Magnetic field directed assembly of magnetic non-spherical microparticles.

This study reports on the fabrication and assembly of anisotropic microparticles as versatile building blocks for directed magnetic assemblies. Although spherical microparticles have received extensive attention, the assembly of non-spherical magnetic microparticles remains underexplored. Herein, we present a fabrication approach that utilizes photolithography and soft lithography to create prism-shaped magnetic microparticles. In order to investigate their assembly, a switching rotating magnetic field was employed. To support our experimental findings, a numerical model which takes into account the magnetic dipole moments induced by the field of other particles was developed. This model helps in understanding the forces and torques governing particle behavior during assembly. Simulations were conducted using the numerical model to complement our experimental findings. In the two particle experiments, attractive magnetic interactions led to various configurations depending on initial positions. For three particles, a tip-to-tip configuration suggested closed or stable ring-like structures. Our work highlights the feasibility of producing highly responsive, non-spherical magnetic microparticles and their potential for assemblies. The versatile fabrication method, coupled with the added degree of freedom conferred by prismatic shapes, opens promising avenues for applications in biology and material science.

Lorentz Reciprocal Theorem in Fluids with Odd Viscosity.

The Lorentz reciprocal theorem-that is used to study various transport phenomena in hydrodynamics-is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here, we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque dipole can lead to directed motion.

Nonreciprocal interactions give rise to fast cilium synchronization in finite systems.

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.

Minimum entropy production by microswimmers with internal dissipation.

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.

Spontaneous Chiral Symmetry Breaking and Lane Formation in Ferromagnetic Ferrofluids.

Ferromagnetic ferrofluids are synthetic materials consisting of magnetic nanoplatelets dispersed in an isotropic fluid. Their main characteristics are the formation of stable magnetic domains and the presence of macroscopic magnetization even in the absence of a magnetic field. Here, the authors report on the experimental observation of spontaneous stripe formation in a ferromagnetic ferrofluid in the presence of an oscillating external magnetic field. The striped structure is identified as elongated magnetic domains, which exhibit reorientation upon reversal of the magnetic field. The stripes are oriented perpendicular to the magnetic field and are separated by alternating flow lanes. The velocity profile is measured using a space-time correlation technique that follows the motion of the thermally excited fluctuations in the sample. The highest velocities are found in the depleted regions between individual domains and reach values up to several µm s-1 . The fluid in adjacent lanes moves in the opposite directions despite the applied magnetic field being uniform. The formation of bidirectional flow lanes can be explained by alternating rotation of magnetic nanoparticles in neighboring stripes, which indicates spontaneous breaking of the chiral symmetry in the sample.

Theoretical efficiency limits and speed-efficiency trade-off in myosin motors.

Muscle myosin is a non-processive molecular motor that generates mechanical work when cooperating in large ensembles. During its cyle, each individual motor keeps attaching and detaching from the actin filament. The random nature of attachment and detachment inevitably leads to losses and imposes theoretical limits on the energetic efficiency. Here, we numerically determine the theoretical efficiency limit of a classical myosin model with a given number of mechano-chemical states. All parameters that are not bounded by physical limits (like rate limiting steps) are determined by numerical efficiency optimization. We show that the efficiency is limited by the number of states, the stiffness and the rate-limiting kinetic steps. There is a trade-off between speed and efficiency. Slow motors are optimal when most of the available free energy is allocated to the working stroke and the stiffness of their elastic element is high. Fast motors, on the other hand, work better with a lower and asymmetric stiffness and allocate a larger fraction of free energy to the release of ADP. Overall, many features found in myosins coincide with the findings from the model optimization: there are at least 3 bound states, the largest part of the working stroke takes place during the first transition, the ADP affinity is adapted differently in slow and fast myosins and there is an asymmetry in elastic elements.

Active Bending of Disordered Microtubule Bundles by Kinesin Motors.

Active networks of biopolymers and motor proteins in vitro self-organize and exhibit dynamic structures on length scales much larger than the interacting individual components of which they consist. How the dynamics is related across the range of length scales is still an open question. Here, we experimentally characterize and quantify the dynamic behavior of isolated microtubule bundles that bend due to the activity of motor proteins. At the motor level, we track and describe the motion features of kinesin-1 clusters stepping within the bending bundles. We find that there is a separation of length scales by at least 1 order of magnitude. At a run length of <1 µm, kinesin-1 activity leads to a bundle curvature in the range of tens of micrometers. We propose that the distribution of microtubule polarity plays a crucial role in the bending dynamics that we observe at both the bundle and motor levels. Our results contribute to the understanding of fundamental principles of vital intracellular processes by disentangling the multiscale dynamics in out-of-equilibrium active networks composed of cytoskeletal elements.

A Synthetic Minimal Beating Axoneme.

