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Register a new userNonlinear excitations in DNA: Aperiodic models vs actual genome sequences
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We study the effects of the sequence on the propagation of nonlinear excitations in simple models of DNA in which we incorporate actual DNA sequences obtained from human genome data. We show that kink propagation requires forces over a certain threshold, a phenomenon already found for aperiodic sequences [F. Domi nguez-Adame {em et al.}, Phys. Rev. E {bf 52}, 2183 (1995)]. For forces below threshold, the final stop positions are highly dependent on the specific sequence. The results of our model are consistent with the stick-slip dynamics of the unzipping process observed in experiments. We also show that the effective potential, a collective coordinate formalism introduced by Salerno and Kivshar [Phys. Lett. A {bf 193}, 263 (1994)] is a useful tool to identify key regions in DNA that control the dynamical behavior of large segments. Additionally, our results lead to further insights in the phenomenology observed in aperiodic systems.
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Repetitive elements are important in genomic structures, functions and regulations, yet effective methods in precisely identifying repetitive elements in DNA sequences are not fully accessible, and the relationship between repetitive elements and periodicities of genomes is not clearly understood. We present an $textit{ab initio}$ method to quantitatively detect repetitive elements and infer the consensus repeat pattern in repetitive elements. The method uses the measure of the distribution uniformity of nucleotides at periodic positions in DNA sequences or genomes. It can identify periodicities, consensus repeat patterns, copy numbers and perfect levels of repetitive elements. The results of using the method on different DNA sequences and genomes demonstrate efficacy and accuracy in identifying repeat patterns and periodicities. The complexity of the method is linear with respect to the lengths of the analyzed sequences.
We study the nonlinear dynamics of a completely inhomogeneous DNA chain which is governed by a perturbed sine-Gordon equation. A multiple scale perturbation analysis provides perturbed kink-antikink solitons to represent open state configuration with small fluctuation. The perturbation due to inhomogeneities changes the velocity of the soliton. However, the width of the soliton remains constant.
We analyze the statistical properties of Poincare recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincare recurrences decays in an algebraic way with the Poincare exponent $beta approx 4$ even if oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent $ u approx 0.6$ that leads to an anomalous super-diffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than million base pairs. We argue that the approach based on Poncare recurrences determines new proximity features between different species and shed a new light on their evolution history.
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