calculating the equilibrium potential (EP) and estimating the resting membrane potential (RMP)

concentrations and permeability of ions responsible for the RMP in a typical mammalian cell

• note that the composition in extracellular fluid is different than in the intracellular fluid

• the relative permeability shows us that K+ and Cl- are 25-30x and 50x MORE permeable than Na+ and A- (intracellular proteins)

what is the electrical gradient AND concentration gradient of K+

• Since K⁺ is positively charged, it is attracted to areas with negative charge and repelled from areas with positive charge

• Inside the cell is more negative than the outside.

• So, the electrical gradient pulls K⁺ into the cell (because opposite charges attract)

• however - There’s also a concentration gradient:

  • K⁺ is more concentrated inside the cell than outside.

  • So, K⁺ tends to diffuse out of the cell down its concentration gradient.

• together known as electrochemical gradient !!!

what is the electrical gradient AND concentration gradient of Na+

• Electrical gradient of Na⁺ (sodium): Na+ is positively charged - the negative inside of the cell attracts it

• Inside the cell is more negative than the outside.

• So the electrical gradient pulls Na⁺ into the cell

• ➕ Plus:

  • Na⁺ is also more concentrated outside the cell than inside.

  • So the concentration gradient also wants Na⁺ to move into the cell

• Both gradients agree:

  • Electrical gradient: Pulls Na⁺ in

  • Concentration gradient: Pulls Na⁺ in

  • So, Na⁺ has a strong drive to enter the cell

• together known as electrochemical gradient

what is the equilibrium potential for K+

• These two forces — electrical gradient (inward) and concentration gradient (outward) — oppose each other.

• The balance point between them is called the equilibrium potential for K⁺, usually around –90 mV in neurons

equilibrium potential for Na+

• It’s around +60 mV, meaning sodium would be at equilibrium if the inside of the cell were that positive — but at rest (around –70 mV), sodium is far from equilibrium, so it’s strongly driven inward

when is equilibrium potential met

• the voltage measured when there is no net influx/movement of an ion

• the movement along concentration gradient is = to movement along electrical gradient

what equation do we use to calculate the equilibrium potential

• calculated using the Nernst equation:

• z = ion’s valence = for Na+ and K+ = 1 and for Cl- = -1

• Co is the extracellular concentration of ion (mM)

• Ci is the intracellular concentration of ion (mM)

• 61 is a constant incorporating the universal gas constant (R), absolute temperature (T), an electrical constant Faraday (F) and the conversion of the natural logarithm (ln) to the logarithm to the base 10 (log); 61 = RT/F

what is the equilibrium potential for Na+, K+ and Cl-

What direction is the driving force for K+, Na+ and Cl- if the RMP is -70mV?

• Driving force for K+ = -90.1mV - outward - RMP is -70mv so K+ will always be trying to make the membrane more polarized/negative as trying to make it go from -70 to -90 - so K+ will have a driving force of outwards of the neuron to do this

• Driving force for Na+ = 61.0mV - inward - RMP is -70mv - so wants to make the membrane more positive - Na+ wants to come into the cell

• Driving force for Cl- = -69.9mV - There is no driving force as it is at equilibrium - extremely close to -70mv

can equilibrium be reached for Na+ and K+

• Na+ and K+ can never reach equilibrium due to the presence of each other / the other ion

• RMP is -70mv - so neither of these ions are at equilibrium at RMP (Na+ is 61mv at RMP and K+ is -90mv)

• the Na+/K+ prevents this from happening - passive diffusion of these ions is prevented by the action of NaK ATPase

what calculation can we use to calculate membrane potential

• Goldman-Hodgkin-Katz (GHK) Equation

• V_m = membrane potential in mV

  61 = a constant representing RT/zF; where z = 1, as it does for K⁺ and Na⁺

  P_K+, P_Na+  = permeabilities for K⁺ and Na⁺, respectively

  [K⁺]_o, [Na⁺]_o = concentration of K⁺ and Na⁺ outside the cell in mV, respectively

  [K⁺]_i, [Na⁺]_i= concentration of K⁺ and Na⁺ inside the cell in mV, respectively

• for permeability : Na+ = 1 and K+ = 25-30 so this means K+ is 25x MORE permeable than Na+ so in the equation K+ permeability will be written as 1 and Na+ will be as 0.04 (1/25 = 0.04)

Why is the RMP closer to E_K than E_Na?

at rest, the membrane is more permeable to K+ than Na+ - K+ has a bigger influence on the RMP

what is the typical value of the RMP with reference to the ICF

-70mv

what ions play an important role in the establishment of the RMP

Na+ and K+