A Magnetic Pincher for the Dynamic Measurement of the Actin Cortex Thickness in Live Cells.

The actin cortex is an essential element of the cytoskeleton allowing cells to control and modify their shape. It is involved in cell division and migration. However, probing precisely the physical properties of the actin cortex has proved to be challenging: it is a thin and dynamic material, and its location in the cell-directly under the plasma membrane-makes it difficult to study with standard light microscopy and cell mechanics techniques. In this chapter, we present a novel protocol to probe dynamically the thickness of the cortex and its fluctuations using superparamagnetic microbeads in a uniform magnetic field. A bead ingested by the cell and another outside the cell attract each other due to dipolar forces. By tracking their position with nanometer precision, one can measure the thickness of the cortex pinched between two beads and monitor its evolution in time. We first present the set of elements necessary to realize this protocol: a magnetic field generator adapted to a specific imaging setup and the aforementioned superparamagnetic microbeads. Then we detail the different steps of a protocol that can be used on diverse cell types, adherent or not.

Asymmetric bistability of chiral particle orientation in viscous shear flows.

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a nonchiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here, we use a high-resolution microprinting technique to fabricate microparticles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these microparticles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments, we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations, and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport and bacterial rheotaxis and might allow the development of targeted delivery applications.

Dynamics of flexible filaments in oscillatory shear flows.

The fluid-structure interactions between flexible fibers and viscous flows play an essential role in various biological phenomena, medical problems, and industrial processes. Of particular interest is the case of particles freely transported in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations, and theoretical modeling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler-Bernoulli rods whose hydrodynamics are described by local slender-body theory.

Fiber Buckling in Confined Viscous Flows: An Absolute Instability Described by the Linear Ginzburg-Landau Equation.

We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between viscous and elastic forces leads to the deformation of the fiber into a wavy shape convolved by a Bell-shaped envelope. We characterize the wavelength and phase velocity of the deformation as well as the growth and spreading of the envelope. Our study of the spatiotemporal evolution of the deformation reveals a linear and absolute instability arising from a local mechanism well described by the Ginzburg-Landau equation.

Shaping Nanoscale Ribbons into Microhelices of Controllable Radius and Pitch.

We report fabrication of highly flexible micron-sized helices from nanometer-thick ribbons. Building upon the helical coiling of such ultrathin ribbons mediated by surface tension, we demonstrate that the enhanced creep properties of highly confined materials can be leveraged to shape helices into the desired geometry with full control of the final shape. The helical radius, total length, and pitch angle are all freely and independently tunable within a wide range: radius within ∼1-100 µm, length within ∼100-3000 µm, and pitch angle within ∼0-70°. This fabrication method is validated for three different materials: poly(methyl methacrylate), poly(dimethylaminoethyl methacrylate), and transition metal chalcogenide quantum dots, each corresponding to a different solid-phase structure: respectively a polymer glass, a cross-linked hydrogel, and a nanoparticle array. This demonstrates excellent versatility with respect to material selection, enabling further control of the helix mechanical properties.

Correction: Non-linear elastic properties of actin patches to partially rescue yeast endocytosis efficiency in the absence of the cross-linker Sac6.

Correction for 'Non-linear elastic properties of actin patches to partially rescue yeast endocytosis efficiency in the absence of the cross-linker Sac6' by Belbahri Reda et al., Soft Matter, 2022, 18, 1479-1488, https://doi.org/10.1039/D1SM01437D.

Pinching the cortex of live cells reveals thickness instabilities caused by myosin II motors.

The cell cortex is a contractile actin meshwork, which determines cell shape and is essential for cell mechanics, migration, and division. Because its thickness is below optical resolution, there is a tendency to consider the cortex as a thin uniform two-dimensional layer. Using two mutually attracted magnetic beads, one inside the cell and the other in the extracellular medium, we pinch the cortex of dendritic cells and provide an accurate and time-resolved measure of its thickness. Our observations draw a new picture of the cell cortex as a highly dynamic layer, harboring large fluctuations in its third dimension because of actomyosin contractility. We propose that the cortex dynamics might be responsible for the fast shape-changing capacity of highly contractile cells that use amoeboid-like migration.

Programmable Design and Performance of Modular Magnetic Microswimmers.

