A human septin octamer complex sensitive to membrane curvature drives membrane deformation with a specific mesh-like organization.

Septins are cytoskeletal proteins interacting with the inner plasma membrane and other cytoskeletal partners. Being key in membrane remodeling processes, they often localize at specific micrometric curvatures. To analyze the behavior of human septins at the membrane and decouple their role from other partners, we used a combination of bottom-up in vitro methods. We assayed their ultrastructural organization, their curvature sensitivity, as well as their role in membrane reshaping. On membranes, human septins organize into a two-layered mesh of orthogonal filaments, instead of generating parallel sheets of filaments observed for budding yeast septins. This peculiar mesh organization is sensitive to micrometric curvature and drives membrane reshaping as well. The observed membrane deformations together with the filamentous organization are recapitulated in a coarse-grained computed simulation to understand their mechanisms. Our results highlight the specific organization and behavior of animal septins at the membrane as opposed to those of fungal proteins.

Dynamics and Stability of the Contractile Actomyosin Ring in the Cell.

Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the midplane of the dividing cell. Assuming boundary driven alignment of the actomyosin filaments at the inner edge of the interface, we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on closure rate. Using these solutions, we perform linear stability analysis for the contracting ring under nonaxisymmetric deformations. Our analysis shows that few low wave number modes, which are unstable during onset of the constriction, later on become stable when the ring shrinks to smaller radii, which is a generic feature of actomyosin ring closure. Our theory also captures how the effective tension in the ring decreases with its radius, causing significant slowdown in the contraction process at later times.

Dynamic surface patterns on cells.

Dynamic pattern formations are commonly observed in multicellular systems, such as cardiac tissue and slime molds, and modeled using reaction-diffusion systems. Recent experiments have revealed dynamic patterns in the concentration profile of various cortical proteins at a much smaller scale, namely, embryos at their single-cell stage. Spiral waves of Rho and F-actin proteins have been reported in Xenopus frog and starfish oocytes [Bement et al., Nat. Cell Biol. 17, 1471 (2015)], while a pulsatile pattern of Rho and myosin proteins has been found in C. elegans embryo [Nishikawa et al., eLife 6, e30537 (2017)]. Here, we propose that these two seemingly distinct dynamic patterns are signatures of a single reaction-diffusion network involving active-Rho, inactive-Rho, actin, and myosin. We show that a small variation in the concentration of other ancillary proteins can give rise to different dynamical states from the same chemical network.

Temperature-dependent self-assembly of biofilaments during red blood cell sickling.

Molecular self-assembly plays a vital role in various biological functions. However, when aberrant molecules self-assemble to form large aggregates, it can give rise to various diseases. For example, sickle cell disease and Alzheimer's disease are caused by self-assembled hemoglobin fibers and amyloid plaques, respectively. Here, we study the assembly kinetics of such fibers using kinetic Monte Carlo simulation. We focus on the initial lag time of these highly stochastic processes, during which self-assembly is very slow. The lag time distributions turn out to be similar for two very different regimes of polymerization, namely, (a) when polymerization is slow and depolymerization is fast and (b) the opposite case, when polymerization is fast and depolymerization is slow. Using temperature-dependent on- and off-rates for hemoglobin fiber growth, reported in recent in vitro experiments, we show that the mean lag time can exhibit non-monotonic behavior with respect to the change in temperature.

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 radii 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., for off-lattice simulations. In our simulation, both conical and short cylindrical tubules emerge, depending on the membrane stiffness and the intrinsic chirality of the molecules. We show that the Helfrich-Prost term, which couples 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 a chiral tweed phase on cones, with varying bandwidths.

Poiseuille Flow of Soft Polycrystals in 2D Rough Channels.

