Neuro 1020 Exam Notes: Active Membrane Properties

Active Membrane Properties

• Key concepts: Ion channels, equilibrium potential, ionic current, voltage clamp, I/V curves, membrane potential, action potential.

Neural Computation

• Decision to swing:
  • Light from the ball reaches the eye at 0 ms.
  • The brain "sees" the ball at 50 ms.
  • Decision to swing occurs at 125 ms.
  • Muscle activated in the spinal cord at 150 ms.
  • Arm begins to move at 200 ms.
  • Bat crosses the plate at 300 ms.
  • Approximately 450 msec from pitcher to plate.

Single Channel vs Macroscopic Currents

• Single channel currents build macroscopic currents.
• Illustrative examples:
  • Na^+ channel at -80 mV showing single channel currents.
  • K^+ channel at +50 mV showing single channel currents.

Macroscopic Current Equation

• The macroscopic current (I) is determined by single channel current, number of channels, and probability of open channel.
  • I = i \cdot n \cdot P_o
    • I = macroscopic current
    • i = single channel current (micro)
    • n = # channels
    • P_o = probability of open channel
• P_o is dynamic and regulation is due to gating and modulation.

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).
• Predictions:
  • During an action potential, the membrane conductance should increase.
  • The membrane potential should reach 0 mV.

Hodgkin and Huxley & Curtis and Cole

• Key figures in understanding action potentials.

Overshoot

• In action potentials, the "overshoot" refers to the portion of the action potential where the membrane potential is more positive than 0 mV.

Role of Sodium

• Is the overshoot due to sodium (Na^+)?
• Is the action potential due to influx of Na^+?
• Hodgkin and Katz (1949) investigated the role of extracellular Na^+ in action potential generation.

Ionic Basis of Action Potential

• E{Na^+} and E{K^+} are the equilibrium potentials for sodium and potassium, respectively.
• Depolarization: Increase in g_{Na^+} (sodium conductance) leads to Na^+ influx.
• Repolarization: Increase in g_{K^+} (potassium conductance) leads to K^+ outflux.
• Equations:
  I{Na^+} = g{Na^+} (Vm - E{Na^+}) \
  I{K^+} = g{K^+} (Vm - E{K^+})
  
• Current clamp: Control current injection, measure change in V_m.
• Voltage clamp: Experimentally set V_m, measure currents.

Voltage Clamp

• Invented by Cole (1949).
• With active conductances, the voltage clamp allows measurement of currents in response to a command voltage.
• Without active conductances, the membrane potential remains at its resting value.
• Demonstrates capacitative currents with and without membrane capacitance.

Squid Axon Experiments

• Depolarizing the squid axon reveals a biphasic current.
• Inward currents disappear with low extracellular Na^+.

Voltage-Dependence of Currents

• Early inward currents and late outward currents exhibit voltage-dependence.
• Peak early current: inward current
• Peak late current: outward current

Selective Channel Blockers

• Allow isolation of currents.
• Sodium channels:
  • Tetrodotoxin (TTX) and Saxitoxin (STX) block Na^+ channels.
• Potassium channels:
  • Tetraethylammonium (TEA) blocks K^+ channels.

Action Potential Threshold

• Depolarization: Na^+ influx
• Repolarization: K^+ outflux
• Increase in g_{Na^+}.
• Non-gated K^+ channels.

Conductance Equations

• 
  g{K^+} = \frac{I{K^+}}{(Vm - E{K^+})} \
  g{Na^+} = \frac{I{Na^+}}{(Vm - E{Na^+})}
  
• Na^+ and K^+ conductances increase with membrane potential independent of actual current flow.
• g = \frac{1}{R} = \frac{I}{V}
• Conductance reflects the time course of channel opening.

Hodgkin and Huxley Model

• Hodgkin and Huxley reconstructed the voltage waveform of the action potential from calculated Na^+ and K^+ conductances.

Action Potential Duration

• Na^+ and K^+ conductances have different inactivation properties.
• Recovery from inactivation takes several ms of hyperpolarization.

Refractory Period

• Na^+ channel inactivation is the basis of the refractory period.
  • Absolute refractory period: No action potential can be generated.
  • Relative refractory period: A larger than normal stimulus is required to generate an action potential.
• "Ball and chain" model for Na^+ channel inactivation.
• Activation and inactivation were thought to be separate processes (not entirely correct).

Patch-Clamp Technique

• Invention of the patch-clamp (1976) allowed single channel recordings.
  • Invented by Erwin Neher and Bert Sakmann.
• Confirmed Hodgkin and Huxley's predictions at the single channel level.
• Illustrative examples:
  • Na^+ channel currents at -80 mV.
  • K^+ channel currents at +50 mV.

Ionic Basis of Action Potential

• Graphical representation of voltage, sodium conductance (g{Na}) and potassium conductance (gK) during an action potential.

Diversity of Voltage-Gated Channels

• Multiple classes of voltage-gated channels exist with different:
  • Ion selectivity
  • Voltage threshold (V_{th}
  • Inactivation properties
  • Sensitivity to blockers
  • Modulation
  • Functions

Examples of Currents in Cortical Neurons

• Sodium Currents
  • Fast (I_{Na(fast)}): Blocked by TTX, involved in spike generation.
  • Slow (I_{Na(slow)}): Blocked by TTX, involved in prepotentials.
• Calcium Currents
  • High-threshold (I{Ca(L)}, I{Ca(N)}, I_{Ca(P)})
  • Low-threshold (I_{Ca(T)})
• Potassium Currents
  • Delayed rectifier (I_{K(DR)}): Blocked by TEA, involved in spike repolarization.
  • Transient (I_{K(A)}): Blocked by 4-AP, involved in spike repolarization.
  • Delay current (I_{K(D)})
  • M current (I_{K(M)}): Affected by various neuromodulators, involved in spike train accommodation.

Spiking Patterns

• Ion channel combinations underlie diversity of spiking patterns and AP shapes.
• Examples: Cortical pyramidal cells, Cerebellar Purkinje cells, Thalamic relay cells, Dopamine neurons.

Alternative Splicing

• Alternative splicing further enhances diversity of channel properties (Diane Lipscombe, 2013).
• Ion channels are unevenly distributed throughout the cell.

Inflammation and Pain Sensitization

• Inflammation increases the distance of the axon initial segment to the soma in dorsal horn inhibitory neurons, causing pain sensitization (Kaspi et al. 2023).
• Increases the action potential threshold of inhibitory neurons.
• Requires stronger depolarization to fire action potentials.
• This imbalance in excitation to inhibition causes inflammatory hyperalgesia (Kaspi et al. 2023).

Important Concepts

1. Action potentials result from temporally coordinated changes in the selective permeability of the membrane to different ions.
2. Experimental manipulations allow us to separate different ionic conductances.
3. Activation and inactivation properties of voltage-gated channels determine the shape and time-course of the action potential.
4. Channel type and density can alter the action potential output of neurons.