Molecular Biology - Free Graduate-Level Course

Introduction to Membrane Biophysics

Biological membranes are not passive barriers but dynamic structures equipped with sophisticated protein machinery that controls the flow of ions and molecules. Ion channels are membrane-spanning proteins that form selective pores, allowing specific ions to cross the lipid bilayer at rates approaching the diffusion limit (~10⁸ ions/second).

These channels are essential for numerous physiological processes: nerve impulse transmission, muscle contraction, hormone secretion, sensory transduction, cell volume regulation, and many others. Understanding their structure, function, and regulation requires integrating concepts from electrophysiology, structural biology, quantum mechanics, and computational modeling.

Key Features of Ion Channels

Ion Selectivity: Discriminate between similar ions (e.g., K⁺ vs. Na⁺) with ratios >1000:1
High Throughput: Conduct ~10⁶-10⁸ ions per second, near diffusion limit
Gating: Open and close in response to voltage, ligands, mechanical force, or temperature
Regulation: Modulated by phosphorylation, lipids, Ca²⁺, and other factors
Pharmacological Targets: Over 13% of approved drugs target ion channels
Disease Relevance: Channelopathies affect nerves, muscle, heart, kidney, and more

1. Membrane Potential & Electrochemical Gradients

The electrical potential difference across the plasma membrane, typically -40 to -90 mV (cytoplasm negative), arises from unequal ion distributions maintained by ATP-driven pumps and selective permeability of the membrane to different ions.

The Nernst Equation

For a membrane permeable to a single ion species, the equilibrium potential (Nernst potential) is given by:

$$E_{\text{ion}} = \frac{RT}{zF}\ln\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} = \frac{61.5\,\text{mV}}{z}\log_{10}\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}$$

R = gas constant, T = absolute temperature, z = ion valence, F = Faraday constant. At 25°C, RT/F ≈ 25.7 mV; at 37°C (body temperature), RT/F ≈ 26.7 mV.

Typical Ion Concentrations (mM)

K⁺ inside:~140

K⁺ outside:~5

Na⁺ inside:~12

Na⁺ outside:~145

Cl⁻ inside:~4

Cl⁻ outside:~110

Ca²⁺ inside:~10⁻⁴

Ca²⁺ outside:~2

Calculated Nernst Potentials (37°C)

E_K:-90 mV

E_Na:+65 mV

E_Cl:-80 mV

E_Ca:+130 mV

Typical V_m (resting):-70 mV

The Goldman-Hodgkin-Katz (GHK) Equation

When the membrane is permeable to multiple ion species, the membrane potential is determined by the weighted contributions of each ion according to their permeabilities:

$$V_m = \frac{RT}{F}\ln\frac{P_K[\text{K}^+]_o + P_{\text{Na}}[\text{Na}^+]_o + P_{\text{Cl}}[\text{Cl}^-]_i}{P_K[\text{K}^+]_i + P_{\text{Na}}[\text{Na}^+]_i + P_{\text{Cl}}[\text{Cl}^-]_o}$$

At rest, neurons are most permeable to K⁺ (P_K > P_Na, P_Cl), so V_m is close to E_K. During an action potential, P_Na increases dramatically, driving V_m toward E_Na.

Video Lecture Series: The Goldman-Hodgkin-Katz Equation

Part 1: Introduction & Derivation

Introduction to the GHK equation and its derivation from first principles.

Part 2: Multiple Ion Species

Extending the equation to account for multiple ion species and their permeabilities.

Part 3: Applications to Membrane Potential

Practical applications of the GHK equation to calculate resting membrane potentials.

Part 4: Worked Examples & Problem Solving

Step-by-step worked examples and problem-solving techniques using the GHK equation.

The Membrane Potential in Animal Cells Depends Mainly on K⁺ Leak Channels and the K⁺ Gradient

In most animal cells at rest, the plasma membrane is far more permeable to K⁺ than to other ions. This high K⁺ permeability is due to constitutively open K⁺ "leak" channels that are open even at rest, allowing K⁺ to flow down its concentration gradient.

