Turning the body into a clock: Accurate timing is facilitated by simple stereotyped interactions with the environment.

How animals adapt their behavior according to regular time intervals between events is not well understood, especially when intervals last several seconds. One possibility is that animals use disembodied internal neuronal representations of time to decide when to initiate a given action at the end of an interval. However, animals rarely remain immobile during time intervals but tend to perform stereotyped behaviors, raising the possibility that motor routines improve timing accuracy. To test this possibility, we used a task in which rats, freely moving on a motorized treadmill, could obtain a reward if they approached it after a fixed interval. Most animals took advantage of the treadmill length and its moving direction to develop, by trial-and-error, the same motor routine whose execution resulted in the precise timing of their reward approaches. Noticeably, when proficient animals did not follow this routine, their temporal accuracy decreased. Then, naïve animals were trained in modified versions of the task designed to prevent the development of this routine. Compared to rats trained in the first protocol, these animals didn't reach a comparable level of timing accuracy. Altogether, our results indicate that timing accuracy in rats is improved when the environment affords cues that animals can incorporate into motor routines.

The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem.

Shoot morphogenetic plasticity is crucial to the adaptation of plants to their fluctuating environments. Major insights into shoot morphogenesis have been compiled studying meristems, especially the shoot apical meristem (SAM), through a methodological effort in multiscale systems biology and biophysics. However, morphogenesis at the SAM is robust to environmental changes. Plasticity emerges later on during post-SAM development. The purpose of this review is to show that multiscale systems biology and biophysics is insightful for the shaping of the whole plant as well. More specifically, we review the shaping of axes and crowns through tropisms and elasticity, combining the recent advances in morphogenetic control using physical cues and by genes. We focus mostly on land angiosperms, but with growth habits ranging from small herbs to big trees. We show that generic (universal) morphogenetic processes have been identified, revealing feedforward and feedback effects of global shape on the local morphogenetic process. In parallel, major advances have been made in the analysis of the major genes involved in shaping axes and crowns, revealing conserved genic networks among angiosperms. Then, we show that these two approaches are now starting to converge, revealing exciting perspectives.

Surfing on Turbulence: A Strategy for Planktonic Navigation.

In marine plankton, many swimming species can perceive their environment with flow sensors. Can they use this flow information to travel faster in turbulence? To address this question, we consider plankters swimming at constant speed, whose goal is to move upward. We propose a robust analytical behavior that allows plankters to choose a swimming direction according to the local flow gradients. We show numerically that such plankters can "surf" on turbulence and reach net vertical speeds up to twice their swimming speed. This new physics-based model suggests that planktonic organisms can exploit turbulence features for navigation.

Rebound and scattering of motile Chlamydomonas algae in confined chambers.

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

Model of Collective Fish Behavior with Hydrodynamic Interactions.

Fish schooling is often modeled with self-propelled particles subject to phenomenological behavioral rules. Although fish are known to sense and exploit flow features, these models usually neglect hydrodynamics. Here, we propose a novel model that couples behavioral rules with far-field hydrodynamic interactions. We show that (1) a new "collective turning" phase emerges, (2) on average, individuals swim faster thanks to the fluid, and (3) the flow enhances behavioral noise. The results of this model suggest that hydrodynamic effects should be considered to fully understand the collective dynamics of fish.

Flow-induced draping.

Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a different sort of forcing. We consider a circular flexible plate clamped at its center and subject to a uniform flow normal to its initial surface. As the flow velocity is gradually increased, the plate exhibits a rich variety of bending deformations: from a cylindrical shape, to isometric developable cones with azimuthal periodicity two or three, to eventually a rolled-up period-three cone. We show that this sequence of flow-induced deformations can be qualitatively predicted by a linear analysis based on the balance between elastic energy and pressure force work.

Growth anisotropy of the extracellular matrix shapes a developing organ.

