arXiv subjects

Karin John

Publications and source records attributed to Karin John.

17 recordsLinked to original sources

arXiv2025

Beyond the tip: Lattice dynamics, seams, and the mechanism of microtubule fracture

The structural integrity of microtubules is paramount for cellular function. We present a theoretical analysis of their lattice fracture, focusing on the influence of multi-seam structures arising from monomer defects and aiming to provide a more accurate estimation of GDP lattice parameters. Our findings reveal that seams function as pre-existing pathways that accelerate damage propagation. Consequently, monomer vacancies destabilize the lattice due to the inherent structural loss of tubulin-tubulin contacts and the additive acceleration of fracture through multiple seams. Importantly, the comparison of our simulations with experiments on lattice fracture suggests that the intrinsic ratio of longitudinal to lateral binding energies is bounded at approximately 1.5, challenging previous predictions of lattice anisotropy from tip-growth models and highlighting the urgent need to incorporate into current growth models parameters obtained from lattice dynamics.

physics.bio-ph↗

arXiv2024

The role of substrate mechanics in osmotic biofilm spreading

Bacteria invade surfaces by forming dense colonies encased in a polymer matrix. Successful settlement of founder bacteria, early microcolony development and later macroscopic spreading of these biofilms on surfaces rely on complex physical mechanisms. Recent data show that on soft hydrogels, substrate rigidity is an important determinant for biofilm initiation and spreading, through mostly unknown mechanisms. Using a thermodynamically consistent thin-film approach for suspensions on soft elastic surfaces supplemented with biomass production we investigate in silico the role of substrate softness in the osmotic spreading of biofilms. We show that on soft substrates with an imposed osmotic pressure spreading is considerably slowed down and may be completely halted depending on the biomass production rate. We find, that the critical slowing down of biofilm spreading on soft surfaces is caused by a reduced osmotic influx of solvent into the biofilm at the edges, which results from the thermodynamic coupling between substrate deformation and interfacial forces. By linking substrate osmotic pressure and mechanical softness through scaling laws, our simple model semi-quantitatively captures a range of experimentally observed biofilm spreading dynamics on hydrogels with different architectures, underscoring the importance of inherent substrate properties in the spreading process.

cond-mat.soft↗

arXiv2022

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.

physics.bio-ph↗

arXiv2022

Molecular motors enhance microtubule lattice plasticity

Microtubules are key structural elements of living cells that are crucial for cell division, intracellular transport and motility. Recent experiments have shown that microtubule severing proteins and molecular motors stimulate the direct and localized incorporation of free tubulin into the shaft. However, a mechanistic picture how microtubule associated proteins affect the lattice is completely missing. Here we theoretically explore a potential mechanism of lattice turnover stimulated by processive molecular motors in which a weak transient destabilization of the lattice by the motor stepping promotes the formation of mobile vacancies. In the absence of free tubulin the defect rapidly propagates leading to a complete fracture. In the presence of free tubulin, the motor walk induces a vacancy drift in the direction opposite of the motor walk. The drift is accompanied by the direct and localized incorporation of free tubulin along the trajectory of the vacancy. Our results are consistent with experiments and strongly suggest that a weak lattice-motor interaction is responsible for an augmented microtubule shaft plasticity.

cond-mat.soft↗

arXiv2021

Thin-Film Modelling 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 profile 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 contact line motion. The model reproduces moving and resting states of polarized droplets: Drops containing domains of opposite polarization are stationary and evolve after long transients into drops with a uniform polarization moving actively over the substrate. In our simple two-dimensional scenario droplet motion sets in at infinitely small self-propulsion force, i.e., it does not need to overcome a critical threshold.

physics.flu-dyn↗

arXiv2018

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.

physics.bio-ph↗

arXiv2018

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-Dupré equation. It relates the interfacial energies with the macroscopic contact angle $θ_e$. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy $f(h)$. Macro- and mesoscale description are consistent if $γ\cos θ_\mathrm{e} =γ+f(h_\mathrm{a})$ where $γ$ and $h_\mathrm{a}$ 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 non-trivial dependence of $θ_\mathrm{e}$ on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are only consistent 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.

physics.flu-dyn↗

arXiv2016

Persistent vs. arrested spreading of biofilms at solid-gas interfaces - the role of surface forces

