Recycling controls membrane domains

We study the coarsening of strongly microphase separated membrane domains in the presence of recycling of material. We study the dynamics of the domain size distribution under both scale-free and size-dependent recycling. Closed form solutions to the steady state distributions and its associated central moments are obtained in both cases. Moreover, for the size-independent case, the~time evolution of the moments is analytically calculated, which provide us with exact results for their corresponding relaxation times. Since these moments and relaxation times are measurable quantities, the biophysically significant free parameters in our model may be determined by comparison with experimental data.Comment: 5 pages, 4 figure

Composition variation and underdamped mechanics near membrane proteins and coats

We study the effect of membrane proteins on the shape, composition and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough the nearby composition and shape both undergo a transition from over-damped to under-damped spatial variation, well before the membrane becomes unstable in the bulk. This transition is associated with a change in the sign of the thermodynamic energy and hence has the unusual features that it can favour the early stages of coat assembly necessary for vesiculation (budding), while suppressing the activity of mechanosensitive membrane channels and transporters. Our results also suggest an approach to obtain physical parameters that are otherwise difficult to measure

Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure

References

The mechanical properties of phospholipid membranes have been extensively studied over the past few decades [1]. Their ability to bend under very low stress is one of the main mechanical properties of such soft materials. This softness is characterized by a very small value of the bending modulus (on the order of 10 kBT). As a result, a flaccid vesicle can attain many thermally allowed shapes at constant volume, which leads the thin-walled vesicles to fluctuate (the so-called flicker phenomenon) [1]. Measurements of these stochastic fluctuations have been used to estimate the bending modulus of red blood cells and artificial vesicles [2, 3, 4]. Here, we re-examine this methodology and discuss some of its limitations; e.g., video-microscopy gives only partial information in the sense that it provides a two-dimensional view of the three-dimensionally fluctuating vesicle. In order to overcome this technical limitation, we develop two new possible methods for inferring mechanical information about membranes from the projected intensity of fluorescent quasi-spherical vesicles