Substrate stiffness impacts early biofilm formation by modulating Pseudomonas aeruginosa twitching motility.

Surface-associated lifestyles dominate in the bacterial world. Large multicellular assemblies, called biofilms, are essential to the survival of bacteria in harsh environments and are closely linked to antibiotic resistance in pathogenic strains. Biofilms stem from the surface colonization of a wide variety of substrates encountered by bacteria, from living tissues to inert materials. Here, we demonstrate experimentally that the promiscuous opportunistic pathogen Pseudomonas aeruginosa explores substrates differently based on their rigidity, leading to striking variations in biofilm structure, exopolysaccharides (EPS) distribution, strain mixing during co-colonization and phenotypic expression. Using simple kinetic models, we show that these phenotypes arise through a mechanical interaction between the elasticity of the substrate and the type IV pilus (T4P) machinery, that mediates the surface-based motility called twitching. Together, our findings reveal a new role for substrate softness in the spatial organization of bacteria in complex microenvironments, with far-reaching consequences on efficient biofilm formation.

Symmetry-breaking, motion and bistability of active drops through polarization-surface coupling.

Cell crawling crucially depends on the collective dynamics of the acto-myosin cytoskeleton. However, it remains an open question to what extent cell polarization and persistent motion depend on continuous regulatory mechanisms and autonomous physical mechanisms. Experiments on cell fragments and theoretical considerations for active polar liquids have highlighted that physical mechanisms induce motility through splay and bend configurations in a nematic director field. Here, we employ a simple model, derived from basic thermodynamic principles, for active polar free-surface droplets to identify a different mechanism of motility. Namely, active stresses drive drop motion through spatial variations of polarization strength. This robustly induces parity-symmetry breaking and motility even for liquid ridges (2D drops) and adds to splay- and bend-driven pumping in 3D geometries. Intriguingly, then, stable polar moving and axisymmetric resting states may coexist, reminiscent of the interconversion of moving and resting keratocytes by external stimuli. The identified additional motility mode originates from a competition between the elastic bulk energy and the polarity control exerted by the drop surface. As it already breaks parity-symmetry for passive drops, the resulting back-forth asymmetry enables active stresses to effectively pump liquid and drop motion ensues.

Self-repair protects microtubules from destruction by molecular motors.

Microtubule instability stems from the low energy of tubulin dimer interactions, which sets the growing polymer close to its disassembly conditions. Molecular motors use ATP hydrolysis to produce mechanical work and move on microtubules. This raises the possibility that the mechanical work produced by walking motors can break dimer interactions and trigger microtubule disassembly. We tested this hypothesis by studying the interplay between microtubules and moving molecular motors in vitro. Our results show that molecular motors can remove tubulin dimers from the lattice and rapidly destroy microtubules. We also found that dimer removal by motors was compensated for by the insertion of free tubulin dimers into the microtubule lattice. This self-repair mechanism allows microtubules to survive the damage induced by molecular motors as they move along their tracks. Our study reveals the existence of coupling between the motion of molecular motors and the renewal of the microtubule lattice.

Thin-film modeling of resting and moving active droplets.

We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energy for a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This gives a consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of living cells on solid substrates. As example, we analyze the dynamics of two-dimensional active drops (i.e., ridges) and demonstrate how active forces compete with passive surface forces to shape droplets and drive their motion. In our simple two-dimensional scenario we find that defect structures within the polarization profile drastically influence the shape and motility of active droplets. Thus, we can observe a transition from resting to motile droplets via the elimination of defects in the polarization profile. Furthermore, droplet motility is modulated by strong active stresses. Contractile stresses even lead to topological changes, i.e., drop splitting, which is naturally encoded in the evolution equations.

CLASP Mediates Microtubule Repair by Restricting Lattice Damage and Regulating Tubulin Incorporation.