K⁺ Leak Channels: Two-pore domain K⁺ channels (K_2P) and inward rectifier K⁺ channels (K_ir) provide background K⁺ conductance
K⁺ Gradient: [K⁺] inside (~140 mM) is much higher than outside (~5 mM), creating a strong driving force for K⁺ efflux
Resting Potential: K⁺ efflux through leak channels leaves excess negative charge inside, creating the negative resting potential (-70 mV)
Equilibrium Tendency: V_m approaches E_K (-90 mV) because P_Kdominates at rest, but small Na⁺ leak slightly depolarizes the membrane

Key Insight: The resting membrane potential is not simply a passive property but results from the active maintenance of ion gradients by the Na⁺/K⁺-ATPase pump combined with the selective permeability of the membrane to K⁺ through leak channels. This establishes the electrical excitability that underlies nerve and muscle function.

The Resting Potential Decays Only Slowly When the Na⁺-K⁺ Pump Is Stopped

The Na⁺-K⁺-ATPase pump continuously works to maintain the ion gradients that underlie the resting potential, hydrolyzing ATP to pump 3 Na⁺ out and 2 K⁺ in per cycle. What happens if this pump is inhibited?

Slow Decay: When the pump is stopped (e.g., by ouabain), the resting potential decays surprisingly slowly—over hours rather than seconds or minutes
Low Leak Rate: The lipid bilayer itself is highly impermeable to ions; leak channels conduct ions selectively and at limited rates
Large Ion Reservoirs: The cell contains large amounts of K⁺ (~140 mM); losing a small fraction through leak channels has minimal effect on concentration
Pump Contribution: The electrogenic pump (3:2 stoichiometry) contributes only ~5-10 mV directly to V_m; its main role is maintaining gradients

Experimental Evidence: Experiments using pump inhibitors show that excitable cells can continue firing action potentials for thousands of cycles even without the pump running, because each action potential involves only tiny changes in ion concentrations. However, without the pump, gradients eventually dissipate and excitability is lost.

🎥 Video Lectures: Membrane Potential

🎥 Armando Hasudungan: Resting Membrane Potential

Hand-drawn illustrated lecture explaining ion gradients, K⁺ leak channels, Nernst equation, Goldman equation, and the role of the Na⁺/K⁺-ATPase in establishing the resting potential

🎥 Armando Hasudungan: Membrane Transport

Illustrated overview of passive and active transport mechanisms, carrier proteins versus ion channels, and how different transport proteins maintain cellular ion homeostasis

Interactive Membrane Equivalent Circuit

The Hodgkin-Huxley equivalent circuit models the plasma membrane as a capacitor (C_m) in parallel with ion-selective conductances (g) and batteries representing Nernst potentials (E).

Na⁺ Conductance (gNa): 0.5 mS/cm²

Opens during depolarization

K⁺ Conductance (gK): 3.0 mS/cm²

Dominant at rest

Leak Conductance (gL): 0.3 mS/cm²

Always open (leak channels)

Show current flow

Calculated Values:

Membrane potential: -68.0 mV

Total conductance: 3.8 mS/cm²

Try This:

• Set gK high, gNa low → resting potential (~-70mV)
• Increase gNa → depolarization (action potential peak)
• High gK, low gNa → hyperpolarization

2. Classes of Ion Channels

Ion channels are classified based on their gating mechanisms—the stimuli that control channel opening and closing.

Voltage-Gated Channels

Open or close in response to changes in membrane potential. Critical for action potentials and electrical signaling in excitable cells.

Voltage-Gated Sodium Channels (Na_v): Rapid depolarization in action potentials
Voltage-Gated Potassium Channels (K_v): Repolarization and regulation of firing
Voltage-Gated Calcium Channels (Ca_v): Ca²⁺ influx for signaling and neurotransmitter release
Hyperpolarization-Activated Cyclic Nucleotide-Gated (HCN): Pacemaker activity

Voltage-Gated Ion Channel Architecture & Mechanism

Voltage-Gated Sodium Channels (Na_v1.1–1.9)

Na_v channels are the molecular engines of the action potential upstroke. The α-subunit (~260 kDa) forms a single polypeptide with four homologous domains (DI–DIV), each containing six transmembrane α-helices (S1–S6). This 4×6TM architecture creates a pseudo-tetrameric pore.

