274 research outputs found
Optimal target search on a fast folding polymer chain with volume exchange
We study the search process of a target on a rapidly folding polymer (`DNA')
by an ensemble of particles (`proteins'), whose search combines 1D diffusion
along the chain, Levy type diffusion mediated by chain looping, and volume
exchange. A rich behavior of the search process is obtained with respect to the
physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe
Aging dynamics in interacting many-body systems
Low-dimensional, complex systems are often characterized by logarithmically
slow dynamics. We study the generic motion of a labeled particle in an ensemble
of identical diffusing particles with hardcore interactions in a strongly
disordered, one-dimensional environment. Each particle in this single file is
trapped for a random waiting time with power law distribution
, such that the values are
independent, local quantities for all particles. From scaling arguments and
simulations, we find that for the scale-free waiting time case ,
the tracer particle dynamics is ultra-slow with a logarithmic mean square
displacement (MSD) . This extreme
slowing down compared to regular single file motion is due to the high likelihood that the labeled
particle keeps encountering strongly immobilized neighbors. For the case
we observe the MSD scaling , where we recover Harris law
.Comment: 5 pages, 4 figure
Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary
We derive the boundary condition for a subdiffusive particle interacting with
a reactive boundary with finite reaction rate. Molecular crowding conditions,
that are found to cause subdiffusion of larger molecules in biological cells,
are shown to effect long-tailed distributions with identical exponent for both
the unbinding times from the boundary to the bulk and the rebinding times from
the bulk. This causes a weak ergodicity breaking: typically, an individual
particle either stays bound or remains in the bulk for very long times. We
discuss why this may be beneficial for in vivo gene regulation by DNA-binding
proteins, whose typical concentrations are nanomolarComment: 4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos
correcte
Well-posedness of Hydrodynamics on the Moving Elastic Surface
The dynamics of a membrane is a coupled system comprising a moving elastic
surface and an incompressible membrane fluid. We will consider a reduced
elastic surface model, which involves the evolution equations of the moving
surface, the dynamic equations of the two-dimensional fluid, and the
incompressible equation, all of which operate within a curved geometry. In this
paper, we prove the local existence and uniqueness of the solution to the
reduced elastic surface model by reformulating the model into a new system in
the isothermal coordinates. One major difficulty is that of constructing an
appropriate iterative scheme such that the limit system is consistent with the
original system.Comment: The introduction is rewritte
Langevin formulation for single-file diffusion
We introduce a stochastic equation for the microscopic motion of a tagged
particle in the single file model. This equation provides a compact
representation of several of the system's properties such as
Fluctuation-Dissipation and Linear Response relations, achieved by means of a
diffusion noise approach. Most important, the proposed Langevin Equation
reproduces quantitatively the \emph{three} temporal regimes and the
corresponding time scales: ballistic, diffusive and subdiffusive.Comment: 9 pages, 5 figures, 1 table, to appear in Physical Review
Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
Mechanics of fluid membranes may be described in terms of the concepts of
mechanical deformations and stresses, or in terms of mechanical free-energy
functions. In this paper, each of the two descriptions is developed by viewing
a membrane from two perspectives: a microscopic perspective, in which the
membrane appears as a thin layer of finite thickness and with highly
inhomogeneous material and force distributions in its transverse direction, and
an effective, two-dimensional perspective, in which the membrane is treated as
an infinitely thin surface, with effective material and mechanical properties.
A connection between these two perspectives is then established. Moreover, the
functional dependence of the variation in the mechanical free energy of the
membrane on its mechanical deformations is first studied in the microscopic
perspective. The result is then used to examine to what extent different,
effective mechanical stresses and forces can be derived from a given, effective
functional of the mechanical free energy.Comment: 37 pages, 3 figures, minor change
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Spatio-temporal correlations can drastically change the response of a MAPK pathway
Multisite covalent modification of proteins is omnipresent in eukaryotic
cells. A well-known example is the mitogen-activated protein kinase (MAPK)
cascade, where in each layer of the cascade a protein is phosphorylated at two
sites. It has long been known that the response of a MAPK pathway strongly
depends on whether the enzymes that modify the protein act processively or
distributively: distributive mechanism, in which the enzyme molecules have to
release the substrate molecules in between the modification of the two sites,
can generate an ultrasensitive response and lead to hysteresis and bistability.
We study by Green's Function Reaction Dynamics, a stochastic scheme that makes
it possible to simulate biochemical networks at the particle level and in time
and space, a dual phosphorylation cycle in which the enzymes act according to a
distributive mechanism. We find that the response of this network can differ
dramatically from that predicted by a mean-field analysis based on the chemical
rate equations. In particular, rapid rebindings of the enzyme molecules to the
substrate molecules after modification of the first site can markedly speed up
the response, and lead to loss of ultrasensitivity and bistability. In essence,
rapid enzyme-substrate rebindings can turn a distributive mechanism into a
processive mechanism. We argue that slow ADP release by the enzymes can protect
the system against these rapid rebindings, thus enabling ultrasensitivity and
bistability
Bulk-mediated surface diffusion on a cylinder: propagators and crossovers
We consider the effective surface motion of a particle that freely diffuses
in the bulk and intermittently binds to that surface. From an exact approach we
derive various regimes of the effective surface motion characterized by
physical rates for binding/unbinding and the bulk diffusivity. We obtain a
transient regime of superdiffusion and, in particular, a saturation regime
characteristic for the cylindrical geometry. This saturation, however, in a
finite system is not terminal but eventually turns over to normal surface
diffusion. The first passage behavior of particles to the cylinder surface is
derived. Consequences for actual systems are discussed.Comment: 4 pages REVTeX4, 2 figure
Determination of the electronic density of states near buried interfaces: Application to Co/Cu multilayers
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