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Уравнение постоянного поля ионных токов

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14

Уравнение постоянного поля

Для того чтобы вычислить точное значение мембранного потенциала для
модели идеальной клетки, необходимо принять во внимание отдельные ионные
токи, протекающие через мембрану. Входящий натриевый ток (iNa) зависит
от величины движущей силы для ионов натрия (Vm-ENa), а также от
натриевой проводимости мембраны (gNa). Проводимость пропорциональна
среднему количеству натриевых каналов, находящихся в открытом состоянии
при потенциале покоя: чем больше открытых каналов, тем выше
проводимость. Таким образом, натриевый ток равен:

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46430100000000000100e207000000000100000054130000000000005413000001000000
6c00000000000000000000006d000000130000000000000000000000400b00000b020000
20454d4600000100541300000c0000000100000000000000000000000000000090060000
1a040000b801000013010000000000000000000000000000c0b606003832040046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000003405000028050000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c000000000000000840000580040000740400000210c0db0100000000000000
00000000000000000000000001000000ffd8ffe000104a46494600010101006000600000
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0b080014006e01011100ffc4001f00000105010101010101000000000000000001020304
05060708090a0bffc400b5100002010303020403050504040000017d0102030004110512
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0d0206090a01010f0105040512292b582d3259594e01010b04015a5b525c5d0902010a15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Тот же подход справедлив и для калия и хлора:
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Если принять iCl, = 0 (т.е. ионы хлора находятся в равновесии), то, для
сохранения неизменного значения мембранного потенциала, калиевый и
натриевый токи должны быть равны по величине и противоположны по
направлению:
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Рассмотрим это уравнение более подробно. Предположим, что gK значительно
больше gNa. Тогда, для того чтобы токи были равны, движущая сила для
выхода калия должна быть значительно меньше движущей силы для натриевого
входа. Другими словами, мембранный потенциал должен быть ближе к ЕK, чем
к ENa. Соответственно, если значение gNa велико, то мембранный потенциал
будет ближе к ENa.

Преобразовав выражение, получим формулу для мембранного потенциала:

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Если по той или иной причине ионы хлора не находятся в равновесии, то
формула приобретает несколько более сложный вид:

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Вышеприведенные расчеты были первоначально проведены Голдманом) и,
независимо от него, Ходжкином и Катцем), с той лишь разницей, что вместо
равновесных потенциалов и проводимостей они оперировали ионными
концентрациями снаружи ([Na] 0,. .) и внутри ([Na] i,. .) клетки, а
также проницаемостью мембраны для каждого из ионов (pNa···):

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0000

Так же как и ранее, хлорные компоненты выражения не рассматриваются,
если ионы хлора находятся в равновесии. Уравнение называется “уравнением
ГХК” по фамилиям авторов, или уравнением постоянного поля, поскольку
одним из допущений при выводе уравнения является равномерное
распределение градиента напряжения (т.е. “поля”) на всем протяжении
мембраны. Уравнение ГХК полностью аналогично уравнению проводимостей, на
его основании можно сделать те же предсказания: когда проницаемости для
натрия и хлора малы по сравнению с калиевой проницаемостью, хлорный и
натриевый компоненты уравнения становятся пренебрежимо малы, и
мембранный потенциал стремится к значению равновесного потенциала для
калия: Vm = 58 log ([K] 0/ [K] 1). При увеличении натриевой
проницаемости мембранный потенциал сдвигается в сторону натриевого
равновесного потенциала.

