title: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¸ Ð²Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð³Ð¾Ð¼ÐµÐ¾ÑÑÐ°Ð·Ð° Ð½ÐµÐ¹ÑÐ¾Ð½Ð°
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: Mathematical modeling of neural ion and water homeostasis ion and water homeostasis in neuron
Creators: name: ÐÐ°Ð´ÑÑÐ¸Ð½Ð°, ÐÐ»Ð¸Ð·Ð°Ð²ÐµÑÐ°
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: Ð¸Ð¾Ð½Ð½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°
Ð²Ð¾Ð´Ð½ÑÐ¹ Ð³Ð¾Ð¼ÐµÐ¾ÑÑÐ°Ð·
Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÐºÐ»ÐµÑÐºÐ¸ Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð½ÐµÐ¹ÑÐ¾Ð½Ð°
ion dynamics
water homeostasis
mathematical model of single neuron cell

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¸Ð¾Ð½Ð½Ð¾Ð¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð½ÐµÐ¹ÑÐ¾Ð½Ð°, Ñ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸ÐµÐ¼ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð¼ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Na+/K+-ÐÐ¢Ð¤Ð°Ð·Ñ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð²ÐºÐ»ÑÑÐ°ÑÑ Ð² ÑÐµÐ±Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð´Ð²ÑÑ ÐºÐ»ÑÑÐµÐ²ÑÑ Ð¸Ð·Ð¾ÑÐ¾ÑÐ¼ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐ¼ÐµÐ½ÑÐ°, Ð²ÑÑÑÐµÑÐ°ÑÑÐ¸ÑÑÑ Ð² ÐºÐ»ÐµÑÐºÐ°Ñ Ð³Ð¾Ð»Ð¾Ð²Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð·Ð³Ð°: Î±1Î²1 Ð¸ Î±3Î²1. Ð¢Ð°ÐºÐ¶Ðµ Ð² ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¾ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¸ Ð½Ð° Ð¾Ð±ÑÐµÐ¼ ÐºÐ»ÐµÑÐºÐ¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð°. ÐÐ»Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð¿Ð°ÐºÐµÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ ÑÐ°ÑÑÐµÑÐ¾Ð² ÑÐ·ÑÐºÐ° Python, Ð° ÑÐ°Ðº Ð¶Ðµ Ð¼ÐµÑÐ¾Ð´ Ð­Ð¹Ð»ÐµÑÐ° Ð´Ð»Ñ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸.
Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ Ð´Ð²ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ( Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Na+/K+-ÐÐ¢Ð¤Ð°Ð·Ñ Ð½Ð° Ð¼ÐµÐ¼Ð±ÑÐ°Ð½Ðµ Ð¸ Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ñ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ¾Ð² Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ ÐºÐ°Ð»Ð¸Ñ Ðº ÑÑÐ¼Ð¼Ð°ÑÐ½Ð¾Ð¹ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¸Ð¾Ð½Ð¾Ð²) Ð´Ð»Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¹ ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð¸Ñ Ð·Ð°ÑÑÐ¶ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¼ÐµÐ¼Ð±ÑÐ°Ð½Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Na+/K+-ÐÐ¢Ð¤Ð°Ð·Ñ, Ð¸ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐµÐ¼Ð° Ð¿ÑÐ¸ Ð¸Ð¼Ð¸ÑÐ°ÑÐ¸Ð¸ Ð¸ÐºÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð·ÑÑÐ´Ð°, ÑÐ¸ÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¹ ÑÐ»Ð¾ÑÐ° Ð¸ Ð¿ÑÐ¸ Ð¾ÑÑÑÑÑÑÐ²Ð¸Ð¸ ÑÐ¾ÐºÐ¾Ð² ÑÐµÑÐµÐ· ÐºÐ¾ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐµÑÑ NKCC1 Ð¸ KCC2. ÐÑÐ»Ð¸ ÑÐ´ÐµÐ»Ð°Ð½Ñ Ð²ÑÐ²Ð¾Ð´Ñ Ð¾Ð± Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ¾Ð¹ Ð¸Ð»Ð¸ Ð¸Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð·Ð°Ð´Ð°ÑÐ¸.
