membrane potentials: where do they come from?
DESCRIPTION
Na +. ATP. K +. V. Membrane Potentials: Where Do They Come From?. Concentration Gradients = Potential Energy. Gibbs Free Energy. out. in. [Na] i ~15 mM. [Na] o ~150 mM. [K] i ~150 mM. [K] o ~15 mM. Chemical potential difference. –. +. K + ‘ Leak ’ Channel. E m ~ -60mV. - PowerPoint PPT PresentationTRANSCRIPT
Membrane Potentials: Where Do They Come From?
K+
Na+
ATP
[Na]o~150 mM
out
in
[K]o ~15 mM
[Na]i ~15 mM
[K]i ~150 mM
Gibbs Free Energy
Concentration Gradients = Potential Energy
Chemical potential difference
= Influx
= Efflux
= Equilibrium
Separation of Charge = Electrical Potential
K+ ‘Leak’ Channel+–
z = charge
V
for an ion:
@ Equilibrium:
NernstPotential
F = constant
@ 23°z=+1
Em~ -60mV
Resting Membrane Potential: Steady State
K+
Na+
ATP
[Na+]o~150 mM
out
in
[K+]o ~15 mM
[Na+]i ~15 mM
[K+]i ~150 mM
= Influx
= Efflux
= Equilibrium
V
Nernst Potential:
[Cl-]o ~150 mM[Cl-]i ~15 mM
PNa
PK
PCl
Em~ -55mV
ENa = ~ +60 mV
EK = ~ -60 mV
ECl = ~ -60 mV
Relative Permeabilities @ Rest (varies) PK : PNa : PCl = ~ 1 : 0.01 : 0.001
Net Fluxes => Steady State @ rest
Goldman-Hodgkin-Katz Potential:
Electromotive Force EMF = Em - Eequil
EMF < 0
EMF > 0
EMF = 0
for cations:
EMFNa = Na/glucose co-transport?
=> ~ 100x glucose gradient!(Em – ENa) = -55mV – 60 mV = -115 mV
Em
Distance from stimulus
‘space constant’ ~1-10 µm
Na+
Na+
K+ K+K+K+
Emrest
~ -55mV
Stimulus = Open Na Channel (typically)
= ⇑ PNa EMFNa <<0
Emrest
Emstim
K+ K+K+K+
Electrotonic Conduction
Fast IonicCurrent
out
in
Fast Spread of Depolarization!
= “electrotonic conduction”
“Depolarize”= Signal
Decay ofDepolarization= Short RangeConduction
K+ efflux = negative feedback
EMFK > 0
V
Graded Potentials = Graded ResponseNa+
K+ K+K+K+ Ca+2Voltage Gated Calcium Channel
Erest
100%
0%
openchannels
E50
large stimulus
small stimulusEm
rest
Depolarization w/o Action Potential
- Small Cells
• Smooth Muscle Cells
• Tonic Muscle Fibers
• Sensory & Brain Cells (Ca+2 => signaling)
• Endocrine Cells (Ca+2 => secretion)
Em dependson stimulus!
= “graded potential”
Retinal Amacrine cells
out
in
Em
?
depolarization
V
Na+
K+K+
Ca+2
Action Potentials = Long Distance Conduction
V
Ca+2
V
Ca+2
V
Ca+2
V
Ca+2
V
Ca+2
Em
out
in
Initial Depolarization
Open Voltage Gated Channels
Electrotonic Conduction
Po
siti
ve F
eed
bac
k!
Electrotonic Conduction
Na+ Ca+2Ca+2 Ca+2Ca+2Ca+2 Ca+2
Distance from stimulus
• Not Graded! “All-or-Nothing” Em
Depolarization
• No Distance Limit!
