RESUMEN
Small unilamellar vesicles (20-100â nm diameter) are model systems for strongly curved lipid membranes, in particular for cell organelles. Routinely, small-angle X-ray scattering (SAXS) is employed to study their size and electron-density profile (EDP). Current SAXS analysis of small unilamellar vesicles (SUVs) often employs a factorization into the structure factor (vesicle shape) and the form factor (lipid bilayer electron-density profile) and invokes additional idealizations: (i) an effective polydispersity distribution of vesicle radii, (ii) a spherical vesicle shape and (iii) an approximate account of membrane asymmetry, a feature particularly relevant for strongly curved membranes. These idealizations do not account for thermal shape fluctuations and also break down for strong salt- or protein-induced deformations, as well as vesicle adhesion and fusion, which complicate the analysis of the lipid bilayer structure. Presented here are simulations of SAXS curves of SUVs with experimentally relevant size, shape and EDPs of the curved bilayer, inferred from coarse-grained simulations and elasticity considerations, to quantify the effects of size polydispersity, thermal fluctuations of the SUV shape and membrane asymmetry. It is observed that the factorization approximation of the scattering intensity holds even for small vesicle radii (â¼30â nm). However, the simulations show that, for very small vesicles, a curvature-induced asymmetry arises in the EDP, with sizeable effects on the SAXS curve. It is also demonstrated that thermal fluctuations in shape and the size polydispersity have distinguishable signatures in the SAXS intensity. Polydispersity gives rise to low-q features, whereas thermal fluctuations predominantly affect the scattering at larger q, related to membrane bending rigidity. Finally, it is shown that simulation of fluctuating vesicle ensembles can be used for analysis of experimental SAXS curves.
RESUMEN
The topological effect of noncrossability of long flexible macromolecules is effectively described by a slip-spring model, which represents entanglements by local, pairwise, translationally invariant interactions that do not alter any equilibrium properties. We demonstrate that the model correctly describes many aspects of the dynamical and rheological behavior of entangled polymer liquids, such as segmental mean-square displacements and shear thinning, in a computationally efficient manner. Furthermore, the model can account for the reduction of entanglements under shear.
RESUMEN
The scaling behavior of the diffusion front, originated by the random motion of particles under a concentration gradient, is studied by means of the Monte Carlo method and solving the diffusion equation. Simulations are performed on the square lattice using confined geometries of size MxL, where the gradient is established along the M direction while periodic boundary conditions are set along the L direction. A dynamic scaling Ansatz is proposed such as the width of the front [w(M,t)] scales as w(M,t) approximately M(alpha)f(t/M(alpha/beta)), where alpha and beta are the roughness and growing exponents, respectively. This proposal is based on the fact that the development of w is constrained by the gradient, that decays as M(-1), in contrast to the standard Family-Vicsek scaling Ansatz where correlations are constrained by the lateral dimension of the sample. It is found that the roughness exponent exhibits a systematic dependence on the sample size that can be rationalized in terms of a finite-size correction. Extrapolation to the thermodynamic limit gives alpha=4/7, in excellent agreement with theoretical predictions linking the diffusion system to the percolation problem. The evaluation of the growing exponent gives beta=0.30+/-0.02, leading us to the conjecture beta=2/7 for the exact value.