Synthetic biomimetic microswimmers are promising agents for in vivo healthcare and important frameworks to advance the understanding of locomotion strategies and collective motion at the microscopic scale. Nevertheless, constructing these devices with design flexibility and in large numbers remains a challenge. Here, a step toward meeting this challenge is taken by assembling such swimmers via the programmed shape and arrangement of superparamagnetic micromodules. The method's capacity for design flexibility is demonstrated through the assembly of a variety of swimmer architectures. On their actuation, strokes characterized by a balance of viscous and magnetic forces are found in all cases, but swimmers formed from a series of size-graded triangular modules swim quicker than more traditional designs comprising a circular "head" and a slender tail. Linking performance to design, rules are extracted informing the construction of a second-generation swimmer with a short tail and an elongated head optimized for speed. Its fast locomotion is attributed to a stroke that better breaks beating symmetry and an ability to beat fully with flex at high frequencies. Finally, production at scale is demonstrated through the assembly and swimming of a flock of the triangle-based architectures to reveal four types of swimmer couplings.

Optimised hyperbolic microchannels for the mechanical characterisation of bio-particles.

The transport of bio-particles in viscous flows exhibits a rich variety of dynamical behaviour, such as morphological transitions, complex orientation dynamics or deformations. Characterising such complex behaviour under well controlled flows is key to understanding the microscopic mechanical properties of biological particles as well as the rheological properties of their suspensions. While generating regions of simple shear flow in microfluidic devices is relatively straightforward, generating straining flows in which the strain rate is maintained constant for a sufficiently long time to observe the objects' morphologic evolution is far from trivial. In this work, we propose an innovative approach based on optimised design of microfluidic converging-diverging channels coupled with a microscope-based tracking method to characterise the dynamic behaviour of individual bio-particles under homogeneous straining flow. The tracking algorithm, combining a motorised stage and a microscopy imaging system controlled by external signals, allows us to follow individual bio-particles transported over long-distances with high-quality images. We demonstrate experimentally the ability of the numerically optimised microchannels to provide linear velocity streamwise gradients along the centreline of the device, allowing for extended consecutive regions of homogeneous elongation and compression. We selected three test cases (DNA, actin filaments and protein aggregates) to highlight the ability of our approach for investigating dynamics of objects with a wide range of sizes, characteristics and behaviours of relevance in the biological world.

Microfluidic In-Situ Measurement of Poisson's Ratio of Hydrogels.

Being able to precisely characterize the mechanical properties of soft microparticles is essential for numerous situations, from the understanding of the flow of biological fluids to the development of soft micro-robots. Here, we present a simple measurement technique for determining Poisson's ratio of soft micron-sized hydrogels in the presence of a surrounding liquid. This method relies on the measurement of the deformation, in two orthogonal directions, of a rectangular hydrogel slab compressed uni-axially inside a microfluidic channel. Due to the in situ character of the method, the sample does not need to be dried, allowing for the measurement of the mechanical properties of swollen hydrogels. Using this method, we determined Poisson's ratio of hydrogel particles composed of polyethylene glycol (PEG) and varying solvents fabricated using a lithography technique. The results demonstrate, with high precision, the dependence of the hydrogel compressibility on the solvent fraction and character. The method is easy to implement and can be adapted for the measurement of a variety of soft and biological materials.

Mechanical stiffness of reconstituted actin patches correlates tightly with endocytosis efficiency.

Clathrin-mediated endocytosis involves the sequential assembly of more than 60 proteins at the plasma membrane. An important fraction of these proteins regulates the assembly of an actin-related protein 2/3 (Arp2/3)-branched actin network, which is essential to generate the force during membrane invagination. We performed, on wild-type (WT) yeast and mutant strains lacking putative actin crosslinkers, a side-by-side comparison of in vivo endocytic phenotypes and in vitro rigidity measurements of reconstituted actin patches. We found a clear correlation between softer actin networks and a decreased efficiency of endocytosis. Our observations support a chain-of-consequences model in which loss of actin crosslinking softens Arp2/3-branched actin networks, directly limiting the transmission of the force. Additionally, the lifetime of failed endocytic patches increases, leading to a larger number of patches and a reduced pool of polymerizable actin, which slows down actin assembly and further impairs endocytosis.

Morphological transitions of elastic filaments in shear flow.

