Deciphering DNA replication dynamics in eukaryotic cell populations in relation with their averaged chromatin conformations.

We propose a non-local model of DNA replication that takes into account the observed uncertainty on the position and time of replication initiation in eukaryote cell populations. By picturing replication initiation as a two-state system and considering all possible transition configurations, and by taking into account the chromatin's fractal dimension, we derive an analytical expression for the rate of replication initiation. This model predicts with no free parameter the temporal profiles of initiation rate, replication fork density and fraction of replicated DNA, in quantitative agreement with corresponding experimental data from both S. cerevisiae and human cells and provides a quantitative estimate of initiation site redundancy. This study shows that, to a large extent, the program that regulates the dynamics of eukaryotic DNA replication is a collective phenomenon that emerges from the stochastic nature of replication origins initiation.

SWDreader: a wavelet-based algorithm using spectral phase to characterize spike-wave morphological variation in genetic models of absence epilepsy.

BACKGROUND: Spike-wave discharges (SWD) found in neuroelectrical recordings are pathognomonic to absence epilepsy. The characteristic spike-wave morphology of the spike-wave complex (SWC) constituents of SWDs can be mathematically described by a subset of possible spectral power and phase values. Morlet wavelet transform (MWT) generates time-frequency representations well-suited to identifying this SWC-associated subset. NEW METHOD: MWT decompositions of SWDs reveal spectral power concentrated at harmonic frequencies. The phase relationships underlying SWC morphology were identified by calculating the differences between phase values at SWD fundamental frequency from the 2nd, 3rd, and 4th harmonics, then using the three phase differences as coordinates to generate a density distribution in a {360°×360°×360°} phase difference space. Strain-specific density distributions were generated from SWDs of mice carrying the Gria4, Gabrg2, or Scn8a mutations to determine whether SWC morphological variants reliably mapped to the same regions of the distribution, and if distribution values could be used to detect SWD. COMPARISON WITH EXISTING METHODS: To the best of our knowledge, this algorithm is the first to employ spectral phase to quantify SWC morphology, making it possible to computationally distinguish SWC morphological subtypes and detect SWDs. RESULTS/CONCLUSIONS: Proof-of-concept testing of the SWDfinder algorithm shows: (1) a major pattern of variation in SWC morphology maps to one axis of the phase difference distribution, (2) variability between the strain-specific distributions reflects differences in the proportions of SWC subtypes generated during SWD, and (3) regularities in the spectral power and phase profiles of SWCs can be used to detect waveforms possessing SWC-like morphology.

Revealing long-range interconnected hubs in human chromatin interaction data using graph theory.

We use graph theory to analyze chromatin interaction (Hi-C) data in the human genome. We show that a key functional feature of the genome--"master" replication origins--corresponds to DNA loci of maximal network centrality. These loci form a set of interconnected hubs both within chromosomes and between different chromosomes. Our results open the way to a fruitful use of graph theory concepts to decipher DNA structural organization in relation to genome functions such as replication and transcription. This quantitative information should prove useful to discriminate between possible polymer models of nuclear organization.

Linking the DNA strand asymmetry to the spatio-temporal replication program: II. Accounting for neighbor-dependent substitution rates.

In paper I, we addressed the impact of the spatio-temporal program on the DNA composition evolution in the case of time homogeneous and neighbor-independent substitution rates. But substitution rates do depend on the flanking nucleotides as exemplified in vertebrates where CpG sites are hypermutable so that the substitution rate C --> T depends dramatically (ten fold) on whether the cytosine belongs to a CG dinucleotide or not. With the specific goal to account for neighbor-dependence, we revisit our minimal modeling of neutral substitution rates in the human genome. When assuming that r = CpG --> TpG and its reverse complement r(c) = CpG --> CpA are (by far) the main neighbor-dependent substitution rates, we demonstrate, using perturbative analysis, that neighbor-dependence does not affect the decomposition of the compositional asymmetry into a transcription- and a replication-associated components, the former increases in magnitude with transcription rate and changes sign with gene orientation, whereas the latter is proportional to the replication fork polarity. Indeed the neighbor dependence case differs from the neighbor-independent model by an additional source term related to the CG dinucleotide content in both the transcription and replication-associated components. We finally discuss the case of time-dependent substitution rates confirming as a very general result the fact that the skew can still be decomposed into a transcription- and a replication-associated components.

