@

Cub

1)(ItM--

~ ~~-

~ ~\~)

V}1A0

Q)I/~

HQ.1 3

~~v~

c~

~

CXaJ

[xi]~ lo~IO~

--

s~ (V~-Vx) 4 C Jv~~I+ -

-

c

. . .-

~ 't':: K CAM. .'.

)( \10\ t~

@\

lOM

lOe

--

J~tQ/\MA~Me ,,~\o.kv~0

-to 1\ ow t~~

[yJ

+~

@ what ~(o~o:t ~

~ o~ MAO+: Co

:be M. M a \A Q.. q, l

k:C\-0

Q) o.j ~@) cb~(Z..~ UJn.tOA

A- t() ~ lMc;.~ck

~~'(loC1J ~

GJ1<: Mot ~{~c.~ Ae\~ch\le J ~

[ x.:J [ Yc:]+

+

coo/J do~M.t~', I, -h'M lOot

[v.]-..

[xi]Vttev

-... .

~c. ~J?Q..<.\u ~ I: ~I\ ~ U,M..\ }

..

[~[cQ:: [~J[clJ( /2XQ.vf'14/ w. \eJ" v M? ::f\: b )

?Co~C~~ON~ ~

. .(OM, Co

Ae~OM ~t<M~J

\Jo\r~ C\O&L~f i \"'UJ\l\lM-\ C\~f ~

QcJ Il Co~ Q.A.\.k) eo.1-e. ~ l)~Ml.

&~fC 1 0 0( =. 0<'0 e.- (1-

r ~ = (10 e

(0

C1J

~

~~ -Po) - p0< (tc;It

700d~-~

01\

'l:

~ ~ ~~ c k ~ \40)

cll\M

~~--

'l'AM

Q)~ ~ tkoA,

Cu 1\ 1\ c..u1 cl Q..v.J.f ?.

0<0 e. $~f~17 - (I-J):! Pi I.1:>0 e /~T

~-=.

~=~ :

?o

{/\GCkoM 01 If ~lJ ~!

9«>? cub0( .4-

NL 0<'+ (l

--

.~

h:cl\M- ,--I

k.+- C~.Me.\

dMCif

Mcc-MTM

--

I~1tJ-Ao

1

-thJ-..

~,v~

, Ie.. IkJa.0 4-

\t \\ so\ved ~ $2..t-uo..ko

1\1\M~ Covt\tt. 4 iL«. ~,

Doo-UJ ~---

GJ

h (VIM - VAlo.)~.. "'1d~' NIl .-

-

a..

v~)It-.l VI5: M-- J.M'L

~CM ((bt~J I","cL \

"'"~-~ 11(:.

=0()AA

=0A

obtCA~~J.ua.k~( ~ 1tt.

(pOt~ ~ .~

U'°-\-~j ~

f.11\M f.1 ?~p\ ~ h,~ l\e\Jiv c. Vt.) v~:~

v ~\o~~ Q~

g

G M\'f J ..v

e NoM- M-\'fe\

CJ\o~~

(i)

CcAAttJt1N.t

AfodL-- ""

a. = ~"t(OM ~etA -\LQ.

.2.~ ~.

bekee.u. M\yel~!tIoM ~ ~ [MAo.kJ ?

cttt~~

Q.

~ 0..1

~ a ~ 1 flAM.

....

,)~MO.pk c. fJ\CLu.5. MAa \:0 M

uW ~ voo \eO\M ~ ~ t\0Jen~~of. ~ qos.t- ~'fMa~c. I\~:CM ~

1+000 would 'feu do iL. .0<{JQA; AMeu1-:+k Meu 1\0 MAU So C u \0'\ t;. '1 MOpf\R. ~ 'feu 1\

-

-

~ s ~ ~f.. ~ .Qx peA 'q\\A ~ cf

6'\MO~'\oQ ~~t,,'\ 6u~OMLolM fo~~ ~

J. a.. CAI\ k \M 0 u tCOt\M e~cat

h"-t --

tb

(L)bCQ}l

(£)

.kD)(Q.LUf

.at~ ~k

:: h. ~ . h. t .-c .1:. t = hM t. M I

A"\

M+M':=.k1

~'.MOM\ ~ J..Co e.{.ftc ~eJ-(~)

rn (L.. tJ

.

i. M ~at~ ' 1\

~ 1\ Iw\ o.U.

~ 0.. S-.MA.

P 011 " ~M¥ ~ c.

('\0'Pf-ik. 0.. V IlM?J. M J l. 4. a.. NA to42.

AJh :: M :: .2.~~,r...

(?(M \ --

-[ o.."J lJ "e.t -").

