Transport of solid bodies along tubular membrane tethers

We study the crucial role of membrane fluctuations in maintaining a narrow gap between a fluid membrane tube and an enclosed solid particle. Solvent flows can occur in this gap, hence giving rise to a finite particle mobility along the tube. While our study has relevance for how cells are able to transport large organelles or other cargo along connecting membrane tubes, known as tunneling nanotubes, our calculations are also framed so that they can be tested by a specific in vitro experiment: A tubular membrane tether can be pulled from a membrane reservoir, such as an aspirated Giant Unilamellar Vesicle (GUV), e.g. using a conjugated bead that binds to the membrane and is held in a laser trap. We compute the subsequent mobility of colloidal particles trapped in the tube, focusing on the case when the particle is large compared to the equilibrium tube radius. We predict that the particle mobility should scale as ∼ σ^−2/3, with σ the membrane tension.

Linear rheology as a potential monitoring tool for sputum in patients with Chronic Obstructive Pulmonary Disease (COPD)

BACKGROUND

The rheological properties of sputum may influence lung function and become modified in disease.

OBJECTIVE

This study aimed to correlate the viscoelastic properties of sputum with clinical data on the severity of disease in patients with chronic obstructive pulmonary disease (COPD).

METHODS

Sputum samples from COPD patients were investigated using rheology, simple mathematical modelling and Scanning Electron Microscopy (SEM). The samples were all collected from patients within two days of their admission to Prince Philip Hospital due to an exacerbation of their COPD. Oscillatory and creep rheological techniques were used to measure changes in viscoelastic properties at different frequencies over time.

RESULTS

COPD sputum was observed to behave as a viscoelastic solid at all frequencies studied. Comparing the rheology of exacerbated COPD sputum with healthy sputum (not diagnosed with a respiratory disease) revealed significant differences in response to oscillatory shear and creep-recovery experiments, which highlights the potential clinical benefits of better understanding sputum viscoelasticity. A common power law model G(t)=G0(tτ0)-m was successfully fitted to experimental rheology data over the range of frequencies studied.

CONCLUSIONS

A comparison between clinical data and the power law index m obtained from rheology, suggested that an important possible future application of this parameter is as a potential biomarker for COPD severity.

Curvature correction to the mobility of fluid membrane inclusions

Using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces, we provide, via a Stokeslet-type approach, a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions.

Theory of simple biochemical "shape recognition" via diffusion from activator coated nanoshapes

Inspired by recent experiments, we model the shape sensitivity, via a typical threshold initiation response, of an underlying complex biochemical reaction network to activator coated nanoshapes. Our theory re-emphasizes that shape effects can be vitally important for the onset of functional behavior in nanopatches and nanoparticles. For certain critical or particular shapes, activator coated nanoshapes do not evoke a threshold response in a complex biochemical network setting, while for different critical or specific shapes, the threshold response is rapidly achieved. The model thus provides a general theoretical understanding for how activator coated nanoshapes can enable a chemical system to perform simple "shape recognition," with an associated "all or nothing" response. The novel and interesting cases of the chemical response due to a nanoshape that shrinks with time is additionally considered, as well as activator coated nanospheres. Possible important applications of this work include the initiation of blood clotting by nanoshapes, nanoshape effects in nanocatalysis, physiological toxicity to nanoparticles, as well as nanoshapes in nanomedicine, drug delivery, and T cell immunological response. The aim of the theory presented here is that it inspires further experimentation on simple biochemical shape recognition via diffusion from activator coated nanoshapes.

Monomer depletion, pressure difference, and membrane tube radius reduction due to fiber polymerization in microspikes

In many processes vital to life, the growth of biological fibers outwards from a membrane surface naturally produces membrane tube tethers or microspikes in biological cells. Here, we investigate the novel effect of pressure difference (due to monomer depletion) on the polymerization dynamics of biological fibers within long membrane tubes. We crucially find that fiber monomers become depleted close to the growing tip as the fiber polymerizes, thus reducing the local pressure, and hence decreasing the membrane tube radius at the tip. This process is found to slow the growth of the fiber, a process which becomes important when we go on to construct a dynamical theory for biopolymer growth in long, narrow tubes. Our result is interesting in that it emphasizes how "passive" biological transport mechanisms such as via pressure differences may play an important role in cell movements.