Linking the DNA strand asymmetry to the spatio-temporal replication program. I. About the role of the replication fork polarity in genome evolution.

Two key cellular processes, namely transcription and replication, require the opening of the DNA double helix and act differently on the two DNA strands, generating different mutational patterns (mutational asymmetry) that may result, after long evolutionary time, in different nucleotide compositions on the two DNA strands (compositional asymmetry). We elaborate on the simplest model of neutral substitution rates that takes into account the strand asymmetries generated by the transcription and replication processes. Using perturbation theory, we then solve the time evolution of the DNA composition under strand-asymmetric substitution rates. In our minimal model, the compositional and substitutional asymmetries are predicted to decompose into a transcription- and a replication-associated components. The transcription-associated asymmetry increases in magnitude with transcription rate and changes sign with gene orientation while the replication-associated asymmetry is proportional to the replication fork polarity. These results are confirmed experimentally in the human genome, using substitution rates obtained by aligning the human and chimpanzee genomes using macaca and orangutan as outgroups, and replication fork polarity determined in the HeLa cell line as estimated from the derivative of the mean replication timing. When further investigating the dynamics of compositional skew evolution, we show that it is not at equilibrium yet and that its evolution is an extremely slow process with characteristic time scales of several hundred Myrs.

Inferring where and when replication initiates from genome-wide replication timing data.

Based on an analogy between DNA replication and one dimensional nucleation-and-growth processes, various attempts to infer the local initiation rate I(x,t) of DNA replication origins from replication timing data have been developed in the framework of phase transition kinetics theories. These works have all used curve-fit strategies to estimate I(x,t) from genome-wide replication timing data. Here, we show how to invert analytically the Kolmogorov-Johnson-Mehl-Avrami model and extract I(x,t) directly. Tests on both simulated and experimental budding-yeast data confirm the location and firing-time distribution of replication origins.

Revisiting polymer statistical physics to account for the presence of long-range-correlated structural disorder in 2D DNA chains.

We elaborate on a generalization of the 2D wormlike chain (WLC) model that accounts for the presence of long-range correlations (LRC) in the intrinsic curvature distribution of eukaryotic DNA. This model predicts some decrease of the DNA persistence length resulting from some large-scale intrinsic curvature induced by sequence-dependent persistent random distribution of local bending sites. When assisting exact analytical calculations by numerical DNA simulations, we show that the conjugated contributions of i) the thermal curvature fluctuations characterized by the "dynamic" persistence length ℓ(p)(d) = 2A, where A is the elastic bending modulus, and ii) the intrinsic LRC curvature disorder of amplitude σ(o) and Hurst exponent H > 1/2, characterized by a "static" persistence length ℓ(p)(H) = A(1/2H)σ(o)(-1/H) Γ(1/2H + 1), can be described by a continuum of generalized WLC (GWLC) models parametrized by the LRC exponent H. We use perturbation analysis to investigate the two limiting cases of weak static disorder (w(H) << 1 and weak dynamical fluctuations (1/w (H) << 1), where w(H) = l(p)(d)/l(p)(H) is a dimensionless parameter. From a quantitative point of view, our study demonstrates that even for a small value of the LRC (H approximately equal 0.6-0.8) static disorder amplitude σ(o) ~ 10(-2), as previously reported for genomic DNA, the decrease of the persistence length from the WLC prediction l(p)(d) can be very significant, up to twofold. The implications of these results on the first steps of compaction of DNA in eukaryotic cells are discussed.

Spontaneous emergence of sequence-dependent rosettelike folding of chromatin fiber.

In the crowded environment of the eukaryotic nucleus, the presence of intrinsic structural defects is shown to predispose chromatin fiber to spontaneously form rosettelike structures. These multilooped patterns self-organize through entropy-driven clustering of sequence-induced fiber defects by depletive forces prior to any external factors coming into play. They provide an attractive description of replication foci that are observed in interphase mammalian nuclei as stable chromatin domains of autonomous DNA replication and gene expression. Experimental perspectives for in vivo visualization of rosettelike organization of the chromatin fiber via the clustering of recently identified putative replication initiation zones are discussed.

