Membrane Potentials: Where Do They Come From?

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Membrane Potentials Where Do They Come From?
Concentration Gradients Potential Energy
Gibbs Free Energy
out
in
Nao150 mM
Nai 15 mM
Ko 15 mM
Ki 150 mM
Chemical potential difference


K Leak Channel
Em -60mV
Separation of Charge Electrical Potential
z charge
Influx
F constant
Efflux
Equilibrium
NernstPotential
for an ion
_at_ Equilibrium
_at_ 23z1
2
Resting Membrane Potential Steady State
out
in
Nernst Potential
PNa
ENa 60 mV
Nao150 mM
Nai 15 mM
PK
EK -60 mV
Ko 15 mM
Ki 150 mM
PCl
ECl -60 mV
Cl-o 150 mM
Cl-i 15 mM
V
Em -55mV
Relative Permeabilities _at_ Rest (varies) PK PNa
PCl 1 0.01 0.001
Electromotive Force EMF Em - Eequil
Net Fluxes gt Steady State _at_ rest
Goldman-Hodgkin-Katz Potential
for cations
Influx
EMF lt 0
Efflux
EMF gt 0
EMF 0
Equilibrium
Na/glucose co-transport? gt 100x glucose
gradient!
EMFNa
(Em ENa) -55mV 60 mV -115 mV
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Stimulus Open Na Channel (typically) ?
PNa EMFNa ltlt0
Electrotonic Conduction
Na
K
K
K
K
K efflux negative feedback
out
Emrest
in
EMFK gt 0
-55mV
Fast Ionic Current
K
Na
K
K
K
Fast Spread of Depolarization! electrotonic
conduction
Emstim
Decay ofDepolarization Short Range Conduction
Depolarize Signal
Em
space constant ???? 1-10 µm
Emrest
Distance from stimulus
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Graded Potentials Graded Response
Na
Ca2
K
K
K
K
Voltage Gated Calcium Channel
out
V
in
?
?Em dependson stimulus! graded potential
Erest
depolarization
large stimulus
E50
Em
Emrest
small stimulus
Smooth Muscle Cells
Depolarization w/o Action Potential - Small
Cells
Tonic Muscle Fibers
 Endocrine Cells (Ca2 gt secretion)
 Sensory Brain Cells (Ca2 gt signaling)
Retinal Amacrine cells
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Action Potentials Long Distance Conduction
Initial Depolarization
Depends on High Density VG Channels
Na
Ca2
Ca2
Ca2
Ca2
Ca2
Ca2
Electrotonic Conduction
out
V
V
V
V
V
V
in
K
K
Open Voltage Gated Channels
Na
Ca2
Ca2
Ca2
Ca2
Ca2
Ca2
Estim
Depolarization
Positive Feedback!
Electrotonic Conduction
Em
E50
Not Graded! All-or-Nothing ?Em
Erest
Distance from stimulus
No Distance Limit!
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Action Potentials Pos Neg Feedback
Na
V
Ca2
Ca2
Ca2
Ca2
Ca2
Ca2
out
V
V
V
V
V
V
in
K
K
Na
Ca2
Ca2
Ca2
Ca2
Ca2
Ca2
Neg feedback
feedback
- Ca-dependent VGCC Inactivation
- Ca-dependent K-Channels
- Voltage Gated K-Channels
Em
Ca2 Action Potential
- Embryonic Smooth Muscle - Cardiac Muscle
(sort of)
time
- Crustacean Muscle
- Plants, Paramecia
Slow!
Low Ca2i _at_rest -gt Hi Ca2i _at_stim
gt Must Pump Out!
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Cardiac Action Potentials Ca2 Na Currents
Slow AP Component VGCC
Ca2 AP
Purkinje
SA node
PNa
Ventricle
AV node
PCa
Voltage Gated Sodium Channels
Fast AP Component!
VG Sodium ChannelFastInactivation
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Na Action Potentials Skeletal Muscle Neurons
Na
V
Na
Na
Na
Na
Na
Na
out
V
V
V
V
V
V
V
V
in
K
K
Neg feedback
PNa
- VGNaC Inactivation
PK
- Voltage Gated K-Channels
Em
Refractory period
- VGNaC Re-activate
Ethreshold
- VGKC Close
Erest
time
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How Many Na Ions Does it Take to Depolarize?
Na
K
K
K
K
Does Depolarization Run Down the Gradients?
out
in
Very Slowly!
Na ?
Emstim
40mV
Q ?Em Cm
of charges (Coulombs)
Capacitance (Farads)
Q (0.100 V) (10-6 F cm-2)
10-7 C cm-2
(96,500 C/mol)
Emrest
-55mV
10 µm cell?
?Nai
10-12 mol Na cm-2
10-8 mM
?Nai ltlt Nai ( 10 mM)
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Action Potentials Long Distance Depolarizations
Motor Neuron
Sensory Neuron
Axon Terminals Electrotonic (? VGCC)
Dendrite/Axon AP (VGSC)
Axon AP (VGSC)
Dendrites,
Soma Electrotonic
interneurons
Typical Motor Neuron (AP)
motor neurons
Inverts 1-4 m/sec
Verts 10-100 m/sec
Limit to Velocity of Conduction?
sensory neurons
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Na Action Potentials Velocity of Conduction?
Na
Na
Na
ChannelPermeation ? SLOW
out
V
V
V
in
Na
Na
Na
Velocity ? VGNaC spacing
Electrotonic Conduction ? FAST
Membrane KConductance (gm)
Internal Na Conductance (gi)
Na
K
gm 1/Rm ? 2??r
gi 1/Ri ? ??r2
VGNaC spacing ? ?
Ethreshold
?
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Na Action Potentials Fast Enough?
Invertebrates
? r
Typical Axon 10µm ? lt 5 m/sec
Giant Axon 500µm ? 10-50 m/sec
Vertebrates 10-100 m/sec
? gm
10 µm
Na
Na
Myelin (Schwann Cells)
1 -2 mm internodal
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AP Initiation Cardiac Pacemaker
Neural Modulation


Parasympathetic (vagus)?Acetylcholinemuscarini
c Ach receptor ?G-protein, etc ?open K
channel
Na
Ca2
Ca2
V
V
V
SA Node
K
K
Sympathetic (accelerans)?Norepinephrine?-adren
ergic receptor ?G-protein, etc ??SR
Ca-ATPase
Na Leak Channel (Funny Channel)
?slow depolarization
Ca2 AP
VGCC InactivationVGKC Opening
Em
Ethreshold
Otto Loewi 1921 (Nobel 1936)