Polycrystals are partially ordered solids where crystalline order extends over mesoscopic length scales, namely, the grain size. We study the Poisuielle flow of such materials in a rough channel. In general, similar to yield stress fluids, three distinct dynamical states, namely, flowing, stick-slip, and jammed can be observed, with a yield threshold dependent on channel width. Importantly, the interplay between the finite channel width, and the intrinsic ordering scale (the grain size) leads to a new type of spatiotemporal heterogeneity. In wide channels, although the average flow profile remains pluglike, at the underlying granular level, there is vigorous grain remodeling activity resulting from the velocity heterogeneity among the grains. As the channel width approaches typical grain size, the flowing polycrystalline state breaks up into a spatially heterogeneous mixture of flowing liquid like patches and chunks of nearly static grains. Despite these static grains, the average velocity still shows a parabolic profile, dominated by the moving liquidlike patches. However, the solid-liquid front moves at nearly constant speed in the opposite direction of the external drive.

Confined filaments in soft vesicles - the case of sickle red blood cells.

Abnormal shapes of red blood cells (RBC) have been associated with various diseases. Diverse RBC shapes have also been intriguing for membrane biophysics. Here we focus on sickle shaped RBC which form due to abnormal growth of semi-rigid hemoglobin (HbS) fibers confined in RBC. Using the area difference elasticity (ADE) model for RBC and worm-like chain model for the confined HbS fibers, we explore shape deformations at equilibrium using Monte-Carlo simulations. We show that while a single HbS fiber is not rigid enough to produce sickle like deformation, a fiber bundle can do so. We also consider multiple disjoint filaments and find that confinement can generate multipolar RBC shapes and can even promote helical filament conformations which have not been discussed before. We show that the same model, when applied to microtubules confined in phospholipid vesicles, predicts vesicle tubulation. In addition we reproduce the tube collapse transition and tennis racket type vesicle shapes, as reported in experiments. We conclude that with a decrease in the surface area to volume ratio, and membrane rigidity, the vesicles prefer tubulation over sickling. The highlight of this work is several important non-axisymmetric RBC and vesicle shapes, which have never been explored in simulations.

Chiral molecules on curved colloidal membranes.

Colloidal membranes, self assembled monolayers of aligned rod like molecules, offer a template for designing membranes with definite shapes and curvature, and possibly new functionalities in the future. Often the constituent rods, due to their molecular chirality, are tilted with respect to the membrane normal. Spatial patterns of this tilt on curved membranes result from a competition among depletion forces, nematic interactions, molecular chirality and boundary effects. We present a covariant theory for the tilt pattern on minimal surfaces, like helicoids and catenoids, which have been generated in the laboratory only recently. We predict several non-uniform tilt patterns, some of which are consistent with experimental observations and some, which are yet to be discovered.

Non-Gaussian subdiffusion of single-molecule tracers in a hydrated polymer network.

Single molecule tracking experiments inside a hydrated polymer network have shown that the tracer motion is subdiffusive due to the viscoelastic environment inside the gel-like network. This property can be related to the negative autocorrelation of the instantaneous displacements at short times. Although the displacements of the individual tracers exhibit Gaussian statistics, the displacement distribution of all the trajectories combined from different spatial locations of the polymer network exhibits a non-Gaussian distribution. Here, we analyze many individual tracer trajectories to show that the central portion of the non-Gaussian distribution can be well approximated by an exponential distribution that spreads sublinearly with time. We explain all these features seen in the experiment by a generalized Langevin model for an overdamped particle with algebraically decaying correlations. We show that the degree of non-Gaussianity can change with the extent of heterogeneity, which is controlled in our model by the experimentally observed distributions of the motion parameters.

Asymmetric Flows in the Intercellular Membrane during Cytokinesis.

