title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¾ÑÑÐ° ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¹ Ð¿Ð»ÑÑÐ¸Ð¿Ð¾ÑÐµÐ½ÑÐ½ÑÑ ÑÑÐ²Ð¾Ð»Ð¾Ð²ÑÑ ÐºÐ»ÐµÑÐ¾Ðº
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 the growth of human pluripotent stem cell colonies
Creators: name: ÐÐ¾Ð²Ð°Ð»ÑÐ²Ð°, ÐÐ»ÑÐ³Ð°
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: 2023
Subjects: Ð¿Ð»ÑÑÐ¸Ð¿Ð¾ÑÐµÐ½ÑÐ½ÑÐµ ÑÑÐ²Ð¾Ð»Ð¾Ð²ÑÐµ ÐºÐ»ÐµÑÐºÐ¸
ÑÐ¸ÑÑÐµÐ¼Ð° Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ Ð¿Ð¾Ð¿ÑÐ»ÑÑÐ¸Ð¸
Ð´Ð¸ÑÑÑÐ·Ð¸Ñ
pluripotent stem cells
system of linear differential equations
popylation dynamics
diffusion

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¾ÑÑÐ° ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¹ Ð¿Ð»ÑÑÐ¸Ð¿Ð¾ÑÐµÐ½ÑÐ½ÑÑ ÑÑÐ²Ð¾Ð»Ð¾Ð²ÑÑ ÐºÐ»ÐµÑÐ¾Ðº ÑÐµÐ»Ð¾Ð²ÐµÐºÐ°Â». Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¸ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ° ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¹ ÑÑÐ²Ð¾Ð»Ð¾Ð²ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ñ ÑÑÐµÑÐ¾Ð¼ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾Ð¹ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ Ð¿Ð¾ÑÐµÑÐ¸ ÐºÐ»Ð¾Ð½Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸. ÐÑÐµÐ´Ð¼ÐµÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÐµÑÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ Ð¿Ð¾Ð¿ÑÐ»ÑÑÐ¸Ð¹ Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½ÑÑ Ð¸ Ð°Ð½Ð¾Ð¼Ð°Ð»ÑÐ½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ð²Ð½ÑÑÑÐ¸ ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¹. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ°ÑÑÑÑÐµÐ¹ ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¸, ÑÐ¾ÑÑÐ¾ÑÑÐµÐ¹ Ð¸Ð· ÑÑÑÑ ÑÐ»Ð¾ÐµÐ² (Ð²Ð½ÑÑÑÐµÐ½Ð½Ð¸Ð¹, ÑÑÐµÐ´Ð½Ð¸Ð¹ Ð¸ Ð²Ð½ÐµÑÐ½Ð¸Ð¹), Ð¸ Ð´Ð¾Ð¿ÑÑÐºÐ°ÑÑÐµÐ¹ Ð¿ÐµÑÐµÑÐ¾Ð´ ÐºÐ»ÐµÑÐ¾Ðº Ð² Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¸ Ð¾Ñ Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ³Ð¾ ÑÐ»Ð¾Ñ Ðº Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸. Ð¢Ð°ÐºÐ°Ñ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¿ÐµÑÐµÐ´Ð°ÐµÑ Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾ÌÐµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ Ð¿Ð¾Ð¿ÑÐ»ÑÑÐ¸Ð¹ Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ, Ð¿Ð¾Ð´Ð¾Ð±Ð½Ð¾ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸. Ð¡Ð»Ð¾Ð¸ Ð¾ÑÐ»Ð¸ÑÐ°ÑÑÑÑ ÑÐ°Ð·Ð½Ð¾Ð¹ ÑÐºÐ¾ÑÐ¾ÑÑÑÑ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½ÑÑ ÑÑÐ²Ð¾Ð»Ð¾Ð²ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ð² Ð°Ð½Ð¾Ð¼Ð°Ð»ÑÐ½ÑÐµ, Ð¿ÑÐ¸ÑÐµÐ¼ ÑÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ð¾Ñ ÑÐµÐ½ÑÑÐ° ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¸ Ðº Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸, ÑÑÐ¾ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÐµÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼ Ð½Ð°Ð±Ð»ÑÐ´ÐµÐ½Ð¸ÑÐ¼. ÐÐ¿Ð¸ÑÐ°Ð½Ñ Ð²ÑÐµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½ÑÐµ ÑÑÐµÐ½Ð°ÑÐ¸Ð¸ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ ÑÐ°ÐºÐ¾Ð¹ ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð° Ð½ÐµÐ¾ÑÑÐ¸ÑÐ°ÑÐµÐ»ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÑ Ð²Ð´Ð¾Ð»Ñ ÑÑÐ°ÐµÐºÑÐ¾ÑÐ¸Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ, Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÑÐ»Ð¾Ð²Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ¾ÑÐºÐ¸ Ð¿Ð¾ÐºÐ¾Ñ, Ð¾Ð¿Ð¸ÑÐ°Ð½Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐµÐ¶Ð¸Ð¼Ñ ÑÐ¾ÑÑÐ° ÐºÐ¾Ð»Ð¾Ð½Ð¸Ð¸ Ñ Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½ÑÐ¼ Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸ÐµÐ¼ ÑÐ¸ÑÐµÐ» Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½ÑÑ Ð¸ Ð°Ð½Ð¾Ð¼Ð°Ð»ÑÐ½ÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ð²Ð½ÑÑÑÐ¸ ÑÐ»Ð¾ÑÐ². ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð´Ð»Ñ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ Ð¿Ð¾Ð¿ÑÐ»ÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ.
description: The topic of the graduate qualification work is "Modeling the growth of human pluripotent stem cell colonies". The aim of the work is to construct and qualitatively study a model of exponential growth of stem cell colonies, taking into account the spatially dependent rate of loss of clonality. The subject of the study is the dynamics of the populations of normal and abnormal cells within colonies. A model of a growing colony consisting of three layers (inner, middle and outer) is constructed, and allowing cells to move in the direction from the inner layer to the periphery. This modification describes the temporal behavior of population numbers in space, similar to diffusion. The layers differ in different rates of transition of normal stem cells to abnormal ones, and the rate increases from the center of the colony to the periphery, which corresponds to experimental observations. All possible scenarios for the development of such a colony are described. The non-negativity of phase variables along the trajectories of the system is shown, the stability conditions of the stationary point are obtained, parametric modes of colony growth with a constant ratio of the numbers of normal and abnormal cells inside the layers are described. The obtained results can be used for a qualitative study of the dynamics of the population system.