Cilia and flagella are beating rod-like organelles that enable the directional movement of microorganisms in fluids and fluid transport along the surface of biological organisms or inside organs. The molecular motor axonemal dynein drives their beating by interacting with microtubules. Constructing synthetic beating systems with axonemal dynein capable of mimicking ciliary beating still represents a major challenge. Here, the bottom-up engineering of a sustained beating synthoneme consisting of a pair of microtubules connected by a series of periodic arrays of approximately eight axonemal dyneins is reported. A model leads to the understanding of the motion through the cooperative, cyclic association-dissociation of the molecular motor from the microtubules. The synthoneme represents a bottom-up self-organized bio-molecular machine at the nanoscale with cilia-like properties.

Active beating modes of two clamped filaments driven by molecular motors.

Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.

Ciliary chemosensitivity is enhanced by cilium geometry and motility.

Cilia are hairlike organelles involved in both sensory functions and motility. We discuss the question of whether the location of chemical receptors on cilia provides an advantage in terms of sensitivity and whether motile sensory cilia have a further advantage. Using a simple advection-diffusion model, we compute the capture rates of diffusive molecules on a cilium. Because of its geometry, a non-motile cilium in a quiescent fluid has a capture rate equivalent to a circular absorbing region with ∼4× its surface area. When the cilium is exposed to an external shear flow, the equivalent surface area increases to ∼6×. Alternatively, if the cilium beats in a non-reciprocal way in an otherwise quiescent fluid, its capture rate increases with the beating frequency to the power of 1/3. Altogether, our results show that the protruding geometry of a cilium could be one of the reasons why so many receptors are located on cilia. They also point to the advantage of combining motility with chemical reception.

Tuning the Properties of Active Microtubule Networks by Depletion Forces.

Suspensions of microtubules and nonadsorbing particles form thick and long bundles due to depletion forces. Such interactions act at the nanometer scale and define the structural and dynamical properties of the resulting networks. In this study, we analyze the depletion forces exerted by two types of nonadsorbing particles, namely, the polymer, poly(ethylene glycol) (PEG), and the block copolymer, Pluronic. We characterize their effects both in passive and active networks by adding motor proteins to the suspensions. By exploiting its bundling effect via entropic forces, we observed that PEG generates a network with thick structures showing a nematic order and larger mesh size. On the other hand, Pluronic builds up a much denser gel-like network without a recognizable mesh structure. This difference is also reflected in the network activity. PEG networks show moderate contraction in lateral directions while Pluronic networks exhibit faster and isotropic contraction. Interestingly, by mixing the two nonadsorbing polymers in different ratios, we observed that the system showed a behavior that exhibited properties of both agents, leading to a robust and fast responsive structure compared to the single-depletant networks. In conclusion, we show how passive osmotic compression modifies the distribution of biopolymers. Its combination with active motors results in a new active material with potential for nanotechnological applications.

Minimum Dissipation Theorem for Microswimmers.

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.

Wrinkling Instability in 3D Active Nematics.

In nature, interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviors. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors, and depleting agent. It shows a rich behavior evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.

Blood Flow Forces in Shaping the Vascular System: A Focus on Endothelial Cell Behavior.

The endothelium is the cell monolayer that lines the interior of the blood vessels separating the vessel lumen where blood circulates, from the surrounding tissues. During embryonic development, endothelial cells (ECs) must ensure that a tight barrier function is maintained whilst dynamically adapting to the growing vascular tree that is being formed and remodeled. Blood circulation generates mechanical forces, such as shear stress and circumferential stretch that are directly acting on the endothelium. ECs actively respond to flow-derived mechanical cues by becoming polarized, migrating and changing neighbors, undergoing shape changes, proliferating or even leaving the tissue and changing identity. It is now accepted that coordinated changes at the single cell level drive fundamental processes governing vascular network morphogenesis such as angiogenic sprouting, network pruning, lumen formation, regulation of vessel caliber and stability or cell fate transitions. Here we summarize the cell biology and mechanics of ECs in response to flow-derived forces, discuss the latest advances made at the single cell level with particular emphasis on in vivo studies and highlight potential implications for vascular pathologies.

Blood Flow Limits Endothelial Cell Extrusion in the Zebrafish Dorsal Aorta.

Blood flow modulates endothelial cell (EC) response during angiogenesis. Shear stress is known to control gene expression related to the endothelial-mesenchymal transition and endothelial-hematopoietic transition. However, the impact of blood flow on the cellular processes associated with EC extrusion is less well understood. To address this question, we dynamically record EC movements and use 3D quantitative methods to segregate the contributions of various cellular processes to the cellular trajectories in the zebrafish dorsal aorta. We find that ECs spread toward the cell extrusion area following the tissue deformation direction dictated by flow-derived mechanical forces. Cell extrusion increases when blood flow is impaired. Similarly, the mechanosensor polycystic kidney disease 2 (pkd2) limits cell extrusion, suggesting that ECs actively sense mechanical forces in the process. These findings identify pkd2 and flow as critical regulators of EC extrusion and suggest that mechanical forces coordinate this process by maintaining ECs within the endothelium.

