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XXI I I

x

1.
| 1 , 100 / . . KCl, 05 , | , -

1 . , . .

.

,

.

. XXIII.1. 1968)
, (2 , ),

(

.

,
-

RC ( +(40{50)

,

. XXIII.1).

t

,

-


x

1.

167

.
K . K K+ ,
+

100{120 K+

.

. , K+ , Na+ . 50{70 , . .

Na+ Cl; .

| . (XVIII.3.1)]
fK fK

?

|

= RT ln Ko]] F Ki K+.
fK

(XXIII.1.1) K K+fK

| , ,

400 K ,
+

;75

+

. ;70

20 . .

-

K+ ( . (XIX.2.10)], Cl; ,..

.

. . (XIX.2.8)] IK + INa + ICl =0
f

IK + INa =0

. Cl; -

= RT ln PK Ko ]+ PNa Nao]] : F PK Ki ]+ PNa Nai K+ , (XXIII.1.2) K+

(XXIII.1.2) Na+ , (XXIII.1.3)

(P

Na

Na+ , PK : PNa =1 :20. PK ) fNa .
fNa

,

.

Na+ (PK : PNa = 1:0 04). (XXIII.1.2), , = RT ln Nao]] : F Nai


168 , .
f

XXIII.

(XXIII.1.3), , ,

+55 Cl; :

, -

]+ P Na ]+ P Cl = RT ln PK Ko]+ P Na Na o]+ P Cl Cloi]] : F PK Ki Na i Cl

(XXIII.1.4)

, , PK : PNa : PCl =1 :20:0 45.

PK : PNa : PCl =1 :0 04 : 0 45,
. XXIII.2). , (XXIII.1.5) . :
f

,

. (XXIII.1.4)] , (

), . XXIII.2. ( . , 1968). , -

i o(

.

fK
g

, fCl , fNa Cl , Na | Cl; , Na+ C f|
g

| K+ , Cl; , Na+ K , K+ , | g

Ii = i (f ; fi )
g g

i|

, fi | , f|

, +
g

, =
gK fK g

+

g

Na fNa
g

gCl fCl g

(XXIII.1.6)
g

g

| (XXIII.1.6) , (XXIII.1.6)

, , , Na+ K+ .

:

=

g

K

+

Na

+

g

Cl

. (XXIII.1.6) ,-

. (XXIII.1.4). .


x

1.

169 . , . K
+

, . Na+ K+ , .

Na+ , K

. .

-

.

( , , . Na+ . 50% , K+ Na , . . . (10 3 / ,
2 + +

, , K2 SO4 ). . 150 Na

K+ . . +

95%

, Na+ , Na+ . , 37 , , . Na , ,
+

Na+ K+ /
2

K Na

-

).
+

), K
+

/ ,

2

,

(6 6

.

1=3

1 1 2 10; . , , ,

Na+ .
12

120 ,

Na+ .

, ,

0 12 10; Na
+

6

Na+ K+ .

Na+

Na+ ,

K+ .

-


170 Na, K+ , Na
x

XXIII.

.

, , , K+ Na+ + ,K+ - acoca ( . x 1 . XXII), Na K+ , .

K, Na+ -

.

+

2.
(. , 1949). Na+ K+ . . . XXIII.3. ()
II

,

: -

()
I

(
f

,

2

E.
, (K0 | , , (E ; f)

,

E
. ).

1 ).

, .. , , ,

,

K0 106

R,

,

E

. XXIII.3 ,

, . . ,

,

.

. -


x

2.

171 , , 1= ,
Na
fK

. 1= K,
g

, , (. , 1= l ,
g

. XXIII.2). C,
fNa

g

.

f

l

. ,

. Na+ K+ ,
i|

. ,

. :

fi

Ii = i (f ; fi )
g g

I

:

,

.

(XXIII.2.1) (XXIII.2.2) . . . -

C| P , I = Ii |
, , (df=dt = 0). , , , ( . x 8 . XXIII) 0 . .

I = C df=dt + I , df=dt |
.

df=dt 6=0
, , , ,

. (. , . XXIII.2).


172 ( . XXIII.4).

XXIII.

IC
, ,

. .

, -

IC

.