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2e2e3a433040214441222b314f383443313a3d3d2f34454e4f4f4f37363332313a2f3e1c
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3a30323040393f2d31404032335a354636313b2f3546464f3745474e4f433d402c2b403b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313131313131313146464f333a3c3a3136302d442d31454a4f343a3e2d2c402b2f2f3236
454f433c3b3c3e3e3e3c3a3030323336384546464e34334e47313c3130302f2f2f303031
3a3546373c41222134333a2b443b36453735432f3d2e2e3e2d44403c3b3e3a3538343c41
443e3e442c2e402b3d323c223e3b31333638464e4a31442b3d3b3d3e3c31364f3838454e
4e31314848322f383c414036494f34374e494d4b49484b52505353524947484b49493339
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055e000025050b222d3d2e2c3d3d3d3c3c3b3b3b30313243333536364646474e4e4f433b
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4546464e34313e2b41442d3e3a2f32333637383846384f47352e2d2f3231313132433334
4f494b462f4142392e3a3b2b3f413d2f3d2d41222a2b3e3a302111422e3a3a3b2f3a344f
432b2a2d3d2d2a1d422b4041212c2f36454536344d4b48383d222a2e2f35474637374953
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155e000016150b3f2c3e2e2d3e3d3d3d3c3c3b3b32433334363738384e4e484949463531
2e212013111d391d444121442c3d2f314545454545464646354f454f46484f3230363632
334e4838384f46474e4746453834433336352f2e3d3c2f36484b49463735333130323437
43323231302f2f3a2239120b090b121d403c303b2c442c3c2239201c222c3c3a34374f38
34433437312f3c2e2e3e3b2f3a2f303132323231434335362f2b403a2f2f3a3a3a303131
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3a3c3a312b2c3e3b2f3131312f2f2f2f3b3c3e2e2c3e3a3a2c212b3c3e3e2e2d2d2e2e3e
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3d4420090c0c0d0e12111c39222c2f34484e464f373634332e3a303a3134353237484835
43384f333637363533303b3e314336464e45333a3c3a32353835313b43303d40442b3e3a
2c2c2c2d2d2d2d2d221d130f0b0f0b0b0d0f1c424222442d2c2b4141402c2c2b412b402c
2c2c2e3d0f113f2b2e3e3e2e2e2e2d2c2b412a22212b2d2d40402e3b3e2e2c402b2b2b2b
2d3d3b3e41200b0e0a11391c42442e2e444121412b21200b1516182614413d2d41130e13
11091e1414091d2b2c442b3e3d2b222a403b3031303b3b2f3c2b2144313334432f3b3033
323a3a3335323031402a1d11203f2b3e314336474a4a45363a364b50514b494947515230
0b04000004051e0b1c2a2b2c2c2c2c2c2d2d2e2e2f30313233343536373636373836322f
2a39101415061f140a0b0b0b0f20212e3a3a3b3c3d3e2e2e2e3d2e212221213f2c30322e
403d3d403e3e3e2e2c4122422b2c3d3043432f3c3b3b3c2e2b2121212a224239391c1112
111120201c1d39390f090c0c0d0d140815071f1e0c0a13203f4239423f39110f081e0d0b
111d1d1c2307140a1013131012121213100f0a09131120201d3f2a2a3f421d2012101010
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2a2a21442122212c1113091e0809121c2b2c3e3c3b3c3c3c2a2b3c3233313c2e2b30432c
0b23000002030405060708080909090a0a0b0b0b0c0d0e090a0f10101112131211130a0d
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140a0b0c0a0a0b0a090c08070c0d0910201d1d1d2122200e15231f0d232315081e060318
1616041b05230615231b1a051515050404022425030515071f071f08080616242426251a
1f140815020203041a1b050505052306062305051b1b1b1a06081e071f07231a16021919
02040607061b031925241818161f08230d071b1b230502171719262728050e0a070d0d23
020316031903150c062525231e0519191b07080715150706192929241b1a1b151e140815
151f1e080623080a1e082302191a15080c0a130f0d0c0a1207071e0e0b0a1e06160c1309
060200000c00000040092900aa00000000000000d2001e0100000000040000002701ffff
030000000000

Рис.1. Зависимость мембранного потенциала от внеклеточной концентрации
калия на аксоне кальмара (полулогарифмическая шкала). Прямая линия
проведена под углом наклона, равным 58 мВ на десятикратное изменение
внеклеточного уровня калия, в соответствии с уравнением Нернста.
Благодаря наличию мембранной проницаемости для натрия, экспериментальные
данные расходятся с прямой линий, особенно при низких концентрациях
калия.

Из уравнения постоянного поля следует один важный принцип. Мембранный
потенциал зависит от проводимости (или проницаемости) мембраны для
важнейших ионов, а также от их равновесных потенциалов. В реальных
клетках проводимости для калия и хлора сравнительно· высоки, поэтому
потенциал покоя клетки близок к равновесным потенциалам для этих двух
ионов. При увеличении натриевой проводимости, например, во время
потенциала действия или возбуждающего постсинаптического потенциала,
мембранный потенциал сдвигается в сторону натриевого равновесного
потенциала.

