118 research outputs found
Mean encounter times for cell adhesion in hydrodynamic flow: analytical progress by dimensional reduction
For a cell moving in hydrodynamic flow above a wall, translational and
rotational degrees of freedom are coupled by the Stokes equation. In addition,
there is a close coupling of convection and diffusion due to the
position-dependent mobility. These couplings render calculation of the mean
encounter time between cell surface receptors and ligands on the substrate very
difficult. Here we show for a two-dimensional model system how analytical
progress can be achieved by treating motion in the vertical direction by an
effective reaction term in the mean first passage time equation for the
rotational degree of freedom. The strength of this reaction term can either be
estimated from equilibrium considerations or used as a fit parameter. Our
analytical results are confirmed by computer simulations and allow to assess
the relative roles of convection and diffusion for different scaling regimes of
interest.Comment: Reftex, postscript figures include
Coexistence of dilute and densely packed domains of ligand-receptor bonds in membrane adhesion
We analyze the stability of micro-domains of ligand-receptor bonds that
mediate the adhesion of biological model membranes. After evaluating the
effects of membrane fluctuations on the binding affinity of a single bond, we
characterize the organization of bonds within the domains by theoretical means.
In a large range of parameters, we find the commonly suggested dense packing to
be separated by a free energy barrier from a regime in which bonds are sparsely
distributed. If bonds are mobile, a coexistence of the two regimes should
emerge, which agrees with recent experimental observations.Comment: 6 pages, 6 figures, accepted by EP
Lateral diffusion of a protein on a fluctuating membrane
Measurements of lateral diffusion of proteins in a membrane typically assume
that the movement of the protein occurs in a flat plane. Real membranes,
however, are subject to thermal fluctuations, leading to movement of an
inclusion into the third dimension. We calculate the magnitude of this effect
by projecting real three-dimensional diffusion onto an effective one on a flat
plane. We consider both a protein that is free to diffuse in the membrane and
one that also couples to the local curvature. For a freely diffusing inclusion
the measured projected diffusion constant is up to 15% smaller than the actual
value. Coupling to the curvature enhances diffusion significantly up to a
factor of two.Comment: 6 pages, 4 figure
Diffusion of active tracers in fluctuating fields
The problem of a particle diffusion in a fluctuating scalar field is studied.
In contrast to most studies of advection diffusion in random fields we analyze
the case where the particle position is also coupled to the dynamics of the
field. Physical realizations of this problem are numerous and range from the
diffusion of proteins in fluctuating membranes and the diffusion of localized
magnetic fields in spin systems. We present exact results for the diffusion
constant of particles diffusing in dynamical Gaussian fields in the adiabatic
limit where the field evolution is much faster than the particle diffusion. In
addition we compute the diffusion constant perturbatively, in the weak coupling
limit where the interaction of the particle with the field is small, using a
Kubo-type relation. Finally we construct a simple toy model which can be solved
exactly.Comment: 13 pages, 1 figur
Brownian motion meets Riemann curvature
The general covariance of the diffusion equation is exploited in order to
explore the curvature effects appearing on brownian motion over a d-dimensional
curved manifold. We use the local frame defined by the so called Riemann normal
coordinates to derive a general formula for the mean-square geodesic distance
(MSD) at the short-time regime. This formula is written in terms of
invariants that depend on the Riemann curvature tensor. We study the
n-dimensional sphere case to validate these results. We also show that the
diffusion for positive constant curvature is slower than the diffusion in a
plane space, while the diffusion for negative constant curvature turns out to
be faster. Finally the two-dimensional case is emphasized, as it is relevant
for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure
Curvature-coupling dependence of membrane protein diffusion coefficients
We consider the lateral diffusion of a protein interacting with the curvature
of the membrane. The interaction energy is minimized if the particle is at a
membrane position with a certain curvature that agrees with the spontaneous
curvature of the particle. We employ stochastic simulations that take into
account both the thermal fluctuations of the membrane and the diffusive
behavior of the particle. In this study we neglect the influence of the
particle on the membrane dynamics, thus the membrane dynamics agrees with that
of a freely fluctuating membrane. Overall, we find that this curvature-coupling
substantially enhances the diffusion coefficient. We compare the ratio of the
projected or measured diffusion coefficient and the free intramembrane
diffusion coefficient, which is a parameter of the simulations, with analytical
results that rely on several approximations. We find that the simulations
always lead to a somewhat smaller diffusion coefficient than our analytical
approach. A detailed study of the correlations of the forces acting on the
particle indicates that the diffusing inclusion tries to follow favorable
positions on the membrane, such that forces along the trajectory are on average
smaller than they would be for random particle positions.Comment: 16 pages, 8 figure
Recommended from our members
Experimental investigations of sensor-based surface following performed by a mobile manipulator
We discuss a series of surface following experiments using a range finder mounted on the end of an arm that is mounted on a vehicle. The goal is to keep the range finder at a fixed distance from an unknown surface and to keep the orientation of the range finder perpendicular to the surface. During the experiments, the vehicle moves along a predefined trajectory while planning software determines the position and orientation of the arm. To keep the range finder perpendicular to the surface, the planning software calculates the surface normal for the unknown surface. We assume that the unknown surface is a cylinder (the surface depends on x and y but does not depend on z). To calculate the surface normal, the planning software must calculate the locations (x,y) of points on the surface in world coordinates. The calculation requires data on the position and orientation of the vehicle, the position and orientation of the arm, and the distance from the range finder to the surface. We discuss four series of experiments. During the first series of experiments, the calculated surface normal values had large high frequency random variations. A filter was used to produce an average value for the surface normal and we limited the rate of change in the yaw angle target for the arm. We performed the experiment for a variety of concave and convex surfaces. While the experiments were qualitative successes, the measured distance to the surface was significantly different than the target. The distance errors were systematic, low frequency, and had magnitudes up to 25 mm. During the second series of experiments, we reduced the variations in the calculated surface normal values. While reviewing the data collected while following the surface of a barrel, we found that the radius of the calculated surface was significantly different than the measured radius of the barrel
Curvature correction to the mobility of fluid membrane inclusions
For the first time, using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces via a Stokeslet-type approach, we provide a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this wholly general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Molecular Dynamics Simulations
A tutorial introduction to the technique of Molecular Dynamics (MD) is given,
and some characteristic examples of applications are described. The purpose and
scope of these simulations and the relation to other simulation methods is
discussed, and the basic MD algorithms are described. The sampling of intensive
variables (temperature T, pressure p) in runs carried out in the microcanonical
(NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as
well as the realization of other ensembles (e.g. the NVT ensemble). For a
typical application example, molten SiO2, the estimation of various transport
coefficients (self-diffusion constants, viscosity, thermal conductivity) is
discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study
of a glass-forming polymer melt under shear is mentioned.Comment: 38 pages, 11 figures, to appear in J. Phys.: Condens. Matte
- …