Bifractality of human DNA strand-asymmetry profiles results from transcription.

We use the wavelet transform modulus maxima method to investigate the multifractal properties of strand-asymmetry DNA walk profiles in the human genome. This study reveals the bifractal nature of these profiles, which involve two competing scale-invariant (up to repeat-masked distances less, or similar 40 kbp) components characterized by Hölder exponents h{1}=0.78 and h{2}=1, respectively. The former corresponds to the long-range-correlated homogeneous fluctuations previously observed in DNA walks generated with structural codings. The latter is associated with the presence of jumps in the original strand-asymmetry noisy signal S. We show that a majority of upward (downward) jumps co-locate with gene transcription start (end) sites. Here 7228 human gene transcription start sites from the refGene database are found within 2 kbp from an upward jump of amplitude DeltaS > or = 0.1 which suggests that about 36% of annotated human genes present significant transcription-induced strand asymmetry and very likely high expression rate.

Experiments confirm the influence of genome long-range correlations on nucleosome positioning.

From the statistical analysis of nucleosome positioning data for chromosome III of S. cerevisiae, we demonstrate that long-range correlations (LRC) in the genomic sequence strongly influence the organization of nucleosomes. We present a physical explanation of how LRC may significantly condition the overall formation and positioning of nucleosomes including the nucleosome-free regions observed at gene promoters. From grand canonical Monte Carlo simulations based upon a simple sequence-dependent nucleosome model, we show that LRC induce a patchy nucleosome occupancy landscape with alternation of "crystal-like" phases of confined regularly spaced nucleosomes and "fluidlike" phases of rather diluted nonpositioned nucleosomes.

DNA replication timing data corroborate in silico human replication origin predictions.

We develop a wavelet-based multiscale pattern recognition methodology to disentangle the replication- from the transcription-associated compositional strand asymmetries observed in the human genome. Comparing replication skew profiles to recent high-resolution replication timing data reveals that most of the putative replication origins that border the so-identified replication domains are replicated earlier than their surroundings whereas the central regions replicate late in the S phase. We discuss the implications of this first experimental confirmation of these replication origin predictions that are likely to be early replicating and active in most tissues.

Formation and positioning of nucleosomes: effect of sequence-dependent long-range correlated structural disorder.

The understanding of the long-range correlations (LRC) observed in DNA sequences is still an open and very challenging problem. In this paper, we start reviewing recent results obtained when exploring the scaling properties of eucaryotic, eubacterial and archaeal genomic sequences using the space-scale decomposition provided by the wavelet transform (WT). These results suggest that the existence of LRC up to distances approximately 20-30 kbp is the signature of the nucleosomal structure and dynamics of the chromatin fiber. Actually the LRC are mainly observed in the DNA bending profiles obtained when using some structural coding of the DNA sequences that accounts for the fluctuations of the local double-helix curvature within the nucleosome complex. Because of the approximate planarity of nucleosomal DNA loops, we then study the influence of the LRC structural disorder on the thermodynamical properties of 2D elastic chains submitted locally to mechanical/topological constraint as loops. The equilibrium properties of the one-loop system are derived numerically and analytically in the quite realistic weak-disorder limit. The LRC are shown to favor the spontaneous formation of small loops, the larger the LRC, the smaller the size of the loop. We further investigate the dynamical behavior of such a loop using the mean first passage time (MFPT) formalism. We show that the typical short-time loop dynamics is superdiffusive in the presence of LRC. For displacements larger than the loop size, we use large-deviation theory to derive a LRC-dependent anomalous-diffusion rule that accounts for the lack of disorder self-averaging. Potential biological implications on DNA loops involved in nucleosome positioning and dynamics in eucaryotic chromatin are discussed.

From DNA sequence analysis to modeling replication in the human genome.