The morphological dynamics, instabilities, and transitions of elastic filaments in viscous flows underlie a wealth of biophysical processes from flagellar propulsion to intracellular streaming and are also key to deciphering the rheological behavior of many complex fluids and soft materials. Here, we combine experiments and computational modeling to elucidate the dynamical regimes and morphological transitions of elastic Brownian filaments in a simple shear flow. Actin filaments are used as an experimental model system and their conformations are investigated through fluorescence microscopy in microfluidic channels. Simulations matching the experimental conditions are also performed using inextensible Euler-Bernoulli beam theory and nonlocal slender-body hydrodynamics in the presence of thermal fluctuations and agree quantitatively with observations. We demonstrate that filament dynamics in this system are primarily governed by a dimensionless elasto-viscous number comparing viscous drag forces to elastic bending forces, with thermal fluctuations playing only a secondary role. While short and rigid filaments perform quasi-periodic tumbling motions, a buckling instability arises above a critical flow strength. A second transition to strongly deformed shapes occurs at a yet larger value of the elasto-viscous number and is characterized by the appearance of localized high-curvature bends that propagate along the filaments in apparent "snaking" motions. A theoretical model for the as yet unexplored onset of snaking accurately predicts the transition and explains the observed dynamics. We present a complete characterization of filament morphologies and transitions as a function of elasto-viscous number and scaled persistence length and demonstrate excellent agreement between theory, experiments, and simulations.

A new method to measure mechanics and dynamic assembly of branched actin networks.

We measured mechanical properties and dynamic assembly of actin networks with a new method based on magnetic microscopic cylinders. Dense actin networks are grown from the cylinders' surfaces using the biochemical Arp2/3-machinery at play in the lamellipodium extension and other force-generating processes in the cell. Under a homogenous magnetic field the magnetic cylinders self-assemble into chains in which forces are attractive and depend on the intensity of the magnetic field. We show that these forces, from piconewtons to nanonewtons, are large enough to slow down the assembly of dense actin networks and controlled enough to access to their non linear mechanical responses. Deformations are measured with nanometer-resolution, well below the optical resolution. Self-assembly of the magnetic particles into chains simplifies experiments and allows for parallel measurements. The combination of accuracy and good throughput of measurements results in a method with high potential for cell and cytoskeleton mechanics. Using this method, we observed in particular a strong non linear mechanical behavior of dense branched actin networks at low forces that has not been reported previously.

Assembly Modulated by Particle Position and Shape: A New Concept in Self-Assembly.

In this communication we outline how the bespoke arrangements and design of micron-sized superparamagnetic shapes provide levers to modulate their assembly under homogeneous magnetic fields. We label this new approach, 'assembly modulated by particle position and shape' (APPS). Specifically, using rectangular lattices of superparamagnetic micron-sized cuboids, we construct distinct microstructures by adjusting lattice pitch and angle of array with respect to a magnetic field. Broadly, we find two modes of assembly: (1) immediate 2D jamming of the cuboids as they rotate to align with the applied field (rotation-induced jamming) and (2) aggregation via translation after their full alignment (dipole-dipole assembly). The boundary between these two assembly pathways is independent on field strength being solely a function of the cuboid's dimensions, lattice pitch, and array angle with respect to field-a relationship which we capture, along with other features of the assembly process, in a 'phase diagram'. In doing so, we set out initial design rules to build custom made assemblies. Moreover, these assemblies can be made flexible thanks to the hinged contacts of their particle building blocks. This flexibility, combined with the superparamagnetic nature of the architectures, renders our assembly method particularly appropriate for the construction of complex actuators at a scale hitherto not possible.

Magnetic fluidized bed for solid phase extraction in microfluidic systems.

Fluidization, a process in which a granular solid phase behaves like a fluid under the influence of an imposed upward fluid flow, is routinely used in many chemical and biological engineering applications. It brings, to applications involving fluid-solid exchanges, advantages such as high surface to volume ratio, constant mixing, low flow resistance, continuous operation and high heat transfer. We present here the physics of a new miniaturized, microfluidic fluidized bed, in which gravity is replaced by a magnetic field created by an external permanent magnet, and the solid phase is composed of magnetic microbeads with diameters ranging from 1 to 5 µm. These beads can be functionalized with different ligands, catalysts or enzymes, in order to use the fluidized bed as a continuous purification column or bioreactor. It allows flow-through operations at flow rates ranging from 100 nL min-1 up to 5 µL min-1 at low driving pressures (<100 mbar) with intimate liquid/solid contact and a continuous recirculation of beads for enhanced target capture efficiencies. The physics of the system presents significant differences as compared to conventional fluidized beds, which are studied here. The effects of magnetic field profile, flow chamber shape and magnetic bead dipolar interactions on flow regimes are investigated, and the different regimes of operation are described. Qualitative rules to obtain optimal operation are deduced. Finally, an exemplary use as a platform for immunocapture is provided, presenting a limit of detection of 0.2 ng mL-1 for 200 µL volume samples.