Microtubules play a key role in cell division, motility, and intracellular trafficking. Microtubule lattices are generally regarded as stable structures that undergo turnover through dynamic instability of their ends [1]. However, recent evidence suggests that microtubules also exchange tubulin dimers at the sites of lattice defects, which can be induced by mechanical stress, severing enzymes, or occur spontaneously during polymerization [2-6]. Tubulin incorporation can restore microtubule integrity; moreover, "islands" of freshly incorporated GTP-tubulin can inhibit microtubule disassembly and promote rescues [3, 4, 6-8]. Microtubule repair occurs in vitro in the presence of tubulin alone [2-6, 9]. However, in cells, it is likely to be regulated by specific factors, the nature of which is currently unknown. CLASPs are interesting candidates for microtubule repair because they induce microtubule nucleation, stimulate rescue, and suppress catastrophes by stabilizing incomplete growing plus ends with lagging protofilaments and promoting their conversion into complete ones [10-17]. Here, we used in vitro reconstitution assays combined with laser microsurgery and microfluidics to show that CLASP2α indeed stimulates microtubule lattice repair. CLASP2α promoted tubulin incorporation into damaged lattice sites, thereby restoring microtubule integrity. Furthermore, it induced the formation of complete tubes from partial protofilament assemblies and inhibited microtubule softening caused by hydrodynamic-flow-induced bending. The catastrophe-suppressing domain of CLASP2α, TOG2, combined with a microtubule-tethering region, was sufficient to stimulate microtubule repair, suggesting that catastrophe suppression and lattice repair are mechanistically similar. Our results suggest that the cellular machinery controlling microtubule nucleation and growth can also help to maintain microtubule integrity.

Lattice defects induce microtubule self-renewal.

Microtubules are dynamic polymers, which grow and shrink by addition and removal of tubulin dimers at their extremities. Within the microtubule shaft, dimers adopt a densely packed and highly ordered crystal-like lattice structure, which is generally not considered to be dynamic. Here we report that thermal forces are sufficient to remodel the microtubule shaft, despite its apparent stability. Our combined experimental data and numerical simulations on lattice dynamics and structure suggest that dimers can spontaneously leave and be incorporated into the lattice at structural defects. We propose a model mechanism, where the lattice dynamics is initiated via a passive breathing mechanism at dislocations, which are frequent in rapidly growing microtubules. These results show that we may need to extend the concept of dissipative dynamics, previously established for microtubule extremities, to the entire shaft, instead of considering it as a passive material.

Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants.

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. It relates the interfacial energies to the macroscopic contact angle θe. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f( h). Macro- and mesoscale descriptions are consistent if γ cos θe = γ + f( ha), where γ and ha are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed, implying a nontrivial dependence of θe on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed. This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.

Modelling of surfactant-driven front instabilities in spreading bacterial colonies.

The spreading of bacterial colonies at solid-air interfaces is determined by the physico-chemical properties of the involved interfaces. The production of surfactant molecules by bacteria is a widespread strategy that allows the colony to efficiently expand over the substrate. On the one hand, surfactant molecules lower the surface tension of the colony, effectively increasing the wettability of the substrate, which facilitates spreading. On the other hand, gradients in the surface concentration of surfactant molecules result in Marangoni flows that drive spreading. These flows may cause an instability of the circular colony shape and the subsequent formation of fingers. In this work, we study the effect of bacterial surfactant production and substrate wettability on colony growth and shape within the framework of a hydrodynamic thin film model. We show that variations in the wettability and surfactant production are sufficient to reproduce four different types of colony growth, which have been described in the literature, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.

Continuous versus Arrested Spreading of Biofilms at Solid-Gas Interfaces: The Role of Surface Forces.

We introduce and analyze a model for osmotically spreading bacterial colonies at solid-air interfaces that includes wetting phenomena, i.e., surface forces. The model is based on a hydrodynamic description for liquid suspensions which is supplemented by bioactive processes. We show that surface forces determine whether a biofilm can expand laterally over a substrate and provide experimental evidence for the existence of a transition between continuous and arrested spreading for Bacillus subtilis biofilms. In the case of arrested spreading, the lateral expansion of the biofilm is confined, albeit the colony is biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading. The incorporation of surface forces into our hydrodynamic model allows us to capture this transition in biofilm spreading behavior.

