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Today’s Topics

Nernst. Today’s Topics. •Ion Transport Across Membranes (A Brief Primer) •The Generation of the Resting Membrane Potential. David S. Weiss Department of Physiology 567-4325 weissd@uthscsa.edu. Transport Across Membranes •Diffusion Through the Lipid Bilayer

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Today’s Topics

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  1. Nernst Today’s Topics •Ion Transport Across Membranes (A Brief Primer) •The Generation of the Resting Membrane Potential David S. Weiss Department of Physiology 567-4325 weissd@uthscsa.edu

  2. Transport Across Membranes •Diffusion Through the Lipid Bilayer •Carrier- or Protein-Mediated Transport

  3. Generation of the Resting Membrane Potential

  4. Measurement of the Resting Potential + - 0 mV -70 mV

  5. Diffusion

  6. Fick’s Law of Diffusion Net rate of diffusion Concentration gradient Diffusion coefficient Area of the plane diffusing across Stokes-Einstein Relation Kinetic energy Viscosity Six 3.14 Molecular radius

  7. Einstein Relationship Diffusion Distance (µM) 1 10 100 1000 (1mm) 10,000 (1cm) Time Required 0.5 msec 50 msec 5 sec 8.3 min 14 hrs

  8. A B Electrochemical Potential µ = µo + RTlnC + zFE

  9. A B µ = µo + RTlnC + zFE We are interested in the difference in the electrochemical potential between the two sides (i.e., intra- and extra-cellular). µA(x) = µo(x)+ RTln[x]A + zFEA µB(x) = µo(x)+ RTln[x]B + zFEB [x]A µ(x) = µA(x) - µB(x) = RTln + zF(EA - EB) [x]B

  10. A B [x]A [x]B µA(x) = µo(x)+ RTln[x]A + zFEA µB(x) = µo(x)+ RTln[x]B + zFEB [x]A µ(x) = µA(x) - µB(x) = RTln + zF(EA - EB) [x]B At equilibrium: µ = 0 RTln + zF(EA - EB) = 0

  11. A B [x]A [x]B -RT RT [x]A [x]B [x]B [x]A zF zF At equilibrium: µ = 0 RTln + zF(EA - EB) = 0 Rearranging gives: EA - EB = ln = ln [x]B RT Nernst Equation Ex = ln [x]A zF

  12. [x]B RT Nernst Equation Ex = ln [x]A zF This equation determines the voltage difference that must be imposed between side A and side B to prevent the movement of ions due to the chemical force. -or- This equation determines the voltage at which the electrical and chemical forces are balanced; that is, there is no net movement of ions.

  13. 0.1 M K+ 0.01 M K+ RT [x]B EK+ = ln [x]A zF Sample Problem Calculate the potential difference required to oppose the movement of K+ ions. A B 60 60 [x]B [0.01]B EK+ = log10 EK+ = log10 [x]A z z [0.1]A EK+ = -60 mV Put -60 mV on side A with respect to side B and there will be no net movement of K+ ions.

  14. 0 mV A More Realistic Situation: 0.1 M NaCl 0.01 M NaCl A B Membrane impermeable to anions, permeable to cations. At time 0, the membrane is made permeable to Na+ only.

  15. 0.1 M NaCl 0.01 M NaCl A B Membrane impermeable to anions, permeable to cations. If we apply -90 mV (Side A with respect to Side B) before the membrane is made permeable to sodium,what will happen?

  16. + 60 mV - - - + - + + + + - + + - + - - 0.1 M NaCl 0.01 M NaCl A B Membrane impermeable to anions, permeable to cations. The +60 mV, or the Nernst potential, is also called the reversal potential (Erev). Also sometimes called the equilibrium potential. Nernst potential = reversal potential = equilibrium potential

  17. Important Point 0 mV 0.1 M NaCl 0.01 M NaCl A B Impermeable membrane If ions cannot move, then no potential difference will be created!

  18. Ion Concentrations in a Typical Mammalian Cell* Out [Na]=145 mM [K]=4 mM [K]=155 mM In [Na]=12 mM [Cl]=4.2 mM [Ca]<=10-7 mM [Cl]=123 mM [Ca]=1.5 mM *actual values may vary

  19. Equivalent Circuit of the Membrane Extracellular RNa RCl RK Cm ENa +67 ECl EK -90 -98 Intracellular

  20. Equivalent Circuit of the Membrane Extracellular RNa RCl RK Cm ENa +67 ECl EK -90 -98 Intracellular Derivation of the chord conductance equation: } IK=gK (Em-EK) INa=gNa (Em-ENa) Ohm’s Law (V=IR) or I=V/R or I=Vg ICl=gCl (Em-ECl) These equations calculate the current flowing across the membrane for each ion.

  21. Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular Derivation of the chord conductance equation: IK=gK (Em-EK) INa=gNa (Em-ENa) ICl=gCl (Em-ECl) At steady state: IK+INa+ICl= 0 Therefore: gK (Em-EK) +gNa (Em-ENa) +gCl (Em-ECl)= 0 Solve for Em: Em =EK+ENa+ECl gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl This is the chord conductance equation. It allows one to calculate the membrane potential given the relative conductances of the ions. It is simply a weighted average.

  22. Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular > > Significance gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV -90 mV -98 mV

  23. Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular > > Significance gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV -90 mV -98 mV

  24. > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV -90 mV -98 mV gK gNa, gCl

  25. > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV -90 mV -98 mV gK gNa, gCl

  26. > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV gNa = gK -90 mV -98 mV gK gNa, gCl

  27. > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ENa+ECl gNa gK, gCl +67 mV gNa = gK -90 mV -98 mV gK gNa, gCl

  28. > > > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ ENa+ECl gNa gK, gCl +67 mV 0 mV gNa = gK -90 mV -98 mV gK gNa, gCl gK gNa, gCl

  29. > > > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ ENa+ECl gNa gK, gCl [K]i= [K]o +67 mV 0 mV gNa = gK -90 mV -98 mV gK gNa, gCl gK gNa, gCl

  30. Measurement of the Resting Potential + - 0 mV -70 mV

  31. So, what is the source of the Resting Membrane Potential?

  32. > > > > > > Significance Extracellular RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ ENa+ECl gNa gK, gCl +67 mV 0 mV gNa = gK -90 mV -98 mV gK gNa, gCl gK gNa, gCl

  33. Ion Concentrations in a Typical Mammalian Cell* Out [Na]=145 mM [K]=4 mM [K]=155 mM In [Na]=12 mM [Cl]=4.2 mM [Ca]<=10-7 mM [Cl]=123 mM [Ca]=1.5 mM *actual values may vary

  34. > > > > > > > > Extracellular Significance RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ ENa+ECl gNa gK, gCl +67 mV 0 mV gNa = gK gCl gNa, gK -90 mV -98 mV gK gNa, gCl gK gNa, gCl

  35. PK[K]o+PNa[Na]o+PCl[Cl]i PK[K]i+PNa[Na]i+PCl[Cl]o RT F Em = ln Extracellular One Last Equation RNa RCl RK Cm ENa +67 EK ECl -98 -90 Intracellular gK gK+gNa+gCl gCl gK+gNa+gCl gNa gK+gNa+gCl Em =EK+ ENa+ECl Goldman-Hodgkin-Katz Equation

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