Greg Huber

Fluid-membrane tethers: Minimal surfaces and elastic boundary layers

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

Stacked Endoplasmic Reticulum Sheets Are Connected by Helicoidal Membrane Motifs

The endoplasmic reticulum (ER) often forms stacked membrane sheets, an arrangement that is likely required to accommodate a maximum of membrane-bound polysomes for secretory protein synthesis. How sheets are stacked is unknown. Here, we used improved staining and automated ultrathin sectioning electron microscopy methods to analyze stacked ER sheets in neuronal cells and secretory salivary gland cells of mice. Our results show that stacked ER sheets form a continuous membrane system in which the sheets are connected by twisted membrane surfaces with helical edges of left- or right-handedness. The three-dimensional structure of tightly stacked ER sheets resembles a parking garage, in which the different levels are connected by helicoidal ramps. A theoretical model explains the experimental observations and indicates that the structure corresponds to a minimum of elastic energy of sheet edges and surfaces. The structure allows the dense packing of ER sheets in the restricted space of a cell.

Kinematics of the Swimming of Spiroplasma

Spiroplasma swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to interkink length and pitch angle, we find that the optimal pitch angle is 35.5 degrees and the optimal interkink length ratio is 0.338, values in good agreement with experimental observations.

Vesicle-like biomechanics governs important aspects of nuclear geometry in fission yeast.

It has long been known that during the closed mitosis of many unicellular eukaryotes, including the fission yeast (Schizosaccharomyces pombe), the nuclear envelope remains intact while the nucleus undergoes a remarkable sequence of shape transformations driven by elongation of an intranuclear mitotic spindle whose ends are capped by spindle pole bodies embedded in the nuclear envelope. However, the mechanical basis of these normal cell cycle transformations, and abnormal nuclear shapes caused by intranuclear elongation of microtubules lacking spindle pole bodies, remain unknown. Although there are models describing the shapes of lipid vesicles deformed by elongation of microtubule bundles, there are no models describing normal or abnormal shape changes in the nucleus. We describe here a novel biophysical model of interphase nuclear geometry in fission yeast that accounts for critical aspects of the mechanics of the fission yeast nucleus, including the biophysical properties of lipid bilayers, forces exerted on the nuclear envelope by elongating microtubules, and access to a lipid reservoir, essential for the large increase in nuclear surface area during the cell cycle. We present experimental confirmation of the novel and non-trivial geometries predicted by our model, which has no free parameters. We also use the model to provide insight into the mechanical basis of previously described defects in nuclear division, including abnormal nuclear shapes and loss of nuclear envelope integrity. The model predicts that (i) despite differences in structure and composition, fission yeast nuclei and vesicles with fluid lipid bilayers have common mechanical properties; (ii) the S. pombe nucleus is not lined with any structure with shear resistance, comparable to the nuclear lamina of higher eukaryotes. We validate the model and its predictions by analyzing wild type cells in which ned1 gene overexpression causes elongation of an intranuclear microtubule bundle that deforms the nucleus of interphase cells.

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of +2 are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

Optimal Filling of Shapes

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

Swimming in Flatsea.

Some of the simplest questions are the hardest to answer. Why flags flap is a long-standing puzzle that becomes easier to solve in a two-dimensional world.

Epinephrine Modulates BCAM/Lu and ICAM-4 Expression on the Sickle Cell Trait Red Blood Cell Membrane

Collapse and sudden death in physical training are the most serious complications of sickle cell trait (SCT). There is evidence that erythrocytes in SCT patients aggregate during strenuous exercise, likely because of adhesive interactions with the extracellular matrix (ECM) and endothelial cells, and because of their irregular viscoelastic properties. This results in inflammation, blood flow impairment, and vaso-occlusive events. However, the exact role of stress conditions and how they lead to these complications is virtually unknown. Using single-molecule atomic force microscopy experiments, we found that epinephrine, a hormone that is secreted under stressful conditions, increases both the frequency and strength of adhesion events between basal cell adhesion molecule (BCAM/Lu) and ECM laminin, and between intercellular adhesion molecule-4 (ICAM-4) and endothelial α(v)β(3), compared with nonstimulated SCT erythrocytes. Increases in adhesion frequency provide significant evidence of the role of epinephrine in BCAM/Lu-laminin and ICAM-4-α(v)β(3) bonding, and suggest mechanisms of vaso-occlusion during physical exertion in SCT.

Micro-swimmers with hydrodynamic interactions

The low-Reynolds-number motions of Purcells three-link swimmer, and of a closely related two-paddle swimmer, are investigated and compared using slender-body theory and resistive-force theory. The results are compared (in the case of the three-link swimmer) with the resistive-force calculations of Becker, Koehler and Stone (BKS). In particular, we examine the effect of hydrodynamic interaction and slenderness on the displacement and efficiency of the swimmers. The BKS analysis is, for the most part, confirmed and extended. However, deviations of up to 43% are found in cases where the swimmer propels itself with large stroke angles. Finally, we discuss recent experimental data in light of our numerical results.

Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses.

The hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Self-similarity in the solutions is discussed as well.