791 research outputs found
A model for enhanced and selective transport through biological membranes with alternating pores
We investigate the outflux of ions through the channels in a cell membrane.
The channels undergo an open/close cycle according to a periodic schedule. Our
study is based both on theoretical considerations relying on homogenization
theory, and on Monte Carlo numerical simulations. We examine the onset of a
limiting boundary behavior characterized by a constant ratio between the
outflux and the local density, in the thermodynamics limit. The focus here is
on the issue of selectivity, that is on the different behavior of the ion
currents through the channel in the cases of the selected and non-selected
species.Comment: arXiv admin note: text overlap with arXiv:1307.418
Flux through a time-periodic gate: Monte Carlo test of a homogenization result
We investigate via Monte Carlo numerical simulations and theoretical
considerations the outflux of random walkers moving in an interval bounded by
an interface exhibiting channels (pores, doors) which undergo an open/close
cycle according to a periodic schedule. We examine the onset of a limiting
boundary behavior characterized by a constant ratio between the outflux and the
local density, in the thermodynamic limit. We compare such a limit with the
predictions of a theoretical model already obtained in the literature as the
homogenization limit of a suitable diffusion problem
Asymptotic analysis for non-local problems in composites with different imperfect contact conditions
We consider a composite material made up of a hosting medium containing an \eps-periodic array of perfect thermal conductors. Comparing with the previous contributions in the literature, in the present paper, the inclusions are completely disconnected and form two families with dissimilar physical behaviour. More specifically, the imperfect contact between the hosting medium and the inclusions
obeys two different laws, according to the two different types of inclusions.
The contact conditions involve the small parameter \eps and two positive constants \contuno,\contdue. We investigate the homogenization limit \eps\to 0 and the limits for \contuno,\contdue going to or , taken in any order, with the aim to find out the cases in which the two limits commute
Well-posedness for a modified bidomain model describing bioelectric activity in damaged heart tissues
We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The main idea is to reduce the problem to an abstract parabolic setting, which requires to introduce several auxiliary differential systems and a non-standard bilinear form.
The main difficulties are due to the degeneracy of the bidomain system and to its non-standard coupling with the diffusion equation
Monte Carlo study of gating and selection in potassium channels
The study of selection and gating in potassium channels is a very important
issue in modern biology. Indeed such structures are known in all types of cells
in all organisms where they play many important functional roles. The mechanism
of gating and selection of ionic species is not clearly understood. In this
paper we study a model in which gating is obtained via an affinity-switching
selectivity filter. We discuss the dependence of selectivity and efficiency on
the cytosolic ionic concentration and on the typical pore open state duration.
We demonstrate that a simple modification of the way in which the selectivity
filter is modeled yields larger channel efficiency
A degenerate pseudo-parabolic equation with memory
We prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials
Homogenization results for a class of parabolic equations with a non-local interface condition via time-periodic unfolding
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