Self-repair promotes microtubule rescue.

The dynamic instability of microtubules is characterized by slow growth phases stochastically interrupted by rapid depolymerizations called catastrophes. Rescue events can arrest the depolymerization and restore microtubule elongation. However, the origin of these rescue events remains unexplained. Here we show that microtubule lattice self-repair, in structurally damaged sites, is responsible for the rescue of microtubule growth. Tubulin photo-conversion in cells revealed that free tubulin dimers can incorporate along the shafts of microtubules, especially in regions where microtubules cross each other, form bundles or become bent due to mechanical constraints. These incorporation sites appeared to act as effective rescue sites ensuring microtubule rejuvenation. By securing damaged microtubule growth, the self-repair process supports a mechanosensitive growth by specifically promoting microtubule assembly in regions where they are subjected to physical constraints.

A variational approach to the growth dynamics of pre-stressed actin filament networks.

In order to model the growth dynamics of elastic bodies with residual stresses a thermodynamically consistent approach is needed such that the cross-coupling between growth and mechanics can be correctly described. In the present work we apply a variational principle to the formulation of the interfacial growth dynamics of dendritic actin filament networks growing from biomimetic beads, an experimentally well studied system, where the buildup of residual stresses governs the network growth. We first introduce the material model for the network via a strain energy density for an isotropic weakly nonlinear elastic material and then derive consistently from this model the dynamic equations for the interfaces, i.e. for a polymerizing internal interface in contact with the bead and a depolymerizing external interface directed towards the solvent. We show that (i) this approach automatically preserves thermodynamic symmetry-properties, which is not the case for the often cited 'rubber-band-model' (Sekimoto et al 2004 Eur. Phys. J. E 13 247-59, Plastino et al 2004 Eur. Biophys. J. 33 310-20) and (ii) leads to a robust morphological instability of the treadmilling network interfaces. The nature of the instability depends on the interplay of the two dynamic interfaces. Depending on the biochemical conditions the network envelope evolves into a comet-like shape (i.e. the actin envelope thins out at one side and thickens on the opposite side of the bead) via a varicose instability or it breaks the symmetry via higher order zigzag modes. We conclude that morphological instabilities due to mechano-chemical coupling mechanisms and the presences of mechancial pre-stresses can play a major role in locally organizing the cytoskeleton of living cells.

Microtubules self-repair in response to mechanical stress.

Microtubules--which define the shape of axons, cilia and flagella, and provide tracks for intracellular transport--can be highly bent by intracellular forces, and microtubule structure and stiffness are thought to be affected by physical constraints. Yet how microtubules tolerate the vast forces exerted on them remains unknown. Here, by using a microfluidic device, we show that microtubule stiffness decreases incrementally with each cycle of bending and release. Similar to other cases of material fatigue, the concentration of mechanical stresses on pre-existing defects in the microtubule lattice is responsible for the generation of more extensive damage, which further decreases microtubule stiffness. Strikingly, damaged microtubules were able to incorporate new tubulin dimers into their lattice and recover their initial stiffness. Our findings demonstrate that microtubules are ductile materials with self-healing properties, that their dynamics does not exclusively occur at their ends, and that their lattice plasticity enables the microtubules' adaptation to mechanical stresses.

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling.

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechanochemical coupling mechanisms that guide the growth process are poorly understood, and a general continuum description combining growth and mechanics is lacking. We develop a theory that bridges the gap between mesoscale and continuum limit and propose a general framework providing the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system.

