Deformation of membrane vesicles due to chiral surface proteins

Chiral, rod-like molecules can self-assemble into cylindrical membrane tubules and helical ribbons. They have been successfully modeled using the theory of chiral nematics. Models have also predicted the role of chiral lipids in forming nanometer-sized membrane buds in the cell. However, in most theoretical studies, the membrane shapes are considered fixed (cylinder, sphere, saddle, etc.), and their optimum radius of curvatures are found variationally by minimizing the energy of the composite system consisting of membrane and chiral nematics. Numerical simulations have only recently started to consider membrane deformation and chiral orientation simultaneously. Here we examine how deformable, closed membrane vesicles and chiral nematic rods mutually influence each other's shape and orientation, respectively, using Monte-Carlo (MC) simulation on a closed triangulated surface. For this, we adopt a discrete form of chiral interaction between rods, originally proposed by Van der Meer et al. (1976) for off-lattice simulations. In our simulation, both conical and short cylindrical tubules emerge, depending on the strength of the chiral interaction and the intrinsic chirality of the molecules. We show that the Helfrich-Prost term, which couple nematic tilt with local membrane curvature in continuum models, can account for most of the observations in the simulation. At higher chirality, our theory also predicts chiral tweed phase on cones, with varying bandwidths.

Beyond the Kármán gait: knifefish swimming in periodic and irregular vortex streets

Neotropical freshwater fishes such as knifefishes are commonly faced with navigating intense and highly unsteady streams. However, our knowledge on locomotion in apteronotids comes from laminar flows, where the ribbon fin dominates over pectoral fins or body bending. Here, we studied the 3D kinematics and swimming control of seven black ghost knifefish (Apteronotus albifrons) moving in laminar flows (flow speed U∞∼1 – 5 Bl/s) and in periodic vortex streets (U∞∼2 – 4 Bl/s). Two different cylinders (∼2 and ∼3 cm diameter) were used to generate the latter. Additionally, fish were exposed to an irregular wake produced by a free oscillating cylinder (∼2 cm diameter; U∞∼2 Bl/s). In laminar flows knifefish mainly used their ribbon fin, with wave frequency, speed and acceleration increasing with U∞. In contrast, knifefish swimming behind a fixed cylinder increased the use of pectoral fins and resulted in changes in body orientation that mimicked steady backward swimming. Meanwhile, individuals behind the oscillating cylinder presented a combination of body bending, ribbon and pectoral fins movements that counteract the out-of-phase yaw oscillations induced by the irregular shedding of vortices. We corroborated passive out-of-phase oscillations by placing a printed knifefish model just downstream of the moving cylinder but, when placed one-cylinder diameter downstream, the model oscillated in phase. Thus, the wake left behind an oscillating body is more challenging than a periodic vortex shedding for an animal located downstream, which may have consequences on inter- and intra-specific interactions.

Nonlinear oscillations of a pendulum wrapped around a cylinder

The large oscillations of a pendulum are studied. The pendulum is a material point that is suspended on an elastic cord with nonlinear characteristics. The mass of the cord is accepted. It is wrapped around a perfectly rigid and fixed cylinder. The system has two degrees of freedom. Nonlinearity is due to a geometric and physical nature. A system of two differential nonlinear equations is derived. A numerical solution was performed with the mathematical package MATLAB. The laws of motion, the generalized velocities and accelerations and the phase trajectories are obtained. In order to continue the task by preparing an actual model and conducting experimental research, the projections of the velocity and acceleration of the material point along the horizontal and vertical axes, as well as their magnitudes, are determined. The obtained results are presented graphically and analysed in detail.