# Properties of Topological Networks of Flexible Polygonal Chains

J. Arsuaga; Y. Diao; M. Klingbeil; V. Rodriguez

Molecular Based Mathematical Biology (2014)

- Volume: 2, Issue: 1
- ISSN: 2299-3266

## Access Full Article

top## Abstract

top## How to cite

topJ. Arsuaga, et al. "Properties of Topological Networks of Flexible Polygonal Chains." Molecular Based Mathematical Biology 2.1 (2014): null. <http://eudml.org/doc/266760>.

@article{J2014,

abstract = {Trypanosomatida parasites, such as Trypanosoma and Leishmania, are the cause of deadly diseases in many third world countries. The three dimensional structure of their mitochondrial DNA, known as kinetoplast DNA (kDNA), is unique since it is organized into several thousands of minicircles that are topologically linked. How and why the minicircles form such a network have remained unanswered questions. In our previous work we have presented a model of network formation that hypothesizes that the network is solely driven by the confinement of minicircles. Our model shows that upon confinement a percolation network forms. This network grows into a space filling network, called saturation network, upon further confinement of minicircles. Our model also shows, in agreement with experimental data, that the mean valence of the network (that is, the average number of minicircles topologically linked to any minicircle in the network) grows linearly with minicircle density. In our previous studies however we disregarded DNA flexibility and used rigid minicircles to model DNA, here we address this limitation by allowing minicircles to be flexible. Our numerical results show that the topological characteristics that describe the growth and topology of the minicircle networks have similar values to those observed in the case of rigid minicircles suggesting that these properties are robust and therefore a potentially adequate description of the networks observed in Trypanosomatid parasites.},

author = {J. Arsuaga, Y. Diao, M. Klingbeil, V. Rodriguez},

journal = {Molecular Based Mathematical Biology},

keywords = {kDNA; minicircles; minicircle networks; random minicircle networks; linking},

language = {eng},

number = {1},

pages = {null},

title = {Properties of Topological Networks of Flexible Polygonal Chains},

url = {http://eudml.org/doc/266760},

volume = {2},

year = {2014},

}

TY - JOUR

AU - J. Arsuaga

AU - Y. Diao

AU - M. Klingbeil

AU - V. Rodriguez

TI - Properties of Topological Networks of Flexible Polygonal Chains

JO - Molecular Based Mathematical Biology

PY - 2014

VL - 2

IS - 1

SP - null

AB - Trypanosomatida parasites, such as Trypanosoma and Leishmania, are the cause of deadly diseases in many third world countries. The three dimensional structure of their mitochondrial DNA, known as kinetoplast DNA (kDNA), is unique since it is organized into several thousands of minicircles that are topologically linked. How and why the minicircles form such a network have remained unanswered questions. In our previous work we have presented a model of network formation that hypothesizes that the network is solely driven by the confinement of minicircles. Our model shows that upon confinement a percolation network forms. This network grows into a space filling network, called saturation network, upon further confinement of minicircles. Our model also shows, in agreement with experimental data, that the mean valence of the network (that is, the average number of minicircles topologically linked to any minicircle in the network) grows linearly with minicircle density. In our previous studies however we disregarded DNA flexibility and used rigid minicircles to model DNA, here we address this limitation by allowing minicircles to be flexible. Our numerical results show that the topological characteristics that describe the growth and topology of the minicircle networks have similar values to those observed in the case of rigid minicircles suggesting that these properties are robust and therefore a potentially adequate description of the networks observed in Trypanosomatid parasites.

LA - eng

KW - kDNA; minicircles; minicircle networks; random minicircle networks; linking

UR - http://eudml.org/doc/266760

ER -

## References

top- [1] J. Arsuaga, Y. Diao, and K. Hinson. The effect of angle restriction on the topological characteristics of minicircle networks. J. Statist. Phys., 146(2):434–445, 2012. Zbl1235.82103
- [2] J. Chen, P. T. Englund, and N. R. Cozzarelli. Changes in network topology during the replication of kinetoplast DNA. EMBO J., 14(24):6339–6347, 1995. [PubMed]
- [3] J. Chen, C. A. Rauch, J. H. White, P. T. Englund, and N. R. Cozzarelli. The topology of the kinetoplast DNA network. Cell, 80(1):61–69, 1995.
- [4] Y. Diao, K. Hinson, and J. Arsuaga. The growth of minicircle networks on regular lattices. J. Phys. A: Math. Theor, 45:doi:10.1088/1751–8113/45/3/035004, 2012. [Crossref][WoS] Zbl1234.92022
- [5] Y. Diao, K. Hinson, R. Kaplan, M. Vazquez, and J. Arsuaga. The effects of minicircle density on the topological structure of the mitochondrial DNA from trypanosomes. J. Math. Biol., 64(6):1087–1108, 2012. [WoS][Crossref] Zbl1311.92145
- [6] M. Ferguson, A. F. Torri, D. C. Ward, and P. T. Englund. In situ hybridization to the crithidia fasciculata kinetoplast reveals two antipodal sites involved in kinetoplast DNA replication. Cell, 70:621–629, 1992. [Crossref][PubMed]
- [7] Rafael Lozano et al. Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the global burden of disease study 2010. The Lancet, 380(9859):2095–2128, 2013.
- [8] C. A. Rauch, D. Perez-Morga, N. R. Cozzarelli, and P. T. Englund. The absence of supercoiling in kinetoplast DNA minicircles. EMBO J., 12(2):403–411, 1993. [PubMed]
- [9] V Rodriguez, Y Diao, and J Arsuaga. Percolation phenomena in disordered topological networks. Journal of Physics: Conference Series, 454(1):012070, 2013.
- [10] Robert G. Scharein. KnotPlot. http://www.knotplot.com. Program for drawing, visualizing, manipulating, and energy minimizing knots.
- [11] T. A. Shapiro and P. T. Englund. The structure and replication of kinetoplast DNA. Annu. Rev. Microbiol., 49:117–143, 1995. [PubMed][Crossref]
- [12] Pere P Simarro, Giuliano Cecchi, José R Franco, Massimo Paone, Abdoulaye Diarra, José Antonio Ruiz-Postigo, Eric M Fèvre, Raffaele C Mattioli, and Jean G Jannin. Estimating and mapping the population at risk of sleeping sickness. PLoS neglected tropical diseases, 6(10):e1859, 2012.
- [13] M. Spera. A survey on the differential and symplectic geometry of linking numbers. Milan J. Math., 74:139–197, 2006. [Crossref] Zbl1165.58004
- [14] R. Varela, K. Hinson, J. Arsuaga, and Y. Diao. A fast ergodic algorithm for generating ensembles of equilateral random polygons. J. Phys. A, 42(9):1–13, 2009. Zbl1158.92019
- [15] A. V. Vologodskii. DNA supercoiling helps to unlink sister duplexes after replication. BioEssays, 32:9–12, 2010. [WoS][Crossref][PubMed]
- [16] A. V. Vologodskii and N. R. Cozzarelli. Monte carlo analysis of the conformation of DNA catenanes. J. Mol. Biol., 232:1130– 1140, 1993.
- [17] A. V. Vologodskii and V. Rybenkov. Simulation of DNA catenanes. Phys. Chem. Chem. Phys., 11:10543–10552, 2009.[Crossref][PubMed]