2,339 research outputs found
Are stress-free membranes really 'tensionless'?
In recent years it has been argued that the tension parameter driving the
fluctuations of fluid membranes, differs from the imposed lateral stress, the
'frame tension'. In particular, stress-free membranes were predicted to have a
residual fluctuation tension. In the present paper, this argument is
reconsidered and shown to be inherently inconsistent -- in the sense that a
linearized theory, the Monge model, is used to predict a nonlinear effect.
Furthermore, numerical simulations of one-dimensional stiff membranes are
presented which clearly demonstrate, first, that the internal 'intrinsic'
stress in membranes indeed differs from the frame tension as conjectured, but
second, that the fluctuations are nevertheless driven by the frame tension.
With this assumption, the predictions of the Monge model agree excellently with
the simulation data for stiffness and tension values spanning several orders of
magnitude
Solid domains in lipid vesicles and scars
The free energy of a crystalline domain coexisting with a liquid phase on a
spherical vesicle may be approximated by an elastic or stretching energy and a
line tension term. The stretching energy generally grows as the area of the
domain, while the line tension term grows with its perimeter. We show that if
the crystalline domain contains defect arrays consisting of finite length grain
boundaries of dislocations (scars) the stretching energy grows linearly with a
characteristic length of the crystalline domain. We show that this result is
critical to understand the existence of solid domains in lipid-bilayers in the
strongly segregated two phase region even for small relative area coverages.
The domains evolve from caps to stripes that become thinner as the line tension
is decreased. We also discuss the implications of the results for other
experimental systems and for the general problem that consists in finding the
ground state of a very large number of particles constrained to move on a fixed
geometry and interacting with an isotropic potential.Comment: 7 pages, 6 eps figure
Clustered bottlenecks in mRNA translation and protein synthesis
We construct an algorithm that generates large, band-diagonal transition
matrices for a totally asymmetric exclusion process (TASEP) with local hopping
rate inhomogeneities. The matrices are diagonalized numerically to find
steady-state currents of TASEPs with local variations in hopping rate. The
results are then used to investigate clustering of slow codons along mRNA.
Ribosome density profiles near neighboring clusters of slow codons interact,
enhancing suppression of ribosome throughput when such bottlenecks are closely
spaced. Increasing the slow codon cluster size, beyond , does not
significantly reduce ribosome current. Our results are verified by extensive
Monte-Carlo simulations and provide a biologically-motivated explanation for
the experimentally-observed clustering of low-usage codons
Lateral migration of a 2D vesicle in unbounded Poiseuille flow
The migration of a suspended vesicle in an unbounded Poiseuille flow is
investigated numerically in the low Reynolds number limit. We consider the
situation without viscosity contrast between the interior of the vesicle and
the exterior. Using the boundary integral method we solve the corresponding
hydrodynamic flow equations and track explicitly the vesicle dynamics in two
dimensions. We find that the interplay between the nonlinear character of the
Poiseuille flow and the vesicle deformation causes a cross-streamline migration
of vesicles towards the center of the Poiseuille flow. This is in a marked
contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12,
435(1980)]according to which the droplet moves away from the center (provided
there is no viscosity contrast between the internal and the external fluids).
The migration velocity is found to increase with the local capillary number
(defined by the time scale of the vesicle relaxation towards its equilibrium
shape times the local shear rate), but reaches a plateau above a certain value
of the capillary number. This plateau value increases with the curvature of the
parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure
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
State Differentiation by Transient Truncation in Coupled Threshold Dynamics
Dynamics with a threshold input--output relation commonly exist in gene,
signal-transduction, and neural networks. Coupled dynamical systems of such
threshold elements are investigated, in an effort to find differentiation of
elements induced by the interaction. Through global diffusive coupling, novel
states are found to be generated that are not the original attractor of
single-element threshold dynamics, but are sustained through the interaction
with the elements located at the original attractor. This stabilization of the
novel state(s) is not related to symmetry breaking, but is explained as the
truncation of transient trajectories to the original attractor due to the
coupling. Single-element dynamics with winding transient trajectories located
at a low-dimensional manifold and having turning points are shown to be
essential to the generation of such novel state(s) in a coupled system.
Universality of this mechanism for the novel state generation and its relevance
to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres
Active Microrheology of Networks Composed of Semiflexible Polymers. II. Theory and comparison with simulations
Building on the results of our computer simulation (ArXiv cond-mat/0503573)we
develop a theoretical description of the motion of a bead, embedded in a
network of semiflexible polymers, and responding to an applied force. The
theory reveals the existence of an osmotic restoring force, generated by the
piling up of filaments in front of the moving bead and first deduced through
computer simulations. The theory predicts that the bead displacement scales
like x ~ t^alfa with time, with alfa=0.5 in an intermediate- and alfa=1 in a
long-time regime. It also predicts that the compliance varies with
concentration like c^(-4/3) in agreement with experiment.Comment: 18 pages and 2 figure
Effect of shear force on the separation of double stranded DNA
Using the Langevin Dynamics simulation, we have studied the effects of the
shear force on the rupture of short double stranded DNA at different
temperatures. We show that the rupture force increases linearly with the chain
length and approaches to the asymptotic value in accordance with the
experiment. The qualitative nature of these curves almost remains same for
different temperatures but with a shift in the force. We observe three
different regimes in the extension of covalent bonds (back bone) under the
shear force.Comment: 4 pages, 4 figure
A variational approach to the stochastic aspects of cellular signal transduction
Cellular signaling networks have evolved to cope with intrinsic fluctuations,
coming from the small numbers of constituents, and the environmental noise.
Stochastic chemical kinetics equations govern the way biochemical networks
process noisy signals. The essential difficulty associated with the master
equation approach to solving the stochastic chemical kinetics problem is the
enormous number of ordinary differential equations involved. In this work, we
show how to achieve tremendous reduction in the dimensionality of specific
reaction cascade dynamics by solving variationally an equivalent quantum field
theoretic formulation of stochastic chemical kinetics. The present formulation
avoids cumbersome commutator computations in the derivation of evolution
equations, making more transparent the physical significance of the variational
method. We propose novel time-dependent basis functions which work well over a
wide range of rate parameters. We apply the new basis functions to describe
stochastic signaling in several enzymatic cascades and compare the results so
obtained with those from alternative solution techniques. The variational
ansatz gives probability distributions that agree well with the exact ones,
even when fluctuations are large and discreteness and nonlinearity are
important. A numerical implementation of our technique is many orders of
magnitude more efficient computationally compared with the traditional Monte
Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure
Universal features of cell polarization processes
Cell polarization plays a central role in the development of complex
organisms. It has been recently shown that cell polarization may follow from
the proximity to a phase separation instability in a bistable network of
chemical reactions. An example which has been thoroughly studied is the
formation of signaling domains during eukaryotic chemotaxis. In this case, the
process of domain growth may be described by the use of a constrained
time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions
{\textit{\`a la}} Lifshitz and Slyozov. The constraint results here from a
mechanism of fast cycling of molecules between a cytosolic, inactive state and
a membrane-bound, active state, which dynamically tunes the chemical potential
for membrane binding to a value corresponding to the coexistence of different
phases on the cell membrane. We provide here a universal description of this
process both in the presence and absence of a gradient in the external
activation field. Universal power laws are derived for the time needed for the
cell to polarize in a chemotactic gradient, and for the value of the smallest
detectable gradient. We also describe a concrete realization of our scheme
based on the analysis of available biochemical and biophysical data.Comment: Submitted to Journal of Statistical Mechanics -Theory and Experiment
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