Fractal genome sequences

Albrecht‐Buehler, Guenter

doi:10.1016/j.gene.2012.01.090

Cited by 25 publications

(20 citation statements)

References 15 publications

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“…GA-sequences, which are composed of hundreds of thousands of segments of DNA containing only guanine and adenine, have been described as a class of fractal genomic sequences, scattered densely throughout the chromosomes. They can be detected in a large number of genomes from different species and are considered to be useful universal natural markers of the non-coding regions of genomes [75]. Repetitive DNA sequences derived from transposable elements are co-clustering with other classes of repeat elements, genes or other components of the genome, and in that way, not randomly distributed.…”

Section: Fractality In the Cell Nucleusmentioning

confidence: 99%

“…According to Albrecht-Buehler, a conceivable linkage between the fractal DNA packing and the GA-fractal sequences has not been established yet [75]. When, however, considering the ubiquitous principle of parsimony in nature, it would be difficult to imagine that the different forms of fractal organization in various levels in the nucleus would all be completely unrelated.…”

Section: Fractality In the Cell Nucleusmentioning

confidence: 99%

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Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

Metze

2013

Expert Review of Molecular Diagnostics

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Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed.

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Section: Fractality In the Cell Nucleusmentioning

confidence: 99%

Section: Fractality In the Cell Nucleusmentioning

confidence: 99%

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

Metze

2013

Expert Review of Molecular Diagnostics

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“…FD takes on non-integer values between the classical Euclidean dimensional values of one, two and three used to define the dimensions of a line, square and a cube. Fractal geometry has been used to describe molecular folding of DNA, and the nucleotide distribution in the genome [16][17][18][19]. In such instances, FD explains the complex structural organization of natural objects.…”

Section: Introductionmentioning

confidence: 99%

On the organization of human T-cell receptor loci: log-periodic distribution of T-cell receptor gene segments

Toor

Rahmani

et al. 2016

J. R. Soc. Interface.

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We dedicate this work to Mr Omair Ahmed Toor and other people with Down's Syndrome and patients with congenital neurological disorders from around the world, whose constant struggle to overcome the challenges of everyday life and better themselves are an inspiration to all.On the organization of human T-cell receptor loci: log-periodic distribution of T-cell receptor gene segments School of Engineering, Virginia Commonwealth University, Richmond, VA, USAThe human T-cell repertoire is complex and is generated by the rearrangement of variable (V), diversity (D) and joining (J) segments on the T-cell receptor (TCR) loci. The T-cell repertoire demonstrates self-similarity in terms clonal frequencies when defined by V, D and J gene segment usage; therefore to determine whether the structural ordering of these gene segments on the TCR loci contributes to the observed clonal frequencies, the TCR loci were examined for self-similarity and periodicity in terms of gene segment organization. Logarithmic transformation of numeric sequence order demonstrated that the V and J gene segments for both T-cell receptor a (TRA) and b (TRB) loci are arranged in a self-similar manner when the spacing between the adjacent segments was considered as a function of the size of the neighbouring gene segment, with an average fractal dimension of approximately 1.5. Accounting for the gene segments occurring on helical DNA molecules with a logarithmic distribution, sine and cosine functions of the log-transformed angular coordinates of the start and stop nucleotides of successive TCR gene segments showed an ordered progression from the 5 0 to the 3 0 end of the locus, supporting a log-periodic organization. T-cell clonal frequency estimates, based on V and J segment usage, from normal stem cell donors were plotted against the V and J segment on TRB locus and demonstrated a periodic distribution. We hypothesize that this quasi-periodic variation in genesegment representation in the T-cell clonal repertoire may be influenced by the location of the gene segments on the periodic-logarithmically scaled TCR loci. Interactions between the two strands of DNA in the double helix may influence the probability of gene segment usage by means of either constructive or destructive interference resulting from the superposition of the two helices.

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“…In view of the prevalence of fractal patterns in nature, some inspiring studies, specially in biology, are reported [1,13,14]. The present subsection is inspired by Fig.…”

Section: Self-similar Compact Timescalesmentioning

confidence: 99%

Non-differentiability and fractional differentiability on timescales

2017

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This work deals with concepts of non-differentiability and a non-integer order differential on timescales. Through an investigation of a local non-integer order derivative on timescales, a mean value theorem (a fractional analog of the mean value theorem on timescales) is presented. Then, by illustrating a vanishing property of this derivative, its objectivity is discussed. As a first-hand result, the potentials and capability of this fractional derivative connected to nonsmooth analysis, including non-differentiable paths and a class of self-similar fractals, are stated. It is stated that the non-integer order derivative never vanishes almost everywhere. It has been shown that with the help of changing the order of differentiability on a q-timescale, the non-differentiability disappears.

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Fractal genome sequences

Cited by 25 publications

References 15 publications

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

On the organization of human T-cell receptor loci: log-periodic distribution of T-cell receptor gene segments

Non-differentiability and fractional differentiability on timescales

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