Swollen-to-globular transition of a self-avoiding polymer confined in a soft tube

Mechano-regulation by clathrin pit-formation and passive cholesterol-dependent tubules during de-adhesion

Adherent cells ensure membrane homeostasis during de-adhesion by various mechanisms, including endocytosis. Although mechano-chemical feedbacks involved in this process have been studied, the step-by-step build-up and resolution of the mechanical changes by endocytosis are poorly understood. To investigate this, we studied the de-adhesion of HeLa cells using a combination of interference reflection microscopy, optical trapping and fluorescence experiments. We found that de-adhesion enhanced membrane height fluctuations of the basal membrane in the presence of an intact cortex. A reduction in the tether force was also noted at the apical side. However, membrane fluctuations reveal phases of an initial drop in effective tension followed by saturation. The area fractions of early (Rab5-labelled) and recycling (Rab4-labelled) endosomes, as well as transferrin-labelled pits close to the basal plasma membrane, also transiently increased. On blocking dynamin-dependent scission of endocytic pits, the regulation of fluctuations was not blocked, but knocking down AP2-dependent pit formation stopped the tension recovery. Interestingly, the regulation could not be suppressed by ATP or cholesterol depletion individually but was arrested by depleting both. The data strongly supports Clathrin and AP2-dependent pit-formation to be central to the reduction in fluctuations confirmed by super-resolution microscopy. Furthermore, we propose that cholesterol-dependent pits spontaneously regulate tension under ATP-depleted conditions.

Stochastic curvature of enclosed semiflexible polymers

The conformational states of a semiflexible polymer enclosed in a compact domain of typical size a are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever 2a/ℓ_{p}>1, where ℓ_{p} is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side a is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.166102] where in this case the critical persistence length is ℓ_{p}^{*}≃a/8 such that the mean-square end-to-end distance exhibits an oscillating behavior for values ℓ_{p}>ℓ_{p}^{*}, whereas for ℓ_{p}<ℓ_{p}^{*} it behaves monotonically increasing.

Pressing soft membrane on a self-avoiding polymer against a flat wall

A polymer-membrane interacting system can produce a variety of structures. Here, we theoretically study a model system in which a membrane pushes a polymer against a hard surface; we show that a first-order structural phase transition can occur. Using a Monte Carlo simulation, we reveal that the system undergoes a transition from a confined (bump) state to a strongly confined (flattened-out) state as the pressure increases. A scaling argument is also made to understand the physical mechanism behind the phase transition and the properties of each state.

Model of a polymer chain adsorbed to a soft membrane surface

The structure of the system consisting of a self-avoiding polymer chain attracted to the surface of a freely supported soft membrane surface by a short-ranged force is investigated. The adhesion of the polymer to the deformed surface can produce distinctive states such as pancake, pinch, and bud, dependent on the phenomenological parameters in the Helfrich model describing the membrane as well as an adsorption energy describing the attraction between a monomer and a membrane surface.

Adhesion between a rigid cylindrical particle and a soft fluid membrane tube

We investigate the structure of a tubular membrane adhering to a rigid cylindrical particle, in various radius ratios. Through a theoretical and numerical analysis of a free-energy model that uses Helfrich energy for the description of the membrane, we show that three distinct phases exist, depending on the ratio between radii of the membrane tube and the rigid cylinder and an adsorption parameter describing the attraction between the cylinder and tube surface. The adhesion transition from the desorbed to weakly adhered states is identified as a second-order phase transition; the wrapping transition from the weakly adhered to strongly adhered states is identified as a first-order phase transition.

Adhesion of cylindrical colloids to the surface of a membrane

We study the system of cylindrical colloids adhering to an originally flat fluid membrane, on the basis of a full treatment of the Helfrich model. Our approach allows for numerical calculation of the free energy in both shallow- and deep-wrapping conformations. We show that the free energy of two cylinders adhering to the same side of a membrane has two branches corresponding to shallow and deep wrapping and that the system of two cylinders adhering to opposite sides of a membrane can undergo a first-order phase transition between two membrane-mediated attractive states.

Structure of a tubular membrane confining spherical particles

We investigate the structure of the system consisting of rigid spherical particles confined in a freely supported soft membrane tube. We show that a number of characteristically different phases exist depending on the phenomenological parameters in the Helfrich model describing the tubular membrane as well as an adsorption energy describing the attraction between the sphere surface and the tube interior wall.

Shapes of semiflexible polymers in confined spaces

Biological macromolecules, living in the confines of a cell, often adopt conformations that are unlikely to occur in free space. In this paper, we investigate the effects of confinement on the shape of a semiflexible chain. Results of Monte Carlo simulations show the existence of a shape transition when the persistence length of the polymer becomes comparable to the dimensions of the box. An order parameter is introduced to quantify this behavior. A simple model is constructed to study the effect of the shape transition on the effective persistence length of the polymer.