Resting Potential - Laboratorium Biofizyki Agregatów...
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Membrane transport
Transcript of Resting Potential - Laboratorium Biofizyki Agregatów...
Membrane transport
Resting Potential
Requirements for cell stability
Cell must be in osmotic balance [particles]i = [particles]e
No net movement of ions.
Intra- & extra-cellular solutions must each be electrically neutral.
The electro-diffusion model assumptions: § A homogeneous membrane slab
§ A constant electric fiels
§ Ions moving independently of ane another
§ A constant permeability coefficient
Iintracellular and extracellular ionic
composition
Na+ 143 mM > 10 mM Na+
K+ 4 mM < 140 mM K+
Cl- 118 mM > 10 mM Cl-
A- 10 mequiv.l-1 < 132 mequiv.l-1 A-
Ca2+ 1.5 mM > 0.1 µM Ca2+
Mg2+ 1.0 mM 1.0 mM Mg2+
HCO3- 24 mM > 10 mM HCO3
-
pH 7.4 > pH 7.0
Extracellular Intracellular
A- are impermeable anions
mout
inoutin zF
ionionRT ΔΨ+=Δ][][ln/µ
ΔµNa ≈ - 13 kJ/mol it requires a lot of energy to pump Na+ out ΔµK ≈ + 1.5 kJ/mol it requires a little of energy to pump K+ in ΔµCl ≈ - 0.5 kJ/mol Cl- is almost at equilibrium
Measuring Membrane Potential Differences
Resting Membrane Potential
of most cells is between -50 and -90 mV (average ~ -70 mV)
Donnan potentials & Donnan Equilibrium:in out ΔΨ
A+out A+
in
B-out B-
in
ratioDonnanRTF
BB
AA
BB
FRT
AA
FRTzz
BB
FzRT
AA
FzRT
out
in
in
out
in
out
in
out
BA
in
out
Bin
out
Ainout
−⎟⎠
⎞⎜⎝
⎛ ΔΨ−==
=−=ΔΨ
=−=
−=−=ΔΨ
−
−
+
+
−
−
+
+
−
−
+
+
exp][][
][][
][][ln
][][ln
1][][ln
][][ln/
in out ΔΨ
A+out A+
in
B-out B-
in
Rn-in
cBAoutRnBAin
outout
ininin
==
+=−+
−−+
][][:][][][:
Electro neutrality:
⎟⎠
⎞⎜⎝
⎛ ΔΨ=
⎟⎠
⎞⎜⎝
⎛ ΔΨ−=
−
+
RTF
Bc
RTF
Ac
in
in
exp][
exp][
out/in
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+=ΔΨ+⎟⎟
⎠
⎞⎜⎜⎝
⎛+=⎟
⎠
⎞⎜⎝
⎛ ΔΨ
=−⎟⎠
⎞⎜⎝
⎛ ΔΨ−⎥
⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ΔΨ
=−⎟⎠
⎞⎜⎝
⎛ ΔΨ−⎟⎠
⎞⎜⎝
⎛ ΔΨ−
−−−−
−
−
12][
2][ln1
2][
2][exp
01][exp
0][expexp
22
2
cRn
cRnRTand
cRn
cRn
RTF
RTF
cRn
RTF
RnRTFc
RTFc
Donnan potentials & Donnan Equilibrium:
Equilibrium potentials If a membrane is permeable to a single ionic species the measured membrane potential can be calculated from the Nernst equation.
Cell Membrane extracell intracell K+ = 4mM K+ = 140mM Na+ = 144mM Na+ = 10mM
Membrane is permeable to K+:
mVVK 951404log5.61 10 −== mVVNa 71
10144log5.61 10 +==
Membrane is permeable to Na+:
mVClCl
FRTV
o
iCl 4.45
][][ln −==
−
−
mVCaCa
FRTV
i
oCa 0.40
][][ln 2
2
+==+
+
A cell permeable to K+ only
A cell permeable to Na+ only
][][lni
oK K
KzRTE ⎟
⎠
⎞⎜⎝
⎛=
ENa =RTz
!
