3B. Membrane Potential

Question 1

• Plasma membrane of all living cells has a membrane potential (polarized electrically)
• Separation of opposite charges across plasma membrane
• Due to differences in concentration and permeability of key ions
• Main equation which relates electical factors is Ohm’s Law

Answer 1

Question 2

Membrane Potential Analogy:

Imagine a waterfall into a____. The height of the waterfall is equivalent to the ____ which supplies the energy for ion flux through the membrane. The flow of water thru the ____ ____ ____ ___ – how many ions are passing the membrane at any time and the diameter of the funnel is equivalent to the resistance of the membrane to the ion flow.

Answer 2

funnel

voltage

funnel is equivalent to the current

Question 3

Excitable cells –2 types:

A

B

Have the ability to produce __, transient ___ in their membrane potential when excited

Answer 3

A. Nerve

B. Muscle

rapid

changes

Question 4

Resting membrane potential–constant membrane potential present in cells of _____ tissues and those of ____ tissues when at rest.

Answer 4

nonexcitable

excitable

Question 5

Na-K pump has a small direct effect on the membrane potential through

Answer 5

its unequal transport of positive ions

Question 6

Concentration (mM) & Permeability of Ions Responsible for Membrane Potential

• Ion / Extracellular / Intracellular / Relative Permeability
• Na+ 150 15 1
• ? 5 150 50-75
• A- 0 65 ?

Answer 6

Ion / Extracellular / Intracellular / Relative Permeability
Na+ 150 15 1
K+ 5 150 50-75
A- 0 65 0

Question 7

Nernst Equation

There is a relationship between the concentration gradient and voltage generated when the ion crosses that membrane (and down that gradient).

Nernst Equation show that relationship:

Answer 7

•E (mV) = (RT/zF) x (ln [ionout]/[ionin])

•For monovalent cations (Na+ or K+) at normal temperatures, the equation is reduced to
E (mV) = 61 mV x log10 [ionout]/[ionin]

Question 8

Nernst Eqn

So for K+, we have about a 30-fold gradient (5 mM outside and 150 mM inside). To solve
1st: log10 (1/30) = -1.48

2nd: E (mV) = -1.48 x 61 mV = -90 mV

-

Answer 8

From

•E (mV) = 61 mV x log10 [ionout]/[ionin]

Question 9

For monovalent cations (Na+ or K+) at normal temperatures, the equation is reduced to

•E (mV) = 61 mV x log10 [ionout]/[ionin]

Answer 9

So for Na+, we have about a 10-fold gradient (15 mM inside and 150 mM outside) or

1st: log10 (10) = 1
2nd: E (mV) = 1 x 61 mV = 61 mV

Question 10

What about Ca++? Its divalent so RT/zF goes to about 30 mV and its also really low inside (~0.1 to1 uM and variable) and about 2 mM outside or about 1000-fold different .

Answer 10

• 1st: log10 (1000) = 3
• 2nd E (mV) = 3 x (61)/2 = +100 but Ca++ inside varies so much that we cannot calculate it definitively

Question 11

•and Cl-? Its similar to Na+ in concentration gradient (it basically follows Na+ but remember its anionic) so
log10 (0.1) = -1 x 61 = ____

Answer 11

-61mV

Question 12

Equilibrium Potential for Na+

1. The concentration gradient for Na+ tends to push this ion into the cell.
2. The inside of the cell becomes more + as the Na+ ions move tothe inside, down the conc’n gradient.
3. The outside becomes more - as the Na+ ions move in. Leaving behind the ECF unbalanced negatively charged Cl-.
4. The resulting electrical gradient tends to move Na+ out of the cell.
5. No further net movement of Na+ occurs when outside electrical gradient is balanced with the inside concentration gradient.
   
   • (E-Na+) = + 60mV

Answer 12

Question 13

Basis of Resting Membrane Potential

1. The Na+/K+ pump actively transports Na+ out of the cell & K+ into the cell. That keeps the concentration of Na+ high in ECF, and K+ concentration high in the ICF.
2. Considering the concentration gradients: K+ drives the membrane potential to K+ equil. potential (-90mV) and Na+ drives it to its equil. potential (+60mV).
3. However, K+ exerts the dominant effect on the resting membrane potential because the membrane is more permeable to K+. As a result, the resting potential (-70mV) is much closer to (E-K+) than to (E-Na+).
   4.

Answer 13

4. When establishing the resting potential, the large net diffusion of K+ outward does not produce a potential of -90mV because the resting membrane is slightly permeable to Na+ inward neutralizes some of the potential created by K+ alone—bringing the resting potential to -70mV, slightly less than (E-K+).
5. The negatively charged intracellular proteins (A-) that cannot permeate the membrane remain unbalanced inside the cell during the net outward movement of the positively charged ions, so the inside of the cell is more negative than the ECF.

Question 14

Answer 14

Resting membrane potential = -70mV

Question 15

Additional factoids on the Resting Membrane Potential

1) Mainly due to dominant resting permeability to K+ (EK= -90 mV)
2) Small contribution of Na+ permeability (ENa=+60 mV) drives Vm slightly positive from EK to ~-70 mV
3) The Goldman equation defines this relationship and allows one to calculate the membrane potential from the known constants of the Nernst potentials and the relative permeability for all ions at any instant in time - not just rest!!!