Iioaioeeae iieiy

Несмотря на то, что во многих случаях уравнение ГХК весьма полезно, оно
не дает возможности правильно вычислить потенциал покоя. Дело в том, что
условие равенства суммарного тока нулю неправомочно: третье условие
равновесия, а именно требование, чтобы каждый отдельный ионный ток
равнялся нулю, не выполняется. В результате клетка будет постепенно
терять калий и наполняться натрием и хлором. В реальных клетках
концентрации натрия и калия поддерживаются на постоянном уровне при
помощи натрий-калиевых насосов. В противовес непрерывному потоку натрия
внутрь клетки и калия наружу, эти насосы переносят оба эти иона в
определенной пропорции в направлении, противоположном их пассивному
движению (рис.1). Следовательно, для поддержания клетки в стабильном
состоянии затрачивается метаболическая энергия.

Чтобы получить более полную формулу потенциала покоя, необходимо принять
во внимание как пассивное движение ионов, так и их активный транспорт,
осуществляемый насосами. Рассмотрим сначала пассивное движение ионов
натрия и калия через мембрану:
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2222220066666600d4d4d400c1c1c100cbcbcb00bababa00161616000707070073737300
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01010906090109010a0a0a0a0a0a0a0a04040404040404040704070a0901130108014011
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0112080f7a0e86f62322d4c28215cb7e15060f91160201020a0a0a0a0a0a0a0a06060609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0a0afeff0101010e1117060f02020202020208080609040a0a0a0a040906080202080709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Отказавшись от предположения о том, что токи эти равны по величине и
противоположны по направлению, но зная соотношение между ними, можно
получить уравнение мембранного потенциала, исходя из равновесных
потенциалов для натрия и калия, а также их относительных проводимостей.
Здесь уже нужно учитывать влияние насоса. Поскольку насос поддерживает
внутриклеточные концентрации натрия и калия на постоянном уровне,
перенося ионы в соотношении 3: 2, то и пассивные токи должны находиться
в том же соотношении: iNa/iK = 3/2. Имеем следующее выражение:
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383c91a603010401010922080a0802080b0b0b0b0508080501d7f47a05220d90890c0102
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2201010109220b0e0202010101220f01010b0c0f01010b050306220601c0f2e301010904
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0503030507090101010101010fee7c11b323534c0308220a07070c923801100501080a09
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9478010e9ae1011c0b080901010a03080601012210010101010a0808050b0b0a01881e1f
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050b01051a01070502090a0a05010101010101010b01090d01120e010a0131012201080a
0e250101010b100501270a0b0c060103b1e4dc31184ce3bf070101060101010101010101
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2323463e250201010144a31dc3d7ecbebe880501080c1ba623bfe3bfbf96464c464ced3e
23e6bf4a41235e41e38989892812e3ee25961b463e7c44a623317c3146bf18233112383e
5e0e2546a6690c0f0c010e0d01010d882369010d13b1080409010112ab16a2bd20c9583c
a60a0103050e694ce34a3e120f01ebb223010b01080101020176ad0e07010a01010a0107
088fb0e89a81b9afbc2bb9ceb091d6667805010301224f317c1b1b69070d01060104d34e
78cd63606348a22176755c7876772a3417d258e520dd7a9c6ab09bce5b6b7ab0cf916a91
e8e86a66d62fe8ceb0b09b2f949a37bc8e9b933217356378e963c99bbc36ea1774916412
03070a010a0b01222701220f010b0c01ded2767584eb2628010a75994a01010801090309
0124ba090b0b0b0d01020a220113e3bf411b44181228019638130ce31b01010101e4a16b
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4a0f4c1307123e46e60f1a3819254f1a271b271a187c040d5e0f4f270f8818383131b1a6
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0f010305030e01010101020101011f99400801010d01daae83a70b010b0b0b140a08080a
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38010b02020705010a0101220c12010f2505120115d20b285f685bcf6dd8a67e41010207
0a06050b020b01010501010a01060e01010b09040f060208030617cb8901010d010178d9
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0b010101010d0e010113a1c6013a212723c74fc8363455c9cacb22194f5d570b0a01010b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08080909050a0a0b0b0b0101010b0a0a0a010308250144617f058081440101121a010e08
0d01018283750406012f4534840508021a012709040d0103855558867b875a880101020b
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01406c6d6e0101080101080105050a0a0a0a0b0b0a0b0101010b0a0a0301020106010734
6f01707112011a010d010409060a0272002101013171735e74410a2701460c4f05060d3e
4b7576776035782d0f08050101795d267a7b7c1022090a09080a0a08020101015d7d1205
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0b0b0b0b0b0b0bd70f010d0f01593d005a05010c01020c01010b0b0b0b0a0a0a050a0b01
010b0b0a020a06010b0301285b165c5d5e0e100a080b0f0b0a0a032e5f60050118613208
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0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b1e0e0a010506124849080b020109060105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Соотношение имеет отрицательную величину, потому что направления
натриевого и калиевого токов противоположны. Преобразовав выражение,
получим:

picscalex100010009000003941a00000000860f00000000860f000026060f00021f574d
464301000000000001008fa30000000001000000e01e000000000000e01e000001000000
6c000000000000000000000082000000210000000000000000000000660d000079030000
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Это уравнение похоже на полученное выше для модели идеальной клетки, и
на его основании можно сделать то же предсказание: значение мембранного
потенциала будет определяться относительными величинами gNa и gК.
Отличие настоящей формулы состоит в том, что члены, относящиеся к калию,
умножены на 1,5. Благодаря этому фактору мембранный потенциал будет
ближе к EK. Таким образом, движущая сила для входа натрия возрастает, а
для выхода калия, наоборот, уменьшается. В результате и пассивные токи
натрия и калия будут находиться в соотношении 3: 2, а не 1: 1.4,Обобщая
вышесказанное, можно сделать вывод, что потенциал покоя – это такое
значение мембранного потенциала, при котором входящий натриевый ток не
равен по величине выходящему калиевому, а превосходит его в 1,5 раза.
Пассивные токи обоих ионов определяются их равновесными потенциалами и
проводимостями, в то время как соотношение токов 3: 2 продиктовано
стехиометрическими характеристиками насоса.

Задачу по выводу формулы потенциала покоя для реальных клеток впервые
взяли на себя Муллинс и Нода. С помощью внутриклеточных микроэлектродов
они исследовали влияние изменения ионных концентраций на мембранный
потенциал мышечной клетки. Подобно Голдману, Ходжкину и Катцу, они
получили выражение, связывающее мембранный потенциал с проницаемостями и
концентрациями отдельных ионов. Результат аналогичен только что
полученному нами уравнению, основанному на проводимостях и равновесных
потенциалах:

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6000000046000000b8090000ac090000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c000000000000000840000504090000f80800000210c0db0100000000000000
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01010f0107010c04090110010c0803081101090b011112070801130107070d0d03040404
0104010c0d02010a0b040e01040c14010507010e01021201040202020201010102868744
0c00000040092900aa000000000000002300a90000000000040000002701ffff03000000
0000

где r – абсолютное значение соотношения ионного транспорта (3: 2).
Уравнение точно описывает потенциал покоя при условии, что все остальные
ионы, проникающие сквозь мембрану (такие как хлор), находятся в
равновесии.

Распределение хлора

Насколько применимы подобные рассуждения для хлора? Как и для других
ионов, суммарный ток хлора должен быть равен нулю. Как показано выше,
равновесие ионов хлора достигается путем простого изменения его
внутриклеточной концентрации, без изменения при этом мембранного
потенциала. Тем не менее, во многих клетках существуют транспортные
системы для хлора. В аксоне кальмара и в мышце активные транспортные
системы переносят ионы хлора внутрь клетки; во многих нервных клетках,
напротив, хлор выводится из клетки (см. рис.1). В результате активного
транспорта хлора в клетку, его внутриклеточная концентрация возрастает,
что приводит к усилению выходящего пассивного тока утечки хлора, равного
по величине активному входящему току. Транспорт хлора из клетки наружу
производит обратное действие.

Электрическая модель мембраны

Потенциалы ENa, ЕK и ЕCl показаны в виде батарей, а проводимости для
натрия, калия и хлора изображены в виде сопротивлений (резисторов).
Пассивные токи через сопротивления равны и противоположны токам,
генерируемым соответствующими насосами, поэтому суммарный ток через
мембрану для каждого иона равен нулю.