Erest
Estim
• Depends on High Density VG Channels
E50
V
Na+
K+K+
Ca+2
V
Ca+2
V
Ca+2
V
Ca+2
V
Ca+2
V
Ca+2
out
in
Na+ Ca+2Ca+2 Ca+2Ca+2Ca+2 Ca+2
Action Potentials = Pos + Neg Feedback
V
Em
time
+ feedback Neg feedback:
- Ca-dependent VGCC Inactivation- Ca-dependent K-Channels- Voltage Gated K-Channels
“Ca+2 Action Potential”
Low [Ca+2]i @rest -> Hi [Ca+2]i @stim => Must Pump Out!
- Embryonic & Smooth Muscle- Cardiac Muscle (sort of)- Crustacean Muscle- Plants, Paramecia
Slow!
K+
V
K+
V
Ventricle
Cardiac Action Potentials = Ca+2 & Na+ Currents
Fast AP Component!Voltage Gated Sodium Channels
VG Sodium Channel:FastInactivation
Slow AP Component: VGCC
PCa
PNa
SA node
AV node
Purkinje
Ca+2 AP
Na+ Na+ Na+Na+Na+Na+K+K+
Na+
V
Na+
K+K+
V VVV Vout
in
V
V
Na+ Na+ Na+Na+Na+Na+
V
Em
time
PNaPK
Erest
Ethreshold
Refractory period:
Na+ Action Potentials: Skeletal Muscle & Neurons
Neg feedback:
- Voltage Gated K-Channels
- VGNaC Inactivation
- VGNaC Re-activate
- VGKC Close
Na+K+ K+K+K+
Emrest
out
in
How Many Na+ Ions Does it Take to Depolarize?
Emstim
Q = Em Cm
# of charges(Coulombs)
Capacitance (Farads)
Q = (0.100 V) (10-6 F cm-2)
-55mV
+40mV
= 10-7 C cm-2
(96,500 C/mol)
= ~ 10-12 mol Na+ cm-210 µm cell? [Na+]i
Does Depolarization Run Down the Gradients?
K+
Na+
ATP
= ~ 10-8 mM
[Na+]i << [Na+]i (~ 10 mM)
Na+ ? Very Slowly!
Action Potentials: Long Distance Depolarizations
Axon = AP(VGSC)
Soma = Electrotonic
Axon Terminals = Electrotonic
(→ VGCC)
‘Typical’’ Motor Neuron (AP):
Inverts: 1-4 m/secVerts: 10-100 m/sec
Limit to Velocity of Conduction?
Motor Neuron: Sensory Neuron:
Dendrite/Axon= AP (VGSC)
motor neurons
sensory neurons
interneuronsinterneurons
Dendrites,
Na+ Na+ Na+
VV Vout
in
Na+ Na+ Na+
Na+ Action Potentials: Velocity of Conduction?
Electrotonic Conduction FAST⇒
ChannelPermeation
⇒ SLOW
Velocity VGNaC spacing∝
Na+
V V
K+
Em
?
gi = 1/Ri ∝ r2
Internal Na+
Conductance (gi)gm = 1/Rm
∝ 2r
Membrane K+
Conductance (gm)
VGNaC spacing ∝
?Ethreshold
Na+ Action Potentials: Fast Enough?
Typical Axon ~10µm ⇒ < 5 m/sec
Giant Axon ~500µm ⇒ 10-50 m/sec
Invertebrates:
Vertebrates: 10-100 m/sec
Myelin (Schwann Cells)
Na+
1 -2 mm internodal
⇓ gm
⇑ r
~10 µmV VV
Na+
AP Initiation: Cardiac Pacemaker
V VV
Em
Na+
Ca+2 Ca+2
K+ K+ SA Node
Neural Modulation:
• Sympathetic (accelerans)⇒Norepinephrine-adrenergic receptor G-protein, etc⇒ SR Ca-ATPase⇒⇑
• Parasympathetic (vagus)⇒Acetylcholinemuscarinic Ach receptor G-protein, etc⇒ open ⇒ K+ channel
+–
Na+ ‘Leak’ Channel(“Funny” Channel)
⇒slow depolarization
Ca+2 AP
Otto Loewi 1921 (Nobel 1936)
VGCC InactivationVGKC Opening
Ethreshold
Purkinje fibers:Na/Ca AP conduction