Final organ size and shape result from volume expansion by growth and shape changes by contractility. Complex morphologies can also arise from differences in growth rate between tissues. We address here how differential growth guides the morphogenesis of the growing Drosophila wing imaginal disc. We report that 3D morphology results from elastic deformation due to differential growth anisotropy between the epithelial cell layer and its enveloping extracellular matrix (ECM). While the tissue layer grows in plane, growth of the bottom ECM occurs in 3D and is reduced in magnitude, thereby causing geometric frustration and tissue bending. The elasticity, growth anisotropy and morphogenesis of the organ are fully captured by a mechanical bilayer model. Moreover, differential expression of the Matrix metalloproteinase MMP2 controls growth anisotropy of the ECM envelope. This study shows that the ECM is a controllable mechanical constraint whose intrinsic growth anisotropy directs tissue morphogenesis in a developing organ.

Kinematics of the most efficient cilium.

In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although cilia have a remarkably conserved internal molecular structure, experimental observations report very diverse kinematics. To address this diversity, we determine numerically the kinematics and energetics of the most efficient cilium. Specifically, we compute the time-periodic deformation of a wall-bound elastic filament leading to transport of a surrounding fluid at minimum energetic cost, where the cost is taken to be the positive work done by all internal molecular motors. The optimal kinematics are found to strongly depend on the cilium bending rigidity through a single dimensionless number, the Sperm number, and closely resemble the two-stroke ciliary beating pattern observed experimentally.

Leonardo's rule, self-similarity, and wind-induced stresses in trees.

Examining botanical trees, Leonardo da Vinci noted that the total cross section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads.

Tree crowns grow into self-similar shapes controlled by gravity and light sensing.

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

Wind loads and competition for light sculpt trees into self-similar structures.

Trees are self-similar structures: their branch lengths and diameters vary allometrically within the tree architecture, with longer and thicker branches near the ground. These tree allometries are often attributed to optimisation of hydraulic sap transport and safety against elastic buckling. Here, we show that these allometries also emerge from a model that includes competition for light, wind biomechanics and no hydraulics. We have developed MECHATREE, a numerical model of trees growing and evolving on a virtual island. With this model, we identify the fittest growth strategy when trees compete for light and allocate their photosynthates to grow seeds, create new branches or reinforce existing ones in response to wind-induced loads. Strikingly, we find that selected trees species are self-similar and follow allometric scalings similar to those observed on dicots and conifers. This result suggests that resistance to wind and competition for light play an essential role in determining tree allometries.

Collective motion with anticipation: flocking, spinning, and swarming.

We investigate the collective dynamics of self-propelled particles able to probe and anticipate the orientation of their neighbors. We show that a simple anticipation strategy hinders the emergence of homogeneous flocking patterns. Yet anticipation promotes two other forms of self-organization: collective spinning and swarming. In the spinning phase, all particles follow synchronous circular orbits, while in the swarming phase, the population condensates into a single compact swarm that cruises coherently without requiring any cohesive interactions. We quantitatively characterize and rationalize these phases of polar active matter and discuss potential applications to the design of swarming robots.

Skin friction on a flapping plate in uniform flow.

To calculate the energy costs of swimming or flying, it is crucial to evaluate the drag force originating from skin friction. This topic seems not to have received a definite answer, given the difficulty in measuring accurately the friction drag along objects in movement. The incoming flow along a flat plate in a flapping normal motion has been considered, as limit case of a yawed cylinder in uniform flow, and applying the laminar boundary layer assumption it is demonstrated that the longitudinal drag scales as the square root of the normal velocity component. This lends credit to the assumption that a swimming-like motion may induce a drag increase because of the compression of the boundary layer, which is known as the 'Bone-Lighthill boundary-layer thinning hypothesis'. The boundary-layer model however cannot predict the genuine three-dimensional flow dynamics and in particular the friction at the leeward side of the plate. A multi-domain, parallel, compact finite-differences Navier-Stokes solution procedure is considered, capable of solving the full problem. The time-dependent flow dynamics is analysed and the general trends predicted by the simplified model are confirmed, with however differences in the magnitude of the friction coefficient. A tentative skin friction formula is proposed for flow states along a plate moving at steady as well as periodic normal velocities.