Answer 15

Question 16

Example: What is the membrane potential if the permeability to all ions is exactly equal or 25% of the total membrane permeability?

V_m = g_KE_K + g_NaE_Na + g_CaE_Ca + g_ClE_Cl

Answer 16

V_m = g_KE_K + g_NaE_Na + g_CaE_Ca + g_ClE_Cl

  = 0.25(-90 mV) + 0.25(61) + 0.25(150) + 0.25(-61)

  = -22.5 + 15 + 37 – 15 mV

  = 14.5 mV

Question 17

What are the basic traits of ion channels and what about the
K+ channels that set the resting membrane potential?

Answer 17

• Selectivity filter:
  
  • Ion channels can discriminate between different ions
• But Na+ is smaller than K+!!! How can this work???

Question 18

Basic structure of ion channels:

• Multiple transmembrane (tm) regions form the main channel structure
• These tm regions may be separate proteins or may a single long protein
• Accessory subunits also are important modifiers of function

Answer 18

Question 19

Inward Rectifier K+ channel / IK_ir

•The RMP is set by a K+ channel known as the ‘resting” or inward rectifying K+ channels denoted as IK_ir channels

(I=ionic K=potassium ir=inward rectifier)

•These are four subunits each w/ only 2 transmembrane regions and a specialized pore-forming region (P) as well which lines the channel

Answer 19

Question 20

Fun facts:

• Potassium and Chloride produce
• Sodium and Calcium
• It is the hyperexcitability of neurons resulting from

Answer 20

• negative, inhibitory potentials
• produce positive, excitatory potentials
• anoxia that kills you, not the anoxia itself. The heart and brain fry themselves.

Question 21

Resting Membrane Potential:

Answer 21

K+ contributes the most due to permeability (-90mV) but Na+ contributes slightly to drive Vm to -70mV

• Goldman Equation: Defines the relationship between ion permeability and Nernst potentials to overall membrane potential

Vm = g_KE_K + g_NaE_Na + g_CaE_Ca + g_ClE_Cl

• g = percent permeability

Question 22

Injection of ___ was used in lethal injections; by doubling ECF K+ conc, the eq potential moves from ____ ___.

This causes all excitatory cells to activate at once, firing all pain receptors and causing a painful death.

Answer 22

potassium

-90mV to -45mV

Question 23

Potassium: eq between conc grad and voltage force rests at ___
o All life exists at -90mV and higher; no biological action can make _____

Answer 23

-90mV

membrane potential lower

Question 24

Na+ and Cl- have opposing charges; if both ion channels are open equivalently, there will be a net membrane potential of __

Answer 24

0mV

Question 25

Electrical interactions between ions and water create a hydrated radius around the ion
o Potassium is a diffuse point source (large radius, delocalized charge) and has less hydrated water, so it has smaller hydration radius that sodium (even though K+ is larger)
o Sodium is a conc point sources with more hydrated water, leading to a larger hydration radius than potassium

Answer 25

This radius can then be filtered
o Potassium channel does not strip hydration, so it accepts the smaller hydrated potassium and blocks the larger hydrated sodium
o Sodium channel does strip hydration, so it accepts the smaller sodium ion and blocks the larger potassium ion

Question 26

Structure of Ion Channels
 Contains a transmembrane region (13 AA in α-helix transmembrane protein)
 Can be made from _____ genes (potassium) or ____ genes (___ channel)

Answer 26

multiple

single

sodium

Question 27

Inward Rectifier K+ channels (IKir)

Answer 27

• The K+ channel which sets the resting membrane potential (also called leak or resting channel)
  
  • 3 regions - 2 transmembrane regions + 1 pore forming region
  • 4 of these sets of 3 come together to form the action ion-selectivity filter (at the pore)
  • Not selective for salts in the same family (i.e. Rubidium, Cesium)

Question 28

Changes in Membrane Potential
 Polarization: State of membrane potential other than ___
 Depolarization: Diminishing polarization (towards 0mV)
 Repolarization: Return to normal resting membrane potential
 Hyperpolarization: Increase in polarization ____

Answer 28

0mV

(away from 0mV)

Question 29

2 Main Kinds of Membrane Potential Changes

• Graded potentials:
  
  • _____ distance, sub-threshold signals in local regions of cell
  • Utilize ____ for cell communication
  • Not ___ by biological processes; passively propagated
• Action potentials:
  
  • Long distance, _____signals
  • Actively regenerated across ___ ___ of cell by specialized voltage-gated ion channels (VGICs)

Answer 29

Short

Small signals

regenerated

super-threshold

large regions

Question 30

Graded Potentials:

• Occurs in small regions of excitable cells (esp. dendrites)
• Magnitude of graded potential varies directly with magnitude of ___
  
  • Ex. When you press something against your finger, greater pressure = greater response
• Electrical signals (depolarization)___ quickly as they are conducted away from initial active area

Answer 30

triggering event

degenerate