Reshaping and enzymatic activity may allow viruses to move through the mucus.

Filamentous viruses like influenza and torovirus often display systematic bends and arcs of mysterious physical origin. We propose that such viruses undergo an instability from a cylindrically symmetric to a toroidally curved state. This "toro-elastic" state emerges via spontaneous symmetry breaking under prestress due to short range spike protein interactions magnified by surface topography. Once surface stresses are sufficiently large, the filament buckles and the curved state constitutes a soft mode that can potentially propagate through the filament's material frame around a Mexican-hat-type potential. In the mucus of our airways, which constitutes a soft, porous 3D network, glycan chains are omnipresent and influenza's spike proteins are known to efficiently bind and cut them. We next show that such a non-equilibrium enzymatic reaction can induce spontaneous rotation of the curved state, leading to a whole body reshaping propulsion similar to - but different from - eukaryotic flagella and spirochetes.

Rolling and ordering of micro rods in shear flow induced by rod wall interactions.

Dynamics of micro particles close to interfaces is a relevant topic in Soft Matter. Translational and rotational dynamics of particles possessing different shapes govern a broad range of interfacial phenomena from biofilm formation, drug delivery and particle active rolling motion. These dynamics usually occur in the presence of external fields such as shear flows, electric fields and gravity. By experiments and theoretical models, we investigate the rolling and translational motion of rod-shaped micro particles close to a solid wall in the presence or absence of a shear flow. Hydrodynamics, long-range surface forces and Brownian motion act on the micro rods, which show non-trivial dynamics such as translational motion orthogonal to the flow direction and preferential ordering with the rod long axis perpendicular to the flow direction.

How Influenza's Spike Motor Works.

While often believed to be a passive agent that merely exploits its host's metabolism, the influenza virus has recently been shown to actively move across glycan-coated surfaces. This form of enzymatically driven surface motility is currently not well understood and has been loosely linked to burnt-bridge Brownian ratchet mechanisms. Starting from known properties of influenza's spike proteins, we develop a physical model that quantitatively describes the observed motility. It predicts a collectively emerging dynamics of spike proteins and surface-bound ligands that combined with the virus' geometry give rise to a self-organized rolling propulsion. We show that in contrast to a Brownian ratchet, the rotary spike drive is not fluctuation driven but operates optimally as a macroscopic engine in the deterministic regime. The mechanism also applies to relatives of influenza and to man-made analogs like DNA monowheels and should give guidelines for their optimization.

Dynamics of fiberboids.

Fiberboids are active filaments trapped at the interface of two phases, able of harnessing energy (and matter) fluxes across the interface in order to produce a rolling-like self-propulsion. We discuss several table-top examples and develop the physical framework for understanding their complex dynamics. In spite of some specific features in the examples studied we conclude that the phenomenon of fiberboids is highly generic and robust across different materials, types of fluxes and timescales. Fiberboid motility should play a role from the macroscopic realm down to the micro scale and, as recently hypothesized, possibly as a means of biological self-propulsion that has escaped previous attention.

Motorizing fibres with geometric zero-energy modes.

Responsive materials1-3 have been used to generate structures with built-in complex geometries4-6, linear actuators7-9 and microswimmers10-12. These results suggest that complex, fully functional machines composed solely from shape-changing materials might be possible 13 . Nonetheless, to accomplish rotary motion in these materials still relies on the classical wheel and axle motifs. Here we explore geometric zero-energy modes to elicit rotary motion in elastic materials in the absence of a rigid wheel travelling around an axle. We show that prestrained polymer fibres closed into rings exhibit self-actuation and continuous motion when placed between two heat baths due to elastic deformations that arise from rotational-symmetry breaking around the rod's axis. Our findings illustrate a simple but robust model to create active motion in mechanically prestrained objects.

Helical Superstructure of Intermediate Filaments.

Intermediate filaments are the least explored among the large cytoskeletal elements. We show here that they display conformational anomalies in narrow microfluidic channels. Their unusual behavior can be understood as the consequence of a previously undetected, large-scale helically curved superstructure. Confinement in a channel orders the otherwise soft, strongly fluctuating helical filaments and enhances their structural correlations, giving rise to experimentally detectable, strongly oscillating tangent correlation functions. We propose an explanation for the detected intrinsic curving phenomenon-an elastic shape instability that we call autocoiling. The mechanism involves self-induced filament buckling via a surface stress located at the outside of the cross section. The results agree with ultrastructural findings and rationalize for the commonly observed looped intermediate filament shapes. Beyond curvature, explaining the molecular origin of the detected helical torsion remains an interesting challenge.

Resonant reshaping of colloidal clusters on a current carrying wire.

