Excess Entropies Suggest the Physiology of Neurons to Be Primed for Higher-Level Computation.

Biological neuronal networks excel over artificial ones in many ways, but the origin of this is still unknown. Our symbolic dynamics-based tool of excess entropies suggests that neuronal cultures naturally implement data structures of a higher level than what we expect from artificial neural networks, or from close-to-biology neural networks. This points to a new pathway for improving artificial neural networks towards a level demonstrated by biology.

Universality in the firing of minicolumnar-type neural networks.

An open question in biological neural networks is whether changes in firing modalities are mainly an individual network property or whether networks follow a joint pathway. For the early developmental period, our study focusing on a simple network class of excitatory and inhibitory neurons suggests the following answer: Networks with considerable variation of topology and dynamical parameters follow a universal firing paradigm that evolves as the overall connectivity strength and firing level increase, as seen in the process of network maturation. A simple macroscopic model reproduces the main features of the paradigm as a result of the competition between the fundamental dynamical system notions of synchronization vs chaos and explains why in simulations the paradigm is robust regarding differences in network topology and largely independent from the neuron model used. The presented findings reflect the first dozen days of dissociated neuronal in vitro cultures (upon following the developmental period bears similarly universal features but is characterized by the processes of neuronal facilitation and depression that do not require to be considered for the first developmental period).

Controlling fracture cascades through twisting and quenching.

Fracture fundamentally limits the structural stability of macroscopic and microscopic matter, from beams and bones to microtubules and nanotubes. Despite substantial recent experimental and theoretical progress, fracture control continues to present profound practical and theoretical challenges. While bending-induced fracture of elongated rod-like objects has been intensely studied, the effects of twist and quench dynamics have yet to be explored systematically. Here, we show how twist and quench protocols may be used to control such fracture processes, by revisiting Feynman's observation that dry spaghetti typically breaks into three or more pieces when exposed to large pure bending stresses. Combining theory and experiment, we demonstrate controlled binary fracture of brittle elastic rods for two distinct protocols based on twisting and nonadiabatic quenching. Our experimental data for twist-controlled fracture agree quantitatively with a theoretically predicted phase diagram, and we establish asymptotic scaling relations for quenched fracture. Due to their general character, these results are expected to apply to torsional and kinetic fracture processes in a wide range of systems.

Geometry of Wave Propagation on Active Deformable Surfaces.

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics remains poorly understood, but it will be essential for the future design of chemically driven soft robots and active materials. Here, we couple prototypical chemical wave and reaction-diffusion models to non-Euclidean shell mechanics to identify and characterize generic features of chemomechanical wave propagation on active deformable surfaces. Our theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes, producing good quantitative agreement in both cases. The theory is then applied to illustrate how geometry and preexisting discrete symmetries can be utilized to focus active elastic surface waves. We highlight the practical potential of chemomechanical coupling by demonstrating spontaneous wave-induced locomotion of elastic shells of various geometries. Altogether, our results show how geometry, elasticity, and chemical signaling can be harnessed to construct dynamically adaptable, autonomously moving mechanical surface waveguides.

Defect formation dynamics in curved elastic surface crystals.

Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for non-thermal transitions in curved and topologically nontrivial systems still poses open questions. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. For both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. Our results suggest that curved elastic bilayers provide an experimentally accessible macroscopic system to study universal properties of non-thermal phase transitions in non-planar geometries.

Curvature-Induced Instabilities of Shells.

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Entropic effects in cell lineage tree packings.

Optimal packings [1, 2] of unconnected objects have been studied for centuries [3-6], but the packing principles of linked objects, such as topologically complex polymers [7, 8] or cell lineages [9, 10], are yet to be fully explored. Here, we identify and investigate a generic class of geometrically frustrated tree packing problems, arising during the initial stages of animal development when interconnected cells assemble within a convex enclosure [10]. Using a combination of 3D imaging, computational image analysis, and mathematical modelling, we study the tree packing problem in Drosophila egg chambers, where 16 germline cells are linked by cytoplasmic bridges to form a branched tree. Our imaging data reveal non-uniformly distributed tree packings, in agreement with predictions from energy-based computations. This departure from uniformity is entropic and affects cell organization during the first stages of the animal's development. Considering mathematical models of increasing complexity, we investigate spherically confined tree packing problems on convex polyhedrons [11] that generalize Platonic and Archimedean solids. Our experimental and theoretical results provide a basis for understanding the principles that govern positional ordering in linked multicellular structures, with implications for tissue organization and dynamics [12, 13].