Ожидаемые значения мембранного потенциала

Для аксона кальмара соотношение констант проницаемости для натрия и
калия приблизительно равно 0,04: 1,0. Воспользовавшись этими данными, а
также значениями ионных концентраций, получим потенциал покоя в морской
воде:

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20454d4600000100103000000c0000000100000000000000000000000000000090060000
1a040000b801000013010000000000000000000000000000c0b606003832040046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000004c0c0000400c0000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c0000000000000008400005980b00008c0b00000210c0db0100000000000000
00000000000000000000000001000000ffd8ffe000104a46494600010101006000600000
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050505050505050503030303030303030103020405111106111111111111111106110402
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030303030402010c060197988b01020236999a01110201043d84989b10019c009d055e60
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220e15017c7d3a0601013d7722017e7f2f01018072810182371683848501786d24130f0f
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020303030303030202020204040404040404040403030303030303030303030303030303
01110104021301525354150d5500330609010d0e33565758331e581f012c03595a010942
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060606060606060605040203030302020303020405051111050402030303030202030301
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0303030303030303030303030303030301130106040d03032a2b152c2d2e2f0114050109
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030303030303030303030303030302020505050505050505040402030303020402020204
050505110504020301010303020203010101030202040505050504020303030303030303
0303030303030303030303030303030303030303030303030303030303030303010c0109
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092829010907010705050505050505050303030303030303030303030303030304040404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Становится очевидным, почему при изменении внеклеточной концентрации
калия мембранный потенциал не строго подчиняется уравнению Нернста для
калия. Если сравнить слагаемые в знаменателе, относящиеся к калию (1,5 x
10 = 15) и к натрию (0,04 x 460 = 18,4), то получится, что вклад калия
составляет всего около 45%. По этой причине, увеличение внеклеточной
концентрации калия вдвое не приведет к удвоению числителя (как было быв
случае полного соответствия с уравнением Нернста), и, следовательно,
эффект изменения уровня калия на мембранный потенциал меньше, чем в
идеальной ситуации, когда калий является единственным проводящим ионом.
Когда внеклеточная концентрация калия возрастает до существенных
значений (100 ммоль), то роль калиевого компонента в знаменателе
становится подавляющей, и кривая зависимости приближается к своему
теоретическому углу наклона (58 мВ на 10-кратное увеличение концентрации
калия). Многие калиевые каналы обладают чувствительностью к мембранному
потенциалу и открываются при деполяризации, вызванной увеличением
внеклеточной концентрации калия. В результате подобного увеличения
проницаемости для калия вклад натрия в формирование мембранного
потенциала дополнительно снижается.

Вообще, потенциал покоя нервных клеток приблизительно равен – 70 мВ. В
некоторых клетках, например в скелетной мышце позвоночных, потенциал
покоя может быть – 90 мВ или даже больше, что объясняется значительным
превосходством калиевой проводимости над натриевой. Натриевая
проводимость глиальных клеток настолько мала, что их потенциал покоя
практически равен калиевому равновесному потенциалу. В таких клетках,
как, например, нейроны ганглиев пиявки или рецепторы сетчатки, натриевая
проводимость достаточно велика, а потенциал покоя составляет всего – 40
мВВклад натрий-калиевого насоса в мембранный потенциал.

Натрий-калиевый насос является электрогенным, потому что за каждый цикл
его работы из клетки выводится один суммарный положительный заряд, тем
самым увеличивая отрицательный заряд на внутренней поверхности мембраны
клетки. Насколько велик этот вклад в заряд на мембране? Чтобы ответить
на этот вопрос, представим себе, что насос не электрогенен, а нейтрален,
то есть соотношение ионов, переносимых насосом внутрь и наружу клетки,
равно единице. С учетом этого условия проведем вычисления:

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030303030303030303030303030303030303030303031302020202020202020203030303
030303030303030303030303030303030303030303030303030303030303030303030303
030303030303030304010105010103060607010108010901010601010a01040b060c0101
0d0e010f0c03010e01010e040101010410110702010901010b090e010101120d13020301
041401010115010a01011601060602020d01020c17141201170103180119130101060109
010402010e0112011201040614010e030d03120112121212121212121203030303121406
121212030301010112121212121212120303030303030303030303030303030303030303
030303030303f9f90c00000040092900aa000000000000002100ea000000000004000000
2701ffff030000000000