. XXIII.4. , Na- KIC |

(

, INa |

(;60 ) () C. M. Armstrong, 1975):
,

()
,I |

-

IK | |

. XXIII.5. ( ( ) 1 Na+ . Na+ K+ . . , , . Na+ Na+ ), 3 5 ).

A. L. Hodgkin, 1964). ( , Na+ -

-

,

(fNa K+ - , ( . XXIII.5).

fNa

.

, Na+ -

-


x

2.

173 K+ ( . . XXIII.6). . Na+ ( . XXIII.7). Na
+

-

. XXIII.6. A. L. Hodgkin, 1964):
1

I

(
2 3

-

|

1

2

, I = INa ,

, I = INa + IK | , I = IK | 85 C

. XXIII.7. 0
I

TTX, :

,
TTX
II

|

+80
III

15

|

,

, , , (2 / )
II

|

-

15 . ,

, . . . ,

,

K+ - . Na - K+ ,
+

| -


174 Na Na+ ( Na+ ,
+

XXIII.

. . XXIII.7, ,

K+ III

, , (.

), . . .

. XXIII.2), (XXIII.2.3) ,

. ,
fK

INa =
, ,

g

Na (f

;

fNa

Na+ - K+ ) I K = K (f ;
g

):

. (XXIII.2.3). (XXIII.2.3)

:

. XXIII.8. 56
06 63

(

A. L. Hodgkin, 1964)
, |

-

. XXIII.9. ()

() -

()

-

Na+ K

+
g

Na

.

g

K

,

(f ; fi ) , :

-

g

i = Ii =(

f

; fi ):

(XXIII.2.4)


x

3.

|

175 (XXIII.2.4) , . XXIII.6. 25 / 2, S. K , +

. XXIII.8 (;56 ) . Na+ 10 Na+ , , . , Na+ Na+ , , . . , . , Na+ Na+ ,

Na+ K+ .

5{6

-

, .

, Na+ , -

. ( . XXI, x 7). . XXIII.9 4{6
x

, . .

-

3.

|
. 1. ( . , . ,
a b

. 3. .

. 2. Na .

. Na+
+

K

+

K+). -

, ( . XXIII.10), ,
b

( Na K

. XXIII.9).

. .

a

.


176 (1 ; x) . (x)

XXIII.

:x

dx=dt = a(1 ; x) ; bx: t =0 x = x1 x = x1 ; (x1 ; x0 ) exp ;t(a + b)]:
0

(XXIII.3.1)

:x=x

t = 1,
(XXIII.3.2)
t

,

t

,

=1=(a + b).

, , -

.

g

i=

x i,
g

i.

g

i|

, ..

. XXIII.10. , :
(1 ; x) |
a b

,

n
, ,
K

. K+ . K+ -

,

p
| -

,-

n4 .
=
g

x|

g

K

n

4

(XXIII.3.3) 0 (XXIII.3.1) 1: (XXIII.3.4) .

n dn=dt = an (1 ; n) ; bnn:

,

,

K+ (n = 0) K+ . . (XXIII.3.2)]

,

n-

n-

. -

n-

n(XXIII.3.5)

n(t)= n1 ; (n1 ; n0 ) exp(;t=tn)


x

3.
tn

|

177

=1=(an + bn ).

n0 =0, n1 =1, n(t)=1 ; exp(;t=tn):
, , .

K+ -

, K+ -

n,
0 7. , . , K+ -

n
.
g

n

4

, tn =1=(an + bn )

..

t

n

K

(t)= n(t)

g

K

= n4 .

, , (XXIII.3.6) ,| g

n
g g g

.
4

(n =1)

n1

n1 =( 1 = )1=
g

1|

(dn=dt)

K+

,
t

.

K+ -

(XXIII.3.4) K+-

,

n1 = an =(an + bn ):

. XXIII.9, ) ,

a

b

(. (XXIII.3.7)

=1=(a + b) (.

n1 = a=(a + b):
. XXIII.9, ): |

(XXIII.3.7), a = n1 =t. | ,

.

Na+ . Na+ -

h,
g

.

,

m.

-

m-

.

Na+ g

Na

=

g

Na

m3 h
, ( . XXIII.10) 0). ,

(XXIII.3.8) ,m -

Na

| 0

Na+ -

m-

, m| , h| . (

1, h


178

XXIII.

