Wavelet-based method to disentangle transcription-and replication-associated strand asymmetries in mammalian genomes

in Applied & Computational Harmonic Analysis (2010), 28

During genome evolution, the two strands of the DNA double helix are not subjected to the same mutation patterns. This mutation bias is considered as a by-product of replicative and transcriptional ... [more ▼]

During genome evolution, the two strands of the DNA double helix are not subjected to the same mutation patterns. This mutation bias is considered as a by-product of replicative and transcriptional activities. In this paper, we develop a wavelet-based methodology to analyze the DNA strand asymmetry profiles with the specific goal to extract the contributions associated with replication and transcription respectively. In a first step, we use an adapted N-shaped analyzing wavelet to perform a multi-scale pattern recognition analysis of the sum of the TA and GC skews along human chromosomes. This method provides an 1 Mbp characteristic objective segmentation of the human genome in skew domains of size, bordered by two putative replication origins recognized as large amplitude upward jumps in the noisy skew profile. In a second step, we use a least-square fitting procedure to disentangle, in these skew domains, the small-scale (the mean human gene size 30 kbp) square-like transcription component from the global N-shaped component induced by replication. When applying this procedure to the 22 human autosomes, we delineate 678 replication domains of mean length L = 1.2 ± 0.6 Mbp spanning 33.8% of the human genome and we predict 1062 replication origins. When investigating the distribution of transcription-associated skew inside the replication N-domains, we reveal some dependence upon the distance to the putative replication origins located at N- domain extremities, the closer the genes to the origin, the larger their transcription bias as the signature of a higher transcriptional activity in the germ-line. As a comparative analysis, we further apply our wavelet-based methodology to skew profiles along the mouse chromosomes. The striking similarity of the results in human and mouse indicates that the remarkable gene organization observed inside the human replication N-domains is likely to be a general feature of mammalian genomes. [less ▲]

Compactly supported wavelets in Sobolev spaces of integer order

in Applied & Computational Harmonic Analysis (1997), 4(1), 51-57

We present a construction of regular compactly supported wavelets in any Sobolev space of integer order. It is based on the existence and suitable estimates of filters defined from polynomial equations ... [more ▼]

We present a construction of regular compactly supported wavelets in any Sobolev space of integer order. It is based on the existence and suitable estimates of filters defined from polynomial equations. We give an implicit study of these filters and use the results obtained to construct scaling functions leading to multiresolution analysis and wavelets. Their regularity increases linearly with the length of their supports as in the L(2) case. One technical problem is to prove that the intersection of the scaling spaces is reduced to 0. This is solved using sharp estimates of Littlewood-Paley type. (C) 1997 Academic Press, Inc. [less ▲]