Highlights of 2012

Actomyosin contractility is essential for biological force generation, and is well understood in highly organized structures such as striated muscle. Additionally, actomyosin bundles devoid of this organization are known to contract both in vivo and in vitro, which cannot be described by standard muscle models. To narrow down the search for possible contraction mechanisms in these systems, we investigate their microscopic symmetries. We show that contractile behavior requires non-identical motors that generate large-enough forces to probe the nonlinear elastic behavior of F-actin. This suggests a role for filament buckling in the contraction of these bundles, consistent with recent experimental results on reconstituted actomyosin bundles.

The growth of a thin elastic sheet imposes constraints on its geometry such as its Gaussian curvature K_G. In this paper, we construct the shapes of sympetalous bell-shaped flowers with a constant Gaussian curvature. Minimizing the bending energies of both the petal and the veins, we are able to predict quantitatively the global shape of these flowers. We discuss two toy problems where the Gaussian curvature is either negative or positive. In the former case, the axisymmetric pseudosphere turns out to mimic the correct shape before edge curling; in the latter case, singularities of the mathematical surface coincide with strong veins. Using a variational minimization of the elastic energy, we find that the optimal number for the veins is either four, five or six, a number that is deceptively close to the statistics on real flowers in nature.

In most instances, tumors have to push their surroundings in order to grow. Thus, during their development, tumors must be able to both exert and sustain mechanical stresses. Using a novel experimental procedure, we study quantitatively the effect of an applied mechanical stress on the long-term growth of a spherical cell aggregate. Our results indicate the possibility to modulate tumor growth depending on the applied pressure. Moreover, we demonstrate quantitatively that the cells located in the core of the spheroid display a different response to stress than those in the periphery. We compare the results to a simple numerical model developed for describing the role of mechanics in cancer progression.

We report the results of the first systematic Lagrangian experimental investigation in a previously unexplored regime of very light (air bubbles in water) and large (D/η ≫ 1) particles in turbulence. Using a traversing camera setup and particle tracking, we study the Lagrangian acceleration statistics of ∼3 mm diameter (D) bubbles in a water tunnel with nearly homogeneous and isotropic turbulence generated by an active grid. The Reynolds number (Re_λ) is varied from 145 to 230, resulting in size ratios, D/η, in the range of 7.3–12.5, where η is the Kolmogorov length scale. The experiments reveal that gravity increases the acceleration variance and reduces the intermittency of the probability density function (PDF) in the vertical direction. Once the gravity offset has been subtracted, the variances of both the horizontal and vertical acceleration components are about 5 ± 2 times larger than those measured in the same flow for fluid tracers. Moreover, for these light particles, the experimental acceleration PDF shows a substantial reduction of intermittency at growing size ratios, in contrast with neutrally buoyant or heavy particles. All these results closely match numerical simulations of finite-sized bubbles with the Faxén corrections.

Colloidal particles dispersed in a liquid crystal (LC) lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short-distance behaviour depends on the structure and dynamics of the topological defects nucleated near the colloidal particles and a full nonlinear theory is required to describe it. Spherical colloidal particles with strong planar degenerate anchoring nucleate a pair of antipodal surface topological defects, known as boojums. We use the Landau–de Gennes theory to resolve the mesoscopic structure of the boojum cores and to determine the pairwise colloidal interactions. We compare the results in three (3D) and two (2D) spatial dimensions for spherical and disc-like colloidal particles, respectively. The corresponding free energy functionals are minimized numerically using finite elements with adaptive meshes. Boojums are always point-like in 2D, but acquire a rather complex structure in 3D, which depends on the combination of the anchoring potential, the radius of the colloid, the temperature and the LC elastic anisotropy. We identify three types of defect cores in 3D that we call single, double and split-core boojums, and investigate the associated structural transitions. The split-core structure is favoured by low temperatures, strong anchoring and small twist to splay or bend ratios. For sufficiently strong anchoring potentials characterized by a well-defined uniaxial minimum, the split-core boojums are the only stable configuration. In the presence of two colloidal particles, we observe substantial re-arrangements of the inner defects in both 3D and 2D. These re-arrangements lead to qualitative changes in the force-distance profile when compared to the asymptotic quadrupole–quadrupole interaction. In line with the experimental results, the presence of the defects prevents coalescence of the colloidal particles in 2D, but not in 3D systems.

A goal of complex system research is to identify the dynamical implications of network structure. While early results focused mainly on local or global structural properties, there is now growing interest in mesoscale structures that comprise more than one node but not the whole network. A central challenge is to discover under what conditions the occurrence of a specific mesoscale motif already allows conclusions on the dynamics of a network as a whole. In this paper, we investigate the dynamics of ecological food webs, complex heterogeneous networks of interacting populations. Generalizing the results of MacArthur and Sánchez-García (2009 Phys. Rev. E 80 26117), we show that certain mesoscale symmetries imply the existence of localized dynamical modes. If these modes are unstable the occurrence of the corresponding mesoscale motif implies dynamical instability regardless of the structure of the embedding network. In contrast, if the mode is stable it means that the symmetry can be exploited to reduce the number of nodes in the model, without changing the dynamics of the system. This result explains a previously observed dynamical equivalence between food webs containing a different number of species.

We studied the snap-off of nematic liquid crystalline droplets originating from the Rayleigh–Taylor instability at the isotropic–nematic interface in suspensions of charged gibbsite in water and sterically stabilized gibbsite in bromotoluene. We found that droplet snap-off strongly depends on the director field structure inside the thinning neck, which is determined by the ratio of the splay elastic constant and the anchoring strength of the nematic phase to the droplet interface relative to the thickness of the thinning neck. If anchoring is weak, which is the case for aqueous gibbsite, this ratio is comparable to the thickness of the breaking thread. As a result, the thinning neck and pending drop have a uniform director field and droplet snap-off is determined by the viscous properties of the liquid crystal as well as by thermal fluctuations of the interface. On the other hand, in sterically stabilized gibbsite where anchoring is strong, this ratio is significantly smaller than the neck thickness. In this case, the neck has an escaped radial director field and the neck thinning is retarded close to snap-off due to a topological energy barrier involved in the separation of the droplet from the thread.

We study excitation energy transfer in a simple model of a photosynthetic complex. The model, described by the Lindblad equation, consists of pigments interacting via dipole–dipole interaction. The overlapping of pigments induces an on-site energy disorder, providing a mechanism for blocking the excitation transfer. Based on the average efficiency as well as the robustness of random configurations of pigments, we calculate the optimal number of pigments that should be enclosed in a pigment–protein complex of a given size. The results suggest that a large fraction of pigment configurations are efficient as well as robust if the number of pigments is properly chosen. We compare the optimal results of the model to the structure of pigment–protein complexes as found in nature, finding good agreement.