Curvature-driven morphing of non-Euclidean shells.

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.

Actomyosin-based tissue folding requires a multicellular myosin gradient.

Tissue folding promotes three-dimensional (3D) form during development. In many cases, folding is associated with myosin accumulation at the apical surface of epithelial cells, as seen in the vertebrate neural tube and the Drosophila ventral furrow. This type of folding is characterized by constriction of apical cell surfaces, and the resulting cell shape change is thought to cause tissue folding. Here, we use quantitative microscopy to measure the pattern of transcription, signaling, myosin activation and cell shape in the Drosophila mesoderm. We found that cells within the ventral domain accumulate different amounts of active apical non-muscle myosin 2 depending on the distance from the ventral midline. This gradient in active myosin depends on a newly quantified gradient in upstream signaling proteins. A 3D continuum model of the embryo with induced contractility demonstrates that contractility gradients, but not contractility per se, promote changes to surface curvature and folding. As predicted by the model, experimental broadening of the myosin domain in vivo disrupts tissue curvature where myosin is uniform. Our data argue that apical contractility gradients are important for tissue folding.

Curvature-Controlled Defect Localization in Elastic Surface Crystals.

We investigate the influence of curvature and topology on crystalline dimpled patterns on the surface of generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal, and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling, or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges.

Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells.

Rheotaxis, the directed response to fluid velocity gradients, has been shown to facilitate stable upstream swimming of mammalian sperm cells along solid surfaces, suggesting a robust physical mechanism for long-distance navigation during fertilization. However, the dynamics by which a human sperm orients itself relative to an ambient flow is poorly understood. Here, we combine microfluidic experiments with mathematical modeling and 3D flagellar beat reconstruction to quantify the response of individual sperm cells in time-varying flow fields. Single-cell tracking reveals two kinematically distinct swimming states that entail opposite turning behaviors under flow reversal. We constrain an effective 2D model for the turning dynamics through systematic large-scale parameter scans, and find good quantitative agreement with experiments at different shear rates and viscosities. Using a 3D reconstruction algorithm to identify the flagellar beat patterns causing left or right turning, we present comprehensive 3D data demonstrating the rolling dynamics of freely swimming sperm cells around their longitudinal axis. Contrary to current beliefs, this 3D analysis uncovers ambidextrous flagellar waveforms and shows that the cell's turning direction is not defined by the rolling direction. Instead, the different rheotactic turning behaviors are linked to a broken mirror symmetry in the midpiece section, likely arising from a buckling instability. These results challenge current theoretical models of sperm locomotion.

Curvature-induced symmetry breaking determines elastic surface patterns.

Symmetry-breaking transitions associated with the buckling and folding of curved multilayered surfaces-which are common to a wide range of systems and processes such as embryogenesis, tissue differentiation and structure formation in heterogeneous thin films or on planetary surfaces-have been characterized experimentally. Yet owing to the nonlinearity of the underlying stretching and bending forces, the transitions cannot be reliably predicted by current theoretical models. Here, we report a generalized Swift-Hohenberg theory that describes wrinkling morphology and pattern selection in curved elastic bilayer materials. By testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions for the critical curves separating labyrinth, hybrid and hexagonal phases. Furthermore, a comparison to earlier experiments suggests that the theory is universally applicable to macroscopic and microscopic systems. Our approach builds on general differential-geometry principles and can thus be extended to arbitrarily shaped surfaces.

Ordered packing of elastic wires in a sphere.

In this paper we study the ordered packing of wires in a sphere. We propose an analytical model and compare the model predictions with the results of our experiments and simulations for the maximum packing fraction, the number of formed coils, the fractal dimension, and bending energy. We show that the relative system size [i.e., the ratio of the wire radius to the sphere radius (a/R)] is the most important control parameter for the maximum packing fraction. We find that the number of coils obeys a power-law relation of the form N∼(R/a){1.5} and the fractal dimension of the structures is 2.5, independent of the system size. Our theoretical results are in good agreement with the experimental data and the predictions of the numerical simulations.

Self-contact and instabilities in the anisotropic growth of elastic membranes.

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e cone solution is energetically minimal any more. Instead, we obtain skewed e cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.