Equilibrium Potentials and Neuronal Action Potentials

Chemical Gradients & Resting Membrane Potential

• Fundamental paradigm: Many physiological processes rely on ions moving down their chemical (concentration) gradients until electrical forces counterbalance them.
• Inside-outside charge separation
  • Interior of most excitable cells ≈ -70\;\text{to}\;-90\;\text{mV} (negative).
  • Exterior is correspondingly positive; overall body remains electrically neutral.
• Key ionic distributions
  • Sodium (Na⁺): high [Na⁺] outside, low inside → strong influx tendency.
  • Potassium (K⁺): high [K⁺] inside, low outside → strong efflux tendency.
• Types of membrane channels
  • Leakage channels (always open) for Na⁺ & K⁺.
  • Voltage-gated channels for Na⁺ & K⁺ (open/close with membrane voltage).
  • All channels render the membrane “selectively permeable.”

Equilibrium Potentials (E₍ion₎)

• Definition (two equivalent phrasings)
  • Voltage at which an ion’s electrical gradient exactly opposes its chemical gradient, halting net diffusion.
  • Point where the ion “ceases” to move down its concentration gradient because the membrane potential has reached a compensating value.
• Canonical values (at 37 °C, typical mammalian neuron)
  • Sodium: E_{\text{Na}} \approx +60\;\text{mV}.
  • Potassium: E_{\text{K}} \approx -90\;\text{mV}.
• Conceptual notes
  • These values arise from the Nernst equation E{\text{ion}} = \frac{RT}{zF}\ln!\left(\frac{[\text{ion}]{\text{out}}}{[\text{ion}]_{\text{in}}}\right) (not derived in video but implicit).
  • Anthropomorphic wording (ions “decide”) is purely pedagogical; ions have no agency.
  • Equilibrium potential is ion-specific; membrane potential will seldom equal either one exactly because multiple ions contribute simultaneously.

Depolarization vs. Repolarization: Idealized Scenario

• Depolarization
  • Na⁺ enters through open channels → interior becomes positive.
  • If channels remained open, depolarization would stop at +60\;\text{mV}: E_{\text{Na}}.
  • Physiological term “depolarize” actually means the polarity reverses (inside turns positive, outside less positive), arguably a misnomer.
• Repolarization / Hyperpolarization
  • K⁺ exits via its channels → interior loses positive charge.
  • Efflux continues until -90\;\text{mV} (≈ E_{\text{K}}), producing hyperpolarization below resting level.
  • Protein anions and phosphate groups inside cell also contribute to negativity.
• Graphical representation
  • Theoretical plot: rise to +60\;\text{mV} (Na⁺ stop), fall to -90\;\text{mV} (K⁺ stop).
  • Real neurons rarely trace this exact line because channel gating kinetics intervene.

Neuron Morphology & Functional Regions

• Cell body (soma)
  • Contains nucleus & organelles.
  • Receives incoming graded potentials across its membrane.
• Dendrites
  • Membranous extensions → ↑ surface area, analogous to microvilli.
• Axon
  • Long conducting fiber; transmits action potentials (AP) to terminals.
• Axon hillock
  • Junction where axon begins; crucial “decision point” for AP initiation.
• Axon terminals (synaptic boutons)
  • House synaptic vesicles loaded with neurotransmitter (NT): acetylcholine (ACh), dopamine, serotonin, norepinephrine, etc.

Graded Potentials vs. Action Potentials

• Graded potential (GP)
  • Local depolarization spreading over dendrites/soma.
  • Magnitude varies with stimulus strength; decays with distance.
• Threshold
  • At axon hillock must reach -55\;\text{mV}.
  • If V \ge -55\;\text{mV}, voltage-gated Na⁺ channels open in axon and an AP is launched.
• Action potential (AP) waveform (realistic)
  1. Resting potential: -70\;\text{mV}.
  2. GP to threshold: slow climb (pink slope) -70 \rightarrow -55.
  3. Rapid upstroke: Na⁺ influx until ≈ +30\;\text{mV} (peak limited by channel closure, not by E_{\text{Na}}).
  4. Repolarization: K⁺ efflux begins; K⁺ channels had opened at threshold but are slow, so they dominate after Na⁺ channels inactivate.
  5. Hyperpolarization (after-potential): membrane may dip toward -90\;\text{mV} because K⁺ channels close sluggishly.
  6. Return to rest: Na⁺ leakage (not Na⁺/K⁺ pump) drifts Vm back to -70\;\text{mV}.
• Channel kinetics mnemonic
  • Na⁺ gate: “flash-open, flash-close.”
  • K⁺ gate: “slow-motion door,” opens at threshold, closes late.

Ionic Contributors to Post-Hyperpolarization Recovery

• Not K⁺: Already at E_{\text{K}}; continued efflux would further hyperpolarize.
• Not Na⁺/K⁺-ATPase: Electrogenic but pumps 3 Na⁺ out / 2 K⁺ in → makes inside more negative.
• Yes: Na⁺ leakage channels
  • Always open; allow small Na⁺ trickle inward.
  • Adds positive charge, drifting Vm from -90 \rightarrow -70\;\text{mV}.

Neurotransmission & Downstream Effects

• Calcium-induced exocytosis
  • AP arriving at terminals opens voltage-gated Ca²⁺ channels → vesicles fuse with membrane → NT release.
• Synaptic cleft distance: nanometer scale; diffusion time negligible.
• Examples
  • ACh released onto heart myocardium → slows heart rate (parasympathetic effect).
  • Norepinephrine onto heart → increases heart rate (sympathetic).
  • ACh onto skeletal muscle endplate → depolarizes fiber → contraction.
• Neural chains
  • One neuron’s NT release generates GP in next neuron; cascade continues.
  • Upstream stimuli can be sensory (e.g., smell of grandmother’s perfume) initiating first neuron’s GP.

Contextual & Conceptual Connections

• Relation to pancreatic β-cells
  • Similar depolarization mechanism (retained K⁺ + incoming Na⁺/Ca²⁺) triggers insulin release; shows conserved principles across tissues.
• Real-world relevance
  • Understanding E₍ion₎ guides clinical use of ion channel drugs (antiarrhythmics, anticonvulsants).
  • Explains why electrolyte disturbances (hyperkalemia, hyponatremia) alter excitability.
• Philosophical/ethical note
  • Anthropomorphizing ions (“decide,” “prefer”) aids teaching but must not mislead; physical forces, not intent, govern movement.

Numerical / Formula Recap

• Resting Vm: -70 \text{ to } -90\;\text{mV}.
• Threshold (axon hillock): -55\;\text{mV}.
• E_{\text{Na}} = +60\;\text{mV} (driven by [Na⁺] gradient).
• E_{\text{K}} = -90\;\text{mV} (driven by [K⁺] gradient).
• Na⁺/K⁺-ATPase stoichiometry: 3\;\text{Na}^+{\text{out}} / 2\;\text{K}^+{\text{in}} per ATP.

Key Take-Home Points

• Equilibrium potentials define voltage limits of passive ion diffusion.
• In neurons, channel gating kinetics, not E₍Na₎/E₍K₎ values, shape the realistic AP waveform.
• The axon hillock’s threshold ensures all-or-none propagation down axon.
• Post-AP hyperpolarization resolves primarily through Na⁺ leak influx.
• Neurotransmitter release couples electrical signals to cell-specific physiological responses (heart rate modulation, muscle contraction, memory formation).