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XXI

x

1.
. , -

.

(

f

= RT ln PK F PK

J = zF fP RT

, : co ; ci exp(zF f=RT ) 1 ; exp(zF f=RT ) Ko ]+ PNa Nao ]+ PCl Clo ] : Ki ]+ PNa Nai ]+ PCl Cli ] : 1) ,

), . (XIX.2.4) (XIX.2.10)],

(XXI.1.1) (XXI.1.2) , (df=dx = .
g

(XXI.1.1) (XXI.1.2), = const) 3) 2)

4)

6 10
. . . . , , ( , | 0 31 0 51 , | 0 45 0 45 ) ,

, | . -


x

1.

115 , . ,| . , ( . . (XIX.2.12.)] , , . , . . ). . . , , , , Na+, ,

1. 2. 3. . 4.

.

. XXI.1. ()
I

()
1

f

co, ci |

( ):
II

( ), 2

, E|

,F|

; ,! |

;| |

, z| -

, . | , ( ( . XXI.1), . ). ,

, ,


116

XXI.

A|
. = F f=RT

. (XIV.1.1)] ! ; = co A exp h; E + fFz i = co n exp ; zF f | RT 2RT 2RT ; = ci A exp h; E ; fFz i = ci n exp zF f : | RT 2RT 2RT , E|

(XXI.1.3) , n| , .
y

F f=RT
:

(XXI.1.3),

=

; I = zF ( ; ; !)= zF n ci exp(z y=2) ; co exp(;z y=2) : |; | (co = ci = c)
I = zF nc exp(z y=2) ; exp(;z y=2) = zF nc sh(z y=2) 1; sh x = 2 exp x ; exp(;x) :
. XXI.2. ( ( ):
II

(XXI.1.4) (XXI.1.5)

;

I, 1

)

(

I,

2

) -

I | , f| f3 | ,

f1 , f

2,

, , . XXI.2 , ,

, ( (.. , ( ).
II

: , ). ()
I

, , .


x

2.

117 , , (
f1 f3

,

2

).

,

, ,

(

(XXI.1.5), ).
1

-

, ( . (XXI.1.6) , , (XXI.1.3){ . . -

( (
f1 f3

).

f2

),

. XXI.2

,

)

! ;= |
(XXI.1.6) .

(XXI.1.3),

; = co exp ; zF f |c RT i
. (XIX.2.12)],

.

,
x

:

2.
. (XIX.2.6)],
g

(

i),
(XXI.2.1) . ,

z2 F 2 P c i = RT i i

:

(XXI.1.3){(XXI.1.5) . , , . ,

.

( . XXI.3).


118 . ,

XXI.

:. , (XXI.2.2) , (XXI.2.3) (XXI.2.4) -

k1 c(1 ; ) = k c|
,k
1

2

, (1 ; ) | . ( 1 =k2 ) g = k k1 c c = 1+k(k =kc)c = 1+cgc + k1 2 12

k2 |

g

= k1 =k2 | (XXI.2.3) ,

. 1 ; =(1 + gc);1 : = gc=(1 + gc)

c

.

. XXI.3.
c| k1 k2 | A B, n |

:

-

10( (

A (1

;

B ),

, | ): = A(1 ; B )n exp ; 2fF : RT (XXI.2.5), . (XIX.2.12) (XXI.1.6)]. . ), 01 (XXI.2.5)

,

! ; |
(1 ; B ) ,,

A

,

-


x

3.

119

! ; |

c,
g 1 = (1 ; )n exp ; 2fF = 1+cgc 1+ gc n exp ; 2fF RT RT gc = (1 + gc)2 , gc 1, , gc(1 , ( (

=
n

exp ; 2fF : (XXI.2.6) RT , , 1 1). ,

+ gc);2 . XXI.4). ,

)

,

, , , . . -

,

( Cs+ . . . -

. XXI.4. , NaCl, .
x

,

, -

5

{5

c;| !| |

:

,

3.
, . , 1 0 01, (XXI.3.1) , l0

: ( ()
g

. XXI.5). (..

1 0 0 1 1 1 0 0).