-

dm=dt = am (1 ; m) ; bm m
a b

dh=dt = ah (1 ; h) ; bhh
Ca2+ ).

(XXIII.3.9) ( (XXIII.3.10) (XXIII.3.11) Na+ -

|

,

m(t)= m1 ; (m1 ; m0 ) exp(;t=tm) tm =1=(am + bm ) h(t)= h1 ; (h1 ; h0 ) exp(;t=th) th =1=(ah + bh ). m1 h1 m1 = am =(am + bm ) h1 = ah=(ah + bh):
. . am , bm , ah , bh , an , bn , . XXIII.11, 12) . ,
bm am

(

m1 , n1
,
f

h1 m-

, . XXIII.11, (XXIII.3.12) . K+Na+ , : -

9F ' exp ; 3 RT
,

exp ; 4F f : RT . XXIII.11, 12 , ,

m

3

h

. . )

,

.

..

).

(.

(..

, ( Na+ . XXI.11) K+ | | ,| ,

| ,

, .

, | ( . XXI, xx 6, 7). ,


x

3.

|

179

.

Ii = m3 h
g

g

Na (f

;

fNa

)+ n

4

g

K (f

; fK )+ 2 (f ; f2 )
g

(XXIII.3.13) , ,

2

|

.

, . ,

h, m, n.
( . XXI, x 7) , , . . XXIII.11.
a
III

b

) ( )(
IV

( .. ., 1981)

I, II,

m, h, n

-

. XXIII.12. 6 3 C.

tm , t

|
h
tn

|

m1 , h1 n1 , m1 n1

h1.

-

( B. Hille, 1970).


180
x

XXIII.

4.
|

m, n
. , , , . , , .

h,

,

,

, ,

, . ,

. XXIII.13. , | ()
2

. ()
1

| -

i, o |

|

, ( , ) , . , , . ,. Na+ . , ,

,

. , . ( , . . XXIII.13). -

.

, ,

-


x

4.

181 , , | , , . . , , 95% N Na+ a+ , Na
+

, -

.

.

. XXIII.14. . (

. XXIII.14 , ).

. XXIII.14.
|95% Na+ |

I

g

I

Na

( C. M. Armstrong, 1975):
Na+ ( ), Na+ 1

()
2

,

Na, Na. | , . , ( , Na+ -

, . XXIII.14, ).

| tm (f) .

.


182 1. . 2. 3. 4. , , . , Na+ , , ,

XXIII.

,

, (. ).

,

, . . , . (XXIII.4.2)
2

Q

10

Na+ -

Q10

tm

.

Zn,

280 ,

Na+ . :

, , ,

Q = i(t)dt:
0

Z1

. XXIII.15. (

XXIII.15 W. Almers, .

/

.

. = Q=Qmax, , -

1978)

f

.

(1 ; ) | (XXIII.4.3) ,

1 ; = exp ; zF f RT , ,

,

|

(XXIII.4.3) . (XXIII.4.4)

h i;1 = 1 + exp ; zF f : RT


x

4.
f f)

183 (
g

( ,
g

z. . XXIII.16)
,

z

. ( 6 Na-

. XXIII.16 . XXIII.15) z =4, 5 . ,
2

K

z=6

g

Na

.

iK i
. )

Na

Na260 e/ 2 ( Na500 e/ g

z = 6,

Nag

e,

), K-

2

,

Ca-

1500{2200 e/ 2 ( 40 250{350 1500{2000 e/ 2 . g

.

. XXIII.16. , , ( ( B. Hille, 1992).

. .

)

,

-

z

z


184

XXIII.

m. , ,

Na+ -

. . (
f

-

m-

), ,d| ,

, ,

h|

zF d=h,
-

.

Q = h1 + exp ; zF fd i;1 Qmax RT h

(XXIII.4.5) , , f

, , ,

. . ,

.
, , ( . XXI, x 7). , ,

, , .

=h (XXIII.4.5)

. .

. ,

, {

,

-

. ,

(-

). | , ( . XXIII, x 3). , K, , { ,

16 (1 1 0 0), (1 0 1 0) ::: (1 1 1 0), (1 1 0 1) ::: (1 1 1 1),

( . . III, x 4). , 4 n- n. (1), (0) . (0 0 0 0), (1 0 0 0), (0 1 0 0) ::: .


x

4.