Deformation and shape of flexible, microscale helices in viscous flow.

We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive-force theory. The deformation of helices by viscous flow is well described by nonlinear finite extensibility. Under distributed loading, the pitch distribution is nonuniform, and from this we identify both linear and nonlinear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at a high flow rate.

Microfluidic in situ mechanical testing of photopolymerized gels.

Gels are a functional template for micro-particle fabrication and microbiology experiments. The control and knowledge of their mechanical properties is critical in a number of applications, but no simple in situ method exists to determine these properties. We propose a novel microfluidic based method that directly measures the mechanical properties of the gel upon its fabrication. We measure the deformation of a gel beam under a controlled flow forcing, which gives us a direct access to the Young's modulus of the material itself. We then use this method to determine the mechanical properties of poly(ethylene glycol) diacrylate (PEGDA) under various experimental conditions. The mechanical properties of the gel can be highly tuned, yielding two order of magnitude in the Young's modulus. The method can be easily implemented to allow for an in situ direct measurement and control of Young's moduli under various experimental conditions.

Impact of branching on the elasticity of actin networks.

Actin filaments play a fundamental role in cell mechanics: assembled into networks by a large number of partners, they ensure cell integrity, deformability, and migration. Here we focus on the mechanics of the dense branched network found at the leading edge of a crawling cell. We develop a new technique based on the dipolar attraction between magnetic colloids to measure mechanical properties of branched actin gels assembled around the colloids. This technique allows us to probe a large number of gels and, through the study of different networks, to access fundamental relationships between their microscopic structure and their mechanical properties. We show that the architecture does regulate the elasticity of the network: increasing both capping and branching concentrations strongly stiffens the networks. These effects occur at protein concentrations that can be regulated by the cell. In addition, the dependence of the elastic modulus on the filaments' flexibility and on increasing internal stress has been studied. Our overall results point toward an elastic regime dominated by enthalpic rather than entropic deformations. This result strongly differs from the elasticity of diluted cross-linked actin networks and can be explained by the dense dendritic structure of lamellipodium-like networks.

Collective beating of artificial microcilia.

We combine technical, experimental, and theoretical efforts to investigate the collective dynamics of artificial microcilia in a viscous fluid. We take advantage of soft lithography and colloidal self-assembly to devise microcarpets made of hundreds of slender magnetic rods. This novel experimental setup is used to investigate the dynamics of extended cilia arrays driven by a precessing magnetic field. Whereas the dynamics of an isolated cilium is a rigid body rotation, collective beating results in a symmetry breaking of the precession patterns. The trajectories of the cilia are anisotropic and experience a significant structural evolution as the actuation frequency increases. We present a minimal model to account for our experimental findings and demonstrate how the global geometry of the array imposes the shape of the trajectories via long-range hydrodynamic interactions.

Force-velocity measurements of a few growing actin filaments.

The polymerization of actin in filaments generates forces that play a pivotal role in many cellular processes. We introduce a novel technique to determine the force-velocity relation when a few independent anchored filaments grow between magnetic colloidal particles. When a magnetic field is applied, the colloidal particles assemble into chains under controlled loading or spacing. As the filaments elongate, the beads separate, allowing the force-velocity curve to be precisely measured. In the widely accepted Brownian ratchet model, the transduced force is associated with the slowing down of the on-rate polymerization. Unexpectedly, in our experiments, filaments are shown to grow at the same rate as when they are free in solution. However, as they elongate, filaments are more confined in the interspace between beads. Higher repulsive forces result from this higher confinement, which is associated with a lower entropy. In this mechanism, the production of force is not controlled by the polymerization rate, but is a consequence of the restriction of filaments' orientational fluctuations at their attachment point.