Поскольку полученный потенциал покоя на 6 мВ менее отрицателен, то можно
сделать вывод о том, что вклад насоса в потенциал покоя равен – 6 мВ.
При условии транспорта ионов в соотношении 3: 2 вклад насоса в потенциал
покоя не может превысить – 11 мВ. При остановке ионообмена его влияние
на величину потенциала покоя прекращается, и потенциал покоя постепенно
снижается по мере накопления в клетке ионов натрия и выхода из нее
калия.

Ионные каналы, участвующие в формировании потенциала покоя

Наличие проводимости для натрия, калия и хлора в состоянии покоя было
показано во многих клетках. Интересно отметить, что ионные каналы,
обеспечивающие эти проводимости, до сих пор не были определены ни в
одном типе клеток. Кандидаты на роль калиевых каналов, активных в
диапазоне потенциала покоя, различны в зависимости от типа клеток. Среди
них есть каналы, активируемые внутриклеточными катионами:
натрий-активируемые и кальций–активируемые калиевые каналы. Кроме того,
многие нервные клетки обладают так называемым калиевым каналом типа “М”,
которые открыты при потенциале покоя и закрываются при участии
внутриклеточных посредников. Активация большого количества
потенциал-зависимых калиевых каналов (то есть “замедленного выпрямителя”
– delayed rectifier, и каналов типа “А”) при потенциале покоя
маловероятна. Однако, даже 0,1-1% от их общего числа было бы достаточно,
чтобы создать проводимость, сравнимую с проводимостью в покое.

Конкретные носители натриевой проводимости в нервных клетках также
неизвестны. В некоторой степени, вход натрия может происходить через
калиевые каналы, для большинства из которых проницаемость для натрия
составляет от 1 до 3% от калиевой проницаемости. Кроме того, открытые
катионные каналы могут способствовать как выходу калия, так и входу
натрия, поскольку большая часть этих каналов не обладает высокой
селективностью к калию по сравнению с натриевой. Дополнительный источник
входящего в клетку натрия – это натрий–зависимые вторичные активные
транспортные системы. Наконец, потенциал–чувствительные натриевые
каналы также вносят свой вклад в натриевую проводимость в покое,
поскольку эта проводимость блокируется тетродотоксином, хотя и в
небольшой степени).

Хлорные каналы семейства CLC широко распространены в нервных и мышечных
клетках. Наличие хлорных каналов обеспечивает стабилизацию мембранного
потенциала. Эти каналы также участвуют в установлении внутриклеточной
концентрации хлора, взаимодействуя с системами хлорного транспорта. При
низком уровне экспрессии каналов CLC, например, в нейронах
эмбрионального гиппокампа, значение ЕCl менее отрицательно по сравнению
с потенциалом покоя, благодаря вкладу активного транспорта ионов хлора
внутрь клетки и их накоплению в цитоплазме. В нейронах взрослого
животного экспрессия каналов CLC более выражена, и мембранная
проводимость для хлора выше, поэтому накопление внутриклеточного хлора
невозможно, и ЕСl равен мембранному потенциалу. В клетках центральной
нервной системы до 10% проводимости мембраны при потенциале покоя
обеспечивается за счет хлорных каналов.

Изменения мембранного потенциала

Равновесный мембранный потенциал представляет собой тот фоновый уровень,
на котором происходят все изменения мембранного потенциала. Как они
происходят? Обычно кратковременные изменения мембранного потенциала
(подобные тем, которые наблюдаются при взаимодействии нейронов между
собой) происходят за счет временных изменений проницаемости мембраны.
Как мы знаем из уравнения постоянного поля, увеличение натриевой
проницаемости (также как и снижение калиевой) приводит к деполяризации,
то есть к смещению мембранного потенциала в сторону натриевого
равновесного потенциала. Напротив, увеличение калиевой проницаемости
вызывает гиперполяризацию. Еше один важный для сигнальных процессов
клетки ион – это кальций. Внутриклеточная концентрация кальция очень
низка, а ЕСа в большинстве клеток превышает +150 мВ. Следовательно,
увеличение кальциевой проницаемости должно приводить к входу кальция в
клетку и деполяризации мембраны.

