Circuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilizing circuit topology relations, namely parallel, series, cross,... Show moreCircuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilizing circuit topology relations, namely parallel, series, cross, and concerted relations. In this article, we further develop this approach to facilitate the analysis of chirality, which is a significant quantity in polymer chemistry. To achieve this, we translate the circuit topology approach to knot engineering into a braid-theoretic framework. This enables us to calculate the Jones polynomial for all possible binary combinations of contacts in cross or concerted relations and to show that, for series and parallel relations, the polynomial factorises. Our results demonstrate that the Jones polynomial provides a powerful tool for analysing the chirality of molecular knots constructed using circuit topology. The framework presented here can be used to design and engineer a wide range of entangled chain with desired chiral properties, with potential applications in fields such as materials science and nanotechnology. Show less
To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces... Show moreTo develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. Our model incorporates active stresses due to a prescribed orientation profile of the cytoskeleton, coupling with the substrate, surface tension and imposed boundary forces. We find a highly non-linear response to forces that we characterise using the drop velocity, its shape, and the traction between the drop and the substrate. There are two main modes of motion: a long and thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. There is a sharp transition between these two modes as a function of the applied forces and indications of drop break-up where large forces stretch the drop in opposite directions. Show less
We investigate the possibility for self-propelled particles to crystallize without reducing their intrinsic speed. We illuminate how, in the absence of any force, the competition between self... Show moreWe investigate the possibility for self-propelled particles to crystallize without reducing their intrinsic speed. We illuminate how, in the absence of any force, the competition between self-propulsion and repulsive torques determines the macroscopic phases of constant-speed active particles. This minimal model expands upon existing approaches for an improved understanding of crystallization of active matter. Show less
Synthetic microswimmers are widely employed model systems in the studies of out-of-equilibrium phenomena. Unlike biological microswimmers which naturally occur in various shapes and forms,... Show moreSynthetic microswimmers are widely employed model systems in the studies of out-of-equilibrium phenomena. Unlike biological microswimmers which naturally occur in various shapes and forms, synthetic microswimmers have so far been limited almost exclusively to spherical shapes. Here, we exploit 3D printing to produce microswimmers with complex shapes in the colloidal size regime. We establish the flexibility of 3D printing by two-photon polymerisation to produce particles smaller than 10 microns with a high-degree of shape complexity. We further demonstrate that 3D printing allows control over the location of the active site through orienting the particles in different directions during printing. We verify that particles behave colloidally by imaging their motion in the passive and active states and by investigating their mean square displacement. In addition, we find that particles exhibit shape-dependant behavior, thereby demonstrating the potential of our method to launch a wide-range of in-depth studies into shape-dependent active motion and behaviour. Show less
Schakenraad K., Ernst J., Pomp W., Danen E.H.J., Merks R.M.H., Schmidt T., Giomi L. 2020
We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical... Show moreWe investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells. Show less
Delivery of naked DNA molecules into living cells via physical disruption of the membrane under electric pulses has potential biomedical applications ranging from gene electro-transfer, electro... Show moreDelivery of naked DNA molecules into living cells via physical disruption of the membrane under electric pulses has potential biomedical applications ranging from gene electro-transfer, electro-chemotherapy, to gene therapy, yet the mechanisms involved in DNA transport remain vague. To investigate the mechanism of DNA translocation across the cell membrane, giant unilamellar vesicles (GUVs) were electroporated in the presence of DNA molecules keeping the size of the DNA molecules as a variable parameter. We experimentally determined the translocation efficiency for each size of the DNA molecule, to compare the results with the existing and conflicting theories of the translocation mechanism i.e. stochastic threading and bulk electrophoresis. We observed that the translocation efficiency is independent of DNA size (ranging from 25-20 000 bp, bp = base pairs), implying that DNA molecules translocate freely across the electro-pores in the lipid membrane in their native polymer conformation, as opposed to unravelling and threading through the electro-pore. Bulk electrophoretic mobility determines the relationship between translocation efficiency and the size of the DNA molecule. This research provides experimental evidence of the mechanistic understanding of DNA translocation across lipid membranes which is essential for devising efficient and predictable protocols for electric field mediated naked DNA delivery. Show less
Hoffmann, L.A.; Schakenraad, K.K.; Merks, R.M.H.; Giomi, L. 2019
Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are... Show moreRecent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation. Show less
Lovrak, M.; Hendriksen, W.E.; Kreutzer, M.T.; Steijn, V. van; Eelkema, R.; Esch, J.H. van 2019
Controlled diffusion, reaction and assembly of hydrogelator precursors can be used to create soft hydrogel objects of defined shape and size. In this study we show that controlling local reaction... Show moreControlled diffusion, reaction and assembly of hydrogelator precursors can be used to create soft hydrogel objects of defined shape and size. In this study we show that controlling local reaction kinetics by means of pH, diffusion length and the concentrations of reactants allows control over the dimensions of formed supramolecular structures. By correlating a reaction diffusion model to experimental results, we show that the influence of all these control parameters can be unified using the Damko hler number, thus providing an easy-to-use relation between experimental parameters and structure dimensions. Finally, our study suggests that control over concentration gradients and chemical reactivity in combination with supramolecular chemistry is a promising platform for the design of soft matter objects of defined sizes, a concept that has received little attention up until now. Show less
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical... Show moreWe study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis–Menten kinetics that governs the motion of individual kinesin motors. Show less
Rinaldin, M.; Verweij, R.W.; Chakraborty, I.; Kraft, D.J. 2018
The use of colloid supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that enable the assembly of structures with internal degrees of flexibility, and to study... Show moreThe use of colloid supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that enable the assembly of structures with internal degrees of flexibility, and to study lipid membranes on curved and closed geometries. These novel applications of CSLBs rely on previously unappreciated properties: the simultaneous fluidity of the bilayer, lateral mobility of inserted (linker) molecules and colloidal stability. Here we characterize every step in the manufacturing of CSLBs in view of these requirements using confocal microscopy and fluorescence recovery after photobleaching (FRAP). Specifically, we have studied the influence of different particle properties (roughness, surface charge, chemical composition, polymer coating) on the quality and mobility of the supported bilayer. We find that the insertion of lipopolymers in the bilayer can affect its homogeneity and fluidity. We improve the colloidal stability by inserting lipopolymers or double-stranded inert DNA into the bilayer. We include surface-mobile DNA linkers and use FRAP to characterize their lateral mobility both in their freely diffusive and bonded state. Finally, we demonstrate the self-assembly of flexibly linked structures from the CSLBs modified with surface-mobile DNA linkers. Our work offers a collection of experimental tools for working with CSLBs in applications ranging from controlled bottom-up self-assembly to model membrane studies. Show less
Molecular conformations of individual polymers during flow through porous media are directly observed by single-DNA imaging in microfluidics. As the Weissenberg number increases during flow (Wi >... Show moreMolecular conformations of individual polymers during flow through porous media are directly observed by single-DNA imaging in microfluidics. As the Weissenberg number increases during flow (Wi > 1), we observe two types of elastic instabilities: (a) stationary dead-zone and (b) time-dependant dead-zone washing. When stretched polymer chains enter a dead-zone, they first re-coil and, once inside the dead-zone, they rotate and re-stretch again. The probability distribution of DNA chains under the stretched condition inside the dead-zone is found to be heterogeneous with a broad distribution. Show less
Dagois-Bohy, S.P.M.; Somfai, E.; Tighe, B.P.; Hecke, M.L. van 2017