"#
$
%&ln[Nao ][Nai ]
Steady state resting membrane potential
The membrane potential exists because • Na+/K+ Pump is active
• Na+ channels is closed
• K+ leaks
q The relationship between the extracellular [K] and membrane potential, Em, is very non-linear.
-140 -120 -100
-80 -60 -40 -20
0
0 50 100 150
E m [mV]
Extracellular K+ [mM]
Intracellular [K] assumed to be 140 mM
-140 -120 -100
-80 -60 -40 -20
0
0 5 10 15 20
E m [mV]
Extracellular K+ [mM]
Normal range
q Small changes of [K] around the normal level have large effects on Em.
][][lni
oK K
KzRTE ⎟
⎠
⎞⎜⎝
⎛=
][][lni
oNa Na
NazRTE ⎟
⎠
⎞⎜⎝
⎛=The potential limits
Equilibrium potentials
Theory Ø The K+ equilibrium potential EK, is about - 95 mV; Ø The Na+ equilibrium potential ENa, is about + 71 mV.
Experiment The measured membrane potential
is between -80 and -90 mV, i.e. close to the K+ equilibrium
potential.
Deduction Ø Because the resting membrane potential is close to EK implies that the membrane is permeable to K+
Ø Because the resting membrane potential is not close to ENa implies that the membrane is impermeable to Na+
A multi-ion steady-state The Goldman-Hodgkin-Katz equation
Assumptions:
(1) The membrane is semi-permeable (2) A constant electrical field across the membrane.
The total current flux across the membrane (Jm = ∑Jn) must equal zero to keep ψm constant.
If ions are in equilibrium across a membrane, then the membrane potential will be given by the Nernst equation. Ions are in constant flux (transport and permeation) and the
capacitative charge is determined by the steady-state distribution of ions.
∑∑ +==anions
jjcations
jjtotal FJzFJzJ 0
K+out K+
in
Cl-out Cl-in
Na+out Na+
in
Goldman – Hodgkin – Katz voltage Equation :
JNa + JK − JCl = 0
PK[Kin+ ]exp FΔΨ
RT$
%&
'
()−PK[Kout
+ ]
1− exp FΔΨRT
$
%&
'
()
+PNa[Nain
+ ]exp FΔΨRT
$
%&
'
()−PNa[Naout
+ ]
1− exp FΔΨRT
$
%&
'
()
+PCl[Clin
− ]exp −FΔΨRT
$
%&
'
()−PCl[Clout
− ]
1− exp −FΔΨRT
$
%&
'
()
= 0
ΔΨ =RTFln PK[Kout
+ ]+PNa[Naout+ ]+PCl[Clin
− ]PK[Kin
+ ]+PNa[Nain+ ]+PCl[Clout
− ]
PK : PNa : PCl = 1 : 0.04 : 0.45
At rest gNa << gk – the membrane potential is close to the potassium equilibrium potential
At rest gNa > 0 – the membrane potential is "pulled" slightly away from VK.
Vm depends on the ratio of sodium to potassium
conductance, gNa/gk Vm = – 68 mV
Resting potential strongly depends upon the external K+ concentration
Resting potential is independent of external Na+ concentration
Changes in Resting Membrane Potential
One strategy for the treatment of stroke and epilepsy is to increase the efficiency of these glial cells as K+ buffers, limiting
neuronal damage.
Neurones become depolarised and die if they are exposed for too long to high
concentrations of extracellular K+.
Astrocytes and other neuroglia have very high resting K+ permeabilities – in fact their resting potentials are very close to the Nernst potential for K+.
They are effective K+ buffers.
Increases in extracellular K+, caused by leakage from nearby neurones, are ‘mopped up’ by astrocytes.
Regulation of Ions Balance: Aldosterone
