Membrane Potentials: Where Do They Come From? K+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 Equilibrium: Nernst Potential F = 23° z=+1 E m ~ -60mV

Resting Membrane Potential: Steady State K+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 P Na PKPK P Cl E m ~ -55mV E Na = ~ +60 mV E K = ~ -60 mV E Cl = ~ -60 mV Relative Rest (varies) P K : P Na : P Cl = ~ 1 : 0.01 : Net Fluxes => Steady rest Goldman-Hodgkin-Katz Potential: Electromotive Force EMF = E m - E equil EMF < 0 EMF > 0 EMF = 0 for cations: EMF Na = Na/glucose co-transport? => ~ 100x glucose gradient! (E m – E Na ) = -55mV – 60 mV = -115 mV

EmEm Distance from stimulus ‘space constant’  ~1-10 µm Na + K+K+ K+K+ K+K+ K+K+ E m rest ~ -55mV Stimulus = Open Na Channel (typically) = ⇑ P Na EMF Na <<0 E m rest E m stim K+K+ K+K+ K+K+ K+K+ Electrotonic Conduction Fast Ionic Current out in Fast Spread of Depolarization! = “electrotonic conduction” “Depolarize” = Signal Decay of Depolarization = Short Range Conduction K + efflux = negative feedback EMF K > 0

V Graded Potentials = Graded Response Na + K+K+ K+K+ K+K+ K+K+ Ca +2 Voltage Gated Calcium Channel E rest 100% 0% open channels E 50 large stimulus small stimulus E m 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)  E m depends on stimulus! = “graded potential” Retinal Amacrine cells out in EmEm ? depolarization

V Na + K+K+ K+K+ Ca +2 Action Potentials = Long Distance Conduction V Ca +2 V V V V EmEm out in Initial Depolarization Open Voltage Gated Channels Electrotonic Conduction Positive Feedback! Electrotonic Conduction Na + Ca +2 Distance from stimulus Not Graded! “All-or-Nothing”  E m Depolarization No Distance Limit! E rest E stim Depends on High Density VG Channels E 50

V Na + K+K+ K+K+ Ca +2 V V V V V out in Na + Ca +2 Action Potentials = Pos + Neg Feedback V EmEm time + feedback Neg feedback: - Ca-dependent VGCC Inactivation - Ca-dependent K-Channels - Voltage Gated K-Channels “Ca +2 Action Potential” Low [Ca +2 ] -> Hi [Ca +2 ] => Must Pump Out! - Embryonic & Smooth Muscle - Cardiac Muscle (sort of) - Crustacean Muscle - Plants, Paramecia Slow! K+K+ V K+K+ V

Ventricle Cardiac Action Potentials = Ca +2 & Na + Currents Fast AP Component! Voltage Gated Sodium Channels VG Sodium Channel: Fast Inactivation Slow AP Component: VGCC P Ca P Na SA node AV node Purkinje Ca +2 AP

Na + K+K+ K+K+ V K+K+ K+K+ VVV V V out in V V Na + V EmEm time P Na PKPK E rest E threshold 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+ K+K+ K+K+ E m rest out in How Many Na + Ions Does it Take to Depolarize? E m stim Q =  E m C m # of charges (Coulombs) Capacitance (Farads) Q = (0.100 V) (10 -6 F cm -2 ) -55mV +40mV = C cm -2 (96,500 C/mol) = ~ mol Na + cm µm cell?  [Na + ] i Does Depolarization Run Down the Gradients? K+K+ Na + ATP = ~ 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/sec Verts: m/sec Limit to Velocity of Conduction? Motor Neuron:Sensory Neuron: Dendrite/Axon = AP (VGSC) motor neurons sensory neurons interneurons Dendrites,

Na + V V V out in Na + Na + Action Potentials: Velocity of Conduction? Electrotonic Conduction ⇒ FAST Channel Permeation ⇒ SLOW Velocity ∝ VGNaC spacing Na + V V K+K+ EmEm ? g i = 1/R i ∝  r 2 Internal Na + Conductance ( g i ) g m = 1/R m ∝ 2  r Membrane K + Conductance ( g m ) VGNaC spacing ∝ ? E threshold

Na + Action Potentials: Fast Enough? Typical Axon ~10µm ⇒ < 5 m/sec Giant Axon ~500µm ⇒ m/sec Invertebrates: Vertebrates: m/sec Myelin (Schwann Cells) Na mm internodal ⇓ gm⇓ gm ⇑ r ~10 µm V V V Na +

AP Initiation: Cardiac Pacemaker VV V EmEm Na + Ca +2 K+K+ K+K+ SA Node Neural Modulation: Sympathetic (accelerans) ⇒ Norepinephrine  -adrenergic receptor ⇒ G-protein, etc ⇒⇑ SR Ca-ATPase Parasympathetic (vagus) ⇒ Acetylcholine muscarinic Ach receptor ⇒ G-protein, etc ⇒ open K + channel + – Na+ ‘Leak’ Channel (“Funny” Channel) ⇒ slow depolarization Ca +2 AP Otto Loewi 1921 (Nobel 1936) VGCC Inactivation VGKC Opening E threshold Purkinje fibers: Na/Ca AP conduction