Resting Membrane Potential

Resting Membrane Potential

I. Signaling Within Neurons

• Key topics include:
  • Ion Channels
  • Equilibrium Potential
  • Ionic current
  • Voltage Clamp
  • I/V curves
  • Membrane Potential

II. Synaptic Signaling Between Neurons

III. Neural Circuits and Plasticity

Neuronal Information Encoding

• Neurons encode information through changes in the membrane potential (Vm).
• These changes are generated by the opening and closing of ion channels.
• Ion channels cause ions to flow down their electrochemical gradients.

Bioelectricity and Membrane Hypothesis

• 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.

Model Cell Equilibrium

• 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.

Nernst Equation

• Determined in 1888 from basic thermodynamic principles.
• Restates concentration gradient in electrical terms.
• Equation: $E<em>{Ion} = \frac{RT}{zF} \ln \frac{[Ion</em>{Out}]}{[Ion_{In}]}$
  • 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):
  • $E<em>K = \frac{RT}{zF} \ln \frac{[K</em>{Out}]}{[K_{In}]}$
  • $RT/F = 25 mV$
  • $E<em>K = 25 \cdot \ln \frac{[K</em>{Out}]}{[K_{In}]}$
  • $E<em>K = 58 \cdot \log \frac{[K</em>{Out}]}{[K_{In}]}$

Nernst Equation Example

• 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

Experimental Data

• Experimental Data showing relationship between $K<em>{out}$ and $V</em>m$
  • Kout (mM) vs. Vm (mV)
    • 2 : -133
    • 10 : -92
    • 20 : -75
    • 200 : -17
• Why is measured Vm different than predicted Vm?

Goldman-Hodgkin-Katz (GHK) Equation

• Calculating Vm for membranes permeable to multiple ions
• Weighted average of Nernst potentials for multiple ions, using relative permeability as weighing factor.
• Equation: $V<em>{mrest} = 58 \cdot \log \frac{p</em>K[K<em>{Out}]+ p</em>{Na}[Na<em>{Out}]+ ….}{p</em>K[K<em>{In}]+ p</em>{Na}[Na_{in}]+ ….}$
  • If $p<em>{Na} = 0$, then $V</em>m = E_K$ (-75 mV)
  • If $p<em>K = 0$, then $V</em>m = E_{Na}$ (+55 mV)
  • If $p<em>K = p</em>{Na}$, then $V<em>m$ = somewhere between $E</em>{Na}$ and $E_K$ (-0 mV)
• For permeant anions (z<0) like Cl(-), invert out and in:
  $V<em>{mrest} = 58 \cdot \log \frac{p</em>K[K<em>{Out}]+ p</em>{Na}[Na<em>{Out}]+ p</em>{Cl}[Cl<em>{in}]}{p</em>K[K<em>{In}]+ p</em>{Na}[Na<em>{in}]+ p</em>{Cl}[Cl_{out}]}$
• 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?

Conductance and Ion Pumps

• GHK equation can be restated as conductances:
  • $I = V/R = Vg$
  • $I<em>{Na} = g</em>{Na}(V<em>m - E</em>{Na})$
  • $I<em>K = g</em>K(V<em>m - E</em>K)$
• At $V<em>{rest}$, $I</em>{Na} = -I_K$
  • $g<em>{Na}(V</em>m - E<em>{Na}) = -g</em>K(V<em>m - E</em>K)$
  • $V<em>m = \frac{g</em>K E<em>K + g</em>{Na}E<em>{Na}}{g</em>K + g_{Na}}$
• 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.

Membrane as an Electrical Circuit

• Membrane can be modeled as an electrical circuit
• Comparison of membrane potential with and without ATPase activity.
• Mitochondria also have a membrane potential driven by $H^+$

Leigh Syndrome

• Leigh syndrome is a neurodegenerative mitochondrial disorder

Key Concepts

• 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.