Voltage sensor (S4 helix): Each domain’s S4 segment contains 4–8 positively charged residues (Arg or Lys) at every third position, forming the voltage-sensing “paddle.” Depolarization drives S4 outward, moving ~12–13 elementary charges (e₀) across the membrane electric field — this “gating charge” is sufficient to account for the steep voltage dependence.
Selectivity filter (DEKA locus): The P-loops between S5 and S6 of each domain form the selectivity filter. The asymmetric Asp-Glu-Lys-Ala (DEKA) ring from domains I–IV creates a high-field-strength site that selects Na⁺ over K⁺ (~10–100:1) based on ionic radius and partial dehydration energy.
Activation gate (S6 bundle crossing): The intracellular ends of the four S6 helices converge to form the activation gate. In the closed state, hydrophobic residues occlude the pore. S4 movement mechanically pulls S6 helices apart via the S4–S5 linker, opening the gate in <1 ms.
Fast inactivation (IFM motif): The short intracellular loop connecting DIII and DIV contains the critical Ile-Phe-Met (IFM) motif that acts as a “hinged lid” — within 1–2 ms of channel opening, the IFM particle swings into the inner vestibule and occludes the pore from the cytoplasmic side.
Three-state gating model: Closed (resting) → Open (activated, ~0.5–1 ms) → Inactivated (refractory). Recovery from inactivation requires membrane repolarization and takes 5–30 ms, underlying the absolute and relative refractory periods.

Clinical Subtypes:

Na_v1.1 (SCN1A) — brain; mutations cause Dravet syndrome (severe epilepsy). Na_v1.5 (SCN5A) — cardiac; mutations cause Long QT syndrome type 3, Brugada syndrome. Na_v1.7 (SCN9A) — pain-sensing DRG neurons; gain-of-function → erythromelalgia; loss-of-function → congenital insensitivity to pain. Na_v1.8/1.9 — peripheral nociceptors; targets for next-gen analgesics.

Voltage-Gated Potassium Channels (K_v1–12)

K_v channels are the most diverse ion channel family (>40 genes in humans). Unlike Na_vchannels, K_v channels are true tetramers — four separate α-subunits assemble to form the functional channel, each contributing one 6TM domain to the pore.

Selectivity filter (TVGYG): The signature sequence Thr-Val-Gly-Tyr-Gly in the P-loop creates 4 K⁺ binding sites (S1–S4) where K⁺ ions are precisely coordinated by backbone carbonyl oxygens, replacing the hydration shell with near-perfect energetic compensation. This achieves >1000:1 selectivity for K⁺ over Na⁺.
Shaker family (K_v1.x): The founding members, discovered in Drosophila; rapid activation, prominent in axonal repolarization. K_v1.1–1.6 form heterotetramers with diverse kinetics.
N-type inactivation (“ball-and-chain”): The N-terminal “inactivation ball” (first ~20 amino acids) is tethered by a flexible linker; after channel opening, the ball swings into the inner pore vestibule and blocks ion flow within 5–50 ms. Can be removed by intracellular trypsin, confirming the physical model.
C-type (slow) inactivation: Conformational rearrangement of the selectivity filter itself over 100s of ms to seconds; the outer mouth of the pore constricts, preventing K⁺ flux even though the activation gate remains open.
Delayed rectifiers (K_v2, K_v3, K_v7): Slower activation kinetics provide sustained repolarization. K_v7.2/7.3 (KCNQ2/3) underlie the M-current; mutations cause benign familial neonatal seizures.