185

. XXIII.17.

Na.

|
.

(

B. Hille, 1978)
m3 h1

Na-

h1

m3 h1 ,

(

h, | , ,

.

. XXIII.17) 3 , , . (

m)

, -

, m0 h1 , m1 h1 , m2 h1 m0 h0 , m1 h0 , m2 h0 , m3 h ( . )

0

h-

.

R

.

|

O, a R ; R ;a R ;a O ! 2! 3!
,

,

-

(

a

! 2a !

3a).

R

,

-


186 , .. . . , K(Shaker) . Na, ,

XXIII.

,

m, . ,

,

(m1 , m2 ), -

70% , ,

.

;; ;; !! R ;; O ;; I
R,
. (+0 1

O R,
t

I.
R!O

R
t

!

O,

O
+50 .

I.
. -

) , , NH2 ,

R!O

( . XXIII.18. . . |

. XXI.14). , (

. NH3 -

-

S

5

, . XXIII.18),

(-

S6

O|

: R| , I| ( C. Miller, 1991). ,

). , { . , .

, -

( . XIV).


x

5.

187 ( . XXI.11) ( , , ,
x

S4 ,

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

. , .

-

(

)

.

5.
, , , ( . x5 . XX). . .

, , , . ,

, , .. . XXIII.19.
l el. El cos b = ed.
, +e

;e
W

. -

E : W = ;edE = ;edf=h, h.
e

f

| ,

. W =(ef=h)(d2 ; d1 )= ;ef,

e

|

= e(d2 ; d1 )=h.

( (

. XXIII.19). . XXIII.20). , :

, , (. -

U0 , . XXIII.19)


188 , , , , , ,

XXIII.

, .

. . ,

-

, (XXIII.5.1) (XXIII.5.2) , -

; (W2 ; W1 )= W ,

W1 W2 |
. ,
ef

. XXIII.20. :
|

,

(. ,

. XXIII.19) ;ef ; W .

, ,-

I, I I

|

(1 ; ), . (1 ; )

,

III

;ef ; W :
ef

k0 |
,

.

1 ; = k0 exp , , ,

+W kT

w

,

= W=k T | e1 = e=e. . , , (.

1 ; exp(;w ) = k0 exp(e1 y) , y = ef=k T |
, ,

w

e1

. XXIII.16). .

, . w =3 5 (XXIII.5.2),

,


x

5.

189 , , . , , 100 10; (.
18

( . x 8 . XXI).

, ,

. .
p6 D L

-

15 10;18 . ,

,

, ( . x 3 . XX). 15D (1D = . ,
1 3

), , -

10;

,

3, 100D.

29

(

).

0 45

. XXIII.19): , e| = 96 5 , .

| ( 96 , =0 1=(3 10
m

W = mF E =e
;1

500 = /. ;7) / , , /

W (XXIII.5.3)
op y a

3

;1 ), E |

1 6 10;19

(XXIII.5.3) ,F| 01 ,E= 67 / . -

100

RT 2 5

N1 =N2 = exp(; W=RT ),

. XXIII.21. :
-

|

(

a-

, . XXIII.21). , , ,
p6 D L

. a

-

-


190 . , . (b. , 103 . , . ), , ,

XXIII.

42

/ ,

. , ,

12 6

25 2

/

01

x

6.

, , .. 50.

.
. . . . , . , , , ( -

,

( . x 5 . XVIII). . , . . ( . XXIII.23). ) , ,

( ,

. XXIII.22). -


x

6.

f

.

191 :

v v = ap ;
bf

p
. | (XXIII.6.1) -

a

b

| .

,

. XXIII.22. :

. XXIII.23.

c1 , c2 | ,v| , v1 , v2 , v;1 , v;2 |

-

RM v

-

. XXIII.24.
I|

(
,

..

, f|

,

., 1981):
f

-

|

, h|

jvj D=h (D |
.

, )

c

1

c

2

. , (
f

c1 ,

v> 0, c2 ,
,

v< 0.

. XXIII.24).

.

,

c

1

c2 ,

,

-


192 ( . , | , . ,

XXIII.

),

,

.

-

, .. ( . XXIII.25.
1, 2

( . . II). . XXIII.25).

|

(
i0 i0 i0 R1 i0 R1 , .
1

..

