by a given coupling function. This effect is included in the three-variable Oregonator model by an additional integral term in the photochemically induced bromide flow. A linear stability analysis of this modified Oregonator model predicts that wave and Turing instabilities of the homogeneous steady state can be induced for experimentally realistic parameter values. In particular, we find that a long-range inhibition in the optical feedback leads to a Turing instability, while a long-range activation induces wave patterns. Using a weakly nonlinear analysis, we derive amplitude equations for the wave instability which are valid close to the instability threshold. Therein, we find that the wave instability occurs supercritically or subcritically and that traveling waves are preferred over standing waves. The results of the theoretical analysis are in good agreement with numerical simulations of the model near the wave instability threshold. For larger distances from threshold, a secondary breathing instability is found for traveling waves.

Drifting pattern domains in a reaction-diffusion system with nonlocal coupling.

Drifting pattern domains (DPDs), i.e., moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this model, a region of bistability between Turing patterns and traveling waves arises from a codimension-2 Turing-wave bifurcation (TWB). DPDs are found within that region in a substantial distance from the TWB. We investigated the dynamics of single interfaces between Turing and wave patterns. It is found that DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.