Eukaryotic cells undergo shape changes during their division and growth. This involves flow of material both in the cell membrane and in the cytoskeletal layer beneath the membrane. Such flows result in redistribution of phospholipid at the cell surface and actomyosin in the cortex. Here we focus on the growth of the intercellular surface during cell division in a Caenorhabditis elegans embryo. The growth of this surface leads to the formation of a double-layer of separating membranes between the two daughter cells. The division plane typically has a circular periphery and the growth starts from the periphery as a membrane invagination, which grows radially inward like the shutter of a camera. The growth is typically not concentric, in the sense that the closing internal ring is located off-center. Cytoskeletal proteins anillin and septin have been found to be responsible for initiating and maintaining the asymmetry of ring closure but the role of possible asymmetry in the material flow into the growing membrane has not been investigated yet. Motivated by experimental evidence of such flow asymmetry, here we explore the patterns of internal ring closure in the growing membrane in response to asymmetric boundary fluxes. We highlight the importance of the flow asymmetry by showing that many of the asymmetric growth patterns observed experimentally can be reproduced by our model, which incorporates the viscous nature of the membrane and contractility of the associated cortex.

Dynamic force balances and cell shape changes during cytokinesis.

During the division of animal cells, an actomyosin ring is formed in the cell cortex. The contraction of this ring induces shape changes of the cell and the formation of a cytokinesis furrow. In many cases, a cell-cell interface forms that separates the two new cells. Here we present a simple physical description of the cell shape changes and the dynamics of the interface closure, based on force balances involving active stresses and viscous friction. We discuss conditions in which the interface closure is either axially symmetric or asymmetric. We show that our model can account for the observed dynamics of ring contraction and interface closure in the C. elegans embryo.

Stuttering Min oscillations within E. coli bacteria: a stochastic polymerization model.

We have developed a 3D off-lattice stochastic polymerization model to study the subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding and fragmentation of MinD filaments due to MinE. Processivity, protection and fragmentation each reduce stuttering, speed oscillations and MinD filament lengths. Neither processivity nor tip protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations is consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization under experimental conditions.

Self-organization of the MinE protein ring in subcellular Min oscillations.

We model the self-organization of the MinE ring that is observed during subcellular oscillations of the proteins MinD and MinE within the rod-shaped bacterium Escherichia coli. With a steady-state approximation, we can study the MinE ring generically--apart from the other details of the Min oscillation. Rebinding of MinE to depolymerizing MinD-filament tips controls MinE-ring formation through a scaled cell shape parameter r. We find two types of E-ring profiles near the filament tip: either a strong plateaulike E ring controlled by one-dimensional diffusion of MinE along the bacterial length or a weak cusplike E ring controlled by three-dimensional diffusion near the filament tip. While the width of a strong E ring depends on r, the occupation fraction of MinE at the MinD-filament tip is saturated and hence the depolymerization speed does not depend strongly on r. Conversely, for weak E rings both r and the MinE to MinD stoichiometry strongly control the tip occupation and hence the depolymerization speed. MinE rings in vivo are close to the threshold between weak and strong, and so MinD-filament depolymerization speed should be sensitive to cell shape, stoichiometry, and MinE-rebinding rate. We also find that the transient to MinE-ring formation is quite long in the appropriate open geometry for assays of ATPase activity in vitro, explaining the long delays of ATPase activity observed for smaller MinE concentrations in those assays without the need to invoke cooperative MinE activity.

Tubulation pattern of membrane vesicles coated with biofilaments.

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.

Effect of hydrodynamic interaction on partially stretched polymers.

We compute the effect of hydrodynamic interaction and stretching on the fluctuation properties of a polymer, with its end points held fixed. Computing the preaveraged hydrodynamic tensor exactly for this geometry, we study both flexible and semiflexible polymer chains, such as Zimm, freely jointed chain, and wormlike chain (WLC) models. We compare the spectra of relaxation-time scales for the effective normal modes of these models. The spectra differ across models with respect to the degree of stretch, but their power-law scaling with low mode numbers turns out to be the same. The characteristics of the transverse modes of WLC agree very well with the experimental data on DNA. The crossover scaling function for (1/r), the inverse of the distance along the polymer contour, yields a modified formula for the size of a "Pincus blob," appropriate for the fixed-end boundary condition.

