4,543 research outputs found
Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes
Inspired by problems in biochemical kinetics, we study statistical properties
of an overdamped Langevin process whose friction coefficient depends on the
state of a similar, unobserved process. Integrating out the latter, we derive
the long time behaviour of the mean square displacement. Anomalous diffusion is
found. Since the diffusion exponent can not be predicted using a simple scaling
argument, anomalous scaling appears as well. We also find that the coupling can
lead to ergodic or non-ergodic behaviour of the studied process. We compare our
theoretical predictions with numerical simulations and find an excellent
agreement. The findings caution against treating biochemical systems coupled
with unobserved dynamical degrees of freedom by means of standard, diffusive
Langevin descriptions
Membrane fluctuations near a plane rigid surface
We use analytical calculations and Monte Carlo simulations to determine the
thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in
size, whose corners are located at a fixed distance above a plane rigid
surface. Our analysis shows that the surface influence on the bilayer
fluctuations can be effectively described in terms of a uniform confining
potential that grows quadratically with the height of the membrane relative
to the surface: . The strength of the harmonic
confining potential vanishes when the corners of the membrane patch are placed
directly on the surface (), and achieves its maximum value when is of
the order of a few nanometers. However, even at maximum strength the
confinement effect is quite small and has noticeable impact only on the
amplitude of the largest bending mode.Comment: Accepted for publication in Phys. Rev.
Surface tension in bilayer membranes with fixed projected area
We study the elastic response of bilayer membranes with fixed projected area
to both stretching and shape deformations. A surface tension is associated to
each of these deformations. By using model amphiphilic membranes and computer
simulations, we are able to observe both the types of deformation, and thus,
both the surface tensions, related to each type of deformation, are measured
for the same system. These surface tensions are found to assume different
values in the same bilayer membrane: in particular they vanish for different
values of the projected area. We introduce a simple theory which relates the
two quantities and successfully apply it to the data obtained with computer
simulations
Fluctuation spectrum of quasispherical membranes with force-dipole activity
The fluctuation spectrum of a quasi-spherical vesicle with active membrane
proteins is calculated. The activity of the proteins is modeled as the proteins
pushing on their surroundings giving rise to non-local force distributions.
Both the contributions from the thermal fluctuations of the active protein
densities and the temporal noise in the individual active force distributions
of the proteins are taken into account. The noise in the individual force
distributions is found to become significant at short wavelengths.Comment: 9 pages, 2 figures, minor changes and addition
Effect of dipolar moments in domain sizes of lipid bilayers and monolayers
Lipid domains are found in systems such as multi-component bilayer membranes
and single component monolayers at the air-water interface. It was shown by
Andelman et al. (Comptes Rendus 301, 675 (1985)) and McConnell et al. (Phys.
Chem. {\bf 91}, 6417 (1987)) that in monolayers, the size of the domains
results from balancing the line tension, which favors the formation of a large
single circular domain, against the electrostatic cost of assembling the
dipolar moments of the lipids. In this paper, we present an exact analytical
expression for the electric potential, ion distribution and electrostatic free
energy for different problems consisting of three different slabs with
different dielectric constants and Debye lengths, with a circular homogeneous
dipolar density in the middle slab. From these solutions, we extend the
calculation of domain sizes for monolayers to include the effects of finite
ionic strength, dielectric discontinuities (or image charges) and the
polarizability of the dipoles and further generalize the calculations to
account for domains in lipid bilayers. In monolayers, the size of the domains
is dependent on the different dielectric constants but independent of ionic
strength. In asymmetric bilayers, where the inner and outer leaflets have
different dipolar densities, domains show a strong size dependence with ionic
strength, with molecular-sized domains that grow to macroscopic phase
separation with increasing ionic strength. We discuss the implications of the
results for experiments and briefly consider their relation to other two
dimensional systems such as Wigner crystals or heteroepitaxial growth.Comment: 13 pages, 5 figues in eps Replaced with new version, one citation
added and a few statements corrected. The results of the paper are unchange
Dynamics of active membranes with internal noise
We study the time-dependent height fluctuations of an active membrane
containing energy-dissipating pumps that drive the membrane out of equilibrium.