ÐÐ°Ðº Ð¸ Ð¾Ð¶Ð¸Ð´Ð°Ð»Ð¾ÑÑ, Ð¿ÑÐ¸ Ð¸ÐºÑÐ°Ð»ÑÐ½Ð¾Ð¼ ÑÐ°Ð·ÑÑÐ´Ðµ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ñ Ð²Ð½ÑÑÑÐ¸ÐºÐ»ÐµÑÐ¾ÑÐ½Ð¾Ð³Ð¾ ÐºÐ°Ð»Ð¸Ñ Ð²Ð¾Ð·ÑÐ°ÑÑÐ°ÐµÑ, Ð° Ð¾Ð±ÑÐµÐ¼ ÐºÐ»ÐµÑÐºÐ¸ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑÑÑ Ð½Ð° Ð´Ð»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¼ Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐºÐµ Ð²ÑÐµÐ¼ÐµÐ½Ð¸.
Ð Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¼, Ð¿ÑÐ¸ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¸ ÑÐ°Ð±Ð¾ÑÑ ÐºÐ¾ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐµÑÐ¾Ð² NKCC1 Ð¸ KCC2 Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ð¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÐ»Ð¾ÑÐ°, Ð¼Ð¾Ð¶Ð½Ð¾ Ð±ÑÐ´ÐµÑ ÑÐ¾Ð·Ð´Ð°ÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð¸ ÑÐµÐ¼ ÑÐ°Ð¼ÑÐ¼ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°ÑÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾Ðµ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÐµÐ¼Ð° ÑÐµÐ»Ð° Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð¿ÑÐ¸ Ð¿Ð°ÑÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸ÑÑ. ÐÐ¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð¾Ð´Ð½Ð¾Ð¹ ÐºÐ»ÐµÑÐºÐ¸,
Ð²ÐºÐ»ÑÑÐµÐ½Ð½Ð¾Ðµ Ð² Ð±Ð¾Ð»ÐµÐµ ÑÐ»Ð¾Ð¶Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÐ¸, Ð¿Ð¾Ð¼Ð¾Ð¶ÐµÑ Ð² Ð±ÑÐ´ÑÑÐµÐ¼ Ð»ÑÑÑÐµ Ð¿Ð¾Ð½ÑÑÑ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ñ Ð½Ð°Ð±ÑÑÐ°Ð½Ð¸Ñ ÐºÐ»ÐµÑÐ¾Ðº Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð²Ð½ÐµÑÐ½Ð¸Ñ ÑÑÐ»Ð¾Ð²Ð¸ÑÑ, Ð½Ð°Ð¿ÑÐ¸Ð¼ÐµÑ, Ð¿ÑÐ¸ ÑÐ¿Ð¸Ð»ÐµÐ¿ÑÐ¸Ð¸.
description: The given work is devoted to ion dynamics analyzes of single neuron with consideration of three Na+/K+-ATPase models, including description of its two main Î±1Î²1 and Î±3Î²1 isoforms that are most common in neuron cell. Numerical and plotting libraries for the Python programming language were used to solve equations as well as Euler method.
As a result , ranges of values for ion dynamics description with different models of Na+/K+-ATPase were obtained. Parameters were density of Na+/K+-ATPase and ratio of conductance of potassium leak current to conductance of ion leak current. Also were plotted graphs of volume changes during simulation of ictal period, while concentrations of chlorine (both intracellular and extracellular) were maintained on the same level. Ion current through cotransporters NKCC1 and KCC2 wasnât included in analyzing of volume dynamics. Recommendations of applying different pump models were made based on task of modeling.
As it was predicted, intracellular potassium concentration increases and neuron swell on long time scale during ictal period.
In the future, with chlorine dynamic and ion traffic through NKCC1 and KCC2 it will be possible to complete model of single neuron and simulate cell volume change under pathological brain activity. Single neuron description can be included in more complex models of neuronal circuits, which provide better
understanding mechanism of cell swelling under different external conditions, such as epilepsy