Long range clustering of oligonucleotides containing the CG signal

Complexity measures for the evolutionary categorization of organisms

Complexity measures are used to compare the genomic characteristics of five organisms belonging to distinct classes spanning the evolutionary tree: higher eukaryotes, amoebae, unicellular eukaryotes and bacteria. The comparisons are undertaken using the full four-letter alphabet and the coarse grained two-letter alphabets AG-CT and AT-CG. We show that the conditional probability matrix for the four-letter and AT-CG alphabet is markedly asymmetric in eukaryotes while it is nearly symmetric in bacterial genomes. Spatial asymmetry is revealed in the four-letter alphabet, signifying that the probability fluxes are nonvanishing and thus the reading sense of a sequence is irreversible for all organisms. Calculations of the block entropy and excess entropy demonstrate that the human genome accommodates better all possible block configurations, especially for long blocks. With respect to point-to-point details and to spatial arrangement of blocks the exit distance distributions from a particular letter demonstrate long distance characteristics in the eukaryotic sequences for all three alphabets, while the bacterial (prokaryotic) genomes deviate indicating short range characteristics. Overall, the conditional probability, the fluxes, the block entropy content and the exit distance distributions can be used as markers, discriminating between eukaryotic and prokaryotic DNA, allowing in many cases to discern details related to finer classes. In all cases the reduction from four letters to two masks some important statistical and spatial properties, with the AT-CG alphabet having higher ability of discrimination than the AG-CT one. In particular, the AT-CG alphabet reduction accentuates the CpG related properties (conditional probabilities w32, long ranged exit distance distribution for A and T nucleotides), but masks sequence asymmetry and irreversibility in all examined organisms.

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. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ^{2} tests shows that DNA can not be described as a low order Markov chain of order up to r=6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs 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 nonequilibrium 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 us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

Coupled intermittent maps modeling the statistics of genomic sequences: A network approach

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long-range correlation features which are observed in the genomic sequences of higher eucaryotes. A weighted network approach to symbolic sequences is introduced, and it is shown that coupled intermittent polynomial maps produce degree and link size distributions with power-law exponents similar to the ones observed in real genomes. The proposed network approach to symbolic sequences is generic and can be applied to any symbol sequence (artificial or natural).

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 four symbols) very closely reproduce the multifractal spectrum D(q) of human genomic sequences for coupling constant α = 0.35 ± 0.01 if q > 0. The presence of rare configurations causes deviations for q < 0, 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.

Hierarchical multifractal representation of symbolic sequences and application to human chromosomes

The two-dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size. The multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences. This method is applied to entire human chromosomes, shuffled human chromosomes, reconstructed human genomic sequences and to artificial random sequences. It is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size. Small deviations are observed between the longer and the shorter chromosomes, especially for the higher (in absolute values) statistical moments. The correlations are crucial for the form of the multifractal spectrum; surrogate shuffled chromosomes present randomlike spectrum, distinctly different from the actual chromosomes. Analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra, especially in the region of negative exponents, due to the underrepresentation of various functional units (such as the cytosine-guanine CG combination and its complementary GC complex). Retaining higher-order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences. This hierarchical approach is generic and is applicable to other correlated symbolic sequences.