title: ÐÐ¾Ð»Ð³Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð°Ñ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°ÑÐ¸Ñ ÑÐ¸Ð½Ð°Ð¿ÑÐ¾Ð² Ð² Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½ÐµÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ½Ð¾Ð³Ð¾ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ° ÐºÐ°ÑÐºÐ°ÑÐ½ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð´ÐµÐ½Ð´ÑÐ¸ÑÐ½ÑÐ¼Ð¸ ÑÐ¸Ð¿Ð¸ÐºÐ°Ð¼Ð¸
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: The long-term potentiation of synapses in the mathematical model of nonequilibrium transport of scaffold proteins between dendritic spines
Creators: name: Ð¢ÑÑÐºÐµÐµÐ²Ð°, ÐÐºÐ°ÑÐµÑÐ¸Ð½Ð°
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´Ð¾Ð»Ð³Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð°Ñ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°ÑÐ¸Ñ ÑÐ¸Ð½Ð°Ð¿ÑÐ¾Ð²
Ð½ÐµÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ½ÑÐ¹ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑ
ÐºÐ°ÑÐºÐ°ÑÐ½ÑÐµ Ð±ÐµÐ»ÐºÐ¸
PSD-95
Ð¿ÑÐ¾ÑÐµÑÑ Ñ Ð½ÑÐ»ÐµÐ²ÑÐ¼ ÑÐ°Ð´Ð¸ÑÑÐ¾Ð¼
long-term potentiation
nonequilibrium transport
scaffold proteins
zero-range process

description: ÐÐ°ÑÐºÐ°ÑÐ½ÑÐµ Ð±ÐµÐ»ÐºÐ¸ ÑÐ²Ð»ÑÑÑÑÑ Ð¾Ð´Ð½Ð¸Ð¼ Ð¸Ð· Ð²Ð°Ð¶Ð½ÐµÐ¹ÑÐ¸Ñ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ¾Ð² Ð¿Ð¾ÑÑÑÐ¸Ð½Ð°Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¿Ð»Ð¾ÑÐ½ÐµÐ½Ð¸Ñ (ÐÐ¡Ð£). ÐÑ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑ ÑÐ°Ð·Ð¼ÐµÑÑ ÐÐ¡Ð£, ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾ ÑÐµÑÐµÐ¿ÑÐ¾ÑÐ¾Ð² AMPA Ð¸ NMDA, Ð° Ð·Ð½Ð°ÑÐ¸Ñ, Ð¸ ÑÐ¸Ð»Ñ ÑÐ¸Ð½Ð°Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸. ÐÐ·Ð²ÐµÑÑÐ½Ð¾, ÑÑÐ¾ Ð¿ÑÐ¸ Ð´Ð¾Ð»Ð³Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°ÑÐ¸Ð¸ (ÐÐ) ÑÐ¸Ð½Ð°Ð¿ÑÐ¾Ð², Ð¾Ð´Ð½Ð¾Ð¹ Ð¸Ð· ÑÐ¾ÑÐ¼ ÑÐ¸Ð½Ð°Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸ÑÐ½Ð¾ÑÑÐ¸, Ð²Ð¾Ð²Ð»ÐµÑÑÐ½Ð½Ð¾Ð¹ Ð² ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð°Ð¼ÑÑÐ¸, Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´Ð¸Ñ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ðµ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð² ÐÐ¡Ð£ Ð·Ð° ÑÑÑÑ Ð¿ÑÐ¸Ð²Ð»ÐµÑÐµÐ½Ð¸Ñ Ð´Ð¾Ð¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð², Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ ÐºÐ°ÑÐºÐ°ÑÐ½Ð¾Ð³Ð¾ Ð±ÐµÐ»ÐºÐ° PSD-95. ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐµÐ¹ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑ ÐºÐ°ÑÐºÐ°ÑÐ½ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð´ÐµÐ½Ð´ÑÐ¸ÑÐ½ÑÐ¼Ð¸ ÑÐ¸Ð¿Ð¸ÐºÐ°Ð¼Ð¸, Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ñ ÐµÐ³Ð¾ ÑÐ¾Ð»Ð¸ Ð² Ð¿Ð¾Ð´Ð´ÐµÑÐ¶Ð°Ð½Ð¸Ð¸ ÐÐ. Ð¢ÑÐ°Ð½ÑÐ¿Ð¾ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð´ÐµÐ½Ð´ÑÐ¸ÑÐ½ÑÐ¼Ð¸ ÑÐ¸Ð¿Ð¸ÐºÐ°Ð¼Ð¸ Ð±ÑÐ» Ð¾Ð¿Ð¸ÑÐ°Ð½ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐ¼ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸ÐµÐ¼. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ¾Ð³Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÐºÐ°ÑÐºÐ°ÑÐ½ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¿Ð¾ Ð´ÐµÐ½Ð´ÑÐ¸ÑÐ½ÑÐ¼ ÑÐ¸Ð¿Ð¸ÐºÐ°Ð¼. ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð° ÐÐ¾Ð½ÑÐµ-ÐÐ°ÑÐ»Ð¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¾ Ð·Ð°ÑÐ¸ÐºÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð¿ÐµÑÐµÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÐºÐ°ÑÐºÐ°ÑÐ½ÑÑ Ð±ÐµÐ»ÐºÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð´ÐµÐ½Ð´ÑÐ¸ÑÐ½ÑÐ¼Ð¸ ÑÐ¸Ð¿Ð¸ÐºÐ°Ð¼Ð¸ Ð¿ÑÐ¸ ÐÐ Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð¸Ð· Ð½Ð¸Ñ.
description: Scaffold proteins are one of the most vital components of the postsynaptic density (PSD). Their number determines the size of the PSD, the number of AMPA and NMDA receptors and the strength of synapses as a result. It is known that during long-term potentiation (LTP), a form of synaptic plasticity involved in memory formation, the size of PSD increases by attracting additional proteins, including the PSD-95 scaffold protein. The given work is devoted to developing the mathematical model of nonequilibrium transport of scaffold proteins between dendritic spines. The transport of proteins was described by the master equation. The analytical expression for stationary distribution of scaffold proteins on dendritic spines was derived. The Monte-Carlo method was used to simulate the redistribution of scaffold proteins between dendritic spines during long-term potentiation.