Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation

Abstract

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamilto-nian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By inten-sively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly docu-mented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.