Resting membrane potential

[Ref: KB2:p232; WG21:p7-8; PK1:p3-4; BL8:p10]

RMP

... is the steady state potential which exists across the cell membrane

Typical values

• myelinated peripheral nerve axon
  = -70mV
• myocyte
  = -90mV

Production of RMP

1. Na-K ATPases pump Na+ out of cells and K+ into cells
2. A concentration gradient across the membrane is produced
3. Na+ and K+ leak down the gradient
4. BUT, the membrane is much more permeable to K+, so much more K+ leaves the cell than Na+ enters the cell
5. This results in net movement of positive charge out of the cell, causing the inside of the cell to be more negative than outside

--> this potential difference is the resting membrane potential

Other contributors

• The Na-K ATPase pump itself is electrogenic because it moves 3 Na+ ions out of cells for every 2 K+ ions.
  i.e. adds a little to RMP
• Gibbs-Donnan effect: large intracellular proteins and organic phosphates are not diffusible, and it results in some redistribution of diffusible ions (e.g. K+, Cl-)
  i.e. also adds a little to RMP

Nernst equation

... calculates the potential difference that any ion (with a concentration gradient across the membrane) would produce if the membrane was permable to it.

E = RT/zF x In{[ion]_o/[ion]_i}
= 61.5 x log{[ion]_o/[ion]_i} @37C

• E = equilibrium potential
• R = gas constant
  * (8.314JK^-1mol^-1)
• F = Faraday's constant
  * (96500 coulombsmol^-1)
• z = ionic valency
• [ion]_o = concentration outside
• [ion]_i = concentration inside

Goldman equation

(Full name: Goldman-Hodgkin-Katz form of Nernst equation)

E = 61.5
x log{(P_K[K]_o+P_Na[Na]_o+P_Cl[Cl]_o)/(P_K[K]_i+P_Na[Na]_i+P_Cl[Cl]_i)}

• Modified from Nernst to take into account the relative concentration and permeability of the important ions

 

Contribution by ions

An electrolyte have greater influence on RMP when:

• high concentration
• large concentration gradient
• high membrane permeability

Also, as an ion's permeability increases, the membrane potential moves towards its equilibrium potential

Other notes

Nernst equation application

For Cl (i:9-10, o:125)

E_Cl = -61.5 x log(125/10)
= -61.5 x 1.0969
= -66.91
~ -70mV

For K (i: 135-150, o: 4-5.5)

E_K = 61.5 x log(4.5/150)
= 61.5 x -1.523
= -93.66
~ -94mV

For Na (i:10-15, o:145-150)

E_Na = 61.5 x log(150/15)
= 61.5 x 1
~ +60mV  

Note

• If Na-K pump stops, the leakage of ions will gradually diminish the RMP
• Na-K pump is inhibited by digitalis

Factors affecting RMP

• Relative conductance to Na and K determines the RMP
• E_K as per Nernst equation
  = -94mV (depends on [K] used)
• RMP is smaller (in absolute term) than E_K because of a small inward leakage of Na.

When extracellular [K+] decreases below 5mM, this small leakage of Na has greater influence on the final RMP. RMP will still become more negative as extracelluar [K+] decreases, but will deviate more from the predicted value (E_K)

[BL8:p12]