F (1 0) l00 |

F (0 1) |

J = l0 F (1 0) ; l00 F (0 1)
10 01


120 :

XXI.

l0 = n exp ; 2fF RT
, (.

l00 = n exp 2fF : RT
. XXI.5, F (1 0) ,
II

(XXI.3.2) . IV). , -

F (0 0), F (1 0)
2

x

dF (1 0) = F (0 0)k c exp ; zF f1 + F (0 1)n exp ; zF f2 + F (1 1)k exp zF f3 ; 1 ;2 dt 2RT 2RT 2RT h zF f1 n exp zF f2 + k c exp ; zF f3 i (XXI.3.3) ; F (1 0) k;1 exp ; 2RT 2 2RT 2RT

+

f1 , f2 f3 f3 = f).

|

dF (0 0)=dt dF (1 1)=dt

(f1 + f2 +

. XXI.5.
c|

.|
I

f

II

, l0 l00 | , 0| ln

, k1 , k;1 , k2 , k;2 | , 1| (XXI.3.2)

|

:
( -

dF (0 1)=dt. F (1 1) + F (1 0) + F (0 1) + F (0 0) = 1:

, (XXI.3.4) .


x

4.
x

121

4.
,

. , ,

, ( ,

, . XXI.6). . . ,

W|

.

10 00 k1 = k1 exp(;W=2RT ) : W = e2 =er r |

(XXI.4.1)

. XXI.6.
k1 |
. , k2 |

-

,

, , , , . , ,

,

,

, . . .

. -


122 , ,
x

XXI.

,, , ( . x 4 . XXII).

, , (.

,

,

. XXIV XXX). --

.

5.
Na+ . ). K
+

.
K+ . . . (1941) . (1902). K+ , , . , , 30 5 / .
ep

:

, ( , . -

.

,

Na+ ,

.

. . (500{700 / ), ,

, .

. -

,

es

. (XXI.5.1)

e2 e2 W = 2a e1p ; e1s ; (a + c)ep


x

5.

.

123

e2 (a + c)ep |

,

(XXI.5.1) . XXI.7, ,

c. . (XVIII.2.6)] W
.

a
. (XXI.5.1)

. .

. : Cs > Rb > K > Na > Li. , ,

-

. XXI.7. :
1 2

W

a

-

1

2

|

3

|

, : Li > Na > K > Rb > Cs. , | , . . , .

, . . Na+ , , | ,

-

, , .

, , . ( . XI, x 3) 10;8{10;9 , ,

, ,


124 ( 03 {0 5 ), , .
x

XXI.

(

, 1991). (COO; , NH+ ) 2

,

K

+

,

(. ,

, . XXIII). : Na+ , . -

6.
.

K+ -

. XXI.8.
1 2

|

Na+ - a

: -

. ( . XXI.8) ( ( Na+ pH Na+ . . . , , , . , ( ).
1

, , . Na+ Na
+

. -

1

2

Na+ -

).

-

,

Na+ (pK 5 2) pH . XXI.8 , ,
2

). -

.


x

6.

125 , . . XXI.9, . . , , , Na+ Na ( 03 05 . XXI.9). Na(;CH2 ;). (H3 N+ ;CH3 ) Na+ , , : . | 0 93 0 02, OH, , Na+ . , 1{3 Na , , -

(;CH3 ) (H3 N+ ;OH) 0 45 0 38 0 38 , 03 . . CH3 .

. ,

,

0 02. . XXI.8.

Na- K| 0 33 2 3, , .

| 0 007 -

.

,

.

, .

f0

2zF f ci ; = co exp ; RT | |
( K+ -

; ! |

, . (XIX.2.12)]

. : f0 = exp 2zF (RT ; f) = exp2(y0 ; y)] .

(XXI.6.1) -

e2

.

! ; |

n, n =2)
(XXI.6.2) , 1 5{2 5, . -

nzF (f0 ; f) ; =exp RT | , .

n


126

XXI.

. XXI.9. ( ) ) . NaNa ) . A, B , C , D E . NaCOO; ( . B. Hille, 1992).

Na- K11

, 0 | COO

2{6

| Na-

A, B , C , D E RT .
, ) | .

C

B.
. ( . , ),

C


x

6.