Особый интерес представляет влияние хлорной проницаемости на мембранный
потенциал. Как было отмечено выше, хлор вносит незначительный вклад в
потенциал покоя. Внутриклеточная концентрация хлора подстраивается под
новые условия за счет работы существующих хлорных транспортных
механизмов. Влияние кратковременного увеличения хлорной проницаемости
может выражаться как в гиперполяризации, так и в деполяризации, в
зависимости от того, положителен или отрицателен ЕС1 по отношению к
потенциалу покоя. Это, в свою очередь, зависит от работы транспортного
механизма, либо наполняющего клетку хлором, либо выводящего его наружу.
В любом случае, влияние хлора на мембранный потенциал обычно невелико.
Тем не менее, увеличение хлорной проницаемости может иметь важное
значение для регулирования сигнальных процессов, поскольку оно
поддерживает мембранный потенциал в диапазоне ЕCl и за счет этого
ослабляет способность других процессов изменить мембранный потенциал.

Поддержание мембранного потенциала на неизменном уровне играет важную
роль в регуляции возбудимости таких клеток, как скелетная мышца, хлорная
проводимость которой в покое достаточно велика. В таких клетках
кратковременный вход положительных ионов вызовет меньшую деполяризацию в
присутствии хлорной проницаемости, нежели в ее отсутствии, поскольку их
вход отчасти балансируется входом хлора через уже открытые каналы.
Мутации хлорных каналов, снижающие хлорную проницаемость мембраны,
приводят к некоторым мышечным заболеваниям. Потерявшие нормальную
высокую хлорную проводимость мышцы находятся в состоянии повышенной
возбудимости (myotonic.

Выводы

Нервные клетки обладают высокой внутриклеточной концентрацией калия и
низкой концентрацией натрия и хлора, так что калий стремится выйти из
клетки, а натрий и хлор стремятся войти в нее. Стремлению калия и хлора
проникнуть через мембрану в направлении концентрационного градиента
противостоит мембранный потенциал.

В модели идеальной клетки, обладающей только калиевой и натриевой
проводимостями, мембранный потенциал может в точности уравновесить
концентрационные градиенты таким образом, чтобы суммарный ток обоих
ионов равнялся нулю. В этом случае мембранный потенциал соответствует
равновесному потенциалу для калия и хлора.

Изменение внеклеточного уровня калия приводит к изменению его
равновесного потенциала и, следовательно, мембранного потенциала.
Напротив, изменение внеклеточной концентрации хлора приводит в конечном
итоге к изменению его внутриклеточного уровня, так что сдвиг хлорного
равновесного потенциала и мембранного потенциала от своих первоначальных
значений носит кратковременный характер.

Мембрана реальных клеток обладает также натриевой проводимостью. В
результате в состоянии покоя происходит постоянная диффузия натрия
внутрь, а калия наружу клетки. Эти токи в точности уравновешиваются
активным ионным транспортным механизмом – натрий-калиевым насосом,
работающим по схеме 3 иона натрия к 2 ионам калия. В этих условиях,
величина мембранного потенциала зависит от натриевого и калиевого
равновесных потенциалов, относительных проводимостей для этих ионов, а
также от соотношения ионов в цикле насоса.

Благодаря тому, что натрий-калиевый насос переносит больше положительных
ионов наружу, чем внутрь клетки, он вносит непосредственный вклад в
мембранный потенциал в размере нескольких мВ.

В зависимости от особенностей хлорных транспортных механизмов,
равновесный потенциал для хлора может быть как более, так и менее
отрицательным по отношению к потенциалу покоя. Несмотря на
незначительное влияние распределения хлора на потенциал покоя, наличие
высокой хлорной проводимости необходимо для поддержания электрической
стабильности клетки.

Литература

1. Блюменфелъд Л.А. Решаемые и не решаемые проблемы биологической
физики.

2. Барышников А. Ю, Шишкин Ю.В. Иммунологические проблемы апоптоза.

3. Крутько В.Н., Славин М.Б., Смирнова Т.М. Математические основания
геронтологии.

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