title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸ ÐºÐ»ÐµÑÐ¾Ðº Ð² Ð³Ð»Ð°Ð·Ð½Ð¾Ð¼ Ð´Ð¸ÑÐºÐµ Ð´ÑÐ¾Ð·Ð¾ÑÐ¸Ð»Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Modeling of cell differentiation in the eye disc of Drosophila
Creators: name: ÐÑÑÐ¾Ð²Ð°, ÐÐ½Ð½Ð°
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: 2021
Subjects: ÑÐºÑÐ¿ÑÐµÑÑÐ¸Ñ Ð³ÐµÐ½Ð¾Ð²
Ð»Ð°ÑÐµÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¸Ð½Ð³Ð¸Ð±Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¾ÑÐµÐ½ÐºÐ° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð²
Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÑÐ¼Ð°
Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸ ÐºÐ»ÐµÑÐ¾Ðº
gene expression
lateral inhibition
estimation of parameters
influence of noise
models of cell differentiation

description: Ð Ð°Ð±Ð¾ÑÐ° Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð° Ð½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸ ÐºÐ»ÐµÑÐ¾Ðº Ð² Ð³Ð»Ð°Ð·Ð½Ð¾Ð¼ Ð´Ð¸ÑÐºÐµ Ð´ÑÐ¾Ð·Ð¾ÑÐ¸Ð»Ñ. ÐÐ°Ð¶Ð½Ð¾Ð¹ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ð¾Ð¹ Ð² ÑÑÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµ ÑÐ²Ð»ÑÐµÑÑÑ Ð²Ð¾Ð¿ÑÐ¾Ñ Ð¾Ð± ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð°ÑÑÐµÑÐ½Ð° Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº. Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ ÑÐ¾ÑÑÐ¾ÑÐ»Ð° Ð² Ð¸Ð·ÑÑÐµÐ½Ð¸Ð¸ ÑÐ¾Ð³Ð¾, ÐºÐ°Ðº ÑÑÐ¼ Ð² Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð²Ð»Ð¸ÑÐµÑ Ð½Ð° Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð² Ð¼Ð¾Ð´ÐµÐ»ÑÑ. ÐÐ»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð±ÑÐ»Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ñ Ð´Ð²Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐµ Ð½Ð° Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸ÑÑ Ð¸ Ð¿Ð¾Â­ÑÐ°Ð·Ð½Ð¾Ð¼Ñ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐ¸Ðµ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð°ÑÑÐµÑÐ½Ð° Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð½Ð°Ð·ÑÐ²Ð°ÐµÑÑÑ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð¾Ð¼ Ð»Ð°ÑÐµÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¸Ð½Ð³Ð¸Ð±Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ°Ð±Ð»Ð¾Ð½Ð°. Ð Ð±Ð°Ð·Ð¾Ð²Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¾Ð±ÑÐ°Ð·ÑÑÑÑÑ ÐºÐ»Ð°ÑÑÐµÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ð¸ Ð¾Ð¿ÑÑÐµÐ½ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ¹ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¾Ð´Ð¸Ð½Ð¾ÑÐ½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº (ÐºÐ»ÐµÑÐ¾Ðº R8) Ð¸Ð· ÑÑÐ¸Ñ ÐºÐ»Ð°ÑÑÐµÑÐ¾Ð². Ð Ð±Ð¾Ð»ÐµÐµ Ð¾Ð±ÑÐµÐ¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÐºÐ»ÐµÑÐ¾Ðº R8 Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸Ð³Ð½Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÑÐ¸ Notch. ÐÑÐ»Ð¸ Ð½Ð°Ð¹Ð´ÐµÐ½Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¸ Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹, Ð¿ÑÐ¸ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¾ÑÐ¼Ð¸ÑÑÐµÑÑÑ Ð¿ÑÐ°Ð²Ð¸Ð»ÑÐ½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð¿Ð°ÑÑÐµÑÐ½Ð° Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸ Ð² ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸ÑÑ Ð² Ð¾Ð±ÐµÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÑ. Ð ÑÐ°Ð¼ÐºÐ°Ñ ÑÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð±ÑÐ»Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð¿Ð°ÑÑÐµÑÐ½Ð¾Ð² Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²ÐºÐ¸ Ðº Ð²Ð½ÐµÑÐµÐ½Ð¸Ñ Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐºÐ¾ÑÐ¾ÑÑÑ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´ÑÑÐ²Ð° Ð±ÐµÐ»ÐºÐ¾Ð², ÐºÐ¾Ð½ÑÑÐ°Ð½ÑÑ Ð´ÐµÐ³ÑÐ°Ð´Ð°ÑÐ¸Ð¸ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¸ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¾Ð½Ð½ÑÐµ ÐºÐ¾Ð½ÑÑÐ°Ð½ÑÑ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¾Ð±Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÑÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²ÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ, ÐµÑÐ»Ð¸ ÑÑÐ¾Ð²ÐµÐ½Ñ Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼ÐµÐ½ÑÑÐµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐ¾Ð³Ð°. ÐÐ´Ð½Ð°ÐºÐ¾ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð¿Ð°ÑÑÐµÑÐ½Ð° Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ñ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð¾Ð¼ Ð¾ÑÐ±Ð¾ÑÐ° ÐºÐ»ÐµÑÐ¾Ðº R8 Ð¿Ð°Ð´Ð°ÐµÑ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð±Ð°Ð·Ð¾Ð²Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»ÑÑ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ Ð³Ð¾Ð²Ð¾ÑÐ¸Ñ Ð¾ Ð½ÐµÑÐ¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ðµ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°Ð½ÐµÐµ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð° Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ð¸ Ð¼Ð¾Ð¶ÐµÑ ÑÐ²Ð¸Ð´ÐµÑÐµÐ»ÑÑÑÐ²Ð¾Ð²Ð°ÑÑ Ð¾ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ ÐµÐ³Ð¾ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸.
description: The work is aimed at the numerical study of models of cell differentiation in the eye disc of Drosophila. An important problem in this problem is the question of the stability of the patterning of differentiated cells. The aim of the work was to study how noise in parameter values affects the dynamics of a numerical solution in models. To solve the problem, two models were implemented, based on differential equations and differently describing the mechanism of the formation of a differentiation pattern, which is called the mechanism of lateral inhibition based on the template. In the basic model, clusters of differentiated cells are formed and the mechanism of subsequent localization of single differentiated cells (R8 cells) from these clusters is omitted. A more general model implements the mechanism of localization of R8 cells using the Notch signaling pathway. We found the values of the parameters and initial conditions under which the correct dynamics of the differentiation pattern is formed in the numerical solutions in both models. Within the framework of these models, the resistance of differentiation patterns to disturbances in the rate of protein production, protein degradation constant, and diffusion constants was investigated. As a result, it is shown that both models demonstrate stable dynamics if the level of disturbance of the parameters is less than a certain threshold. However, the stability of the pattern in the model with the R8 cell selection mechanism decreases compared to the baseline model. The obtained result indicates the imperfection of the previously proposed mechanism of localization of differentiated cells and may indicate the need for its modification.