127 . XXI.10.
1 2

()
I

| |

( ):
II

, 4

(

,|
3

1

), ,

o, i |

,|
5

| ,

. ( . 08 . 03 O, Na 10 130 K+ ,
+

. XXI.10). , K
+

, -

K+ , . . , , 0 26 O , K+ K+ 07 , , , 1 . 1 0 4{0 5 . . . , , , . K+O, . , , (. Na Na, . ,

0 26

03 . K , , Na+ K+ -

. XXI.9).

. . .

. . XXI.10, .
II

, , .. .

, K+ -


128

XXI.

(
, . . 5 . 100 . , : 1) , 3) , 4) ). . . . , . , . ( , ), . . . 1976 . .

-

).
. , 0 5-1 , ,

-

, , ( , , 2) .

-

(

10{20

)

, , -

, . . ,

Na+ -, K+ .

.

XXIII Na+ - K+ -

-


x

6.

129

. XXI.11. . ,

( B. Hille, 1992). . , | -

,

| ,

,

. XXI.11 ( ,

, 1993) . 1900{4000 , .

-

.

, , -

, . .

,


130 , , . , Na+ - K+ ( Na+ , Na+ Na+ . (t K+ . K+ . 4{5 ) . . . , . XXI.12). (

XXI.

.

. , -

. , . XXI.12). . Na+ -

,

. . (;15 , ) ,

.

.

I
,

K

( (500 )

)

.

-

(10{20 )

R, R
w

O
'

I-

o

/

O
o

/

I: I, O,

,

R

.

.


x

6.

131

. XXI.12. )

;80

Na-

Na. Cs.

.

-

(

B. Hille, 1992). 10

. ).

;40

( )

) K-

,

> 10 NaK+50 . . ,

. . . -

,

3

.

;100

20

.

9 ( 20


132
x

XXI.

7.
, . , 70, , , , . ( : CH3 ;CO;OCH2 CH;N+ ;(CH3 )3 : ( . 0 ), ( , (a, b,
g d)

1960-x Na+ , .

.

,

-

, ).

.

Na+ .
a2 bgd

. , , )

. ,

a

-

40, 50, 60 65

,

.

, . , ( ( . . ) ) .

,

.

54 ,

.

: o-

. -

, , ,
Escherichia coli

.

-

-

, ,


x

7.

133 . , . XXI.13 , , . , . ,
a

a

M1 {M4 . , M1 ,M2 ,M3 ,M4 , 20{30 b, g, d,
; ).
a, b, g, d,

.

.

430{500 . ) . M3 , M . . , .

. . XXI.13 M
2

,

(

(

;,

;, M2 -

.

4

Na-, K-, Ca. Na- Ca, S4 ,

.
,

, (

a

( Na. XXI.14)

a

(S1 S2 S3 S4 S5 S6 ) . S4 , . Na- Ca.S1 {S6 , . K, Shaker . KS5 S K,

) a1 ( Ca300{400 6 4 , 8

) , -

(

. XXI.14) ( . , 10). ,

KShaker A).

4 S
6 4

,

Na-

Ca, .

a-

K-

Shaker.

(

K-


134
XXI.

. XXI.13. . ,

,

( B. Hille, 1992). , .

N- C-

M1 ,M2 ,M3 M4 .


x

7.

135

. XXI.14. I, II, III IV. (y), (ScTX), (n),

( B. Hille, 1992). .

. (+)

P,

,

(CbTX),


136

XXI.

. XXI.15. B. Hille, 1992).
(STX)

(
(TTX) , (TEA) .

-

NaK. .

,

.
. , . ( . XIV). STX, TTX ) TEA ( (. ( . XXIII, x 3). , . . XXI.15) .

. : 1) 2) , ( :
Tetraodontidae.

-

TTX, . TEA -

, . XXIII, x 3) STX, , T

.

,

;; T + Rec ;k;! TRec k;;
1 1

K
,

K( )

.

; = kk 1 : 1 TEA,

(XXI.7.1) , , -

.


x

7.

137 K. (TRec) ( TTX STX Na. NapH. . ( ) , . , , , TEA Na(COO; ), K. , ) (iK ) . , K+, , , -

.

