Wrapping transition and wrapping-mediated interactions for discrete binding along an elastic filament: An exact solution

Ordering of adsorbed rigid rods mediated by the Boussinesq interaction on a soft substrate

Orientational ordering driven by mechanical distortion of soft substrates plays a major role in material transformation processes such as elastocapillarity and surface anchoring. We present a theoretical model of the orientational response of anisotropic rods deposited onto a surface of a soft, elastic substrate of finite thickness. We show that anisotropic rods exhibit a continuous isotropic-nematic phase transition, driven by orientational interactions between surface deposited rods. This interaction is mediated by the deformation of the underlying elastic substrate and is quantified by the Boussinesq solution adapted to the case of slender, surface deposited rods. From the microscopic rod-rod interactions, we derive the appropriate Maier-Saupe mean-field description, which includes the Boussinesq elastic free energy contribution due to the substrate elasticity, derive the conditions for the existence of a continuous orientational ordering transition, and discuss the implication of results in the soft (bio)system context.

Interactions of rod-like particles on responsive elastic sheets

What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers

Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application.

Modeling DNA condensation on freestanding cationic lipid membranes

Motivated by recent experimental observations of a rapid spontaneous DNA coil-globule transition on freestanding cationic lipid bilayers, we propose simple theoretical models for DNA condensation on cationic lipid membranes. First, for a single DNA rod, we examine the conditions of full wrapping of a cylindrical DNA-like semi-flexible polyelectrolyte by an oppositely charged membrane. Then, for two parallel DNA rods, we self-consistently analyze the shape and the extent of the membrane enveloping them, focusing on membrane elastic deformations and the membrane-DNA embracing angle, which enables us to compute the membrane-mediated DNA-DNA interactions. We examine the effects of the membrane composition and its charge density, which are the experimentally tunable parameters. We show that membrane-driven rod-rod attraction is more pronounced for higher charge densities and for smaller surface tensions of the membrane. Thus, we demonstrate that for a long DNA chain adhered to a cationic lipid membrane, such membrane-induced DNA-DNA attraction can trigger compaction of DNA.

Elastocapillary interaction of particles on the surfaces of ultrasoft gels: a novel route to study self-assembly and soft lubrication

We study the interaction of small hydrophobic particles on the surface of an ultrasoft elastic gel, in which a small amount of elasticity of the medium balances the weights of the particles. The excess energy of the surface of the deformed gel causes them to attract as is the case with the generic capillary interactions of particles on a liquid surface. The variation of the gravitational potential energies of the particles resulting from their descents in the gel coupled with the superposition principle of Nicolson allow a fair estimation of the distance dependent attractive energy of the particles. This energy follows a modified Bessel function of the second kind with a characteristic elastocapillary decay length that decreases with the elasticity of the medium. An interesting finding of this study is that the particles on the gel move toward each other as if the system possesses a negative diffusivity that is inversely proportional to friction. This study illustrates how the capillary interaction of particles is modified by the elasticity of the medium, which is expected to have important implications in the surface force driven self-assembly of particles. In particular, this study points out that the range and the strength of the capillary interaction can be tuned in by appropriate choices of the elasticity of the support and the interfacial tension of the surrounding medium. Manipulation of the particle interactions is exemplified in such fascinating mimicry of the biological processes as the tubulation and phagocytic engulfment and in the assembly of particles that can be used to study nucleation and clustering phenomena in well-controlled settings.

Global analysis of the ground-state wrapping conformation of a charged polymer on an oppositely charged nano-sphere

We investigate the wrapping conformations of a single, strongly adsorbed polymer chain on an oppositely charged nano-sphere by employing a reduced (dimensionless) representation of a primitive chain-sphere model. This enables us to determine the global behavior of the chain conformation in a wide range of values for the system parameters including the chain contour length, its linear charge density and persistence length as well as the nano-sphere charge and radius, and also the salt concentration in the bathing solution. The structural behavior of a charged chain-sphere complex can be described in terms of a few distinct conformational symmetry classes separated by continuous or discontinuous transition lines which are determined by means of appropriately defined (order) parameters. Our results can be applied to a wide class of strongly coupled polymer-sphere complexes including, for instance, complexes that comprise a mechanically flexible or semiflexible polymer chain or an extremely short or long chain and, as a special case, include the biologically relevant example of DNA-histone complexes.