,|
3

., 1981):
f

R1 |
. i0

-

,

(XXIII.7.1)

.
2

i0 R2 ,

i0 , i0 R2 .
f

R2 | i0 R2 > f , -

i0 R2

.

( ).
1

()

i0 R2 < f ,

,

, .

, , . ,

, .

2, (XXIII.6.1), , .. . XXIII.26
f

.

,

, | (.
xx

, 2, 3 . XXIII) .

.

-

x

7.
.


x

7.

193

t

m

( . x3

m

nh
, ,

10;4 ,

t

n

t

. II). , h 2 10;3 . |

,

n

h.

Na+ - -

m (m = m1 ).

m

nh h + n = G =const ( 0 85):
. XXIII.26. ( ( ..
1

m1 .

(XXIII.7.1) . XXIII.25)
, ,

,

,

, ., 1981).
i0 ,
, ,

p

1

p

2

i0 i0
, .

p1 . ,

p1
N-

2

i0 .

p1 ,
. ,

i0 ,

3

p2 ,

|

(XXIII.2.2), (XXIII.2.3), (XXIII.3.3)
g

(XXIII.3.8),
g

Cdf=dt = ; m, n h |
Na+ ,K+

Na

m3 h(f ;
,

fNa

)+ Kn4 (f ;
g

fK

)+ l (f ; fl ) + I

(XXIII.7.2)

,

(XXIII.7.1),

m

g

l (f

; fl ).
fNa

| ,

.

I h n

,

Cdf=dt = ;

g

3 Na m1

(G ; n)(f ;

)+

g

K

n4 (f ; fK )+ l (f ; fl ) + I
g

(XXIII.7.3) (XXIII.7.4)

:

n dn=dt =(n1 ; n)=t:
(n
f

( . xx 3, 5 . XXIII). (XXIII.7.3) (XXIII.7.4) -

)


194 (XXIII.7.2). | (

XXIII.

, 10{15%).

-

(XXIII.7.3) (XXIII.7.4), . . (XXIII.7.4) , dn=dt = 0

df=dt =0 dn=dt =0.
(XXIII.7.5)

n = n1 n1 |
g

df=dt = 0
g

f

(.

. XXIII.11). (XXIII.7.3):
fNa

K

n4 (f ; fK )+

3 Na m1

(G ; n)(f ;

)+ l (f ; fl ) ; I
g

=0: -

(XXIII.7.6)

N-

. XXIII.27. . .

,

df=dt =0

. | |

df=dt =0 df=dt =0

dn=dt =0
.

. XXIII.27. ..
K+ -

|

S|

( ., 1978):

n|

-

, Na+ ,

,

.
K+.

.

,

, , (f) . XXIII.27. . , ,

. -

df=dt = 0

),

( . x 2 . II). df=dt =0, , | , n (tf =tn 10;1). , , ( ), . . ( ( . XXIII.28, ).
I


x

7.

195 , ) , . ( ( . , . XXIII.28, ).
II

df=dt = 0,
, (.. , , , KCl . -

,

. XXIII.29).

df=dt = 0 df=dt = 0
. .

.

.

. XXIII.28.
I

| | ) n|

,

( K+ -

S
( (

,

) , ., 1978)

:

II

S ..

. XXIII.29. ( | / 2, . XXIII.28) ( .. , ., 1978)

-


196 , , , (. ,

XXIII.

). |

| , . , : . XXIII.31). . . XXIII.30. ..
. XXIII.28 ,
fK

. XXIII.30). CsF, ,

(XXIII.7.6) ,

df=dt = 0

.

, ,

(

|

( ,

. XXIII.31,

I

II

| |

K+ ( ., 1978):

-

. XXIII.31. (
I

|

..
):
II

, |

| ., 1978):
(-

: . , .

.

-


x

8.
x

197

8.
. , , , -

, | .

( .

) .

(

. XXIII.32). ,

, ..

. , . XXIII.32, ).
II

.

,

( , ,

).

(

. XXIII.32.
I

|

,

( A. L. Hodgkin, 1964):
II

|

, . , ,

, , ( ) . , ,(

. ,

-


198 , ). ,

XXIII.