Voltage-Gated Calcium Channels (Ca_v1–3)

Ca_v channels share the 4×6TM architecture of Na_v channels but select for Ca²⁺ using an EEEE (or EEDD) glutamate ring in the selectivity filter. Ca²⁺ influx serves as both an electrical signal and a second messenger.

L-type (Ca_v1.1–1.4): Large, long-lasting currents. Ca_v1.1 in skeletal muscle (excitation-contraction coupling); Ca_v1.2 in cardiac muscle and smooth muscle (target of dihydropyridines: nifedipine, amlodipine); Ca_v1.3 in neurons (pacemaker activity in substantia nigra); Ca_v1.4 in retina.
N-type (Ca_v2.2): Neuronal; concentrated at presynaptic terminals; triggers neurotransmitter release at many peripheral and some central synapses. Blocked by ω-conotoxin GVIA (cone snail).
P/Q-type (Ca_v2.1): Predominant presynaptic Ca²⁺ channel at most central synapses; mutations cause familial hemiplegic migraine type 1 and episodic ataxia type 2. Blocked by ω-agatoxin IVA (spider).
T-type (Ca_v3.1–3.3): Low-voltage-activated (activate near −60 mV); small, transient currents. Generate rebound burst firing in thalamic relay neurons; pacemaker role in sinoatrial node; target of ethosuximide for absence seizures.
Auxiliary subunits: α₂δ (target of gabapentin/pregabalin for neuropathic pain), β subunits (trafficking and kinetics), γ subunits, and calmodulin (Ca²⁺-dependent inactivation/facilitation).

The Voltage-Sensing Mechanism: A Unified View

Decades of research have converged on a consensus model: the S4 helix moves through a “focused electric field” — a narrow (~5 Å) hydrophobic gasket formed by conserved residues in S1–S3 (including the “charge transfer center” with Phe233 and two acidic residues). The S4 arginine residues sequentially transfer through this gasket, each moving ~5–10 Å physically but traversing most of the membrane voltage drop. This explains how ~12–13 elementary charges can transfer with only modest physical displacement of the S4 helix. The resulting conformational change is transmitted to the pore domain via the S4–S5 linker, which acts as a mechanical lever to open the activation gate.

Ligand-Gated Channels (Ionotropic Receptors)

Open in response to binding of neurotransmitters or other ligands. Mediate fast synaptic transmission.

Nicotinic Acetylcholine Receptors (nAChR): Excitatory transmission at NMJ and CNS
GABA_A and Glycine Receptors: Inhibitory chloride channels
Glutamate Receptors (AMPA, NMDA, Kainate): Excitatory transmission, synaptic plasticity
Purinergic Receptors (P2X): ATP-gated cation channels

Mechanosensitive Channels

Activated by mechanical forces: membrane stretch, pressure, or touch.

Piezo Channels: Mechanosensation, proprioception, touch
TRP Channels (TRPV, TRPA, TRPM): Multimodal sensors (mechanical, thermal, chemical)
MscL/MscS (bacteria): Osmotic stress response

Other Channel Types

Temperature-Gated (TRP channels): Thermosensation (TRPV1 for heat, TRPM8 for cold)
Store-Operated Channels (Orai/CRAC): ER calcium store depletion
Two-Pore Domain K⁺ Channels (K_2P): Background leak conductance
Inward Rectifier K⁺ Channels (K_ir): Maintain resting potential
Calcium-Activated Channels: BK, SK, IK channels; chloride channels (TMEM16)

Detailed Ligand-Gated Ion Channel Pharmacology & Structure

Nicotinic Acetylcholine Receptors (nAChR)

The nAChR is the founding member and structural prototype of the Cys-loop superfamily of pentameric ligand-gated ion channels (pLGICs). The Torpedo (electric ray) nAChR provided the first high-resolution structure of any ion channel.