G)

l ~k~d ,feA d&

(;Me) 'hue , tM.t~ ~ f<,Ult-..(.M

"'1

~

ks. ~tA.

M

~

0.. pi 0-1- I.?

~Clk.e.- -

M/lu $c\e e~~ h ~ ~

io~ 0.. " ~ cb tv..A. C La "- M

\ ~t \... c1. '" Ut. ~ UJ~ Leo

C.tV kJ k p p~ ~ dtc. clo.. ~ M ~ QI\ Ao\M e

~~I\:cHCM.{ ~ it~ I\MOVR..wJ!

",.,

~~

.,

~

AJLc..

~OVJ<..\MJ I .~

~

Do M-AAO. M. ~ ~~\~ :

~ Meu I\~AA.,

....

kh~

-tk. c.e.\\ 1\M~/'DM.l AA 6>RAMAeJ.~ r!c

but Mcd 40 kJ~+ ~ A-

4\ Is ~

I:> ) T- "" UJ U J ~ I\e J> 0 -'" c.u l /I ea.ckA) h J: QI\1.. ~ ~ M ol CX7v\ CJlM 1\ cJ\ 0 M- ~ .

LVWc) ~~~ ~~O\~

at\..l

J ) wa:\:~ ~[ow ?

1'>0

100

L.SO

0110

k'" ~ cl-

- -

~

\

lOM. AMOV.c.}

~oLh~~~it. ft MJ1ft. va.lv~

~~

C~-'I()(C\o -)() ::: (ch ~)()(l!i. +)()

ko (10 - Ico ~ - C!o1. ~:: C\J~.~ 4- ct, J( 4-1(;,( ~

koc\o - t.l ~ +do) -::. c\;. b -1-)( (c\~ -I- "=l)

~

K

.

~ eM. S : J.c... 6 ... -r'"

~+ 1..00 100

AJ~-+ 10 'bO -C\- 160 "LOO

JA" \\0 I 0

. .

v

~C\ ,eM...

CI, t- xclo - x

)( --+-1..

~ do - C\, tc.~ - ':I. Q)o--

'°0sr,-'oo--

-

~-4-~~ ~Oo ~C\(

S6x

5~ IO~'6 ~ ~ , '}s I\A,\ vi--

Quick review

1. The flow of ions through an ion channel depends on thedriving force for that ion and on the conductance of the channel.

The driving force for a specific ion is detmnined by the differencebetween the voltage and the equilibrium potential for that ion. Theequilibrium potential is detmnined by the internal and externalconcentrations of that ion.

At room temperature:

2. Ion channels have an inherent conductance that is measuredin Siemens (S), which are the reciprocal of Ohms (Q). Typicalsingle channel conductances (1) are around lOpS. The currentthrough K+ channels, for example, may be detennined by:

3. The cellmem

R C

Current applied to the membrane chargesfllSt.

~

EA = 58 mVloglO{[A]J[A]iJ

IK = 8K(V-VK)

brane acts both as a resistor and as a capacitor.

~ I :J I

v I

the capacitive element

CHANNELS AND THE PASSIVE DISTRIBUTION OF IONS

Consider a cell that contains an impenneant ion S- and ispenneable to K+ and cr.

Since we know that it takes only a very smallltage we know that the concentrations of positive

and negative ions inside and outside the cell must be equal to

If the cell membrane is freely permeable to K+ and cr, both willdistribute themselves such that they will be at equilibrium.

Therefore

And using the Nemst equation:

Which is equivalent to

This is called the Donnan Ratio.

Combining this with the requirements for charge neutrality

to cause aimbalance

VK=VM=VCI

VM = (58 mV/+l)loglO{[K1J[K1i}= (58 m V 1-1 )loglO {[CllJ[Cll i}

[K1J[Kli = [crJ/[cllo

.gIves:

D'JJP'Ji = ([KJi-(SlYP'Jo

Multiplying:

Rearranging:

Therefore..

This makes intuitive sense because the impenneant anions insidethe cell attract K+ and repel cr ions. Even in the absence of ionpumps, therefore, K+ and cr gradients are present and give the cella negative potential. Both ion pumps and passive distribution ofions contribute to the resting membrane potential of cells.

A calculation

A cell has the following ion concentrations inside (mM):K+ 150, Na+ 10, cr 50, and S- 110;and the following outside:K+ 150, Na+ 100, cr 250, and S. O.

suddenly made penneable to K+ and cr, butwhat are the final concentrations of each of the ions

potential of the cell?

