41 research outputs found
A continuum membrane model for small deformations of a spider orb-web
In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider web. The model is derived in the simple context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane static equilibrium and the free transverse and in-plane vibration of a supported circular orb-web are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated.Part of this work has been developed during visits of A. Morassi to the Department of Continuum Mechanics and Structural Analysis of the Universidad Carlos III de Madrid in the years 2015 and 2016. A. Morassi wishes to thank the colleagues for the warm hospitality at UC3M; his work was developed within the National Research Project PRIN2015 Identificazione e diagnostica di sistemi strutturali complessi, whose financial support is gratefully acknowledged. The authors of the Universidad Carlos III de Madrid are indebted to the Ministerio de Economía y Competitividad de España for financial support under grant DPI2014-57989-P
A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins
Membrane proteins constitute a large portion of the human proteome and
perform a variety of important functions as membrane receptors, transport
proteins, enzymes, signaling proteins, and more. The computational studies of
membrane proteins are usually much more complicated than those of globular
proteins. Here we propose a new continuum model for Poisson-Boltzmann
calculations of membrane channel proteins. Major improvements over the existing
continuum slab model are as follows: 1) The location and thickness of the slab
model are fine-tuned based on explicit-solvent MD simulations. 2) The highly
different accessibility in the membrane and water regions are addressed with a
two-step, two-probe grid labeling procedure, and 3) The water pores/channels
are automatically identified. The new continuum membrane model is optimized (by
adjusting the membrane probe, as well as the slab thickness and center) to best
reproduce the distributions of buried water molecules in the membrane region as
sampled in explicit water simulations. Our optimization also shows that the
widely adopted water probe of 1.4 {\AA} for globular proteins is a very
reasonable default value for membrane protein simulations. It gives an overall
minimum number of inconsistencies between the continuum and explicit
representations of water distributions in membrane channel proteins, at least
in the water accessible pore/channel regions that we focus on. Finally, we
validate the new membrane model by carrying out binding affinity calculations
for a potassium channel, and we observe a good agreement with experiment
results.Comment: 40 pages, 6 figures, 5 table
A proposal for a membrane model for the small deformations of a spider orb-web
Abstract In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider orb-web. The model is derived in the context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. The continuous model inherits a specific fibrous structure from the original discrete web. In particular, a singularity arises at the centre of the membrane as a consequence of the intensification of the density of radial threads towards the centre of the web. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane free transverse vibrations of a circular orb-web supported at the boundary are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated
Wrapping of ellipsoidal nano-particles by fluid membranes
Membrane budding and wrapping of particles, such as viruses and
nano-particles, play a key role in intracellular transport and have been
studied for a variety of biological and soft matter systems. We study
nano-particle wrapping by numerical minimization of bending, surface tension,
and adhesion energies. We calculate deformation and adhesion energies as a
function of membrane elastic parameters and adhesion strength to obtain
wrapping diagrams. We predict unwrapped, partially-wrapped, and
completely-wrapped states for prolate and oblate ellipsoids for various aspect
ratios and particle sizes. In contrast to spherical particles, where
partially-wrapped states exist only for finite surface tensions,
partially-wrapped states for ellipsoids occur already for tensionless
membranes. In addition, the partially-wrapped states are long-lived, because of
an increased energy cost for wrapping of the highly-curved tips. Our results
suggest a lower uptake rate of ellipsoidal particles by cells and thereby a
higher virulence of tubular viruses compared with icosahedral viruses, as well
as co-operative budding of ellipsoidal particles on membranes.Comment: 10 pages, 11 figure
Backmapping triangulated surfaces to coarse-grained membrane models
Many biological processes involve large-scale changes in membrane shape. Computer simulations of these processes are challenging since they occur across a wide range of spatiotemporal scales that cannot be investigated in full by any single current simulation technique. A potential solution is to combine different levels of resolution through a multiscale scheme. Here, we present a multiscale algorithm that backmaps a continuum membrane model represented as a dynamically triangulated surface (DTS) to its corresponding molecular model based on the coarse-grained (CG) Martini force field. Thus, we can use DTS simulations to equilibrate slow large-scale membrane conformational changes and then explore the local properties at CG resolution. We demonstrate the power of our method by backmapping a vesicular bud induced by binding of Shiga toxin and by transforming the membranes of an entire mitochondrion to near-atomic resolution. Our approach opens the way to whole cell simulations at molecular detail
Electrostatic forces on charged surfaces of bilayer lipid membranes
Simulating protein-membrane interactions is an important and dynamic area of
research. A proper definition of electrostatic forces on membrane surfaces is
necessary for developing electromechanical models of protein-membrane
interactions. Here we modeled the bilayer membrane as a continuum with general
continuous distributions of lipids charges on membrane surfaces. A new
electrostatic potential energy functional was then defined for this solvated
protein-membrane system. We investigated the geometrical transformation
properties of the membrane surfaces under a smooth velocity field. These
properties allows us to apply the Hadamard-Zolesio structure theorem, and the
electrostatic forces on membrane surfaces can be computed as the shape
derivative of the electrostatic energy functional