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Membrane Potentials: Where Do They Come From?

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.

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Membrane Potentials: Where Do They Come From?

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  1. 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 Em~ -60mV Separation of Charge = Electrical Potential z = charge = Influx F = constant = Efflux = Equilibrium NernstPotential for an ion: @ Equilibrium: @ 23°z=+1

  2. Na+ ATP K+ Resting Membrane Potential: Steady State out in Nernst Potential: PNa ENa = ~ +60 mV [Na+]i ~15 mM [Na+]o~150 mM PK EK = ~ -60 mV [K+]i ~150 mM [K+]o ~15 mM PCl ECl = ~ -60 mV [Cl-]i ~15 mM [Cl-]o ~150 mM V Em~ -55mV Relative Permeabilities @ Rest (varies) PK : PNa : PCl = ~ 1 : 0.01 : 0.001 Electromotive Force EMF = Em - Eequil Net Fluxes => Steady State @ rest Goldman-Hodgkin-Katz Potential: for cations: = Influx EMF < 0 = Efflux EMF > 0 EMF = 0 = Equilibrium Na/glucose co-transport? => ~ 100x glucose gradient! EMFNa = (Em – ENa) = -55mV – 60 mV = -115 mV

  3. Stimulus = Open Na Channel (typically) = ⇑ PNa EMFNa <<0  Electrotonic Conduction Na+ K+ K+ K+ K+ K+ efflux= negative feedback out Emrest in EMFK > 0 ~ -55mV Fast Ionic Current K+ K+ Na+ 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

  4. 100% openchannels 0% Graded Potentials = Graded Response Na+ Ca+2 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 (Ca+2 => secretion) • Sensory & Brain Cells (Ca+2 => signaling) Retinal Amacrine cells

  5. Action Potentials = Long Distance Conduction Initial Depolarization • Depends on High Density VG Channels Na+ Ca+2 Ca+2 Ca+2 Ca+2 Ca+2 Ca+2 Electrotonic Conduction out V V V V V V in K+ K+ Open Voltage Gated Channels Ca+2 Ca+2 Ca+2 Ca+2 Ca+2 Ca+2 Na+ Estim Depolarization Positive Feedback! Electrotonic Conduction Em E50 • Not Graded! “All-or-Nothing”Em Erest Distance from stimulus • No Distance Limit!

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

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

  8. K+ K+ Na+ Na+ Na+ Na+ Na+ Na+ Na+ Na+ Action Potentials: Skeletal Muscle & Neurons Na+ Na+ Na+ V 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

  9. Na+ ATP K+ 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? [Na+]i = ~ 10-12 mol Na+ cm-2 = ~ 10-8 mM [Na+]i<< [Na+]i (~ 10mM)

  10. 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

  11. ? V V Em 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 K+Conductance (gm) Internal Na+Conductance (gi) Na+ K+ gm = 1/Rm ∝ 2r gi = 1/Ri ∝r2 VGNaC spacing ∝  Ethreshold ?

  12. V V V Na+ Action Potentials: Fast Enough? Invertebrates: ⇑ r Typical Axon ~10µm ⇒ < 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

  13. Purkinje fibers: Na/Ca AP conduction AP Initiation: Cardiac Pacemaker Neural Modulation: – + • Parasympathetic (vagus)⇒Acetylcholinemuscarinic Ach receptor ⇒G-protein, etc ⇒open K+ channel Na+ Ca+2 Ca+2 V V V SA Node K+ K+ • Sympathetic (accelerans)⇒Norepinephrine-adrenergic receptor ⇒G-protein, etc ⇒⇑SR Ca-ATPase Na+ ‘Leak’ Channel (“Funny” Channel) ⇒slow depolarization Ca+2 AP VGCC InactivationVGKC Opening Em Ethreshold Otto Loewi 1921 (Nobel 1936)

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