Two-Photon Polymerization 3D-Printing of Micro-scale Neuronal Cell Culture Devices.

Neuronal cultures have been a reference experimental model for several decades. However, 3D cell arrangement, spatial constraints on neurite outgrowth, and realistic synaptic connectivity are missing. The latter limits the study of structure and function in the context of compartmentalization and diminishes the significance of cultures in neuroscience. Approximating ex vivo the structured anatomical arrangement of synaptic connectivity is not trivial, despite being key for the emergence of rhythms, synaptic plasticity, and ultimately, brain pathophysiology. Here, two-photon polymerization (2PP) is employed as a 3D printing technique, enabling the rapid fabrication of polymeric cell culture devices using polydimethyl-siloxane (PDMS) at the micrometer scale. Compared to conventional replica molding techniques based on microphotolitography, 2PP micro-scale printing enables rapid and affordable turnaround of prototypes. This protocol illustrates the design and fabrication of PDMS-based microfluidic devices aimed at culturing modular neuronal networks. As a proof-of-principle, a two-chamber device is presented to physically constrain connectivity. Specifically, an asymmetric axonal outgrowth during ex vivo development is favored and allowed to be directed from one chamber to the other. In order to probe the functional consequences of unidirectional synaptic interactions, commercial microelectrode arrays are chosen to monitor the bioelectrical activity of interconnected neuronal modules. Here, methods to 1) fabricate molds with micrometer precision and 2) perform in vitro multisite extracellular recordings in rat cortical neuronal cultures are illustrated. By decreasing costs and future widespread accessibility of 2PP 3D-printing, this method will become more and more relevant across research labs worldwide. Especially in neurotechnology and high-throughput neural data recording, the ease and rapidity of prototyping simplified in vitro models will improve experimental control and theoretical understanding of in vivo large-scale neural systems.

Transient shape morphing of active gel plates: geometry and physics.

The control of shape in active structures is a key problem for the realization of smart sensors and actuators, which often draw inspiration from natural systems. In this context, slender structures, such as thin plates, have been studied as a relevant example of shape morphing systems where curvature is generated by in-plane incompatibilities. In particular, in hydrogel plates these incompatibilities can be programmed at fabrication time, such that a target configuration is attained at equilibrium upon swelling or shrinking. While these aspects have been examined in detail, understanding the transient morphing of such active structures deserves further investigation. In this study, we develop a geometrical model for the transient shaping of thin hydrogel plates by extending the theory of non-Euclidean plates. We validate the proposed model using experiments on gel samples that are programmed to reach axisymmetric equilibrium shapes. Interestingly, our experiments show the emergence of non-axisymmetric shapes for early times, as a consequence of boundary layer effects induced by solvent transport. We rationalize these observations using numerical simulations based on a detailed poroelastic model. Overall, this work highlights the limitations of purely geometrical models and the importance of transient, reduced theories for morphing plates that account for the coupled physics driving the evolution of shape. Computational approaches employing these theories will allow to achieve accurate control on the morphing dynamics and ultimately advance 4D printing technologies.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis.

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

Nutations in Plant Shoots: Endogenous and Exogenous Factors in the Presence of Mechanical Deformations.

We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

How Euglena gracilis swims: Flow field reconstruction and analysis.

Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.

Swimming Euglena respond to confinement with a behavioral change enabling effective crawling.

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large amplitude peristaltic body deformations. This remarkable behavior has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behavior is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modeling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.

Detecting singular weak-dissipation limit for flutter onset in reversible systems.

A "flutter machine" is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.

A Fluorescent Dye Method Suitable for Visualization of One or More Rat Whiskers.

Visualization and tracking of the facial whiskers is critical to many studies of rodent behavior. High-speed videography is the most robust methodology for characterizing whisker kinematics, but whisker visualization is challenging due to the low contrast of the whisker against its background. Recently, we showed that fluorescent dye(s) can be applied to enhance visualization and tracking of whisker(s) ( Rigosa et al., 2017 ), and this protocol provides additional details on the technique.

Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes.

The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.

Dye-enhanced visualization of rat whiskers for behavioral studies.

Visualization and tracking of the facial whiskers is required in an increasing number of rodent studies. Although many approaches have been employed, only high-speed videography has proven adequate for measuring whisker motion and deformation during interaction with an object. However, whisker visualization and tracking is challenging for multiple reasons, primary among them the low contrast of the whisker against its background. Here, we demonstrate a fluorescent dye method suitable for visualization of one or more rat whiskers. The process makes the dyed whisker(s) easily visible against a dark background. The coloring does not influence the behavioral performance of rats trained on a vibrissal vibrotactile discrimination task, nor does it affect the whiskers' mechanical properties.

Hydraulic Fracture and Toughening of a Brittle Layer Bonded to a Hydrogel.

Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.