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1. A continuum membrane model can predict curvature sensing by helix insertion

   https://doi.org/10.1039/d1sm01333e  

   Fu, Yiben ; Zeno, Wade F. ; Stachowiak, Jeanne C. ; Johnson, Margaret E. ( December 2021 , Soft Matter)

   Protein domains, such as ENTH (epsin N-terminal homology) and BAR (bin/amphiphysin/rvs), contain amphipathic helices that drive preferential binding to curved membranes. However, predicting how the physical parameters of these domains control this ‘curvature sensing’ behavior is challenging due to the local membrane deformations generated by the nanoscopic helix on the surface of a large sphere. We here use a deformable continuum model that accounts for the physical properties of the membrane and the helix insertion to predict curvature sensing behavior, with direct validation against multiple experimental datasets. We show that the insertion can be modeled as a local change tomore »the membrane's spontaneous curvature, c ins0, producing excellent agreement with the energetics extracted from experiments on ENTH binding to vesicles and cylinders, and of ArfGAP helices to vesicles. For small vesicles with high curvature, the insertion lowers the membrane energy by relieving strain on a membrane that is far from its preferred curvature of zero. For larger vesicles, however, the insertion has the inverse effect, de-stabilizing the membrane by introducing more strain. We formulate here an empirical expression that accurately captures numerically calculated membrane energies as a function of both basic membrane properties (bending modulus κ and radius R ) as well as stresses applied by the inserted helix ( c ins0 and area A ins ). We therefore predict how these physical parameters will alter the energetics of helix binding to curved vesicles, which is an essential step in understanding their localization dynamics during membrane remodeling processes.« less
2. Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers

   https://doi.org/10.1039/D1SM00827G  

   Jia, Leroy L. ; Pei, Steven ; Pelcovits, Robert A. ; Powers, Thomas R. ( August 2021 , Soft Matter)

   We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a soap film. In our problem, we find infinitely many branches of solutions for the shape and external force as functions of the separation of the rings, analogous to the infinite family of eigenmodes for the Euler buckling of a slender rod. Special attention is paid to the catenoid, which emerges as the shape of maximal allowable separation when the area ismore »less than a critical area equal to the planar area enclosed by the two rings. A perturbation theory argument directly relates the tension of catenoidal membranes to the stability of catenoidal soap films in this regime. When the membrane area is larger than the critical area, we find additional cylindrical tether solutions to the shape equations at large ring separation, and that arbitrarily large ring separations are possible. These results apply for the case of vanishing Gaussian curvature modulus; when the Gaussian curvature modulus is nonzero and the area is below the critical area, the force and the membrane tension diverge as the ring separation approaches its maximum value. We also examine the stability of our shapes and analytically show that catenoidal membranes have markedly different stability properties than their soap film counterparts.« less
3. Deformation and orientational order of chiral membranes with free edges

   https://doi.org/10.1039/d1sm00629k  

   Ding, Lijie ; Pelcovits, Robert A. ; Powers, Thomas R. ( July 2021 , Soft Matter)

   Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to simulate these systems and determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl–Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. Themore »beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist.« less
4. Slender body theory for particles with non-circular cross-sections with application to particle dynamics in shear flows

   https://doi.org/10.1017/jfm.2019.625  

   Borker, Neeraj S. ; Koch, Donald L. ( October 2019 , Journal of Fluid Mechanics)

   This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ( $A=l/a_{0}$ ) is defined as the ratio of the particle size ( $l$ ) to the cross-sectional dimensionmore »( $a_{0}$ ) and $\unicode[STIX]{x1D6FC}$ is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e. $\unicode[STIX]{x1D6FC}\sim O(1)$ ). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section, and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios ( ${\sim}10$ ) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers.« less
5. A comprehensive mathematical model for nanofibre formation in centrifugal spinning methods

   https://doi.org/10.1017/jfm.2020.196  

   Noroozi, S. ; Arne, W. ; Larson, R. G. ; Taghavi, S. M. ( June 2020 , Journal of Fluid Mechanics)

   Motivated by our experimental observations of nanofibre formation via the centrifugal spinning process, we develop a string model to study the behaviours of a Newtonian, viscous curved jet, in a non-orthogonal curvilinear coordinate system including both air-drag effects and solvent evaporation for the first time. In centrifugal spinning a polymeric solution emerges from the nozzle of a spinneret rotating at high speeds around its axis of symmetry and thins as it moves away from the nozzle exit until it finally lands on the collector. Except for the Newtonian fluid assumption, our model includes the key parameters of the curved jetmore »flow, e.g. viscous, inertial, rotational, surface tension, gravitational, mass diffusion within the jet, mass diffusion into air and aerodynamic effects, via Rossby ( $Rb$ ), Reynolds ( $Re$ ), Weber ( $We$ ), Froude ( $Fr$ ), Péclet ( $Pe$ ), air Reynolds ( $Re^{\ast }$ ) and air Péclet ( $Pe^{\ast }$ ) numbers, and the collector radial position ( ${\mathcal{R}}$ ). Our results, including comparison to experiments, reveal that the aerodynamic effects must be considered to enable a correct prediction of the jet trajectory and radius. Decreasing $Rb$ not only renders the jet thinning much faster, but also forces the jet to wrap tighter around the rotation axis. Increasing $Re$ , $Re^{\ast }$ and ${\mathcal{R}}$ leads to a longer jet. Decreasing $We$ causes the jet to wrap tighter around the spinneret but it shows trivial effects on the solvent evaporation. Changes in $Pe$ and $Pe^{\ast }$ do not significantly affect the jet trajectory. Finally, we propose simple relations to estimate the jet radius and the jet breakup length.« less