264 research outputs found
Short-range plasma model for intermediate spectral statistics
We propose a plasma model for spectral statistics displaying level repulsion
without long-range spectral rigidity, i.e. statistics intermediate between
random matrix and Poisson statistics similar to the ones found numerically at
the critical point of the Anderson metal-insulator transition in disordered
systems and in certain dynamical systems. The model emerges from Dysons
one-dimensional gas corresponding to the eigenvalue distribution of the
classical random matrix ensembles by restricting the logarithmic pair
interaction to a finite number of nearest neighbors. We calculate
analytically the spacing distributions and the two-level statistics. In
particular we show that the number variance has the asymptotic form
for large and the nearest-neighbor distribution
decreases exponentially when , with
, where is the inverse temperature of the gas
(1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class
respectively). In the simplest case of , the model leads to the
so-called Semi-Poisson statistics characterized by particular simple
correlation functions e.g. . Furthermore we investigate the
spectral statistics of several pseudointegrable quantum billiards numerically
and compare them to the Semi-Poisson statistics.Comment: 24 pages, 4 figure
Translocation of structured polynucleotides through nanopores
We investigate theoretically the translocation of structured RNA/DNA
molecules through narrow pores which allow single but not double strands to
pass. The unzipping of basepaired regions within the molecules presents
significant kinetic barriers for the translocation process. We show that this
circumstance may be exploited to determine the full basepairing pattern of
polynucleotides, including RNA pseudoknots. The crucial requirement is that the
translocation dynamics (i.e., the length of the translocated molecular segment)
needs to be recorded as a function of time with a spatial resolution of a few
nucleotides. This could be achieved, for instance, by applying a mechanical
driving force for translocation and recording force-extension curves (FEC's)
with a device such as an atomic force microscope or optical tweezers. Our
analysis suggests that with this added spatial resolution, nanopores could be
transformed into a powerful experimental tool to study the folding of nucleic
acids.Comment: 9 pages, 5 figure
Inferring DNA sequences from mechanical unzipping: an ideal-case study
We introduce and test a method to predict the sequence of DNA molecules from
in silico unzipping experiments. The method is based on Bayesian inference and
on the Viterbi decoding algorithm. The probability of misprediction decreases
exponentially with the number of unzippings, with a decay rate depending on the
applied force and the sequence content.Comment: Source as TeX file with ps figure
Dynamics of Competitive Evolution on a Smooth Landscape
We study competitive DNA sequence evolution directed by {\it in vitro}
protein binding. The steady-state dynamics of this process is well described by
a shape-preserving pulse which decelerates and eventually reaches equilibrium.
We explain this dynamical behavior within a continuum mean-field framework.
Analytical results obtained on the motion of the pulse agree with simulations.
Furthermore, finite population correction to the mean-field results are found
to be insignificant.Comment: 4 pages, 2 figures, revised, to appear in Phys. Rev. Let
Emergence of robust nucleosome patterns from an interplay of positioning mechanisms
Proper positioning of nucleosomes in eukaryotic cells is determined by a complex interplay of factors, including nucleosome-nucleosome interactions, DNA sequence, and active chromatin remodeling. Yet, characteristic features of nucleosome positioning, such as geneaveraged nucleosome patterns, are surprisingly robust across perturbations, conditions, and species. Here, we explore how this robustness arises despite the underlying complexity. We leverage mathematical models to show that a large class of positioning mechanisms merely affects the quantitative characteristics of qualitatively robust positioning patterns. We demonstrate how statistical positioning emerges as an effective description from the complex interplay of different positioning mechanisms, which ultimately only renormalize the model parameter quantifying the effective softness of nucleosomes. This renormalization can be species-specific, rationalizing a puzzling discrepancy between the effective nucleosome softness of S. pombe and S. cerevisiae. More generally, we establish a quantitative framework for dissecting the interplay of different nucleosome positioning determinants
Quasispecies evolution in general mean-field landscapes
I consider a class of fitness landscapes, in which the fitness is a function
of a finite number of phenotypic "traits", which are themselves linear
functions of the genotype. I show that the stationary trait distribution in
such a landscape can be explicitly evaluated in a suitably defined
"thermodynamic limit", which is a combination of infinite-genome and strong
selection limits. These considerations can be applied in particular to identify
relevant features of the evolution of promoter binding sites, in spite of the
shortness of the corresponding sequences.Comment: 6 pages, 2 figures, Europhysics Letters style (included) Finite-size
scaling analysis sketched. To appear in Europhysics Letter
Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures
Large RNA molecules often carry multiple functional domains whose spatial
arrangement is an important determinant of their function. Pre-mRNA splicing,
furthermore, relies on the spatial proximity of the splice junctions that can
be separated by very long introns. Similar effects appear in the processing of
RNA virus genomes. Albeit a crude measure, the distribution of spatial
distances in thermodynamic equilibrium therefore provides useful information on
the overall shape of the molecule can provide insights into the interplay of
its functional domains. Spatial distance can be approximated by the
graph-distance in RNA secondary structure. We show here that the equilibrium
distribution of graph-distances between arbitrary nucleotides can be computed
in polynomial time by means of dynamic programming. A naive implementation
would yield recursions with a very high time complexity of O(n^11). Although we
were able to reduce this to O(n^6) for many practical applications a further
reduction seems difficult. We conclude, therefore, that sampling approaches,
which are much easier to implement, are also theoretically favorable for most
real-life applications, in particular since these primarily concern long-range
interactions in very large RNA molecules.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Random RNA under tension
The Laessig-Wiese (LW) field theory for the freezing transition of random RNA
secondary structures is generalized to the situation of an external force. We
find a second-order phase transition at a critical applied force f = f_c. For f
f_c, the extension L as a function of
pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated
in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to
the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly
mentioned. Using a locking argument, we speculate that this result extends to
the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking
argument improve
Exact steady-state velocity of ratchets driven by random sequential adsorption
We solve the problem of discrete translocation of a polymer through a pore,
driven by the irreversible, random sequential adsorption of particles on one
side of the pore. Although the kinetics of the wall motion and the deposition
are coupled, we find the exact steady-state distribution for the gap between
the wall and the nearest deposited particle. This result enables us to
construct the mean translocation velocity demonstrating that translocation is
faster when the adsorbing particles are smaller. Monte-Carlo simulations also
show that smaller particles gives less dispersion in the ratcheted motion. We
also define and compare the relative efficiencies of ratcheting by deposition
of particles with different sizes and we describe an associated
"zone-refinement" process.Comment: 11 pages, 4 figures New asymptotic result for low chaperone density
added. Exact translocation velocity is proportional to (chaperone
density)^(1/3
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