2,895 research outputs found
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
Stretching short biopolymers by fields and forces
We study the mechanical properties of semiflexible polymers when the contour
length of the polymer is comparable to its persistence length. We compute the
exact average end-to-end distance and shape of the polymer for different
boundary conditions, and show that boundary effects can lead to significant
deviations from the well-known long-polymer results. We also consider the case
of stretching a uniformly charged biopolymer by an electric field, for which we
compute the average extension and the average shape, which is shown to be
trumpetlike. Our results also apply to long biopolymers when thermal
fluctuations have been smoothed out by a large applied field or force.Comment: 10 pages, 7 figure
A model for the orientational ordering of the plant microtubule cortical array
The plant microtubule cortical array is a striking feature of all growing
plant cells. It consists of a more or less homogeneously distributed array of
highly aligned microtubules connected to the inner side of the plasma membrane
and oriented transversely to the cell growth axis. Here we formulate a
continuum model to describe the origin of orientational order in such confined
arrays of dynamical microtubules. The model is based on recent experimental
observations that show that a growing cortical microtubule can interact through
angle dependent collisions with pre-existing microtubules that can lead either
to co-alignment of the growth, retraction through catastrophe induction or
crossing over the encountered microtubule. We identify a single control
parameter, which is fully determined by the nucleation rate and intrinsic
dynamics of individual microtubules. We solve the model analytically in the
stationary isotropic phase, discuss the limits of stability of this isotropic
phase, and explicitly solve for the ordered stationary states in a simplified
version of the model.Comment: 15 pages, 5 figure
The Continuum Directed Random Polymer
Motivated by discrete directed polymers in one space and one time dimension,
we construct a continuum directed random polymer that is modeled by a
continuous path interacting with a space-time white noise. The strength of the
interaction is determined by an inverse temperature parameter beta, and for a
given beta and realization of the noise the path evolves in a Markovian way.
The transition probabilities are determined by solutions to the one-dimensional
stochastic heat equation. We show that for all beta > 0 and for almost all
realizations of the white noise the path measure has the same Holder continuity
and quadratic variation properties as Brownian motion, but that it is actually
singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page
Quenched central limit theorem for the stochastic heat equation in weak disorder
We continue with the study of the mollified stochastic heat equation in
given by with spatially
smoothened cylindrical Wiener process , whose (renormalized) Feynman-Kac
solution describes the partition function of the continuous directed polymer.
In an earlier work (\cite{MSZ16}), a phase transition was obtained, depending
on the value of in the limiting object of the smoothened solution
as the smoothing parameter This partition function
naturally defines a quenched polymer path measure and we prove that as long as
stays small enough while converges to a strictly
positive non-degenerate random variable, the distribution of the diffusively
rescaled Brownian path converges under the aforementioned polymer path measure
to standard Gaussian distribution.Comment: Minor revisio
Power spectra of TASEPs with a localized slow site
The totally asymmetric simple exclusion process (TASEP) with a localized
defect is revisited in this article with attention paid to the power spectra of
the particle occupancy N(t). Intrigued by the oscillatory behaviors in the
power spectra of an ordinary TASEP in high/low density phase(HD/LD) observed by
Adams et al. (2007 Phys. Rev. Lett. 99 020601), we introduce a single slow site
with hopping rate q<1 to the system. As the power spectrum contains
time-correlation information of the particle occupancy of the system, we are
particularly interested in how the defect affects fluctuation in particle
number of the left and right subsystems as well as that of the entire system.
Exploiting Monte Carlo simulations, we observe the disappearance of
oscillations when the defect is located at the center of the system. When the
defect is off center, oscillations are restored. To explore the origin of such
phenomenon, we use a linearized Langevin equation to calculate the power
spectrum for the sublattices and the whole lattice. We provide insights into
the interactions between the sublattices coupled through the defect site for
both simulation and analytical results.Comment: 16 pages, 6 figures; v2: Minor revision
Entropic phase separation of linked beads
We study theoretically a model system of a transient network of microemulsion
droplets connected by telechelic polymers and explain recent experimental
findings. Despite the absence of any specific interactions between either the
droplets or polymer chains, we predict that as the number of polymers per drop
is increased, the system undergoes a first order phase separation into a dense,
highly connected phase, in equilibrium with dilute droplets, decorated by
polymer loops. The phase transition is purely entropic and is driven by the
interplay between the translational entropy of the drops and the
configurational entropy of the polymer connections between them. Because it is
dominated by entropic effects, the phase separation mechanism of the system is
extremely robust and does not depend on the particlular physical realization of
the network. The discussed model applies as well to other polymer linked
particle aggregates, such as nano-particles connected with short DNA linkers
Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior in a two-dimensional system of particles
with two bonding sites that, by decreasing temperature or increasing density,
polymerize reversibly into chains with discrete orientational degrees of
freedom and, at the same time, undergo a continuous isotropic-nematic (IN)
transition. A complete phase diagram was obtained as a function of temperature
and density. The numerical results were compared with mean field (MF) and real
space renormalization group (RSRG) analytical predictions about the IN
transformation. While the RSRG approach supports the continuous nature of the
transition, the MF solution predicts a first-order transition line and a
tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio
Compression modulus of macroscopic fiber bundles
We study dense, disordered stacks of elastic macroscopic fibers. These stacks
often exhibit non-linear elasticity, due to the coupling between the applied
stress and the internal distribution of fiber contacts. We propose a
theoretical model for the compression modulus of such systems, and illustrate
our method by studying the conical shapes frequently observed at the
extremities of ropes and other fiber structures. studying the conical shapes
frequently observed at theextremities of ropes and other fiber structures
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