.

TTX

pKa Na. , , , . ( . ( ). . , . . . , TRecTTX, STX , , Na, , . . XXI.16 c

,

7{9.

-

Na+ H+ , , . , . , . ),

N-

.
( ) ,


138

XXI.

. XXI.16. B. Hille, 1992). () Na( () () H
+

( : R| , (resting state), O | (inactivated state). -

(open state), I | ) . . . . Na, .

.

Na

+

Na-

-

. | , III .

-

IV ( . XXI.14) , , TTX STX.


x

8.
a

139 , , , | , . , Nax

, , . . ( , . . , .

(

) , . , , . Na( ( pH, . )

.

. ,-

,

) -

)

,

,

,

. XXI.17

8.
.

:

. , , . . 70-

-

R
t0

O q p

. q,

=1=q

t0

q ; ! O ;;R: p

nO nO = pnR ; qnO _ nR = ;pnR + qnO _ nO + nR = N

nR

-


140

XXI.

. XXI.17.
1| , ScX (b-ScTx) ( ,

Na( ATX (

( B. Hille, 1992). :
2| BTX) 3 | ). (LA) ) 4| ( Na .
b

),

, -

t

nO | 1 = p+ q.
),

nO (t)= nO ; (nO ; n0 ) exp ;(p + q)t] O 0| , nO nO nO nR
. ( , -

-


x

8.
t

141 =1=(p + q). , , (t0 =1=p) (XIX.25) = dI =df.
g

. . tg a,
a

:

, ( |

) -

I (f).
. . XXI.18.
(t),
g

t
(t + t)
g

-

g

t.

,
g

(t + t) (t + t),

(t), . . (t + t) g(t)
g

, , .
g

, , .

c2

c c2

:
g g

g

= h( ; )2 i ,
g

(XXI.8.1) (t + t) .

(

. XXI.18). . (XI.1.9){(XI.1.15)].
g

(t),
t

,
g

. (XI.1.9)]:
g

, (t)

t
(XXI.8.2)

C (t)= h (t) (t + t)i:
g


142 (..
c2 t

XXI.

, . (XI.1.11)]. .
t

; 0,
,
t

,

). , ,
t

,

t

=0 ,

. -

|

,

.

C (t)
, , ,

.

{

.

. (N = N0 exp(;t=t0 )), . (XI.1.13)] . XXI.19. ,
t

t0 t0

c2

(

. XXI.19)

-

()
1

0|

:

()
2

(XI.1.15):

C (t)= c2 exp(;t=t0 ):
,

(XXI.8.3) ,(XXI.8.4) (XXI.8.5) (XXI.8.6)
e

,

-

P (w)= (2=p) C (t) cos(wt)dt:
0

Z1

,

( :

. XXI.20).

C (t)= C0 exp(;t=t0 )
exp(;t=t0 )cos(wt)d
t

2 P (w)= p C

0

Z1
0

0 P (w)= 2 C0 1+tw2 t2 : p 0

f (f =2pw)
e

S (f )= SVn (f ) ; f )Ve (f ) SVe (

(f ):

-

(XXI.8.7)


x

8.

143

SVn (f ) | n), a SVe (f ) |
, , (1928): , | e). ,
e

V
(f ) , ,

(

f
(

| . (XXI.8.8)

.
Z (f ) |

SVe (f )=4k T Re Z (f ):
, .. ( : ).

Rs =Re Z | =Im Z |

Z = Rs + iXs =Re Z + i Im Z
(

), a Xs =

. XXI.20.
( ) P (w) . 1=t0 . 1=t0 . | 1=t0 , , -

(XIII.3.16)].

,

.

R ReZ =
(XXI.8.9) 1=Z :

C,
R R = : 1+ w2 C 2 R2 1+ 4p2 (fC R)2 ,

, (XXI.8.9) 1=R

wCR CR2 Z = 1+ iR CR = R(1 ;2iC 2 R2) = 1+ wRC 2 R2 ; i 1+ww2 C 2 R2 : 2 w 1+ w

,

1=Z =1=R + i 1=1 C =1=R + iwC: w


144 ( ) (XXI.8.8) ( ) .