Emergent collective colloidal currents generated via exchange dynamics in a broken dimer state.

Controlling the flow of matter down to micrometer-scale confinement is of central importance in material and environmental sciences, with direct applications in nano and microfluidics, drug delivery, and biotechnology. Currents of microparticles are usually generated with external field gradients of different nature (e.g., electric, magnetic, optical, thermal, or chemical ones), which are difficult to control over spatially extended regions and samples. Here, we demonstrate a general strategy to assemble and transport polarizable microparticles in fluid media through combination of confinement and magnetic dipolar interactions. We use a homogeneous magnetic modulation to assemble dispersed particles into rotating dimeric state and frustrated binary lattices, and generate collective currents that arise from a novel, field-synchronized particle exchange process. These dynamic states are similar to cyclotron and skipping orbits in electronic and molecular systems, thus paving the way toward understanding and engineering similar processes at different length scales across condensed matter.

The cilium as a force sensor-myth versus reality.

Cells need to sense their mechanical environment during the growth of developing tissues and maintenance of adult tissues. The concept of force-sensing mechanisms that act through cell-cell and cell-matrix adhesions is now well established and accepted. Additionally, it is widely believed that force sensing can be mediated through cilia. Yet, this hypothesis is still debated. By using primary cilia sensing as a paradigm, we describe the physical requirements for cilium-mediated mechanical sensing and discuss the different hypotheses of how this could work. We review the different mechanosensitive channels within the cilium, their potential mode of action and their biological implications. In addition, we describe the biological contexts in which cilia are acting - in particular, the left-right organizer - and discuss the challenges to discriminate between cilium-mediated chemosensitivity and mechanosensitivity. Throughout, we provide perspectives on how quantitative analysis and physics-based arguments might help to better understand the biological mechanisms by which cells use cilia to probe their mechanical environment.

Diffusive ferromagnetic roller gas.

An ensemble of actively rotating ferromagnetic particles is used to realize an active roller gas. Here, we investigate the diffusive properties of such a gas in experiments and simulations. We reveal that ferromagnetic rollers demonstrate a normal (Fickian) diffusion with a characteristic linear growth of the mean-squared displacement, while statistics of displacements stay non-Gaussian. At short times the system has a bimodal distribution of the displacements that transitions with time to a quasi-Gaussian distribution (Gaussian core with overpopulated tails) for a range of studied particle number densities. Inert particles introduced into the active roller gas exhibit similar diffusive behavior. The results provide insights into diffusive properties of active colloidal systems with activity originating from spinning degrees of freedom.

Flagella-like Beating of a Single Microtubule.

Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simultaneously on a microtubule. The tangential forces exerted by a cluster are mostly in the range 0-8 pN toward the microtubule minus end, indicating the action of 1 or 2 kinesin motors. The lateral forces are distributed symmetrically and mainly below 10 pN, while the lateral velocity has a strong peak around zero. Unlike well-known models for flapping filaments, kinesins are found to have a strong "pinning" effect on the beating filaments. Our results suggest new strategies to utilize molecular motors in dynamic roles that depend sensitively on the stress built-up in the system.

Prolines Affect the Nucleation Phase of Amyloid Fibrillation Reaction; Mutational Analysis of Human Stefin B.

Proline residues play a prominent role in protein folding and aggregation. We investigated the influence of single prolines and their combination on oligomerization and the amyloid fibrillation reaction of human stefin B (stB). The proline mutants influenced the distribution of oligomers between monomers, dimers, and tetramers as shown by the size-exclusion chromatography. Only P74S showed higher oligomers, reminiscent of the molten globule reported previously for the P74S of stB-Y31 variant. The proline mutants also inhibited to various degree the amyloid fibrillation reaction. At 30 and 37 °C, inhibition was complete for the P74S single mutant, two double mutants (P6L P74S and P74S P79S), and for the triple mutant P6L P11S P74S. At 30 °C the single mutant P6L completely inhibited the reaction, while P11S and P79S formed amyloid fibrils with a prolonged lag phase. P36D did not show a lag phase, reminiscent of a downhill polymerization model. At 37 °C in addition to P36D, P11S, and P79S, P6L and P11S P74S also started to fibrillate; however, the yield of the fibrils was much lower than that of the wild-type protein as judged by transmission electron microscopy. Thus, Pro 74 cis/trans isomerization proves to be the key event, acting as a switch toward an amyloid transition. Using our previous model of nucleation and growth, we simulated the kinetics of all the mutants that exhibited sigmoidal fibrillation curves. To our surprise, the nucleation phase was most affected by Pro cis/trans isomerism, rather than the fibril elongation phase.