1,591 research outputs found
Force-induced misfolding in RNA
RNA folding is a kinetic process governed by the competition of a large
number of structures stabilized by the transient formation of base pairs that
may induce complex folding pathways and the formation of misfolded structures.
Despite of its importance in modern biophysics, the current understanding of
RNA folding kinetics is limited by the complex interplay between the weak
base-pair interactions that stabilize the native structure and the disordering
effect of thermal forces. The possibility of mechanically pulling individual
molecules offers a new perspective to understand the folding of nucleic acids.
Here we investigate the folding and misfolding mechanism in RNA secondary
structures pulled by mechanical forces. We introduce a model based on the
identification of the minimal set of structures that reproduce the patterns of
force-extension curves obtained in single molecule experiments. The model
requires only two fitting parameters: the attempt frequency at the level of
individual base pairs and a parameter associated to a free energy correction
that accounts for the configurational entropy of an exponentially large number
of neglected secondary structures. We apply the model to interpret results
recently obtained in pulling experiments in the three-helix junction S15 RNA
molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where
force favors the formation of a stable non-native hairpin. The model reproduces
the pattern of unfolding and refolding force-extension curves, the distribution
of breakage forces and the misfolding probability obtained in the experiments.Comment: 28 pages, 11 figure
Grand canonical and canonical solution of self-avoiding walks with up to three monomers per site on the Bethe lattice
We solve a model of polymers represented by self-avoiding walks on a lattice
which may visit the same site up to three times in the grand-canonical
formalism on the Bethe lattice. This may be a model for the collapse transition
of polymers where only interactions between monomers at the same site are
considered. The phase diagram of the model is very rich, displaying coexistence
and critical surfaces, critical, critical endpoint and tricritical lines, as
well as a multicritical point. From the grand-canonical results, we present an
argument to obtain the properties of the model in the canonical ensemble, and
compare our results with simulations in the literature. We do actually find
extended and collapsed phases, but the transition between them, composed by a
line of critical endpoints and a line of tricritical points, separated by the
multicritical point, is always continuous. This result is at variance with the
simulations for the model, which suggest that part of the line should be a
discontinuous transition. Finally, we discuss the connection of the present
model with the standard model for the collapse of polymers (self-avoiding
self-attracting walks), where the transition between the extended and collapsed
phases is a tricritical point.Comment: 34 pages, including 10 figure
Surface critical behaviour of the Interacting Self-Avoiding Trail on the square lattice
The surface critical behaviour of the interacting self-avoiding trail is
examined using transfer matrix methods coupled with finite-size scaling.
Particular attention is paid to the critical exponents at the ordinary and
special points along the collapse transition line. The phase diagram is also
presented.Comment: Journal of Physics A (accepted
Diffusive transport of light in three-dimensional disordered Voronoi structures
The origin of diffusive transport of light in dry foams is still under
debate. In this paper, we consider the random walks of photons as they are
reflected or transmitted by liquid films according to the rules of ray optics.
The foams are approximately modeled by three-dimensional Voronoi tessellations
with varying degree of disorder. We study two cases: a constant intensity
reflectance and the reflectance of thin films. Especially in the second case,
we find that in the experimentally important regime for the film thicknesses,
the transport-mean-free path does not significantly depend on the topological
and geometrical disorder of the Voronoi foams including the periodic Kelvin
foam. This may indicate that the detailed structure of foams is not crucial for
understanding the diffusive transport of light. Furthermore, our theoretical
values for transport-mean-free path fall in the same range as the experimental
values observed in dry foams. One can therefore argue that liquid films
contribute substantially to the diffusive transport of light in {dry} foams.Comment: 8 pages, 8 figure
Diffusive transport of light in two-dimensional granular materials
We study photon diffusion in a two-dimensional random packing of monodisperse
disks as a simple model of granular material. We apply ray optics approximation
to set up a persistent random walk for the photons. We employ Fresnel's
intensity reflectance with its rich dependence on the incidence angle and
polarization state of the light. We present an analytic expression for the
transport-mean-free path in terms of the refractive indices of grains and host
medium, grain radius, and packing fraction. We perform numerical simulations to
examine our analytical result.Comment: 9 pages, 3 figure
Polymer Brushes in Cylindrical Pores: Simulation versus Scaling Theory
The structure of flexible polymers endgrafted in cylindrical pores of
diameter D is studied as a function of chain length N and grafting density
\sigma, assuming good solvent conditions. A phenomenological scaling theory,
describing the variation of the linear dimensions of the chains with \sigma, is
developed and tested by Molecular Dynamics simulations of a bead-spring model.Comment: 35 pages, 38 figure
Distance dependence of angular correlations in dense polymer solutions
Angular correlations in dense solutions and melts of flexible polymer chains
are investigated with respect to the distance between the bonds by
comparing quantitative predictions of perturbation calculations with numerical
data obtained by Monte Carlo simulation of the bond-fluctuation model. We
consider both monodisperse systems and grand-canonical (Flory-distributed)
equilibrium polymers. Density effects are discussed as well as finite chain
length corrections. The intrachain bond-bond correlation function is
shown to decay as for \xi \ll r \ll \r^* with being
the screening length of the density fluctuations and a novel
length scale increasing slowly with (mean) chain length .Comment: 17 pages, 5 figures, accepted for publication at Macromolecule
Critical Indices as Limits of Control Functions
A variant of self-similar approximation theory is suggested, permitting an
easy and accurate summation of divergent series consisting of only a few terms.
The method is based on a power-law algebraic transformation, whose powers play
the role of control functions governing the fastest convergence of the
renormalized series. A striking relation between the theory of critical
phenomena and optimal control theory is discovered: The critical indices are
found to be directly related to limits of control functions at critical points.
The method is applied to calculating the critical indices for several difficult
problems. The results are in very good agreement with accurate numerical data.Comment: 1 file, 5 pages, RevTe
Critical Dynamics of Gelation
Shear relaxation and dynamic density fluctuations are studied within a Rouse
model, generalized to include the effects of permanent random crosslinks. We
derive an exact correspondence between the static shear viscosity and the
resistance of a random resistor network. This relation allows us to compute the
static shear viscosity exactly for uncorrelated crosslinks. For more general
percolation models, which are amenable to a scaling description, it yields the
scaling relation for the critical exponent of the shear
viscosity. Here is the thermal exponent for the gel fraction and
is the crossover exponent of the resistor network. The results on the shear
viscosity are also used in deriving upper and lower bounds on the incoherent
scattering function in the long-time limit, thereby corroborating previous
results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor
changes
Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions
A monomer-dimer reaction lattice model with lateral repulsion among the same
species is studied using a mean-field analysis and Monte Carlo simulations. For
weak repulsions, the model exhibits a first-order irreversible phase transition
between two absorbing states saturated by each different species. Increasing
the repulsion, a reactive stationary state appears in addition to the saturated
states. The irreversible phase transitions from the reactive phase to any of
the saturated states are continuous and belong to the directed percolation
universality class. However, a different critical behavior is found at the
point where the directed percolation phase boundaries meet. The values of the
critical exponents calculated at the bicritical point are in good agreement
with the exponents corresponding to the parity-conserving universality class.
Since the adsorption-reaction processes does not lead to a non-trivial local
parity-conserving dynamics, this result confirms that the twofold symmetry
between absorbing states plays a relevant role in determining the universality
class. The value of the exponent , which characterizes the
fluctuations of an interface at the bicritical point, supports the
Bassler-Brown's conjecture which states that this is a new exponent in the
parity-conserving universality class.Comment: 19 pages, 22 figures, to be published in Phys. Rev
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