XXI.

(XXI.8.9), (XXI.8.10)

SVe (f )=
,

4k TR : 1+4p2 (RC f )2

I,

-

SI (f )=4k T=R:
. , , , ,

(XXI.8.11) . ,
t0

, (XXI.8.8) (XXI.8.10).
t

h

0

,
e

,

-

V|
:

,
e

20 2 1 (f )= tk hTV t0 1+ (2pf t)2 , t=
t

(XXI.8.12)
t0 t (t0

+ t );1 . (XX.8.12) (XXI.8.13) . , . . XXI.22.

t0

,

1 V2 (f )= t0kh0T 1+(2pf t0 )

2

;100

. XXI.21.

. ( . XXI.20)

S (f )

f|
. XXI.22 2

S (f )= 1+ , S (0)

S (0) = S (0) (f=fc )2 1+(2pf t0 )2 fc | , , fc | , t0 =1=2pfc | t0 , ,

, ,

.

-


x

8.

145

. XXI.21. (
, . , . . , , . 8 C. , .

-

, |

B. Hille, 1992)
| , . ,

. XXI.22. ,

-

.

S (f )

( C. R. Anderson, C. F. Stevens, 1973)
( . ).


146

XXI.

1 = p+q 1 ,
t0

.

.

;50
p

20 C (p

t0

q),

= -

t0

1 = p + q ' 1: p
.
2

.

,

.
c2

. ,

,

P

P2 P n 1X 2 1X = n (Ik ; I )2 = nIk ; 2I n Ik + I 2 = n Ik ; I k=1 k Ik =n = I . , i. , , i2 p. (XXI.8.14) ,
c2 c2 i

I:

(XXI.8.14)

ip,

p,

-

= i2p ; i2p2 = i2 p(1 ; p)= i2 pq

(XXI.8.15) (XXI.8.16) (XXI.8.17)

q|

,
c2 I

I

.

N

= N (i2 p ; i2 p2 )= Ni2pq

I = N ip:
,
c2 I

= Iiq.

i
(XXI.8.18) .

. .i

,

c

2 2 I i = cI = I (1c; p) Iq 2 I I

p

q,

,

i = cII : i,

2

I

.


x

9.

147 )
g

(

(XIX.2.5)
g

= dI =df:

h0 : h0 = di=df:
, .

i(f).

. XXI.23

. XXI.23. (
Ca. 160 KCl 160 KCl

Y. Yellen, 1984).
Koutside-out NaCl, a KCl. 265 .

-

( . XXI, x 6) (QIO Na1 0{2 5). 2.
x

(

NaK-

4

24 K(h
0

. XXI.24), . 500{2000

h

0

h0

, 100{300

). Ca -

9.
. , , Mn, Co La, K+2+

Ca

Ca2+ Ca2+ - a a a.

.


148

XXI.

. XXI.24. () () . () () 28 . KNa. , . . ,

( Cl. ).

B. Hille, 1992). . +40 . ;80
Torpedo,

(

;80

. 0, 14 -


x

9.

149 Na+ . Ca2+ , , , , Na+ ). . | , , Ca2+ , , K . K+ , Ca2+ x , . Na+ , , Na
+ +

. , , Ca2+ | D-600. 2+ Na+ Ca , Ca2+ . Ca2+ . . (.. , 20 . , Na+ K+. , , . , , ..

.

,

Ca ,

2+

|

Mn, Ca2+ -

Ca2+ -

D-600.

Na+ - . Ca2+ Cd, Mn, Co, Ni, La,

,

,

-

F
4-

, ,

,

. Ca2+ - a c
Chaetopterus

Ca2+ .

Ca2+ , Ca2+ Na+ ,

Ca2+ Ca2+ Ca . . . ,

F ;.

-


150 Ca2+ , (10; . . , Ca2+ : . Ca2+ ; Na+ , , Ca , , . , Ca2+ . Ca2+ Cl; , ,
8

XXI.

), Ca
2+ 2+

. , , , Ca2+ .

Ca ,

, -

, Ca Cl; Ca2+
2+

, Cl; . Ca Ca2+
2+

Ca

.

. , . .

10;

9