We explore the large-scale behavior of nucleotide compositional strand asymmetries along human chromosomes. As we observe for 7 of 9 origins of replication experimentally identified so far, the (TA+GC) skew displays rather sharp upward jumps, with a linear decreasing profile in between two successive jumps. We present a model of replication with well positioned replication origins and random terminations that accounts for the observed characteristic serrated skew profiles. We succeed in identifying 287 pairs of putative adjacent replication origins with an origin spacing approximately 1-2 Mbp that are likely to correspond to replication foci observed in interphase nuclei and recognized as stable structures that persist throughout subsequent cell generations.

Thermodynamics of DNA loops with long-range correlated structural disorder.

We study the influence of a structural disorder on the thermodynamical properties of 2D-elastic chains submitted to mechanical/topological constraint as loops. The disorder is introduced via a spontaneous curvature whose distribution along the chain presents either no correlation or long-range correlations (LRC). The equilibrium properties of the one-loop system are derived numerically and analytically for weak disorder. LRC are shown to favor the formation of small loop, larger the LRC, smaller the loop size. We use the mean first passage time formalism to show that the typical short time loop dynamics is superdiffusive in the presence of LRC. Potential biological implications on nucleosome positioning and dynamics in eukaryotic chromatin are discussed.

Influence of the sequence on elastic properties of long DNA chains.

We revisit the results of single-molecule DNA stretching experiments using a rodlike chain (RLC) model that explicitly includes some intrinsic structural disorder induced by the sequence. The investigation of artificial and real genomic sequences shows that the wormlike chain model reproduces quite well the data but with an effective bend stiffness A(eff), which underestimates the true elastic bend stiffness A, independently of the elastic twist stiffness C. Mainly dominated by the amplitude of the structural disorder, this correction seems rather insensitive to the presence of long-range correlations. This RLC model is shown to remarkably fit the experimental data for lambda-DNA when considering A approximately 70+/-10 nm (>A(eff) approximately 50 nm), in good agreement with previous experimental estimates of the "dynamic" persistent length. From the analysis of large human contigs, we speculate about the possible dependence of A(eff) and/or A upon the (G+C) content of the considered sequence.

Strain-specific genes of Helicobacter pylori: distribution, function and dynamics.

Whole-genome clustering of the two available genome sequences of Helicobacter pylori strains 26695 and J99 allows the detection of 110 and 52 strain-specific genes, respectively. This set of strain-specific genes was compared with the sets obtained with other computational approaches of direct genome comparison as well as experimental data from microarray analysis. A considerable number of novel function assignments is possible using database-driven sequence annotation, although the function of the majority of the identified genes remains unknown. Using whole-genome clustering, it is also possible to detect species-specific genes by comparing the two H.pylori strains against the genome sequence of Campylobacter jejuni. It is interesting that the majority of strain-specific genes appear to be species specific. Finally, we introduce a novel approach to gene position analysis by employing measures from directional statistics. We show that although the two strains exhibit differences with respect to strain-specific gene distributions, this is due to the extensive genome rearrangements. If these are taken into account, a common pattern for the genome dynamics of the two Helicobacter strains emerges, suggestive of certain spatial constraints that may act as control mechanisms of gene flux.

Long-range correlations in genomic DNA: a signature of the nucleosomal structure.

We use the "wavelet transform microscope" to carry out a comparative statistical analysis of DNA bending profiles and of the corresponding DNA texts. In the three kingdoms, one reveals on both signals a characteristic scale of 100-200 bp that separates two different regimes of power-law correlations (PLC). In the small-scale regime, PLC are observed in eukaryotic, in double-strand DNA viral, and in archaeal genomes, which contrasts with their total absence in the genomes of eubacteria and their viruses. This strongly suggests that small-scale PLC are related to the mechanisms underlying the wrapping of DNA in the nucleosomal structure. We further speculate that the large scale PLC are the signature of the higher-order structure and dynamics of chromatin.

Genome sequences and great expectations.

To assess how automatic function assignment will contribute to genome annotation in the next five years, we have performed an analysis of 31 available genome sequences. An emerging pattern is that function can be predicted for almost two-thirds of the 73,500 genes that were analyzed. Despite progress in computational biology, there will always be a great need for large-scale experimental determination of protein function.