Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Three-dimensional organization of fenestrae labyrinths in liver sinusoidal endothelial cells

- Background/Aims Liver sinusoidal endothelial cell (LSEC) fenestrae are membrane-bound pores that are grouped in sieve plates and act as a bidirectional guardian in regulating transendothelial liver transport. The high permeability of the endothelial lining is explained by the presence of fenestrae and by various membrane-bound transport vesicles. The question as to whether fenestrae relate to other transport compartments remains unclear and has been debated since their discovery almost 40 years ago. - Methods In this study, novel insights concerning the three-dimensional (3D) organization of the fenestrated cytoplasm were built on transmission electron tomographical observations on isolated and cultured whole-mount LSECs. Classical transmission electron microscopy and atomic force microscopy imaging was performed to accumulate cross-correlative structural evidence. - Results and Conclusions The data presented here indicate that different arrangements of fenestrae have to be considered: i.e. open fenestrae that lack any structural obstruction mainly located in the thin peripheral cytoplasm and complexes of multifolded fenestrae organized as labyrinth-like structures that are found in the proximity of the perinuclear area. Fenestrae in labyrinths constitute about one-third of the total LSEC porosity. The 3D reconstructions also revealed that coated pits and small membrane-bound vesicles are exclusively interspersed in the non-fenestrated cytoplasmic arms.