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![psm.edu
Ex = RT * ln [ X ]o
[ X ]i
___
zF
Ex = 60 * log
[ X ]o
[ X ]i
EK = 60 * log
[ 5 ]o
[ 100 ]i
At 37 °C and a
valence = +1
= -78 mV
The Nernst Equation
• The Nernst potential for a single ion is
its equilibrium potential.
z = valence of ion](https://image.slidesharecdn.com/membranepotentials1-260123035659-13da5f65/85/Membrane-Potentials-for-SCU-MSMS-Program-10-320.jpg)
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Membrane Potentials for SCU MSMS Program
- 1.
- 2. psm.edu Membrane Potentials James T.Porter, Ph.D.
- 3. psm.edu • Use Fick’sLaw of diffusion to explain how changes in the concentration gradient will influence the diffusional movement of a compound. • Based on the principle of ionic attraction, explain how a potential difference across a membrane will influence the distribution of a cation and an anion. • Write the Nernst equation, and explain the effects of altering the intracellular or extracellular Na+, K+, Cl-, or Ca2+ concentration on the equilibrium potential for that ion. • List the values for membrane potential, ENa, EK, ECl, and ECa in a typical mammalian cell. • Explain the direction that an ion will move when the membrane potential is at its equilibrium potential, is higher than its equilibrium potential, or is less than its equilibrium potential. Objectives
- 4. psm.edu Objectives • Describe thenormal distribution of Na+, K+, and Cl- across the cell membrane, and use the Goldman equation to explain how the relative permeabilities of these ions create a resting membrane potential. • Define gating, activation, and inactivation of ion channels. • Explain how driving force and conductance affect current flow across a membrane. • Contrast the gating of ion channels by extracellular ligands, intracellular ligands, stretch, and voltage. • Describe the effects of hyperkalemia, hypokalemia, and hypoxia on resting membrane potential. • Explain how changes in membrane resistance, axial resistance, and capacitance affect the propagation of membrane potentials and action potentials.
- 5.
- 6. psm.edu Voltage KCL 5 mM KCL 100 mM Semi-permeable membrane K+ Thecell as a potassium battery Cl- Inside Outside
- 7. psm.edu Voltage KCL 5 mM KCL 100 mM Permeableonly to K+ K+ Cl- K+ Fick’s Law of Diffusion • Ions flow from high to low concentration Inside Outside
- 8. psm.edu Concentration Gradient isOpposed by Electrical Gradient
- 9. psm.edu Equilibrium Potential • Atequilibrium: the diffusion gradient pushing K+ out of the cell is equal to the electrical gradient pulling K+ back into the cell.
- 10. psm.edu Ex = RT* ln [ X ]o [ X ]i ___ zF Ex = 60 * log [ X ]o [ X ]i EK = 60 * log [ 5 ]o [ 100 ]i At 37 °C and a valence = +1 = -78 mV The Nernst Equation • The Nernst potential for a single ion is its equilibrium potential. z = valence of ion
- 11. psm.edu Nernst Potential Affects Directionof Ion Movement EK -78 mV -50 mV -90 mV K+ K+ Influx Efflux
- 12. psm.edu Ion Out (mM)In (mM) Eion 37 C K+ 5 100 -78 mV Na+ 150 15 +60 mV Ca2+ 2 0.0002 +120 mV Cl- 150 13 -64 mV Equilibrium Potentials
- 13. psm.edu • Includes permeabilityof ions. • Permeability varies with time. • So why is normal resting membrane potential -70 mV? Goldman Equation Vm
- 14. psm.edu Leak K+ Channels •Always open • Produce K+ permeability at the resting membrane potential http://www.neurology.org/content/72/7/664/F1.large.jpg
- 15. psm.edu To Establish theResting Membrane Potential - Only need a concentration difference and diffusion through a semipermeable membrane - No ATP is required - No pump is required
- 16. psm.edu Na+K+ATPase Pump • UsesATP to move 3Na+ out for every 2K+ into neuron • Electrogenic pump helps maintain concentration gradients and membrane potential. • Ischemia causes some depolarization of resting membrane potential.
- 17. psm.edu Changes in Concentrationsof Ions in the Blood Modify the Nernst Potentials: Effects of hypo- and hyperkalemia Muscle and cardiac cell depolarization and hyperpolarization are affected by extracellular potassium. Muscle contraction requires cells to depolarize from the resting potential (RP) to the threshold potential (TP). Hyperkalemia moves the RP closer to the TP and can result in depolarization muscle paralysis. Hypokalemia hyperpolarizes cells and this also impairs depolarization.
- 18. psm.edu • How dothe values in this equation change during: • Upstroke of action potential? • Downstroke of action potential? • What if permeability of Na+ and K+ were equal? Ionic Permeability is Dynamic Vm
- 19. psm.edu Ohm’s law: V= I R or I = V V = Vm-E g = 1 I = g (Vm-E) Therefore the amount of current flow depends on: 1. driving force: distance of membrane potential from Nernst potential: (Vm-E) 2. conductance (g; related to permeability and is the inverse of resistance) as channels open the resistance decreases and conductance increases What determines the amount of current (I) flowing through the membrane? R R
- 20. psm.edu Schematic of thesodium channel. The sodium channel is a transmembrane protein that can be conceptualized as having two gates. Sodium ions pass only when both gates are open. Opening of the gates is time dependent and voltage dependent; therefore, the channel possesses three functional states. At rest, the lower gate is open, but the upper gate is closed (A). When the muscle membrane reaches threshold voltage depolarization, the upper gate opens, and sodium can pass (B). Shortly after the upper gate opens, the time-dependent lower gate closes (C). When the membrane repolarizes to its resting voltage, the upper gate closes, and the lower gate opens (A). Voltage-Gated Channels
- 21. psm.edu Ligand-Gated Channels • Openin response to binding of neurotransmitter • Close when neurotransmitter is degraded or reuptaken from synapse
- 22. psm.edu Second Messenger-Regulated Channels •Cyclic nucleotides like cAMP or cGMP open some channels • Phosphorylation can open some channels • For example, sympathetic nerves increase heart rate by cAMP activation of Funny Channels/ “pacemaker channels”/ Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and PKA phosphorylation of calcium channels in SA node.
- 23. psm.edu Mechanically-Gated Channels • Openor close in response to physical deformation of receptor that is tethered to intracellular and extracellular proteins • Particularly important for sensing deformation of various tissues • Baroreceptor Reflex
- 24. psm.edu How fast doessurrounding membrane depolarize? I Membrane Time Constant () = time to charge membrane to 63% of maximum Rm is proportional to number of closed channels Cm is membrane capacitance Each section of membrane must be charged before moving to next section. The larger the time constant the slower the conduction velocity. 63% τ = RmCm mV
- 25. psm.edu • Capacitance isthe ability to store charge. • The cell membrane’s lipid bilayer is a great capacitor. • The closer together are the different charges, the stronger the interaction and the larger the capacitance (i.e. the more charges can be stored). Capacitance + - + - +
- 26. psm.edu How far doEPSPs and end plate potentials propogate? • Length Constant (λ): distance that a given amount of charge (i.e. end plate potential or EPSP) can travel before it is reduced to 37% of its original magnitude. • The larger the length constant the faster the conduction velocity. Ra Rm
- 27. psm.edu Length Constant (λ) •Charge is lost either by flowing out through open channels (Rm) or to impedance of intracellular material (Ra). Injection site