474 research outputs found
A lattice polymer study of DNA renaturation dynamics
DNA renaturation is the recombination of two complementary single strands to
form a double helix. It is experimentally known that renaturation proceeds
through the formation of a double stranded nucleus of several base pairs (the
rate limiting step) followed by a much faster zippering. We consider a lattice
polymer model undergoing Rouse dynamics and focus on the nucleation of two
diffusing strands. We study numerically the dependence of various nucleation
rates on the strand lengths and on an additional local nucleation barrier. When
the local barrier is sufficiently high, all renaturation rates considered scale
with the length as predicted by Kramers' rate theory and are also in agreement
with experiments: their scaling behavior is governed by exponents describing
equilibrium properties of polymers. When the local barrier is lowered
renaturation occurs in a regime of genuine non-equilibrium behavior and the
scaling deviates from the rate theory prediction.Comment: 13 pages, 6 figures. To appear in Journal of Statistical Mechanic
Breakdown of thermodynamic equilibrium for DNA hybridization in microarrays
Test experiments of hybridization in DNA microarrays show systematic
deviations from the equilibrium isotherms. We argue that these deviations are
due to the presence of a partially hybridized long-lived state, which we
include in a kinetic model. Experiments confirm the model predictions for the
intensity vs. free energy behavior. The existence of slow relaxation phenomena
has important consequences for the specificity of microarrays as devices for
the detection of a target sequence from a complex mixture of nucleic acids.Comment: 4 pages, 4 figure
Coexistence of excited states in confined Ising systems
Using the density-matrix renormalization-group method we study the
two-dimensional Ising model in strip geometry. This renormalization scheme
enables us to consider the system up to the size 300 x infinity and study the
influence of the bulk magnetic field on the system at full range of
temperature. We have found out the crossover in the behavior of the correlation
length on the line of coexistence of the excited states. A detailed study of
scaling of this line is performed. Our numerical results support and specify
previous conclusions by Abraham, Parry, and Upton based on the related bubble
model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been
rewritten without including new result
Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type
A mean field theory is developed for the calculation of the surface free
energy of the staggered BCSOS, (or six vertex) model as function of the surface
orientation and of temperature. The model approximately describes surfaces of
crystals with nearest neighbor attractions and next nearest neighbor
repulsions. The mean field free energy is calculated by expressing the model in
terms of interacting directed walks on a lattice. The resulting equilibrium
shape is very rich with facet boundaries and boundaries between reconstructed
and unreconstructed regions which can be either sharp (first order) or smooth
(continuous). In addition there are tricritical points where a smooth boundary
changes into a sharp one and triple points where three sharp boundaries meet.
Finally our numerical results strongly suggest the existence of conical points,
at which tangent planes of a finite range of orientations all intersect each
other. The thermal evolution of the equilibrium shape in this model shows
strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include
Crossover from reptation to Rouse dynamics in a one-dimensional model
A simple one-dimensional model is constructed for polymer motion. It exhibits
the crossover from reptation to Rouse dynamics through gradually allowing
hernia creation and annihilation. The model is treated by the density matrix
technique which permits an accurate finite-size-scaling analysis of the
behavior of long polymers.Comment: 5 Pages RevTeX and 5 PostScript figures included (to appear in
Physical Review E
The generalized contact process with n absorbing states
We investigate the critical properties of a one dimensional stochastic
lattice model with n (permutation symmetric) absorbing states. We analyze the
cases with by means of the non-hermitian density matrix
renormalization group. For n=1 and n=2 we find that the model is respectively
in the directed percolation and parity conserving universality class,
consistent with previous studies. For n=3 and n=4, the model is in the active
phase in the whole parameter space and the critical point is shifted to the
limit of one infinite reaction rate. We show that in this limit the dynamics of
the model can be mapped onto that of a zero temperature n-state Potts model. On
the basis of our numerical and analytical results we conjecture that the model
is in the same universality class for all with exponents , and . These exponents
coincide with those of the multispecies (bosonic) branching annihilating random
walks. For n=3 we also show that, upon breaking the symmetry to a lower one
(), one gets a transition either in the directed percolation, or in the
parity conserving class, depending on the choice of parameters.Comment: 10 pages, RevTeX, and 10 PostScript figures include
Reptation in the Rubinstein-Duke model: the influence of end-reptons dynamics
We investigate the Rubinstein-Duke model for polymer reptation by means of
density-matrix renormalization group techniques both in absence and presence of
a driving field. In the former case the renewal time \tau and the diffusion
coefficient D are calculated for chains up to N=150 reptons and their scaling
behavior in N is analyzed. Both quantities scale as powers of N: and with the asymptotic exponents z=3 and x=2, in agreement
with the reptation theory. For an intermediate range of lengths, however, the
data are well-fitted by some effective exponents whose values are quite
sensitive to the dynamics of the end reptons. We find 2.7 <z< 3.3 and 1.8 <x<
2.1 for the range of parameters considered and we suggest how to influence the
end reptons dynamics in order to bring out such a behavior. At finite and not
too small driving field, we observe the onset of the so-called band inversion
phenomenon according to which long polymers migrate faster than shorter ones as
opposed to the small field dynamics. For chains in the range of 20 reptons we
present detailed shapes of the reptating chain as function of the driving field
and the end repton dynamics.Comment: RevTeX 12 Pages and 14 figure
Effective affinities in microarray data
In the past couple of years several studies have shown that hybridization in
Affymetrix DNA microarrays can be rather well understood on the basis of simple
models of physical chemistry. In the majority of the cases a Langmuir isotherm
was used to fit experimental data. Although there is a general consensus about
this approach, some discrepancies between different studies are evident. For
instance, some authors have fitted the hybridization affinities from the
microarray fluorescent intensities, while others used affinities obtained from
melting experiments in solution. The former approach yields fitted affinities
that at first sight are only partially consistent with solution values. In this
paper we show that this discrepancy exists only superficially: a sufficiently
complete model provides effective affinities which are fully consistent with
those fitted to experimental data. This link provides new insight on the
relevant processes underlying the functioning of DNA microarrays.Comment: 8 pages, 6 figure
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