Curvature instability of chiral colloidal membranes on crystallization.

Buckling and wrinkling instabilities are failure modes of elastic sheets that are avoided in the traditional material design. Recently, a new paradigm has appeared where these instabilities are instead being utilized for high-performance applications. Multiple approaches such as heterogeneous gelation, capillary stresses, and confinement have been used to shape thin macroscopic elastic sheets. However, it remains a challenge to shape two-dimensional self-assembled monolayers at colloidal or molecular length scales. Here, we show the existence of a curvature instability that arises during the crystallization of finite-sized monolayer membranes of chiral colloidal rods. While the bulk of the membrane crystallizes, its edge remains fluid like and exhibits chiral ordering. The resulting internal stresses cause the flat membrane to buckle macroscopically and wrinkle locally. Our results demonstrate an alternate pathway based on intrinsic stresses instead of the usual external ones to assemble non-Euclidean sheets at the colloidal length scale.

Rupture of an extended object: a many-body Kramers calculation.

We show how an extended object's strain field is redistributed when the material ruptures under by thermal activation. Through analytical calculations and molecular dynamics simulations, we show that in a polymer chain the distribution is exponentially localized around the point of rupture. The length scale of localization is determined by the strain and microscopic parameters of the interaction potential. We also derive an analytic expression for the rate of bond rupture by consistently treating the collective modes of the chain and the effect of dissipation on those modes. Our theoretical estimates are of the same order of magnitude as those obtained by simulations, as compared to earlier theories which had overestimated the rate of rupture by approximately two orders of magnitude. It is also noteworthy that the correction comes about through the effective attempt frequency rather than the effective barrier height.

Shape transitions during clathrin-induced endocytosis.

Endocytosis is among the most common transport mechanisms which cells employ to receive macromolecules, the so-called cargo, from its extra cellular environment. Clathrin-mediated endocytosis (CME), in particular, involves the cytoplasmic protein clathrin which induces formation and internalization of clathrin-coated membrane buds that contain extra-cellular cargo. Decades of experimental work have established that the morphology of the clathrin coat evolves with time and induces its curvature on the membrane bud; but energetics of the process remain unclear. Recent experiments by Avinoam et al. [Science 348, 1369 (2015)SCIEAS0036-807510.1126/science.aaa9555] reported that the area of the clathrin coat remains fixed while its curvature increases with time and also the clathrin molecules in the coat turn over rapidly. We show that these observations challenge existing models of coated membrane bud formation. We analyze their data to bring out certain features consistent with the underlying lattice structure of the coat. We hypothesize that membrane curvature inhibits clathrin deposition and propose a kinetic model that explains the area distribution of clathrin coats. We also show that their data on shape evolution of the coated membrane bud can be approximately understood from simple geometric considerations. However, the energetics of the coat formation which controls the kinetics of the process remains a puzzle.

Influence of tether dynamics on forced Kramers escape from a kinetic trap.

When a trapped particle is subject to the tension of a massive frictional spring (the "tether"), the escape rate increases due to a lowering of the escape barrier. However, in addition, the escape-rate prefactor is influenced by the mass and drag contributed by the spring. We solve the full Kramers escape problem for the coupled system using a technique attributed to Langer. The prefactor in the escape rate is significantly modified by the spring parameters even in the strong-damping limit. The biophysical relevance of this problem is briefly discussed.

Chain persistency in single-stranded DNA.

We develop a theoretical approach to hairpin-loop formation of single-stranded (ss) DNA by treating the strand as a two-state system in which bases are either "stacked" or "unstacked." The looping kinetics of ssDNA is shown to be intrinsically different from that of a wormlike chain; it is mainly controlled by stacking-breakage probability, not by the mean curvature of loops, and highly sensitive to the composition of the loop as seen in recent experiments. Our estimate of a stacking energy for poly ( dA ), -3.9 kcal/mol, is consistent with known results.