Exogenous lysophospholipids with large head groups perturb clathrin-mediated endocytosis.

In this study, we have investigated how clathrin-dependent endocytosis is affected by exogenously added lysophospholipids (LPLs). Addition of LPLs with large head groups strongly inhibits transferrin (Tf) endocytosis in various cell lines, while LPLs with small head groups do not. Electron and total internal reflection fluorescence microscopy (EM and TIRF) reveal that treatment with lysophosphatidylinositol (LPI) with the fatty acyl group C18:0 leads to reduced numbers of invaginated clathrin-coated pits (CCPs) at the plasma membrane, fewer endocytic events per membrane area and increased lifetime of CCPs. Also, endocytosis of Tf becomes dependent on actin upon LPI treatment. Thus, our results demonstrate that one can regulate the kinetics and properties of clathrin-dependent endocytosis by addition of LPLs in a head group size- and fatty acyl-dependent manner. Furthermore, studies performed with optical tweezers show that less force is required to pull membrane tubules outwards from the plasma membrane when LPI is added to the cells. The results are in agreement with the notion that insertion of LPLs with large head groups creates a positive membrane curvature which might have a negative impact on events that require plasma membrane invagination, while it may facilitate membrane bending toward the cell exterior.

Dynamin recruitment by clathrin coats: a physical step?

Recent structural findings have shown that dynamin, a cytosol protein playing a key-role in clathrin-mediated endocytosis, inserts partly within the lipid bilayer and tends to self-assemble around lipid tubules. Taking into account these observations, we make the hypothesis that individual membrane-inserted dynamins imprint a local cylindrical curvature to the membrane. This imprint may give rise to long-range mechanical forces mediated by the elasticity of the membrane. Calculating the resulting many-body interaction between a collection of inserted dynamins and a membrane bud, we find a regime in which the dynamins are elastically recruited by the bud to form a collar around its neck, which is reminiscent of the actual process preempting vesicle scission. This physical mechanism might therefore be implied in the recruitment of dynamins by clathrin coats.

Knots in charged polymers.

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.

Tightness of slip-linked polymer chains.

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

Fluctuations of the Casimir-like force between two membrane inclusions.

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d2. This distance dependence shares a common physical origin with the Casimir force itself.

The many-body problem for anisotropic membrane inclusions and the self-assembly of "saddle" defects into an "egg carton".

We calculate the many-body, nonpairwise interaction between N rigid, anisotropic membrane inclusions by modeling them as point-like constraints on the membrane's curvature tensor and by minimizing the membrane's curvature energy. Because multipolar distortions of higher-order decay on very short distances, our calculation gives the correct elastic interaction energy for inclusions separated by distances of the order of several times their size. As an application, we show by thermally equilibrating the many-body elastic energy using a Monte Carlo algorithm, that inclusions shaped as "saddles" attract each other and build an "egg-carton" structure. The latter is reminiscent of some patterns observed in membranes obtained from biological extracts, the origin of which is still mysterious.

Helical packaging of semiflexible polymers in bacteriophages.

We investigate multilayered helical packaging of double-stranded DNA, or of a general polymer chain with persistence length lb, into an ideal, inert cylindrical container, reaching densities slightly below close packaging. We calculate the free energy as a function of the packaged length, based on the energies for bending, twisting, the suffered entropy loss, and the electrostatic energy in a Debye-Hückel model. In the absence of charges on the packaged polymer, a critical packaging force can be determined, similar to the mechanism involved in DNA unzipping models. When charges are taken into consideration, in the final packaging state the charges which are chemically distant become geometrically close, and therefore a steep rise is seen in the free energy. We argue that due to the extremely ordered and almost closely packaged final state the actual packaging geometry does not influence the behaviour of the free energy, pointing towards a certain universality of this state of the polymer. Our findings are compared to a recent simulations study, showing that the model is sensitive to the screening length.

Equilibrium shapes of flat knots.

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.