Karin John

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.

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.

Transport of free surface liquid films and drops by external ratchets and self-ratcheting mechanisms

We discuss the usage of ratchet mechanisms to transport a continuous phase in several micro-fluidic settings. In particular, we study the transport of a dielectric liquid in a heterogeneous ratchet capacitor that is periodically switched on and off. The second system consists of drops on a solid substrate that are transported by different types of harmonic substrate vibrations. We argue that the latter can be seen as a self-ratcheting process and discuss analogies between the employed class of thin film equations and Fokker–Planck equations for transport of discrete objects in a ‘particle ratchet’.

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.

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.

From a thin film model for passive suspensions towards the description of osmotic biofilm spreading

Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid- liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bac- teria to an interface, where they proliferate and produce a slimy polymeric matrix - two processes that result in colony growth and spreading. Recent experiments on the growth of biofilms on agar substrates under air have shown that for certain bacterial strains, the production of the extracellular matrix and the resulting osmotic influx of nutrient-rich water from the agar into the biofilm are more crucial for the spreading behaviour of a biofilm than the motility of individual bacteria. We present a model which de- scribes the biofilm evolution and the advancing biofilm edge for this spreading mechanism. The model is based on a gradient dynamics formulation for thin films of biologically passive liquid mixtures and suspensions, supplemented by bioactive processes which play a decisive role in the osmotic spreading of biofilms. It explicitly includes the wetting properties of the biofilm on the agar substrate via a dis- joining pressure and can therefore give insight into the interplay between passive surface forces and bioactive growth processes.

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.

Lattice defects induce microtubule self-renewal

The dynamic instability of microtubules is powered by the addition and removal of tubulin dimers at the ends of the microtubule. Apart from the end, the microtubule shaft is not considered to be dynamic. However recent evidence suggests that free dimers can be incorporated into the shaft of a microtubule damaged by mechanical stress. Here we explored whether dimer exchange was a core property of the microtubule lattice independently of any external constraint. We found that dimers can be removed from and incorporated into the lattice at sites along the microtubule shaft. Furthermore, we showed by experiment and by modeling that rapid dimer renewal requires structural defects in the lattice, which occur in fast growing microtubules. Hence long-lived microtubules have the capacity to self-renew despite their apparent stability and thereby can potentially regulate signaling pathways and structural rearrangements associated with tubulin-dimer exchange at sites along their entire length.

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.

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.