title: ÐÐ¾Ð´ÐµÐ»Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² Ð² Ð³ÐµÐ½Ð¾Ð¼Ðµ Ñ ÑÑÐµÑÐ¾Ð¼ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸ Ð·Ð° ÐºÐ»ÐµÑÐ¾ÑÐ½ÑÐµ ÑÐµÑÑÑÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Model of transposons' dynamics over the genome with competition for cellular resources
Creators: name: ÐÐ°Ð²Ð»Ð¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ñ
Ð¼Ð¾Ð´ÐµÐ»Ñ "Ñ Ð¸ÑÐ½Ð¸Ðº-Ð¶ÐµÑÑÐ²Ð°"
Ð°Ð½Ð°Ð»Ð¸Ð· Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼
Ð±Ð¸ÑÑÑÐºÐ°ÑÐ¸Ñ
transposons
"predator-prey" model
linear stability analysis
bifurcation

description: Ð¡ ÑÐµÐ»ÑÑ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¿Ð°ÑÑ Ð°Ð²ÑÐ¾Ð½Ð¾Ð¼Ð½ÑÑ Ð¸ Ð½ÐµÐ°Ð²ÑÐ¾Ð½Ð¾Ð¼Ð½ÑÑ ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² (LINE Ð¸ SINE) Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ Ð´Ð²Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¸Ð¿Ð° Â«ÑÐ¸ÑÐ½Ð¸Ðº-Ð¶ÐµÑÑÐ²Ð°Â». ÐÐ´Ð½Ð° Ð¸Ð· Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÑÐ¸ÑÑÐ²Ð°ÐµÑ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° ÑÐ²Ð¾Ð±Ð¾Ð´Ð½ÑÐµ ÑÐ¸Ð±Ð¾ÑÐ¾Ð¼Ñ, Ð²ÑÐ¾ÑÐ°Ñ â ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° Ð´Ð¾ÑÑÑÐ¿Ð½ÑÑ ÑÐ½ÐµÑÐ³Ð¸Ñ Ð² ÐºÐ»ÐµÑÐºÐµ. Ð ÑÑÐ»Ð¾Ð²Ð¸ÑÑ Ð½ÐµÐ¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐµÑÑÑÑÐ¾Ð², Ð² ÐºÐ»ÐµÑÐºÐµ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÑÑÑÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²ÑÐµ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ»ÑÐºÑÑÐ°ÑÐ¸Ð¸ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð¼Ð¾Ð»ÐµÐºÑÐ» ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² Ð²Ð±Ð»Ð¸Ð·Ð¸ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ, ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÐµÐ¼ÑÐµ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¾Ð¼ Ð¸ ÑÑÐµÐ´Ð½ÐµÐ¹ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ð¾Ð¹ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹. ÐÐ²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸Ð¹ Ð½Ð° Ð´Ð¾ÑÑÑÐ¿Ð½ÑÐµ ÐºÐ»ÐµÑÐ¾ÑÐ½ÑÐµ ÑÐµÑÑÑÑÑ Ð¸ Ð¿Ð¾ÑÑÐµÐ¿ÐµÐ½Ð½Ð¾Ðµ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ðµ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´Ð°ÐµÑÑÑ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸ÑÐ¼Ð¸ Ð² ÑÐ°ÑÐ°ÐºÑÐµÑÐµ ÑÐ»ÑÐºÑÑÐ°ÑÐ¸Ð¹, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸ÐµÐ¼ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° SINE. Ð Ð¾Ð±ÐµÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÑ Ð±ÑÐ»Ð¾ Ð¾ÑÐ¼ÐµÑÐµÐ½Ð¾ Ð½Ð°Ð»Ð¸ÑÐ¸Ðµ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÑÐ¾Ð²Ð½Ñ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸, Ð¿ÑÐ¸ Ð¿ÐµÑÐµÑÐµÑÐµÐ½Ð¸Ð¸ ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ Ð² Ð¾Ð±ÐµÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÑ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÑÑÑ Ð¿Ð¾ÑÐµÑÑ Ð°ÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¾Ð±Ð¾Ð¸Ñ ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð². ÐÑÐ¸ ÑÑÐ¾Ð¼ Ð¼Ð¾Ð´ÐµÐ»Ñ, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐ°Ñ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° ÑÐ¸Ð±Ð¾ÑÐ¾Ð¼Ñ, Ð¿ÑÐ¸ ÑÑÐ¾Ð²Ð½Ðµ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸ Ð½Ð¸Ð¶Ðµ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾, Ð´Ð¾Ð¿ÑÑÐºÐ°ÐµÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ Ð¿Ð¾ÑÐµÑÐ¸ Ð°ÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ ÐºÐ°Ðº SINE, ÑÐ°Ðº Ð¸ LINE, Ð² ÑÐ¾ Ð²ÑÐµÐ¼Ñ ÐºÐ°Ðº Ð¼Ð¾Ð´ÐµÐ»Ñ, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐ°Ñ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° ÑÐ½ÐµÑÐ³Ð¸Ñ, ÑÐ°Ð·Ð³ÑÐ°Ð½Ð¸ÑÐ¸Ð²Ð°ÐµÑ ÑÑÐ¸ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐ¸ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÑÑÐ¾Ð²Ð½ÐµÐ¼ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸. Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ¾ÑÐµÑÐ°ÑÑÑÑ Ð¼ÐµÑÐ¾Ð´Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÐ¸ÑÑÐµÐ¼ Ð¾Ð±ÑÐºÐ½Ð¾Ð²ÐµÐ½Ð½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¸ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. ÐÐ»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐµÐ¹ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° ÑÐ¸Ð±Ð¾ÑÐ¾Ð¼Ñ, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¾ Ð½ÐµÑÐºÐ¾Ð»ÑÐºÐ¾ ÑÐµÑÐµÐ½Ð¸Ð¹ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ð°, Ð¾ÑÑÐ°Ð¶Ð°ÑÑÐ¸Ñ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² Ð½Ð° Ð¸Ñ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ. Ð Ð¼Ð¾Ð´ÐµÐ»Ð¸, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐµÐ¹ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ñ Ð·Ð° Ð´Ð¾ÑÑÑÐ¿Ð½ÑÑ ÑÐ½ÐµÑÐ³Ð¸Ñ, Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² Ð½Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð¾Ñ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¸Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð°, Ð° Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ Ð»Ð¸ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¸ ÑÑÐ¾Ð²Ð½ÐµÐ¼ ÐºÐ¾Ð½ÐºÑÑÐµÐ½ÑÐ¸Ð¸. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿Ð¾Ð¼Ð¾Ð³Ð°ÑÑ Ð¿Ð¾Ð½ÑÑÑ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ñ, ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐ¸Ðµ Ð²Ð°ÑÐ¸Ð°ÑÐ¸ÐµÐ¹ ÑÐ¸ÑÐ»Ð° ÑÑÐ°Ð½ÑÐ¿Ð¾Ð·Ð¾Ð½Ð¾Ð² Ð² Ð³ÐµÐ½Ð¾Ð¼Ðµ.
description: Two mathematical âpredator-preyâ models were created to describe the dynamics of spreading of a pair of autonomous and nonautonomous transposons (LINE and SINE). One model considers the case of competition for free ribosomes, and another â competition for the available energy in a cell. In case of unlimited resources, stable stochastic fluctuations of the number of molecules of transposons near the stationary state are observed in a cell. Fluctuations have characteristic period and average amplitude of oscillations. Limiting available cellular resources and stepwise increasing of competition is accompanied with change in character of fluctuations and decreasing of stationary state number of SINE. It was noticed, that in both models after exceeding some critical level of competition, all transposons lost their activity. Moreover, at a given level of competition, below critical, the model with competition for ribosomes allows the loss of activity of either SINE or both LINE and SINE transposons. Meanwhile the model with competition for the energy differentiates these two cases with critical level of competition. In this work, we combined such methods as linear stability analysis for analyzing systems of ODE and stochastic simulations. We made several phase space sections for the model with competition for the ribosomes to show the impact of the initial copy number of molecules of transposons on their following dynamics. In the model with competition for the available energy, transposonsâ dynamics does not depend on their initial copy number, but it is determined by systemâs parameters and competition level. Obtained results help to understand the mechanisms that control the variation in the number of transposons in the genome.