447 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
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
Fixed Point of the Finite System DMRG
The density matrix renormalization group (DMRG) is a numerical method that
optimizes a variational state expressed by a tensor product. We show that the
ground state is not fully optimized as far as we use the standard finite system
algorithm, that uses the block structure B**B. This is because the tensors are
not improved directly. We overcome this problem by using the simpler block
structure B*B for the final several sweeps in the finite iteration process. It
is possible to increase the numerical precision of the finite system algorithm
without increasing the computational effort.Comment: 6 pages, 4 figure
Crossover from Reptation to Rouse dynamics in the Cage Model
The two-dimensional cage model for polymer motion is discussed with an
emphasis on the effect of sideways motions, which cross the barriers imposed by
the lattice. Using the Density Matrix Method as a solver of the Master
Equation, the renewal time and the diffusion coefficient are calculated as a
function of the strength of the barrier crossings. A strong crossover influence
of the barrier crossings is found and it is analyzed in terms of effective
exponents for a given chain length. The crossover scaling functions and the
crossover scaling exponents are calculated.Comment: RevTeX, 11 PostScript figures include
Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the
Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase
transition in the directed percolation universality class. Estimates for the
stochastic time evolution, phase boundaries and critical exponents can be
obtained with high precision. This is possible using only modest numerical
effort since the thermodynamic limit can be taken analytically in our approach.
We also point out further advantages of the TMRG over other numerical
approaches, such as classical DMRG or Monte-Carlo simulations.Comment: 9 pages, 9 figures, uses IOP styl
Stability domains of actin genes and genomic evolution
In eukaryotic genes the protein coding sequence is split into several
fragments, the exons, separated by non-coding DNA stretches, the introns.
Prokaryotes do not have introns in their genome. We report the calculations of
stability domains of actin genes for various organisms in the animal, plant and
fungi kingdoms. Actin genes have been chosen because they have been highly
conserved during evolution. In these genes all introns were removed so as to
mimic ancient genes at the time of the early eukaryotic development, i.e.
before introns insertion. Common stability boundaries are found in evolutionary
distant organisms, which implies that these boundaries date from the early
origin of eukaryotes. In general boundaries correspond with introns positions
of vertebrates and other animals actins, but not much for plants and fungi. The
sharpest boundary is found in a locus where fungi, algae and animals have
introns in positions separated by one nucleotide only, which identifies a
hot-spot for insertion. These results suggest that some introns may have been
incorporated into the genomes through a thermodynamic driven mechanism, in
agreement with previous observations on human genes. They also suggest a
different mechanism for introns insertion in plants and animals.Comment: 9 Pages, 7 figures. Phys. Rev. E in pres
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