Membrane Potentials and Action Potentials

Introduction

• if you place an electrode into a cell comparing inside to outside assuming the net charge outside of the cell is 0

  • proteins make cells more (-)

    • skew distribution of Na, K, Cl

    • to around -70mV

  • conductance is ability to move across the membrane

    • K most permeable

    • Na least perm

Do ions tend to move across membrane or just sit there?

• move if there is a net force

  • electrical

  • concentration

  • for sodium both electrical and concentration are inward

  • if Na wants to move it can move and will move

• potassium

  • Nernst potential equation

  • electrical force weak thus tends to diffuse out the cell

  • what about the driving force?

    • outward

How much do ions tend to move?

• Total Diffusion (Flux): The movement of ions across a membrane

  • The equation defined as:     J=(Permeability)×(Driving Force)

• Ion-Specific Flux Profiles:

  • Potassium (K+): Characterized by high permeability but a low driving force.

  • Sodium (Na+): Characterized by low permeability but a large driving force.

• The Sodium-Potassium Pump Mechanics:

  • The pump functions at a specific 3/2 ratio, transporting 3 sodium ions out of the cell for every 2 potassium ions transported back in.

  • The purpose of the pump is to compensate for those ions that previously spontaneously diffused across the cell membrane.

  • Net Flux Relationship: Based on the pump's activity, the net flux of sodium into the cell is 50% greater (150%) than the net flux of potassium out of the cell.

The Goldman Equation and Resting Membrane Potential

• Permeability and Potential: The most permeable ion possesses the ability to move most freely across the membrane. Consequently, any change in the membrane potential will first alter the net diffusion of the most permeable ion.

• The Governance Rule: The membrane potential ($E_m$) of a cell will always most closely resemble the Nernst Potential ($E_{ion}$) of the most permeable ion.

• The Goldman Equation: This equation is used to estimate the resting membrane potential by factoring in the Nernst potentials and the relative permeabilities of the three major ions (Sodium, Potassium, and Chloride).     $E_m = -61 \log \left( \frac{[Na^+]_{in} P_{Na^+} + [K^+]_{in} P_{K^+} + [Cl^-]_{out} P_{Cl^-}}{[Na^+]_{out} P_{Na^+} + [K^+]_{out} P_{K^+} + [Cl^-]_{in} P_{Cl^-}} \right)$

  • Applying this equation results in a calculated value of $-65\,mV$.

The Role of Electrogenicity and the Sodium-Potassium Pump

• Calculated vs. Measured Values: While the Goldman Equation yields a value of $-65\,mV$, the actual measured membrane potential is $-70\,mV$.

• The $5\,mV$ Difference: The discrepancy is attributed to the electrogenic nature of the sodium-potassium pump.

  • As a $3/2$ pump, for every $3$ positive charges pumped out (sodium), only $2$ positive charges are pumped in (potassium).

  • This resultantly removes a net positive charge from the interior of the cell, contributing an additional $-5\,mV$ of negativity to the resting potential.

• Chemical Inhibition (Ouabain): Adding ouabain to the extracellular fluid poisons the pump. This leads to an immediate $5\,mV$ depolarization, bringing the membrane potential to exactly $-65\,mV$, confirming the prediction of the Goldman Equation.

The most permeable influences membrane potential the most

• most permeable is K, and membrane potential is -70mV

  • close to Nernst for K at -94mV

  • sets stage to generate AP by altering permeability of Na and K through voltage gated selective channels

Ionic Principles of the Action Potential (all or none)

• action potential is basic unit of the nervous system

• resting membrane around -70mV and with neural input, neuron release neurotransmitters and produce small fluctuations, EPSPs and IPSPs (elaborated on later)

  • first rapid depolarization phase, the inside of the neuron becomes positive (overshoot)

  • followed by depolarization goes back to resting -70mV

  • followed by after hyper-polarization, neuron is more negative than rest

    • less likely to reach threshold (relative refractory period)

• Electrical Change Mechanics: Action potentials result from simple electrical changes involving positive charge entering the cell followed by positive charge leaving the cell.

• Permeability Alterations: To produce an action potential, the cell must alter the membrane permeabilities for sodium and potassium using voltage-gated channels.

  • Sodium (at rest): High driving force entering the neuron, but low permeability. $E_{Na} = +50\,mV$.

  • Potassium (at rest): Low driving force, but relatively high permeability. $E_K = -90\,mV$.

• Membrane Potential Shift: Because the membrane potential follows the Nernst Potential of the most permeable ion, opening voltage-gated channels shifts the potential toward the specific Nernst potential of the ion being permitted.

Anatomy and Physiology of Voltage-Gated Channels

• Channel Inventory:

  • Voltage-gated Sodium Channel: Features two "gates."

  • Voltage-gated Potassium Channel: Features one "gate."

  • Non-gated Potassium Channel: Remains open at all times.

  • when threshold reached both (Na and K) open

    • Na movement predominate - much larger driving force

    • and K channels open more slowly than Na

    • repolarize when Na permeability is at rest while K peaks

• Components of the Sodium Channel:

  • Selectivity Filter: Selectively allows sodium to enter. It utilizes specific negative charges in the protein to stabilize the sodium atom after it sheds most of its hydration sphere to enter the pore.

  • Tetrodotoxin (TTX): A toxin derived from puffer fish that binds to the selectivity filter and blocks the channel. Reversibly referred to by the phrase "Sushi kills!"

  • Voltage Sensor: A protein conformation that recognizes shifts in charge as the inside of the cell becomes less negative. Approximately $6$ positive charges must shift to open the gate.

  • Inactivation Gate: Located on the intracellular end of the channel. It is open at rest but closes shortly after the activation gate opens, typically at the peak of the action potential. This returns sodium conductance to zero.

    • Protease Inhibition: Intracellular injection of proteases like Pronase or Papain can destroy the inactivation gate.

    • Reset Requirement: The membrane potential must pass back below the threshold before the inactivation gate reopens.

  • Activation Gate: Located near the selectivity filter and remains closed until the threshold is reached.

• Absolute Refractory Period: The timeframe during which the inactivation gate is closed, preventing the initiation of another action potential.

• Components of the Potassium Channel:

  • there is only one gate either open or closed

  • charges in conductance pore arranged to stabilize potassium rather than sodium

Pharmacological agents that act on voltage gated channels:

Calcium: stabilize membrane and increase threshold

Tetrodotoxin: blocks Na channels from extracellular side

Local anesthetic: lidocaine, procaine etc insert into conductance pore and block Na permeability increases

Batrachtotoxin: from skin of poisonous frogs irreversibly opens Na channels

scorpion toxins: block K channel from opening

TEA: tetraethylammonium blocks voltage gated K channels only from the intracellular fluids side of the channel

Quantitative Dynamics and Neuroimaging Applications

• Ion Concentration Changes: In a typical sized cell body, only about $53\,million$ sodium atoms enter to depolarize the membrane from $-70\,mV$ to $+30\,mV$. This represents a mere $0.012\%$ increase in intracellular sodium concentration. Thus, sodium does not "flood" the cell, but rather "squirts" in.

• Gradient Restoration: By the end of the afterhyperpolarization phase, the neuron has gained some sodium and lost some potassium. The sodium-potassium pumps work to return these ions to their proper locations to prevent the collapse of gradients.

• Glucose Demand and PET Scanning: Increased action potential frequency leads to increased ion pumping, which in turn increases the demand for glucose. This metabolic relationship led to the use of the glucose analog $2\text{-deoxyglucose}$ and the development of Positron Emission Tomography (PET scanning) as a research and diagnostic tool in neuroscience.