Colloids in confined geometries promise a path towards tailored microscopic superstructures. Yet, a major roadblock is posed by kinetically trapped states that prevent the assemblies from reaching their anticipated shapes. We investigate magnetic colloids trapped on a cylindrical surface of a current carrying wire. If kinetic traps could be avoided the wire's surface would act as an ideal mold for colloidal rings and helical fibers. We devise here a way to dynamically shake down the clusters and avoid kinetic traps in their energy landscape. A low frequency magnetic modulation wave around the wire axis effectively eliminates defects from the clusters and stretches them into slender rings and helical filaments. A theoretical model is developed that qualitatively explains the observed resonant reshaping response of clusters.

How bio-filaments twist membranes.

We study the deformations of a fluid membrane imposed by adhering stiff bio-filaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical bio-filaments. In particular, we analyse interface-mediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.

Squeezed helical elastica.

We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters. We explore the conformation space in detail and show that the shapes can be understood as the mutual elastic interaction of conformational quasi-particles. Our theoretical results are potentially useful to determine the material parameters of such helical filaments in an experimental setting.

Why microtubules run in circles: mechanical hysteresis of the tubulin lattice.

The fate of every eukaryotic cell subtly relies on the exceptional mechanical properties of microtubules. Despite significant efforts, understanding their unusual mechanics remains elusive. One persistent, unresolved mystery is the formation of long-lived arcs and rings, e.g., in kinesin-driven gliding assays. To elucidate their physical origin we develop a model of the inner workings of the microtubule's lattice, based on recent experimental evidence for a conformational switch of the tubulin dimer. We show that the microtubule lattice itself coexists in discrete polymorphic states. Metastable curved states can be induced via a mechanical hysteresis involving torques and forces typical of few molecular motors acting in unison, in agreement with the observations.

Topological energy storage of work generated by nanomotors.

Most macroscopic machines rely on wheels and gears. Yet, rigid gears are entirely impractical on the nano-scale. Here we propose a more useful method to couple any rotary engine to any other mechanical elements on the nano- and micro-scale. We argue that a rotary molecular motor attached to an entangled polymer energy storage unit, which together form what we call the "tanglotron" device, is a viable concept that can be experimentally implemented. We derive the torque-entanglement relationship for a tanglotron (its "equation of state") and show that it can be understood by simple statistical mechanics arguments. We find that a typical entanglement at low packing density costs around 6kT. In the high entanglement regime, the free energy diverges logarithmically close to a maximal geometric packing density. We outline several promising applications of the tanglotron idea and conclude that the transmission, storage and back-conversion of topological entanglement energy are not only physically feasible but also practical for a number of reasons.

A nonequilibrium power balance relation for analyzing dissipative filament dynamics.

Biofilaments like F-actin or microtubules, as well as cilia, flagella, or filament bundles, are often deformed by distributed and time-dependent external forces. It is highly desirable to characterize these filaments' mechanics in an efficient way, either using a single experiment or a high throughput method. We here propose a dynamic power balance approach to study nonequilibrium filament dynamics and exemplify it both experimentally and theoretically by applying it to microtubule gliding assay dynamics. Its usefulness is highlighted by the experimental determination of the lateral friction coefficient for microtubules on kinesins. In contrast to what is usually assumed, friction is anisotropic, in a similar fashion as hydrodynamic friction. We also exemplify, by considering a microtubule buckling event, that if at least one parameter is known in advance, all other parameters can be determined by analyzing a single time-dependent experiment.

Confotronic dynamics of tubular filaments.

Tubular lattices are ubiquitous in nature and technology. Microtubules and nanotubes of all kinds act as important pillars of biological cells and the man-made nano-world. We show that when prestress is introduced in such structures, localized conformational quasiparticles emerge and govern the collective shape dynamics of the lattice. When coupled via cooperative interactions these quasiparticles form larger-scale quasipolymer superstructures exhibiting collective dynamic modes and giving rise to a hallmark behavior radically different from semiflexible beams.

Self-assembly of colloidal superstructures in coherently fluctuating fields.

From microscopic fluid clusters to macroscopic droplets, the structure of fluids is governed by the van der Waals force, a force that acts between polarizable objects. In this Letter, we derive a general theory that describes the nonequilibrium counterpart to the van der Waals force, which emerges in spatially coherently fluctuating electromagnetic fields. We describe the formation of a novel and complex hierarchy of self-organized morphologies in magnetic and dielectric colloid systems. Most striking among these morphologies are dipolar foams--colloidal superstructures that swell against gravity and display a high sensitivity to the applied field. We discuss the dominance of many-body forces and derive the equation of state for a material formed by the coherent van der Waals force. Our theory is applied to recent experiments in paramagnetic colloidal systems and a new experiment is suggested to test the theory.

