Stall, spiculate, or run away: The fate of fibers growing towards fluctuating membranes

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.

Snap-buckling in asymmetrically constrained elastic strips

When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking, forming a cylindrical arc. This is a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called "snap-through buckling" and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating mechanical behaviors, including largely hysteretic but reproducible force responses and switchlike discontinuous shape changes. We establish the set of exact analytical solutions to fully explain all our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end. The introduction of asymmetry through boundary conditions yields new insight into complex and programmable functionalities in material and industrial design.

Slip Morphology of Elastic Strips on Frictional Rigid Substrates

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

Modelling the effect of myosin X motors on filopodia growth

We present a numerical simulation study of the dynamics of filopodial growth in the presence of active transport by myosin X motors. We employ both a microscopic agent-based model, which captures the stochasticity of the growth process, and a continuum mean-field theory which neglects fluctuations. We show that in the absence of motors, filopodia growth is overestimated by the continuum mean-field theory. Thus fluctuations slow down the growth, especially when the protrusions are driven by a small number (10 or less) of F-actin fibres, and when the force opposing growth (coming from membrane elasticity) is large enough. We also show that, with typical parameter values for eukaryotic cells, motors are unlikely to provide an actin transport mechanism which enhances filopodial size significantly, unless the G-actin concentration within the filopodium greatly exceeds that of the cytosol bulk. We explain these observations in terms of order-of-magnitude estimates of diffusion-induced and advection-induced growth of a bundle of Brownian ratchets.

The physical foundation of vasoocclusion in sickle cell disease

The pathology of sickle cell disease arises from the occlusion of small blood vessels because of polymerization of the sickle hemoglobin within the red cells. We present measurements using a microfluidic method we have developed to determine the pressure required to eject individual red cells from a capillary-sized channel after the cell has sickled. We find that the maximum pressure is only ∼100 Pa, much smaller than typically found in the microcirculation. This explains why experiments using animal models have not observed occlusion beginning in capillaries. The magnitude of the pressure and its dependence on intracellular concentration are both well described as consequences of sickle hemoglobin polymerization acting as a Brownian ratchet. Given the recently determined stiffness of sickle hemoglobin gels, the observed obstruction seen in sickle cell disease as mediated by adherent cells can now be rationalized, and surprisingly suggests a window of maximum vulnerability during circulation of sickle cells.

Quantifying the rheological and hemodynamic characteristics of sickle cell anemia

Sickle erythrocytes exhibit abnormal morphology and membrane mechanics under deoxygenated conditions due to the polymerization of hemoglobin S. We employed dissipative particle dynamics to extend a validated multiscale model of red blood cells (RBCs) to represent different sickle cell morphologies based on a simulated annealing procedure and experimental observations. We quantified cell distortion using asphericity and elliptical shape factors, and the results were consistent with a medical image analysis. We then studied the rheology and dynamics of sickle RBC suspensions under constant shear and in a tube. In shear flow, the transition from shear-thinning to shear-independent flow revealed a profound effect of cell membrane stiffening during deoxygenation, with granular RBC shapes leading to the greatest viscosity. In tube flow, the increase of flow resistance by granular RBCs was also greater than the resistance of blood flow with sickle-shape RBCs. However, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into simulations that partially trapped sickle RBCs, which led to full occlusion in some cases.

Cell spreading as a hydrodynamic process

Many cell types have the ability to move themselves by crawling on extra-cellular matrices. Although cell motility is governed by actin and myosin filament assembly, the pattern of the movement follows the physical properties of the network ensemble average. The first step of motility, cell spreading on matrix substrates, involves a transition from round cells in suspension to polarized cells on substrates. Here we show that the spreading dynamics on 2D surfaces can be described as a hydrodynamic process. In particular, we show that the transition from isotropic spreading at early time to anisotropic spreading is reminiscent of the fingering instability observed in many spreading fluids. During cell spreading, the main driving force is the polymerization of actin filaments that push the membrane forward. From the equilibrium between the membrane force and the cytoskeleton, we derive a first order expression of the polymerization stress that reproduces the observed behavior. Our model also allows an interpretation of the effects of pharmacological agents altering the polymerization of actin. In particular we describe the influence of Cytochalasin D on the nucleation of the fingering instability.