Chromatin pattern by variogram analysis

Many cytological processes such as cell proliferation, differentiation, transformation, apoptosis, etc., are accompanied by specific chromatin changes, usually identified on the basis of the relative content of euchromatin and heterochromatin. In order to achieve a quantitative, non-subjective evaluation of the chromatin pattern, two different approaches may be undertaken, one consisting in the analysis of the several morphological features of chromatin grains (size, shape, density, arrangement, and distribution), and the second consisting in the analysis of the chromatin globally considered as a coherent texture. Although the second approach appears to be simpler and more suitable, methods of texture analysis--including those specifically designed for the analysis of the chromatin pattern--are rarely applied due mainly to the unsuitability of sampling procedures and the excessive crypticism of results. As an alternative to traditional texture analysis, we suggest a method supported by a sound mathematical theory and approximately 30 years of applications in the field of geostatistics. The method, called variogram, analyzes the intrinsic structure of data sampled at different distance intervals and directions, and outputs easily understandable results. Recently, variogram analysis has successfully been exported from geostatistics to other fields (for example, ecology and epidemiology) that make use of spatially referenced variables. Based on the fact that pixels represent a perfect array of data ordered at regular distance intervals and directions, the variogram can be adopted to explore nuclear images and recognize chromatin patterns. Variograms of different nuclei can be summarized by multivariate methods without the need of previous standardization of data. This allows comparison and discrimination of chromatin patterns from mixed cell populations. Preliminary data obtained from young neurons undergoing massive apoptosis reveal a self-consistent map of nuclear changes correlated to the degenerative process.