Cooperative lattice dynamics and anomalous fluctuations of microtubules.

Microtubules have been in the focus of biophysical research for several decades. However, the confusing and mutually contradictory results regarding their elasticity and fluctuations have cast doubt on their present understanding. In this paper, we present the empirical evidence for the existence of discrete guanosine diphosphate (GDP)-tubulin fluctuations between a curved and a straight configuration at room temperature as well as for conformational tubulin cooperativity. Guided by a number of experimental findings, we build the case for a novel microtubule model, with the principal result that microtubules can spontaneously form micron-sized cooperative helical states with unique elastic and dynamic features. The polymorphic dynamics of the microtubule lattice resulting from the tubulin bistability quantitatively explains several experimental puzzles, including anomalous scaling of dynamic fluctuations of grafted microtubules, their apparent length-stiffness relation, and their remarkable curved-helical appearance in general. We point out that the multistability and cooperative switching of tubulin dimers could participate in important cellular processes, and could in particular lead to efficient mechanochemical signaling along single microtubules.

Physics of self-rolling viruses.

Viruses are right at the interface of inanimate matter and life. However, recent experiments [Sakai et al., J. Virol. 92, e01522-17 (2018)0022-538X10.1128/JVI.01522-17] have shown that some influenza strains can actively roll on glycan-covered surfaces. In a previous letter [Ziebert and Kulic, Phys. Rev. Lett. 126, 218101 (2021)0031-900710.1103/PhysRevLett.126.218101] we suggested this to be a form of viral surface metabolism: a collection of spike proteins that attach to and cut the glycans act as a self-organized mechano-chemical motor. Here we study in more depth the physics of the emergent self-rolling states. We give scaling arguments how the motion arises, substantiated by a detailed analytical theory that yields the full torque-angular velocity relation of the self-organized motor. Stochastic Gillespie simulations are used to validate the theory and to quantify stochastic effects like virus detachment and reversals of its direction. Finally, we also cross-check several approximations made previously and show that the proposed mechanism is very robust. All these results point together to the statistical inevitability of viral rolling in the presence of enzymatic activity.

The role of microtubule movement in bidirectional organelle transport.

We study the role of microtubule movement in bidirectional organelle transport in Drosophila S2 cells and show that EGFP-tagged peroxisomes in cells serve as sensitive probes of motor induced, noisy cytoskeletal motions. Multiple peroxisomes move in unison over large time windows and show correlations with microtubule tip positions, indicating rapid microtubule fluctuations in the longitudinal direction. We report the first high-resolution measurement of longitudinal microtubule fluctuations performed by tracing such pairs of co-moving peroxisomes. The resulting picture shows that motor-dependent longitudinal microtubule oscillations contribute significantly to cargo movement along microtubules. Thus, contrary to the conventional view, organelle transport cannot be described solely in terms of cargo movement along stationary microtubule tracks, but instead includes a strong contribution from the movement of the tracks.

Tubulin bistability and polymorphic dynamics of microtubules.

Based on the hypothesis that the GDP-tubulin dimer is a conformationally bistable molecule-rapidly fluctuating between a discrete curved and a straight state-we develop a model for polymorphic dynamics of the microtubule lattice. We show that GDP-tubulin bistability consistently explains unusual dynamic fluctuations, the apparent length-stiffness relation of grafted taxol-stabilized microtubules, and the curved-helical appearance of microtubules in general. When clamped by one end the microtubules undergo an unusual zero energy motion-in its effect reminiscent of a limited rotational hinge. We conclude that microtubules exist in highly cooperative energy-degenerate helical states and discuss possible implications in vivo.

Counterrotation of magnetic beads in spinning fields.

A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau et al. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.

MAP6 is an intraluminal protein that induces neuronal microtubules to coil.

Neuronal activities depend heavily on microtubules, which shape neuronal processes and transport myriad molecules within them. Although constantly remodeled through growth and shrinkage events, neuronal microtubules must be sufficiently stable to maintain nervous system wiring. This stability is somehow maintained by various microtubule-associated proteins (MAPs), but little is known about how these proteins work. Here, we show that MAP6, previously known to confer cold stability to microtubules, promotes growth. More unexpectedly, MAP6 localizes in the lumen of microtubules, induces the microtubules to coil into a left-handed helix, and forms apertures in the lattice, likely to relieve mechanical stress. These features have not been seen in microtubules before and could play roles in maintaining axonal width or providing flexibility in the face of compressive forces during development.