Pentameric structure: Five subunits arranged around a central ion pore. Muscle-type: (α1)₂β1δε (adult) or (α1)₂β1δγ (fetal). Each subunit has a large extracellular domain (ECD), 4 transmembrane helices (M1–M4), and an intracellular domain.
ACh binding sites: Two ACh molecules bind at α–δ and α–ε subunit interfaces in the ECD. The binding pocket is formed by loops A–C from the α-subunit (+) face and loops D–F from the complementary (−) face. A conserved “aromatic box” (Trp, Tyr residues) forms a cation–π interaction with the quaternary ammonium of ACh.
Ion pore (M2 helix): The five M2 helices line the pore. Rings of negatively charged residues at the extracellular and intracellular entrances attract cations. The gate is formed by hydrophobic leucine residues (9′ position) that rotate apart upon activation.
Desensitization: Prolonged agonist exposure drives the receptor into a high-affinity, closed “desensitized” state. Recovery requires agonist removal and takes seconds to minutes. Clinically relevant: succinylcholine (depolarizing neuromuscular blocker) causes initial fasciculation then flaccid paralysis via desensitization.
Neuronal subtypes: α4β2 (high-affinity nicotine binding, major brain subtype; target of varenicline for smoking cessation); α7 (homomeric, high Ca²⁺ permeability, rapid desensitization; roles in cognition and inflammation)

GABA_A Receptors

GABA_A receptors are the major inhibitory ligand-gated channels in the brain. They are pentameric Cl−-selective channels of the Cys-loop superfamily.

Subunit composition: 19 subunit genes (α1–6, β1–3, γ1–3, δ, ε, θ, π, ρ1–3). Most common synaptic receptor: α1β2γ2 (constitutes ~60% of brain GABA_ARs). Two GABA molecules bind at β–α interfaces.
Benzodiazepine binding: Benzodiazepines (diazepam, midazolam) bind at the α–γ interface — a site distinct from the GABA binding site. They are positive allosteric modulators: they increase GABA affinity and channel open frequency without activating the channel alone. α1-containing receptors mediate sedation; α2/α3 mediate anxiolysis.
Barbiturate binding: Barbiturates bind within the M2–M3 transmembrane region. At low doses, they increase channel open duration (positive allosteric modulation); at high doses, they can directly activate the channel without GABA (hence overdose risk).
Neurosteroid modulation: Endogenous neurosteroids (allopregnanolone, THDOC) are potent positive allosteric modulators binding at transmembrane α–β and α–γ interfaces. Brexanolone (allopregnanolone) is FDA-approved for postpartum depression.
Ethanol, anesthetics, Zn²⁺: Ethanol enhances GABA_A function at δ-containing extrasynaptic receptors. Propofol and isoflurane potentiate at transmembrane sites. Zn²⁺ is an endogenous negative modulator.

AMPA Receptors (GluA1–4)

Tetrameric structure: iGluRs are tetramers (dimer of dimers) with a distinct architecture from Cys-loop receptors. Each subunit has an amino-terminal domain (ATD), ligand-binding domain (LBD, “clamshell”), 3 transmembrane helices (M1, M3, M4) + 1 re-entrant loop (M2), and an intracellular C-terminal domain.
Fast synaptic transmission: AMPARs mediate the fast component of excitatory postsynaptic currents (EPSCs). Rise time ~0.5 ms; decay ~5–10 ms. Permeant to Na⁺/K⁺ (E_rev ≈ 0 mV).
Q/R editing: GluA2 undergoes RNA editing at the Q/R site (Gln → Arg in M2 pore loop) by ADAR2 enzyme. Edited GluA2 makes the channel Ca²⁺-impermeable and linear (no polyamine block). Most adult AMPARs contain GluA2 → Ca²⁺-impermeable.
TARPs (γ-2/stargazin): Transmembrane AMPAR regulatory proteins are obligate auxiliary subunits that control trafficking, surface expression, pharmacology, and gating kinetics of AMPARs.