During pattern formation in spatially extended systems, different mechanisms with different characteristic length scales, e.g., reaction-diffusion processes or molecular interactions, can be active. Such multiscale effects may generate new phenomena, which are not observed in systems where pattern formation occurs on a single scale. Here, we derive and analyze a reaction-diffusion model of the FitzHugh-Nagumo type with short-range attractive molecular interactions of the activator species. The model exhibits a wave instability. Simulations in one and two dimensions show traveling waves with a wavelength set by the parameters of the molecular interaction in the model. In two dimensions, simulations reveal a labyrinthine arrangement of the waves in systems with isotropic diffusion, whereas parallel bands of counterpropagating waves are formed in simulations of a model with anisotropic diffusion. The latter findings are in good qualitative agreement with experimental observation in the catalytic NO+H_{2} reaction on an anisotropic Rh(110) surface. In addition we have identified a transition regime in the simulations, where a short scale instability triggers global oscillations in an excitable regime.

Nonlinear elasticity of cross-linked networks.

Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.

Complex wave patterns in an effective reaction-diffusion model for chemical reactions in microemulsions.

An effective medium theory is employed to derive a simple qualitative model of a pattern forming chemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction-diffusion equations and then derive an equivalent effective spatially homogeneous reaction-diffusion model by using earlier results on homogenization in heterogeneous reaction-diffusion systems [S.Alonso, M.Bär, and R.Kapral, J. Chem. Phys. 134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov-Zhabotinsky reaction in an aerosol OT (AOT)-water-in-oil microemulsion [V.K.Vanag and I.R.Epstein, Phys. Rev. Lett. 87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov-Zhabotinsky reaction in an AOT oil-in-water microemulsion by direct numerical simulations.

Self-ratcheting Stokes drops driven by oblique vibrations.

We develop and analyze a minimal hydrodynamic model to understand why a drop climbs a smooth homogeneous incline that is harmonically vibrated at an angle different from the substrate normal [P. Brunet, J. Eggers, and R. D. Deegan, Phys. Rev. Lett. 99, 144501 (2007)]. We find that the vibration component orthogonal to the substrate induces a nonlinear (anharmonic) response in the drop shape. This results in an asymmetric response of the drop to the parallel vibration and, as a consequence, in the observed net motion. In addition to establishing the basic mechanism, we identify scaling laws valid in a broad frequency range and a flow reversal at high frequencies.

Nonlinear study of symmetry breaking in actin gels: implications for cellular motility.

Force generation by actin polymerization is an important step in cellular motility and can induce the motion of organelles or bacteria, which move inside their host cells by trailing an actin tail behind. Biomimetic experiments on beads and droplets have identified the biochemical ingredients to induce this motion, which requires a spontaneous symmetry breaking in the absence of external fields. We find that the symmetry breaking can be captured on the basis of elasticity theory and linear flux-force relationships. Furthermore, we develop a phase-field approach to study the fully nonlinear regime and show that actin-comet formation is a robust feature, triggered by growth and mechanical stresses. We discuss the implications of symmetry breaking for self-propulsion.

Ratchet-driven fluid transport in bounded two-layer films of immiscible liquids.

We present a two-layer thin film model allowing us to study the behavior of a general class of 'wettability ratchets' that can be employed to transport a continuous phase. Brownian ratchets, in contrast, are normally used to transport particles or molecules within a continuous carrier fluid without transporting the fluid itself. The wettability ratchet is based on a switchable, spatially asymmetric, periodic interaction of the free surface of the film and the walls. To illustrate the general concept, we focus on an electrical dewetting mechanism based on the effective force exercised by a static electric field on the liquid-liquid interface between two dielectric liquids. In particular, we analyse (i) an on-off ratchet with a constant lateral force resulting in a dewetting-spreading cycle, (ii) a ratchet switching between two shifted potentials that shows a transition between oscillating and sliding drops, and (iii) a flashing external force ratchet. For the three cases, the macroscopic transport is studied in its dependence on spatial and temporal characteristics of the ratchet, and physical properties and volume of the liquids.