According to the Donnan role of equilibrium:

£KiJ[KJi = [Cll/[Cr]o

[Kio 2 = [Ki? - [Kii[Sl

[Kii2 = [Ki02 + £Kii[Sl

£KJi > £KJo and [Cllo> [Clli

Since the movements ofK+ and cr will have to be equal tomaintain charge neutrality, the flow of X mM will result in

(150 + X)/(l50 - X) = (250 - X)/(50 + X)

Therefore X = 50 mM and the final concentrations are:

inside K+ 200, Na + 10, cr 100, and S. 110;

and outside:K+ 100, Na + 100, cr 200, and S- O.

(A I HYI'BPOLARJZA TlON

~65 "'¥

--, - UOmVEM

m D£I'OlAIUZATION

EM

6 VOLTAGE-CLAMP CUIlRENTS IN SQUID AXON

An axon IS tHllht.-d in sea wOller and voIta~.damped by d1r II!rii&J wiremrthnd (Figure 5). The memtwalW' pok"nlill is held OIl . fIi lilY andtMn hyperpularized in a srep 10 -130 mY or d4!poIarized in a si4!p 10 0mY. Outward Ionic CUrft'nt is Mown "" an upward d~. 1114!

membrane pl'nneabilily mt'Chani8nt11 are ck..rly asymmd1t..-1. Hyp.r-pdariutiun produces only I sman inward currrnt. whilr JepoIeriza-tion elicits.. JarKCr and bipha'lic C'UlTI!nt. T - 3.8"<: (Ad:lpWd fromHodgkin rt OIl.. 19521

J .9..V L.IIIV1..

I,.,

~_..~ .. - v'--. =-", ".e."!"': :-

J

r..

..:-

I "I.!,

"1a- ..L . - r- . ---r--'"~...

TIme (ms)

r ~~11&ft1o-

'-", " -.

,

1111 £QU1VALl!Nt claron Of AXON MliMnAN"I""""'" m.J I~\, d<-Ornbo-d ~ ~ .., .to ..w.-w 1.",<UIt wid. lour ".t~ ~ T1w ("~f"'CI"Ii"'" bnmd> .." ", thin dwloo."!Jit ~... IIw.- ~'}IW" n... ,""'" nJndUdIW~ ...~ JWxfb>",. I"~""'J""" ""d ,...k o.",d~ rihIMjtd~ ~-m"-. The< ~ WIth .""".. ""'>Uj\h~ "" tinM'1IJOd "~'inlt c<>nd~ ukifll! In.,,,, thtl'f"!'Ii.. an4 ~ ,of lOA" ""'nh<'k. If-rorn I"~'n """, H..d<-y.1'6h11

'M No CXII\'tIVCTANCIi 4.. It tlNfUTANL'11

a. 1

ke -tI~v

1

~lj'~ r-'-;a;':'.1T___011_,......

U CONDtICTANn OtAN<iES AT MANY VOlTAGESTI.- uI (AI .nd ~ (II) doomtI ~"II -.. 10 .hI'iNIaIIod ...I~ (ltdn .~ dw - --- in .01 """" .. . :I"C. h .- - 1M aMldl8ttll'ft ~

'""" .hI' I"""""""'" 1. ,"'- HodaJdn. I"'"ad8""" '""" IInd .1Id II ,.. 1952d I

~--"-

11 10HtC L"ONOUCTI\NCf. CHANGI'fi IN JQUIDTI mu of ",odium ..n.1 ",--" ~ ,~~~'tlepl" ..""V (-.ond,lCUnMI"*,,,-bon' 2-2.mot 2-~ from fh<. ..."",aIOd cumont tnK1'O InIin oIoow ~ .h., dec-_'.pidIv "'-"""""""""1IS n.~'<1 "" mV ,,'0.6:1 -, w""":f>... k hWo.

- ,} ~ tho. """""'..,.. to """tIomrd .",-,. ]a ~ T 8. ore. Ifrum HDdM',n. 1'l'1li. ~~nd U...Iey. 1'ISU.b.d)

,., ANAL \'SIS(I\) No nlk11l:Nf

-OIl\""---.. ,"""

,~:;E1...

.;I.

~)

t

IAI 11IVO.PUlM~.

_I -,~ s-1.rl"'

[i ,.. .. .

~,~

181 lI!COyuy CW1/E

ii .,~ ~.liJ \ /l[" -

6.3"<:Squid axon

Membrane pot~ntial (mV)

MODELOFHH17 VOLTAGE-DEPENDENT PARAMETERSTime ronstants T.." T", and T.. and steady-state values m~. hn and "...cakulated from the empirical equatitms of the Hodgkin-Huxley modelfor squid giant axon membrane at 6.3°c. Depolarizations increase m...and n.,. and decrease h~. The time ronstants of relaxation are maximalnear the resting potential and become shorter on either side. (FromHille. 1970.)