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

Metze, Konradin

doi:10.1586/14737159.2013.828889

Cited by 80 publications

(78 citation statements)

References 148 publications

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“…Thus, alterations in the FD could be suggestive of modifications in chromatin packing and might be of prognostic or diagnostic importance in multiple cancer pathologies, as is discussed in the ‘Pathology’ section of this Review. 38 Of note, bright-light and confocal microscopy images of nuclei can be quickly and easily used to measure the FD of chromatin and/or the nucleus. 38 …”

Section: Fractal Nature Of the Normal Lungmentioning

confidence: 99%

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Lung cancer—a fractal viewpoint

et al. 2015

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Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.

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Section: Fractal Nature Of the Normal Lungmentioning

confidence: 99%

“…38 Of note, bright-light and confocal microscopy images of nuclei can be quickly and easily used to measure the FD of chromatin and/or the nucleus. 38 …”

Section: Fractal Nature Of the Normal Lungmentioning

confidence: 99%

Lung cancer—a fractal viewpoint

et al. 2015

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“…The large-scale organization of chromatin is fundamentally different from its small-scale structure [16][17][18][19][20][21]. At present the most popular model describing the three-dimensional configuration of chromatin packaging in a cell nucleus is represented by a crumpled or fractal globule.…”

Section: Introductionmentioning

confidence: 99%

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

et al. 2017

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Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei Iashina Important noteTo cite this publication, please use the final published version (if applicable). Please check the document version above. CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policyPlease contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q −3 in the range of momentum transfer Q ∈ 10 −3 -10 −2 nm −1 . Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3 × 10 2 )-(3 × 10 4 ) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ (r) = ln(ξ/r) for r < ξ, where ξ = (3.69 ± 0.07) × 10 3 nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal γ (r/a) = γ (r) + ln(a), i.e., the scaling down by a gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.

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“…A number of literatures addressed the successful applications of box-counting dimension [23][24][25][26]. For the case of CGR situation, the CGR pictures of protein sequences are plane images-two dimensional geometries.…”

Section: Gpcr Familymentioning

confidence: 99%

A novel fractal approach for predicting G-protein–coupled receptors and their subfamilies with support vector machines

Nie

Wang

et al. 2015

BME

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Abstract. G-protein-coupled receptors (GPCRs) are seven membrane-spanning proteins and regulate many important physiological processes, such as vision, neurotransmission, immune response and so on. GPCRs-related pathways are the targets of a large number of marketed drugs. Therefore, the design of a reliable computational model for predicting GPCRs from amino acid sequence has long been a significant biomedical problem. Chaos game representation (CGR) reveals the fractal patterns hidden in protein sequences, and then fractal dimension (FD) is an important feature of these highly irregular geometries with concise mathematical expression. Here, in order to extract important features from GPCR protein sequences, CGR algorithm, fractal dimension and amino acid composition (AAC) are employed to formulate the numerical features of protein samples. Four groups of features are considered, and each group is evaluated by support vector machine (SVM) and 10-fold cross-validation test. To test the performance of the present method, a new non-redundant dataset was built based on latest GPCRDB database. Comparing the results of numerical experiments, the group of combined features with AAC and FD gets the best result, the accuracy is 99.22% and Matthew's correlation coefficient (MCC) is 0.9845 for identifying GPCRs from non-GPCRs. Moreover, if it is classified as a GPCR, it will be further put into the second level, which will classify a GPCR into one of the five main subfamilies. At this level, the group of combined features with AAC and FD also gets best accuracy 85.73%. Finally, the proposed predictor is also compared with existing methods and shows better performances.

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

Cited by 80 publications

References 148 publications

Lung cancer—a fractal viewpoint

Lung cancer—a fractal viewpoint

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

A novel fractal approach for predicting G-protein–coupled receptors and their subfamilies with support vector machines

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