Unlike previous investigations based on models that neglect either curvature
couplings or random fluctuations in pump activities, our formulation explores
two new models that take both of these effects into account. In the first
model, the magnitude of the nonequilibrium forces generated by the pumps is
allowed to fluctuate temporally. In the second model, the pumps are allowed to
switch between "on" and "off" states. We compute the mean squared displacement
of a membrane point for both models, and show that they exhibit distinct
dynamical behaviors from previous models, and in particular, a superdiffusive
regime specifically arising from the shot noise.Comment: 7 pages, 4 figure
Proton transport and torque generation in rotary biomotors
We analyze the dynamics of rotary biomotors within a simple
nano-electromechanical model, consisting of a stator part and a ring-shaped
rotor having twelve proton-binding sites. This model is closely related to the
membrane-embedded F motor of adenosine triphosphate (ATP) synthase, which
converts the energy of the transmembrane electrochemical gradient of protons
into mechanical motion of the rotor. It is shown that the Coulomb coupling
between the negative charge of the empty rotor site and the positive stator
charge, located near the periplasmic proton-conducting channel (proton source),
plays a dominant role in the torque-generating process. When approaching the
source outlet, the rotor site has a proton energy level higher than the energy
level of the site, located near the cytoplasmic channel (proton drain). In the
first stage of this torque-generating process, the energy of the
electrochemical potential is converted into potential energy of the
proton-binding sites on the rotor. Afterwards, the tangential component of the
Coulomb force produces a mechanical torque. We demonstrate that, at low
temperatures, the loaded motor works in the shuttling regime where the energy
of the electrochemical potential is consumed without producing any
unidirectional rotation. The motor switches to the torque-generating regime at
high temperatures, when the Brownian ratchet mechanism turns on. In the
presence of a significant external torque, created by ATP hydrolysis, the
system operates as a proton pump, which translocates protons against the
transmembrane potential gradient. Here we focus on the F motor, even though
our analysis is applicable to the bacterial flagellar motor.Comment: 24 pages, 5 figure
Discreteness-induced Transition in Catalytic Reaction Networks
Drastic change in dynamics and statistics in a chemical reaction system,
induced by smallness in the molecule number, is reported. Through stochastic
simulations for random catalytic reaction networks, transition to a novel state
is observed with the decrease in the total molecule number N, characterized by:
i) large fluctuations in chemical concentrations as a result of intermittent
switching over several states with extinction of some molecule species and ii)
strong deviation of time averaged distribution of chemical concentrations from
that expected in the continuum limit, i.e., . The origin of
transition is explained by the deficiency of molecule leading to termination of
some reactions. The critical number of molecules for the transition is obtained
as a function of the number of molecules species M and that of reaction paths
K, while total reaction rates, scaled properly, are shown to follow a universal
form as a function of NK/M
Semiflexible polymers: Dependence on ensemble and boundary orientations
We show that the mechanical properties of a worm-like-chain (WLC) polymer, of
contour length and persistence length \l such that t=L/\l\sim{\cal
O}(1), depend both on the ensemble and the constraint on end-orientations. In
the Helmholtz ensemble, multiple minima in free energy near persists for
all kinds of orientational boundary conditions. The qualitative features of
projected probability distribution of end to end vector depend crucially on the
embedding dimensions. A mapping of the WLC model, to a quantum particle moving
on the surface of an unit sphere, is used to obtain the statistical and
mechanical properties of the polymer under various boundary conditions and
ensembles. The results show excellent agreement with Monte-Carlo simulations.Comment: 15 pages, 15 figures; version accepted for publication in Phys. Rev.
E; one new figure and discussions adde
Fluctuation induced interactions between domains in membranes
We study a model lipid bilayer composed of a mixture of two incompatible
lipid types which have a natural tendency to segregate in the absence of
membrane fluctuations. The membrane is mechanically characterized by a local
bending rigidity which varies with the average local lipid
composition . We show, in the case where varies weakly with
, that the effective interaction between lipids of the same type can
either be everywhere attractive or can have a repulsive component at
intermediate distances greater than the typical lipid size. When this
interaction has a repulsive component, it can prevent macro-phase separation
and lead to separation in mesophases with a finite domain size. This effect
could be relevant to certain experimental and numerical observations of
mesoscopic domains in such systems.Comment: 9 pages RevTex, 1 eps figur
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