,

. XXIII.33. . ,

,

, , : (XXIII.8.1)

f0

|r ( ,

). .

ri ( / ),
. ,

il

x

il = ; r1 df : i dx dx,
.

-

i
(XXIII.8.2)

2 i = ; dil = r1 d f : dx i dx2

. XXIII.33. ()
I

,
,C | , il | ,i | ,R |

l

|

x =0 ( ):
II

x

, Ri |

,

x
l2

i = f=r ,
r d2 f = ri dx2
f

f0

.

f

|

-

(XXIII.8.3)

l2

d2 f = f, dx2

= r =ri .


x

8.

199 (XXIII.8.3)
f

=

f0

exp(;x=l): , 1
2

(XXIII.8.4)

Ri

x = l. r ri

l

= r =ri : r = RD p , . . 30

p

R
p

1

3

.

f0

=e
-

i ri = 4R2

D| . (DR =4Ri )1=2 , . .
1 , 27 .

D

(XXIII.8.5)
2

R =5 R
| ,
2

R =10

,

Ri =50
,

3

.

-

, . ,
f

: (XXIII.8.6) , , ri | .

. . (XXIII. 2.2)]:

i

. (XXIII.8.2)]

,

(x t)

C|
( . x 2 . XXIII). , | , . .

1 @2f = I + C @f ri @x2 @t
,
f

,I| : | . (XXIII.8.6) ,

I

-

( , | , , (XXIII.8.6), ,

. XXIII.34).

,


200

XXIII.

i2 .

i1 .
, . ,

,

t

1

,

-

t2 (
,

: i1 t1 = i1 t2 . (XXIII.8.6) , )

. XXIII.34, ). , , , ,
II

,

(

x

. (XXIII.8.6) = x ; vt, v|

Na+ - K+-

. XXIII.34. Na+ ..
1 3

,

| |

, ., 1981):

(

.| ,
I
2

II

,

,

| K+ t1 t2 |
|

)(
-

18 5 C

| , i1 i2 |

.
f(x

)

.
x

,

,

() ( . x 4 . II). (XXIII.8.6)

x xf

x
(XXIII.8.7)

@ 2 f + vr C @ f ; r i(x)=0 i @x i @ x2

..

,

.

, . . f(0) = f ,

f

|


x

8.

201 . t2 =0 55
I

t1 =0 35
( ,

i1 = 63
, , : , |

/

2 , i2

=40

/

2

, -

. XXIII.34, ). ,

. ,

(XXIII.8.8) , .. . -

v1 =

f

i1 1=2 : ri C 2

. XXIII.35.

v
1, 2

.|
I II

,
3

|

:

|
|

, 21 / . . .

. , , , , , -

( , , , , , , . , . , . ,

. XXIII.35)

, (XXIII.8.9)

r2 3=2 > k +1 11k1=2 ; 1 69 = K (k) r1


202

XXIII.

r

1

r2 |
. , , .

, k|

. .

, ,

-

.

. .

.

,

,

. , , , , . XXIII.36.
I

,

, -

,

. .

|
II

.
|

-

(

. XXIII.36),
3 3 r2=2 + r3=2 >K (k): 3 r1=2

(XXIII.8.10) ,

3 r3=2 3 3 >K (k): r1=2 + r2=2

(XXIII.8.11) . , , , . , , .

, ,

. , , . ,

. ,

,


x

8.

203 , . ( , : , | . , . . 10%, ) ), , . . . , (XXIII.8.6), .
t t

.

-

:

( . . , -

I
,

. ,

m, n h

,

m

t

n

t

h

n , th , tm |

Na+ , (XXIII.8.12) (XXIII.8.6) | : dy = 1 d2 y + m3 ;1 < x < 1 dx u2 dx2 dm = ; 1 m ; m (y)] 1 dx t(y) Na+ t(y)

(XXIII.8.12) : K+, . m, (XXIII.8.13) . :u= (XXIII.8.14) . ,

= v(RC

2f

=i)1=2 , y = f=f . u =1
. . v=

m

x = t + x=v m1 (y) |

i RC 2

1=2
f

t

!

0.

(XXIII.8.8) ,


204 | |

XXIII.

Na+ t3

. (XXIII.8.15) -

v ' 1 25
(XXIII.8.15) Na+ -

C 5 f R4 ,

i

1=8

:

.