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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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Statistics of Poincare recurrences is studied for the base-pair breathing dynamics of an all-atom DNA molecule in realistic aqueous environment with thousands of degrees of freedom. It is found that at least over five decades in time the decay of recurrences is described by an algebraic law with the Poincare exponent close to $beta=1.2$. This value is directly related to the correlation decay exponent $ u = beta -1$, which is close to $ uapprox 0.15$ observed in the time resolved Stokes shift experiments. By applying the virial theorem we analyse the chaotic dynamics in polynomial potentials and demonstrate analytically that exponent $beta=1.2$ is obtained assuming the dominance of dipole-dipole interactions in the relevant DNA dynamics. Molecular dynamics simulations also reveal the presence of strong low frequency noise with the exponent $eta=1.6$. We trace parallels with the chaotic dynamics of symplectic maps with a few degrees of freedom characterized by the Poincare exponent $beta sim 1.5$.
DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of proteins lead to variations in the replication time. We analyse these stochastic properties of DNA and derive the positions of origins corresponding to the minimum replication time. We show that under some conditions the minimization of replication time leads to the grouping of origins, and relate this to experimental data in a number of species showing origin grouping.
Several experiments show that the three dimensional (3D) organization of chromosomes affects genetic processes such as transcription and gene regulation. To better understand this connection, researchers developed the Hi-C method that is able to detect the pairwise physical contacts of all chromosomal loci. The Hi-C data show that chromosomes are composed of 3D compartments that range over a variety of scales. However, it is challenging to systematically detect these cross-scale structures. Most studies have therefore designed methods for specific scales to study foremost topologically associated domains (TADs) and A/B compartments. To go beyond this limitation, we tailor a network community detection method that finds communities in compact fractal globule polymer systems. Our method allows us to continuously scan through all scales with a single resolution parameter. We found: (i) polymer segments belonging to the same 3D community do not have to be in consecutive order along the polymer chain. In other words, several TADs may belong to the same 3D community. (ii) CTCF proteins---a loop-stabilizing protein that is ascribed a big role in TAD formation---are well correlated with community borders only at one level of organization. (iii) TADs and A/B compartments are traditionally treated as two weakly related 3D structures and detected with different algorithms. With our method, we detect both by simply adjusting the resolution parameter. We therefore argue that they represent two specific levels of a continuous spectrum 3D communities, rather than seeing them as different structural entities.
The flexibility and stiffness of small DNA play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) having length ranging from 12 base-pairs (bps) to 56 bps, paranemic crossover (PX) DNA, and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grain models $-$ Martini and oxDNA. To calculate the persistence length ($L_p$) and the stretch modulus ($gamma$) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for DNT, we implement our previously developed theoretical framework. We compare and contrast all the results with previously reported all-atom molecular dynamics (MD) simulation and experimental results. The mechanical properties of dsDNA ($L_p$ $sim$ 50nm, $gamma sim$ 800-1500 pN), PX DNA ($gamma sim$ 1600-2000 pN) and DNTs ($L_p sim 1-10 mu$m, $gamma sim$ 6000-8000 pN) estimated using Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces order of magnitude higher values of $L_p$ and $gamma$. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. OxDNA captures the salt concentration effect on small dsDNA mechanics. But it is found to be ineffective to reproduce the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.
We investigate the dynamics of DNA translocation through a nanopore using 2D Langevin dynamics simulations, focusing on the dependence of the translocation dynamics on the details of DNA sequences. The DNA molecules studied in this work are built from two types of bases $A$ and $C$, which has been shown previously to have different interactions with the pore. We study DNA with repeating blocks $A_nC_n$ for various values of $n$, and find that the translocation time depends strongly on the {em block length} $2n$ as well as on the {em orientation} of which base entering the pore first. Thus, we demonstrate that the measurement of translocation dynamics of DNA through nanopore can yield detailed information about its structure. We have also found that the periodicity of the block sequences are contained in the periodicity of the residence time of the individual nucleotides inside the pore.
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