113 research outputs found
Non-extensive Trends in the Size Distribution of Coding and Non-coding DNA Sequences in the Human Genome
We study the primary DNA structure of four of the most completely sequenced
human chromosomes (including chromosome 19 which is the most dense in coding),
using Non-extensive Statistics. We show that the exponents governing the decay
of the coding size distributions vary between for the short
scales and for the large scales. On the contrary, the
exponents governing the decay of the non-coding size distributions in these
four chromosomes, take the values for the short scales and
for the large scales. This quantitative difference, in
particular in the tail exponent , indicates that the non-coding (coding)
size distributions have long (short) range correlations. This non-trivial
difference in the DNA statistics is attributed to the non-conservative
(conservative) evolution dynamics acting on the non-coding (coding) DNA
sequences.Comment: 13 pages, 10 figures, 2 table
DNA viewed as an out-of-equilibrium structure
The complexity of the primary structure of human DNA is explored using
methods from nonequilibrium statistical mechanics, dynamical systems theory and
information theory. The use of chi-square tests shows that DNA cannot be
described as a low order Markov chain of order up to . Although detailed
balance seems to hold at the level of purine-pyrimidine notation it fails when
all four basepairs are considered, suggesting spatial asymmetry and
irreversibility. Furthermore, the block entropy does not increase linearly with
the block size, reflecting the long range nature of the correlations in the
human genomic sequences. To probe locally the spatial structure of the chain we
study the exit distances from a specific symbol, the distribution of recurrence
distances and the Hurst exponent, all of which show power law tails and long
range characteristics. These results suggest that human DNA can be viewed as a
non-equilibrium structure maintained in its state through interactions with a
constantly changing environment. Based solely on the exit distance distribution
accounting for the nonequilibrium statistics and using the Monte Carlo
rejection sampling method we construct a model DNA sequence. This method allows
to keep all long range and short range statistical characteristics of the
original sequence. The model sequence presents the same characteristic
exponents as the natural DNA but fails to capture point-to-point details
Effective Mean Field Approach to Kinetic Monte Carlo Simulations in Limit Cycle Dynamics with Reactive and Diffusive Rewiring
The dynamics of complex reactive schemes is known to deviate from the Mean
Field (MF) theory when restricted on low dimensional spatial supports. This
failure has been attributed to the limited number of species-neighbours which
are available for interactions. In the current study, we introduce effective
reactive parameters, which depend on the type of the spatial support and which
allow for an effective MF description. As working example the Lattice Limit
Cycle dynamics is used, restricted on a 2D square lattice with nearest
neighbour interactions. We show that the MF steady state results are recovered
when the kinetic rates are replaced with their effective values. The same
conclusion holds when reactive stochastic rewiring is introduced in the system
via long distance reactive coupling. Instead, when the stochastic coupling
becomes diffusive the effective parameters no longer predict the steady state.
This is attributed to the diffusion process which is an additional factor
introduced into the dynamics and is not accounted for, in the kinetic MF
scheme.Comment: 8 pages, 6 figure
Reactive dynamics on fractal sets: anomalous fluctuations and memory effects
We study the effect of fractal initial conditions in closed reactive systems
in the cases of both mobile and immobile reactants. For the reaction , in the absence of diffusion, the mean number of particles is shown to
decay exponentially to a steady state which depends on the details of the
initial conditions. The nature of this dependence is demonstrated both
analytically and numerically. In contrast, when diffusion is incorporated, it
is shown that the mean number of particles decays asymptotically as
, the memory of the initial conditions being now carried by the
dynamical power law exponent. The latter is fully determined by the fractal
dimension of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl
Power law exponents characterizing human DNA
The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc S of size S present long tails Pnc S S−1− nc, with exponents nc ranging between 0.71 for chromosome 13 and 1.2 for chromosome 19 . On the contrary, the exponential, short-range decay terms dominate in the distributions of coding exon segments Pc S in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are
proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two
systems coding and noncoding coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium on
Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences
Symbolic sequences generated by coupled map lattices (CMLs) can be used to
model the chaotic-like structure of genomic sequences. In this study it is
shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a
shift of 4 symbols) very closely reproduce the multifractal spectrum of
human genomic sequences for coupling constant if .
The presence of rare configurations causes deviations for , which
disappear if the rare event statistics of the CML is modified. Such rare
configurations are known to play specific functional roles in genomic sequences
serving as promoters or regulatory elements.Comment: 7 pages, 6 picture
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