Deforming biological membranes: how the cytoskeleton affects a polymerizing fiber

We give a theoretical treatment of the force exerted by a fluctuating membrane on a polymer rod tip, taking into account the effects of an underlying biological cytoskeleton by way of a simple harmonic dependence on displacement. We also consider theoretically and experimentally the dynamics of a growing fiber tip under the influence of such a fluctuation-induced membrane force, including the effects of an underlying cytoskeletal network. We compare our model with new experimental data for the growth of hemoglobin fibers within red blood cells, revealing a good agreement. We are also able to estimate the force and membrane/cytoskeletal displacement required to stall growth of, or buckle, a growing fiber. We discuss the significance of our results in a biological context, including how the properties of the membrane and cytoskeleton relate to the thermodynamics of rod polymerization.

Diffusion on membrane tubes: a highly discriminatory test of the Saffman-Delbruck theory

The efficient transport of membrane proteins is vital in maintaining life. In this work, we investigate the transport of such membrane proteins along long thin membrane tubes or tethers. We calculate the diffusion constant to leading order in the low Reynolds number regime to be D = (4 pi eta)-1 log(r/a), with r and a being the tube and protein radii, respectively, and eta being the membrane viscosity. Thus we propose an exact limiting form for the controversial logarithmic correction, such as originally introduced by Saffman and Delbruck, that involves the tube radius rather than some "frame size". Our work suggests a test of this logarithmic correction could be achieved by measuring diffusion on membrane tubes, exploiting the fact that the equilibrium tube radius can be controlled by the membrane tension and varied over several orders of magnitude. We analyze the time taken for a protein to transit a membrane tube between cells and find that this can vary by an order of magnitude over physiological tensions. This is a strong effect in biological terms and suggests a possible regulatory coupling between membrane tension and signaling.

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

We study the dynamics of a growing semiflexible fiber approaching a membrane at an angle. At late times we find three regimes: fiber stalling, when growth stops, runaway, in which the fiber bends away from the membrane, and another regime in which spicules form. We discuss which regions of the resulting "phase diagram" are explored by (i) single and bundled actin fibers in living cells, (ii) sickle hemoglobin fibers, and (iii) microtubules inside vesicles. We complement our analysis with 3D stochastic simulations.

Spicules and the effect of rigid rods on enclosing membrane tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force f exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between f approximately square root of (sigma) and f approximately sigma as the membrane tension sigma increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.

The force generated by biological membranes on a polymer rod and its response: Statics and dynamics

We propose a theory for the force exerted by a fluctuating membrane on a polymer rod tip. Using statistical mechanical methods, the expression for the generated force is written in terms of the distance of the rod tip from the membrane "frame." We apply the theory in calculating the stall force and membrane displacement required to cease the growth of a growing fiber induced by membrane fluctuations, as well as the membrane force and membrane displacement required for rod/fiber buckling. We also consider the dynamics of a growing fiber tip under the influence of a fluctuation-induced membrane force. We discuss the importance of our results in various biological contexts. Finally, we present a method to simultaneously extract both the rigidity of the semiflexible rod and the force applied by, e.g., the membrane from the measurements of the bending fluctuations of the rod. Such a measurement of the force would give information about the thermodynamics of the rod polymerization that involves the usual Brownian ratchet mechanism.

An improved model for analyzing the small angle x-ray scattering of starch granules

The structure of starch was studied using small-angle x-ray scattering (SAXS). The scattering data was modeled by considering a finite stack of alternating lamellae that are allowed to fluctuate both along the layer repeat direction and along the transverse layer direction. Analysis in this way of the SAXS data from starch allowed fresh insights into the native structure of several starch species, particularly potato starch. The novel model presented in this work was able to capture the experimentally observed SAXS patterns much better than previous models, which did not incorporate transverse layer fluctuations.