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

Abstract

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.

Keywords::

• acute leukemia
• fractal
• fractal dimension
• fractal globule
• goodness-of-fit
• heterochromatin
• higher-order chromatin
• multiple myeloma
• nucleus
• prognostic marker
• self-organization
• systems biology

Acknowledgments

The author would like to thank AA Piaza for assistance with the creation of the figures.

Financial & competing interests disclosure

The author has received grants from the São Paulo Research Foundation FAPESP (project 2007/52015–0) and the National Council of Technological and Scientific Development CNPq (project 307270/2010-6). The author has no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this manuscript.

Key issues

• • The fractal concept has improved our understanding of many phenomena in biomedical sciences.

• • Recently, a fractal globule model describing the 3D configuration of the cell nucleus has been introduced.

• • In histology and cytology, fractal characteristics of chromatin have been described during the last 20 years.

• • Fractal features, such as the fractal dimension or the goodness-of-fit of the regression curve can easily be estimated in digitalized microscopic images.

• • During carcinogenesis and tumor progression, the fractal dimension (FD) of chromatin usually increases.

• • In various tumors, an increased FD is an unfavorable prognostic facture.

• • The goodness-of-fit of the regression line may predict outcome, with a closer fit to the ideal fractal structure indicating a better prognosis.

• • Accumulating genetic and epigenetic alterations cause progressive chromatin remodeling.

• • A more complex chromatin structure, less heterochromatin and a less perfect self-organization of the nucleus are expected in more aggressive neoplasias.

Notes