Lecture 17

Readings

http://umdberg.pbworks.com/w/page/73084895/Nernst%20potential%20%282013%29

Nernst Potential

• Situation:

• Not worrying at the momement about how this situation with [Na] occured

  • It just exists

• But still, each side has equal positive and negative ions due to other ions not shown here.

• Na⁺ wants to move from outside to inside (extracellular to intracellular) due to random diffusion/entropy effect:

• Now a few extra positive ions are inside:

• Another Na₊ wants to go inside, but what does it see?

  • A wall of positive charges on the inside membrane

• So it's tougher to move inside

• Eventually, the random motion/entropy effect (Na⁺ wanting to move inside) is balanced by the opposing electric field:

• Which resists + charges moving inside

• Now there's a potential difference between inside and outside, with the inside potential being higher than outside.

  • This is not the "normal" case for biological cells.
  • This was what would happen if only Na⁺ were involved.

• This potential difference is called the Nernst potential for sodium

• For resting/normal membranes, it is potassium, K⁺ , that primarily determines the membrane potential:

• The intracellular space is at $-70mV$$-70\ mV$ or $-80mV$$-80\ mV$ relative to the extracellular space

• Membranes normally are much more permeable to $K^{+}$$K^+$ than $N{a}^{+}$$Na^+$

• Notice two concepts: "Membrane potential" and "Nernst Potential"

  • Each ion has a Nernst potential

  • So there are many Nernst potentials for a single membrane, one for each ion $N{a}^{+}$$Na^+$ , $K^{+}$$K^+$ , $C{l}^{-}$$Cl^-$ , etc.

  • The membrane potential is a weighted average of each Nernst potential

  • The ions that can move through membrane most easily ( highest permeability ) get the most weight

  • The membrane is much more permeable to $K^{+}$$K^+$ and to $N{a}^{+}$$Na^+$.

    • Therefore, the membrane potential is close to the $K^{+}$$K^+$ Nernst potential

  • Typical Numbers:

    • Nernst: $K^{+}=-80mV$$K^+ = -80\ mV$
    • Nernst: $N{a}^{+}=+60mV$$Na^+ = +60\ mV$
    • Membrane Potential $=-75mV$$= -75\ mV$

• Value of the Nernst potential is determined by a Boltzmann distribution:

• The "$q\ast \mathrm{\Delta }V$$q*\Delta V$" term is energy ( units = Joules )
• $\mathrm{\Delta }V=V_2-V_1=V_{in}-V_{out}=V_{intracellular}-V_{extracellular}$$\Delta V = V_2 - V_1 = V_{in} - V_{out} = V_{intracellular} - V_{extracellular}$
• Rearranging:

• OR:

• This says that the Nernst potential across a membrane for an ion is determined by the concentrations of that ion on each side of the membrane.

• The Nernst potential reflects the electrical energy difference that opposes the thermal/entropy tendency to even out the concentration

• Reminder: something else caused the concentration of $N{a}^{+}$$Na^+$ to be unequal in the first place

  • We aren't dealing with why concentration of $N{a}^{+}$$Na^+$ is unequal.

    • It just is