We introduce and analyze a model for osmotically spreading biofilm colonies at solid-air interfaces that includes wetting phenomena, i.e. surface forces. The model combines a hydrodynamic description for biologically passive liquid suspensions with bioactive processes. We show that wetting effects are responsible for a transition between persistent and arrested spreading and provide experimental evidence for the existence of this transition for Bacillus subtilis biofilms growing on agar substrates. In the case of arrested spreading, the biofilm is non-invasive albeit being biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading.

physics.bio-ph↗

arXiv2016

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 bacteria 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 describes 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 disjoining pressure and can therefore give insight into the interplay between passive surface forces and bioactive growth processes.

physics.bio-ph↗

arXiv2014

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechano-chemical coupling

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechano-chemical coupling mechanisms which 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.

cond-mat.soft↗

arXiv2010

A constitutive law for cross-linked actin networks by homogenization techniques

Inspired by experiments on the actin driven propulsion of micrometer sized beads we develop and study a minimal mechanical model of a two-dimensional network of stiff elastic filaments grown from the surface of a cylinder. Starting out from a discrete model of the network structure and of its microscopic mechanical behavior we derive a macroscopic constitutive law by homogenization techniques. We calculate the axisymmetric equilibrium state and study its linear stability depending on the microscopic mechanical properties. We find that thin networks are linearly stable, whereas thick networks are unstable. The critical thickness for the change in stability depends on the ratio of the microscopic elastic constants. The instability is induced by the increase in the compressive load on the inner network layers as the thickness of the network increases. The here employed homogenization approach combined with more elaborate microscopic models can serve as a basis to study the evolution of polymerizing actin networks and the mechanism of actin driven motion.

cond-mat.soft↗

arXiv2010

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'.

cond-mat.soft↗

arXiv2009

Actin based propulsion: Intriguing interplay between material properties and growth processes

Eukaryotic cells and intracellular pathogens such as bacteria or viruses utilize the actin polymerization machinery to propel themselves forward. Thereby, the onset of motion and choice of direction may be the result of a spontaneous symmetry-breaking or might be triggered by external signals and preexisting asymmetries, e.g. through a previous septation in bacteria. Although very complex, a key feature of cellular motility is the ability of actin to form dense polymeric networks, whose microstructure is tightly regulated by the cell. These polar actin networks produce the forces necessary for propulsion but may also be at the origin of a spontaneous symmetry-breaking. Understanding the exact role of actin dynamics in cell motility requires multiscale approaches which capture at the same time the polymer network structure and dynamics on the scale of a few nanometers and the macroscopic distribution of elastic stresses on the scale of the whole cell. In this chapter we review a selection of theories on how mechanical material properties and growth processes interact to induce the onset of actin based motion.

cond-mat.soft↗

arXiv2009

Self-ratcheting Stokes drops driven by oblique vibrations

We develop and analyze a minimal hydrodynamic model in the overdamped limit to understand why a drop climbs a smooth homogeneous incline that is harmonically vibrated at an angle different from the substrate normal [Brunet, Eggers and 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, in consequence, in the observed net motion. Beside establishing the basic mechanism, we identify scaling laws valid in a broad frequency range and a flow reversal at high frequencies.

cond-mat.soft↗

arXiv2006

Alternative mechanisms of structuring biomembranes: Self-assembly vs. self-organization

We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to a nonequilibrium biochemical reaction cycle of proteins near the membrane. While both processes lead eventually to quite similar patterns, their evolution occurs on very different length and time scales. Self-assembly produces periodic protein patterns on a spatial scale below 0.1 micron in a few seconds followed by extremely slow coarsening, whereas self-organization results in a pattern wavelength comparable to the typical cell size of 100 micron within a few minutes suggesting different biological functions for the two processes.

q-bio.CB↗

arXiv2006

Liquid transport generated by a flashing field-induced wettability ratchet

We develop and analyze a model for ratchet-driven macroscopic transport of a continuous phase. The transport relies on a field-induced dewetting-spreading cycle of a liquid film with a free surface based on a switchable, spatially asymmetric, periodic interaction of the liquid-gas interface and the substrate. The concept is exemplified using an evolution equation for a dielectric liquid film under an inhomogeneous voltage. We analyse the influence of the various phases of the ratchet cycle on the transport properties. Conditions for maximal transport and the efficiency of transport under load are discussed.

physics.flu-dyn↗

arXiv2004

Dynamical Model for Chemically Driven Running Droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets -- reaction-limited and saturated regime -- are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.

cond-mat.soft↗