Cylindrical confinement of semiflexible polymers

Packing a flexible fiber into a cavity

The insertion of an elastic rod or fiber into a confining cavity is studied. Such an insertion is a feature of a variety of problems, including packing and unpacking of DNA in viral capsids and the insertion of catheters during surgery. We consider a simplified geometry in which the container is a smooth (frictionless) circular cylinder of radius a. The fiber is pushed through a hole in the curved surface of the cylinder and is then assumed to stay in a cross-sectional plane perpendicular to the cylinder axis. A solution is found for the fiber shape in which most of the fiber lies against the curved interior surface of the cylinder, apart from the final end section of the fiber, of length 2.0888a, which crosses the interior of the cylinder before ending at the opposite side, which it meets at an angle 1.15 rad to the normal. The force required to push the fiber into the cylinder is EI/2a^{2}, where E is the fiber's Young's modulus and I its cross-sectional moment of inertia. The shape of the final end section of the fiber is confirmed by experiment.

Dynamin's helical geometry does not destabilize membranes during fission

It is now widely accepted that dynamin-mediated fission is a fundamentally mechanical process: dynamin undergoes a GTP-dependent conformational change, constricting the neck between two compartments, somehow inducing their fission. However, the exact connection between dynamin's conformational change and the scission of the neck is still unclear. In this paper, we re-evaluate the suggestion that a change in the pitch or radius of dynamin's helical geometry drives the lipid bilayer through a mechanical instability, similar to a well-known phenomenon occurring in soap films. We find that, contrary to previous claims, there is no such instability. This lends credence to an alternative model, in which dynamin drives the membrane up an energy barrier, allowing thermal fluctuations to take it into the hemifission state.

Generalized elastica patterns in a curved rotating Hele-Shaw cell

We study a family of generalized elasticalike equilibrium shapes that arise at the interface separating two fluids in a curved rotating Hele-Shaw cell. This family of stationary interface solutions consists of shapes that balance the competing capillary and centrifugal forces in such a curved flow environment. We investigate how the emerging interfacial patterns are impacted by changes in the geometric properties of the curved Hele-Shaw cell. A vortex-sheet formalism is used to calculate the two-fluid interface curvature, and a gallery of possible shapes is provided to highlight a number of peculiar morphological features. A linear perturbation theory is employed to show that the most prominent aspects of these complex stationary patterns can be fairly well reproduced by the interplay of just two interfacial modes. The connection of these dominant modes to the geometry of the curved cell, as well as to the fluid dynamic properties of the flow, is discussed.

Constriction by Dynamin: Elasticity versus Adhesion

Any cellular fission process is completed when the neck connecting almost-separate membrane compartments is severed. This crucial step is somehow accomplished by proteins from the dynamin family, which polymerize into helical spirals around such necks. Much research has been devoted to elucidating the specifics of that somehow, but despite no shortage of ideas, the question is not settled. Pictorially obvious notions of strangling or pushing are difficult to render in mechanically precise terms. Moreover, because dynamin is a GTPase, it is tempting to speculate that it has a motor activity that assists the necessary severing action, but again the underlying mechanics is not obvious. We believe the difficulty to be the mechanically nontrivial nature of confining elastic filaments onto curved surfaces, for which efficient methods to conceptualize the associated forces and torques have only recently appeared. Here we investigate the implications of a conceptually simple yet mechanically challenging model: consider an elastic helical filament confined to a surface mimicking the neck between two membrane compartments, which we assume to take the shape of a catenoid. What can we say about the expected length of such adsorbed filaments, their shapes, and the forces they exert, as a function of the key parameters in the model? While real dynamin is surely more complex, we consider such a minimal model to be the indispensable baseline. Without knowing what such a model can and cannot explain, it is difficult to justify more complex mechanisms, or understand the constraints under which this machinery evolved in the first place.

How bio-filaments twist membranes

We study the deformations of a fluid membrane imposed by adhering stiff bio-filaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical bio-filaments. In particular, we analyse interface-mediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.

Confined semiflexible polymers suppress fluctuations of soft membrane tubes

We use Monte Carlo computer simulations to investigate tubular membrane structures with and without semiflexible polymers confined inside. At small values of membrane bending rigidity, empty fluid and non-fluid membrane tubes exhibit markedly different behavior, with fluid membranes adopting irregular, highly fluctuating shapes and non-fluid membranes maintaining extended tube-like structures. Fluid membranes, unlike non-fluid membranes, exhibit a local maximum in specific heat as their bending rigidity increases. The peak is coincident with a transition to extended tube-like structures. We further find that confining a semiflexible polymer within a fluid membrane tube reduces the specific heat of the membrane, which is a consequence of suppressed membrane shape fluctuations. Polymers with a sufficiently large persistence length can significantly deform the membrane tube, with long polymers leading to localized bulges in the membrane that accommodate regions in which the polymer forms loops. Analytical calculations of the energies of idealized polymer-membrane configurations provide additional insight into the formation of polymer-induced membrane deformations.

Curvature-induced crosshatched order in two-dimensional semiflexible polymer networks

A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-two-dimensional (2D) geometries adopt a characteristic order: the fibers wrap around the central axis at an angle which varies with radius and, in several cases, is strongly bimodally distributed. In this Rapid Communication, we investigate the general problem of a 2D crosslinked network of semiflexible fibers confined to a cylindrical substrate, and demonstrate that in such systems the trade-off between bending and stretching energies, very generically, gives rise to crosshatched order. We discuss its general dependency on the radius of the confining cylinder, and present an intuitive model that illustrates the basic physical principle of curvature-induced order. Our findings shed new light on the potential origin of some curiously universal fiber orientational distributions in tissue biology, and suggests novel ways in which synthetic polymeric soft materials may be instructed or programmed to exhibit preselected macromolecular ordering.