Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation

Author(s)
Carlos Antonio Marante Valdés,
Fidel Antonio Castro Smirnov,
Oscar Rodríguez Hoyos,
João Dias de Toledo Arruda-Neto

Affiliation(s)

Centro de Estudios Avanzados de Cuba (CEAC), Havana, Cuba.

Universidad de las Ciencias Informáticas (UCI), Havana, Cuba.

Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC), Havana, Cuba.

Physics Institute, University of S?o Paulo, S?o Paulo, Brasil.

Centro de Estudios Avanzados de Cuba (CEAC), Havana, Cuba.

Universidad de las Ciencias Informáticas (UCI), Havana, Cuba.

Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC), Havana, Cuba.

Physics Institute, University of S?o Paulo, S?o Paulo, Brasil.

ABSTRACT

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian 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 intensively 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 documented 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.

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian 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 intensively 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 documented 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.

Cite this paper

C. Valdés, F. Smirnov, O. Hoyos and J. Arruda-Neto, "Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation,"*Journal of Modern Physics*, Vol. 3 No. 6, 2012, pp. 431-437. doi: 10.4236/jmp.2012.36059.

C. Valdés, F. Smirnov, O. Hoyos and J. Arruda-Neto, "Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation,"

References

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[11] D. Pang, J. E. Rodgers, B. L. Berman, S. Chasovskikh and A. Dritschilo, “Spatial Distribution of Radiation-In- duced Double-Strand Breaks in Plasmid DNA as Resolved by Atomic Force Microscopy,” Radiation Re- search, Vol. 164, No. 6, 2005, pp. 755-765. doi:10.1667/RR3425.1

[12] J. D. T. Arruda-Neto, et al., “Personal Communication,” Journal of Biological Physics, in Press.

[13] D. Pang, B. L. Berman, S. Chasovskikh, J. E. Rodgers and A. Dritschilo, “Investigation of Neutron-Induced Damage in DNA by Aromic Force Microscopy: Experimental Evidence of Clustered DNA Lesions,” Radiation Research, Vol. 150, No. 6, 1998, pp. 612-618. doi:10.2307/3579883

[14] D. Pang, et al., “Radiation-Generated Short DNA Fragments May Perturb Non-homologous End-joining and Induce Genomic Instability,” Journal of Radiation Research, Vol. 52, No. 3, 2011, pp. 309-319. doi:10.1269/jrr.10147

[1] K. Fuquan, et al., “Analysis of Length Distribution of Short DNA Fragments Induced by 7Li Ions Using the Random-Breakage Model,” Chinese Science Bulletin, Vol. 50, No. 9, 2005, pp. 841-844. doi:10.1360/982004-827

[2] M. L?brich, P. K. Cooper and B. Rydberg, “Non-Random Distribution of DNA Double-Strand Breaks Induced by Particle Irradiation,” International Journal of Radiation Biology, Vol. 70, No. 5, 1996, pp. 493-503. doi:10.1080/095530096144680

[3] F. A. Castro, O. Rodriguez and J. D. T. Arruda-Neto. “Present Status of Radiation Interaction with DNA- Strand-Break Cross-Section and Fragment-Size Distributions,” Radiation Effects and Defects in Solids, Vol. 162, No. 3-4, 2007, pp. 237-245. doi:10.1080/10420150601134616

[4] O. Sotolongo-Costa, et al., “A Non Extensive Approach for DNA Breaking by Ionizing Radiation,” 2002.

[5] T. Els?sser, et al., “Biophysical Modeling of Fragment Length Distributions of DNA Plasmids after X and Heavy-Ion Irradiation Analyzed by Atomic Force Microscopy,” Radiation Research, Vol. 169, No. 6, 2008, pp. 649-59. doi:10.1667/RR1028.1

[6] C. Tsallis, F. Baldovin, R. Cerbino and P. Pierobon. “Introduction to Nonextensive Statistical Mechanics and Thermodynamics,” 2003.

[7] C. Tsallis, R. Mendes and A. Plastino, “The Role of Constraints within Generalized Nonextensive Statistics,” Phy- sica A, Vol. 261, No. 3-4, 1998, pp. 534-554. doi:10.1016/S0378-4371(98)00437-3

[8] S. Curilef, “Generalized Statistical Mechanics for the N Body Quantum Problem—Ideal Gases,” Zeitschrift Für Physik B Condensed Matter, Vol. 100, No. 3, 1995, pp. 433-440.

[9] L. V. Yakushevich, “Nonlinear Physics of DNA,” 2nd Edition, Wiley-VCH Verlag-GmbH & Co. KGaA, Weinheim, 2004.

[10] S. Li, et al., “Atomic Force Microscopy Measurement of DNA Fragment Induced by Heavy Ions,” Chinese Physics Letters, Vol. 22, No. 4, 2005, pp. 1010-1013. doi:10.1088/0256-307X/22/4/064

[11] D. Pang, J. E. Rodgers, B. L. Berman, S. Chasovskikh and A. Dritschilo, “Spatial Distribution of Radiation-In- duced Double-Strand Breaks in Plasmid DNA as Resolved by Atomic Force Microscopy,” Radiation Re- search, Vol. 164, No. 6, 2005, pp. 755-765. doi:10.1667/RR3425.1

[12] J. D. T. Arruda-Neto, et al., “Personal Communication,” Journal of Biological Physics, in Press.

[13] D. Pang, B. L. Berman, S. Chasovskikh, J. E. Rodgers and A. Dritschilo, “Investigation of Neutron-Induced Damage in DNA by Aromic Force Microscopy: Experimental Evidence of Clustered DNA Lesions,” Radiation Research, Vol. 150, No. 6, 1998, pp. 612-618. doi:10.2307/3579883

[14] D. Pang, et al., “Radiation-Generated Short DNA Fragments May Perturb Non-homologous End-joining and Induce Genomic Instability,” Journal of Radiation Research, Vol. 52, No. 3, 2011, pp. 309-319. doi:10.1269/jrr.10147