The nucleotide sequences complexity in chromosome 3 of Caenorhabditis elegans (C. elegans) is studied. The complexity of these sequences is compared with some random sequences. Moreover, by using some parameters related to complexity such as fractal dimension and frequency, indicator matrix is given a first classification of sequences of C. elegans. In particular, the sequences with highest and lowest fractal value are singled out. It is shown that the intrinsic nature of the low fractal dimension sequences has many common features with the random sequences. 1. Introduction The Caenorhabditis elegans (C. elegans) is a 1？mm length transparent nematode. Thanks to its simple organic structure, it was taken as a model for research into genetic field. Early studies on C. elegans began in 1962 with some works on cell lineage and apoptosis [1, 2]. There are 2 distinct sexual types of the C. elegans, the hermaphrodite and the male. The second one is very rarely represented in nature (being approximately only the 0.05% of the population). We have 959 cells in the hermaphroditic species and 1031 cells for the male. The sexual difference at the chromosomal level provides: XX chromosomes for hermafrodite and X0 for the male. The sexual reproduction of C. elegans is realized by 2 distinct pathways: mating or, in case of the hermaphrodite, by a self-fertilization. The life cycle of C. elegans consists of 4 larval stages (from L1 to L4); however, if there exists some hard environment conditions, such as lacking of food, the C. elegans remains in the L3 larval stage, until the conditions improve. The complete sequencing of C. elegans genome was completed in 2002. The C. elegans has 5 chromosomes autosomes plus the sex chromosome X. Totally, it is made up of nearly 100 million base pairs and 19000 genes [3–5]. Study on fractal analysis of multigenome of C. elegans has shown that chromosome 3 is the one with multifractal characteristics higher than the others, the less multifractal appears to be the chromosome sexual X [6]. For the first time, in this work, we have analyzed the different types of sequences belonging to the genome of C. elegans, focusing our investigation on those that show fractal characteristics. Thus, chromosome 3 of C. elegans has been carefully studied because its unsymmetrical and inhomogeneous statistical characteristics. Through the analysis of this chromosome we can investigate what are the features that make it more “complex” from a biostatistical point of view and in particular with the use of statistical parameters such as the complexity, the
P. E. Velez, L. E. Garreta, E. Martinez et al., “The Caenorhabditis elegans genome: a multifractal analysis,” Genetics and Molecular Research, vol. 9, no. 2, pp. 949–965, 2010.
S. S. Cross and D. W. K. Cotton, “The fractal dimension may be a useful morphometric discriminant in histopathology,” Journal of Pathology, vol. 166, no. 4, pp. 409–411, 1992.
Z. G. Yu, V. Anh, and K. S. Lau, “Measure representation and multifractal analysis of complete genomes,” Physical Review E, vol. 64, no. 3, Article ID 031903, pp. 319031–319039, 2001.
Z. G. Yu, V. Anh, and K. S. Lau, “Multifractal and correlation analyses of protein sequences from complete genomes,” Physical Review E, vol. 68, no. 2, Article ID 021913, pp. 021913-1–021913-10, 2003.
G. A. Losa and T. F. Nonnenmacher, “Self-similarity and fractal irregularity in pathologic tissues,” Modern Pathology, vol. 9, no. 3, pp. 174–182, 1996.
Y. Xiao, R. Chen, R. Shen, J. Sun, and J. Xu, “Fractal dimension, of exon and intron sequences,” Journal of Theoretical Biology, vol. 175, no. 1, pp. 23–26, 1995.
R. L. Adam, R. C. Silva, F. G. Pereira, N. J. Leite, I. Lorand-Metze, and K. Metze, “The fractal dimension of nuclear chromatin as a prognostic factor in acute precursor B lymphoblastic leukemia,” Cellular Oncology, vol. 28, no. 1-2, pp. 55–59, 2006.
D. P. Ferro, M. A. Falconi, R. L. Adam et al., “Fractal characteristics of May-Grünwald-Giemsa stained chromatin are independent prognostic factors for survival in multiple myeloma,” PLoS ONE, vol. 6, no. 6, Article ID e20706, 2011.
C. Cattani and G. Pierro, “Complexity on acute myeloid leukemia mRNA transcript variant,” Mathematical Problems in Engineering, vol. 2011, Article ID 379873, 16 pages, 2011.
C. Cattani, “Wavelet algorithms for DNA analysis,” in Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications, M. Elloumi and A. Y. Zomaya, Eds., Wiley Series in Bioinformatics, chapter 35, pp. 799–842, John Wiley & Sons, New York, NY, USA, 2010.
C. Cattani, “On the existence of wavelet symmetries in archaea DNA,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 673934, 21 pages, 2012.
C. Cattani, “Complexity and simmetries in DNA sequences,” in Handbook of Biological Discovery, (Wiley Series in Bioinformatics), M. Elloumi and A. Y. Zomaya, Eds., Chapter 5, pp. 700–742, John Wiley & Sons, New York, NY, USA, 2012.
R. F. Voss, “Evolution of long-range fractal correlations and 1/f noise in DNA base sequences,” Physical Review Letters, vol. 68, no. 25, pp. 3805–3808, 1992.