Geodesic
Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 400-411 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules.
Keywords: Cayley tree, Potts model, Gibbs measure, Holliday junction. 
@article{TMF_2024_218_2_a10,
     author = {N. M. Khatamov and N. N. Malikov},
     title = {Holliday junctions in the~set of {DNA} molecules for new translation-invariant {Gibbs} measures of {the~Potts} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {400--411},
     year = {2024},
     volume = {218},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a10/}
}
TY  - JOUR
AU  - N. M. Khatamov
AU  - N. N. Malikov
TI  - Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 400
EP  - 411
VL  - 218
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a10/
LA  - ru
ID  - TMF_2024_218_2_a10
ER  - 
%0 Journal Article
%A N. M. Khatamov
%A N. N. Malikov
%T Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 400-411
%V 218
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a10/
%G ru
%F TMF_2024_218_2_a10
N. M. Khatamov; N. N. Malikov. Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 400-411. http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a10/

[1] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | MR | Zbl

[2] F. Y. Wu, “The Potts model”, Rev. Modern Phys., 54:1 (1982), 235–268 | DOI | MR

[3] N. N. Ganikhodzhaev, “O chistykh fazakh ferromagnitnoi modeli Pottsa na reshetke Bete”, Dokl. AN RUz, 1992, no. 6–7, 4–7

[4] N. N. Ganikhodzhaev, “O chistykh fazakh ferromagnitnoi modeli Pottsa s tremya sostoyaniyami na reshetke Bete vtorogo poryadka”, TMF, 85:2 (1990), 163–175 | DOI | MR

[5] N. N. Ganikhodzhaev, U. A. Rozikov, “Opisanie periodicheskikh krainikh gibbsovskikh mer nekotorykh modelei na dereve Keli”, TMF, 111:1 (1997), 109–117 | DOI | DOI | MR | Zbl

[6] N. N. Ganikhodjaev, U. A. Rozikov, “On Potts model with countable set of spin values on Cayley tree”, Lett. Math. Phys., 75:1 (2006), 99–109 | DOI | MR

[7] U. A. Rozikov, M. M. Rakhmatullaev, “Opisanie slabo periodicheskikh mer Gibbsa modeli Izinga na dereve Keli”, TMF, 156:2 (2008), 292–302 | DOI | DOI | MR | Zbl

[8] U. A. Rozikov, M. M. Rakhmatullaev, “Slabo periodicheskie osnovnye sostoyaniya i mery Gibbsa dlya modeli Izinga s konkuriruyuschimi vzaimodeistviyami na dereve Keli”, TMF, 160:3 (2009), 507–516 | DOI | DOI | MR | Zbl

[9] U. A. Rozikov, “Tree-hierarchy of DNA and distribution of Holliday junctions”, J. Math. Biol., 75:6–7 (2017), 1715–1733 | DOI | MR

[10] U. A. Rozikov, “Holliday junctions for the Potts model of DNA”, Algebra, Complex Analysis, and Pluripotential Theory (Urgench, Uzbekistan, August 8–12, 2017), Springer Proceedings in Mathematics and Statistics, 264, eds. Z. Ibragimov, N. Levenberg, U. Rozikov, A. Sadullaev, Springer, Cham, 2018, 151–165 | DOI | MR | Zbl

[11] U. A. Rozikov, “Termodinamika vzaimodeistvuyuschikh sistem molekul DNK”, TMF, 206:2 (2021), 199–209 | DOI | DOI | MR

[12] N. M. Khatamov, “Struktury Khollideya v modeli Blyuma–Kapelya molekuly DNK”, TMF, 206:3 (2021), 439–447 | DOI | DOI | MR

[13] N. M. Khatamov, “Holliday junctions in the HC Blume–Capel model in ‘one case’ on DNA”, Nanosytems: Physics, Chemisry, Mathematics, 12:5 (2021), 563–568 | DOI

[14] U. A. Rozikov, “Thermodynamics of DNA-RNA renaturation”, Int. J. Geom. Methods Mod. Phys., 18:6 (2021), 2150096, 14 pp. | DOI | MR

[15] U. A. Rozikov, Gibbs measures in Biology and Physics: The Potts Model, World Sci., Singapore, 2022 | DOI

[16] B. Alberts, A. Dzhonson, D. Lyuis, M. Reff, K. Roberts, P. Uolter, Molekulyarnaya biologiya kletki, NITs “Regulyarnaya i khaotichnaya dinamika”, M.–Izhevsk, 2013 | DOI

[17] R. Holliday, “A mechanism for gene conversion in fungi”, Genetics Research, 5:2 (1964), 282–304 | DOI

[18] U. A. Rozikov, F. T. Ishankulov, “Description of periodic $p$-harmonic functions on Cayley trees”, Nonlinear Differ. Equ. Appl., 17:2 (2010), 153–160 | DOI | MR

[19] D. Swigon, “The mathematics of DNA structure, mechanics, and dynamics”, Mathematics of DNA Structure, Function and Interactions, The IMA Volumes in Mathematics and its Applications, 150, eds. C. Benham, S. Harvey, W. Olson, D. Sumners, D. Swigon, Springer, New York, 2009, 293–320 | DOI | MR

[20] Kh.-O. Georgi, Gibbsovskie mery i fazovye perekhody, Mir, M., 1992 | DOI | MR | MR | Zbl