Resting Membrane Potential

Luigi Galvani (1737 - 1798):
- Proposed that animal tissues generate electricity using a “vital energy”.
Alessandro Volta (1745 - 1827):
- Suggested that tissue response is due to electric current generated by different metals.
Membrane Hypothesis (1902, 1912):
- Resting membrane potential: Arises from high resting selective permeability to K^+ and a concentration gradient for K^+ ions across the membrane.
- Action potential: Produced by a transient change in the membrane, losing its exclusive permeability to K^+ ions and becoming permeable to all ions (membrane breakdown).
- Hypothesis predicts that changes in K^+ ion concentrations should alter the resting membrane potential.

Must be electroneutral (equal - and + charges).
Osmotically balanced.
No net movement of ions.
Equilibrium of a membrane permeant to one ion (K^+) is determined by 2 opposing forces: chemical vs. electrical gradients at equilibrium
Nernst equation takes into account both forces.

Determined in 1888 from basic thermodynamic principles.
Restates concentration gradient in electrical terms.
Equation: E{Ion} = \frac{RT}{zF} \ln \frac{[Ion{Out}]}{[Ion_{In}]}
- R = Gas constant (8.31 J/K.mol)
- T = Absolute temperature (K)
- z = Valence of ion
- F = Faraday constant (96,485.34 C/mol)
- E = Vm at which there is no net movement of ions and at which membrane will be drawn to when channels are open
Calculating E_K (at 20°C):
- EK = \frac{RT}{zF} \ln \frac{[K{Out}]}{[K_{In}]}
- RT/F = 25 mV
- EK = 25 \cdot \ln \frac{[K{Out}]}{[K_{In}]}
- EK = 58 \cdot \log \frac{[K{Out}]}{[K_{In}]}

Example calculation:
- E_K = 58mV \cdot \log \frac{[3mM]}{[90mM]}
- E_K = -85.7mV
Experimental support for membrane hypothesis
Squid Giant Axon
- Loligo pealei ~1 mm thick
- Hodgkin and Huxley, Nature, 1939
- Preparation developed by K.S. Cole at MBL

Calculating Vm for membranes permeable to multiple ions
Weighted average of Nernst potentials for multiple ions, using relative permeability as weighing factor.
Equation: V{mrest} = 58 \cdot \log \frac{pK[K{Out}]+ p{Na}[Na{Out}]+ ….}{pK[K{In}]+ p{Na}[Na_{in}]+ ….}
- If p{Na} = 0, then Vm = E_K (-75 mV)
- If pK = 0, then Vm = E_{Na} (+55 mV)
- If pK = p{Na}, then Vm = somewhere between E{Na} and E_K (-0 mV)
For permeant anions (z<0) like Cl(-), invert out and in:
V{mrest} = 58 \cdot \log \frac{pK[K{Out}]+ p{Na}[Na{Out}]+ p{Cl}[Cl{in}]}{pK[K{In}]+ p{Na}[Na{in}]+ p{Cl}[Cl_{out}]}
Example Calculation:
- Calculate Vm, at 20°C, using concentrations shown in the table, assuming relative permeabilities of: PK:PNa:PCl = 100 : 4 : 45
  | Ion | Out | In |
  | ---- | --- | --- |
  | K+ | 10 | 200 |
  | Na+ | 88 | 10 |
  | Cl- | 112 | 8 |
- What happens if you increase PCl 5-fold?
- Is Chloride playing a major role in setting Vm?

GHK equation can be restated as conductances:
- I = V/R = Vg
- I{Na} = g{Na}(Vm - E{Na})
- IK = gK(Vm - EK)
At V{rest}, I{Na} = -I_K
- g{Na}(Vm - E{Na}) = -gK(Vm - EK)
- Vm = \frac{gK EK + g{Na}E{Na}}{gK + g_{Na}}
At rest the cell is at a steady state and there is no net current, however individual ions are still in flux.
Why doesn’t concentration gradient eventually run out?
Ion pumps maintain concentration gradient.
- Na-K ATPase - exchanges 3Na to 2 K: electrogenic and will contribute ~ -5 mV to Vm.

Resting membrane potential is determined by selective membrane permeability to specific ions at rest.
1. At rest there is no net current flow, but individual ions are still flowing across the membrane.
2. K^+, Na^+ and Cl^- are the main determinants of the RMP. Their gradients are maintained by use of pumps and exchangers.
3. The GHK equation is a weighted average of the equilibrium potentials of permeant ions, where relative permeability is the weighing factor.