NMDA Receptors (GluN1/GluN2A–D)

Obligate heterotetramers: Functional NMDARs require 2 GluN1 subunits (bind glycine/D-serine) + 2 GluN2 subunits (bind glutamate). GluN2 subtype determines channel kinetics, Mg²⁺ sensitivity, and synaptic localization.
Mg²⁺ block (voltage dependence): At resting potential (−70 mV), extracellular Mg²⁺ (~1 mM) physically plugs the open channel pore at the M2 re-entrant loop. Depolarization to −40 mV or above electrostatically repels Mg²⁺, relieving the block. This makes the NMDAR a molecular AND gate: requires both glutamate binding AND postsynaptic depolarization.
High Ca²⁺ permeability: P_Ca/P_Na ≈ 10:1; the Ca²⁺ influx activates CaMKII, calcineurin, and other signaling cascades essential for synaptic plasticity.
Coincidence detection for LTP: Presynaptic glutamate release (binds GluN2) + postsynaptic depolarization (relieves Mg²⁺ block) → Ca²⁺ influx → CaMKII autophosphorylation → AMPAR insertion → long-term potentiation.
Excitotoxicity: Excessive NMDA receptor activation (stroke, traumatic brain injury) leads to lethal Ca²⁺ overload, activating calpains, mitochondrial permeability transition, and apoptotic/necrotic pathways.

Kainate Receptors (GluK1–5)

Tetrameric: GluK1–3 can form homomers or heteromers; GluK4–5 require GluK1–3 for functional expression
Roles in both pre- and postsynaptic modulation; presynaptic kainate receptors regulate glutamate and GABA release
Prominent at mossy fiber → CA3 synapses in hippocampus; involved in seizure susceptibility
Unique feature: some kainate receptors activate metabotropic signaling pathways (G-protein coupled) in addition to ionotropic function

5-HT₃ Receptor

Cys-loop superfamily pentamer; the only ionotropic serotonin receptor
Cation-selective (Na⁺/K⁺); homomeric 5-HT_3A or heteromeric
Expressed in brainstem (area postrema), peripheral sensory neurons, enteric nervous system
Target of ondansetron (Zofran) for chemotherapy-induced nausea

Glycine Receptor (GlyR)

Cys-loop pentamer; Cl−-selective (inhibitory)
Primary inhibitory receptor in spinal cord and brainstem
Mutations cause hyperekplexia (startle disease)
Strychnine is a competitive antagonist (lethal convulsant)

P2X Receptors (Trimeric)

Structurally distinct: trimeric with 2 TM helices per subunit
Activated by extracellular ATP; 7 subtypes (P2X1–7)
P2X3: nociception; P2X4: microglial activation; P2X7: inflammasome/IL-1β

Key Structural Comparison

The three LGIC superfamilies represent convergent evolution: Cys-loop receptors are pentameric with 4 TM helices per subunit (20 TM total); iGluRs are tetrameric with 3 TM helices + 1 re-entrant loop per subunit; P2X receptors are trimeric with 2 TM helices per subunit (6 TM total). Despite these differences, all three families use similar gating principles: agonist binding in the extracellular domain propagates conformational changes to the transmembrane gate.

🎥 Video Lectures: Ion Channel Structure & Function

🎥 Ninja Nerd: Cell Membrane Structure & Function

Comprehensive 46-minute lecture covering phospholipid bilayer, integral & peripheral proteins, ion channel proteins, carriers, and the molecular basis of selective membrane permeability

🎥 Armando Hasudungan: The Neuron

Illustrated lecture on neuron structure and function: soma, axon, dendrites, axon terminal, Na⁺ channels, and the functional classification of sensory, motor, and interneurons

3. Ion Selectivity Mechanisms

The remarkable ability of ion channels to discriminate between chemically similar ions (e.g., K⁺ vs. Na⁺) with selectivity ratios exceeding 1000:1 while maintaining near-diffusion-limited throughput is one of the most elegant solutions in molecular biology.

Ion Channels Are Ion-Selective and Fluctuate Between Open and Closed States

Ion channels exhibit two fundamental properties that define their function: ion selectivity and gating. Unlike simple pores, ion channels actively discriminate between different ion species and transition stochastically between open (conducting) and closed (nonconducting) conformational states.

Gating Behavior: Individual ion channels do not remain permanently open; they fluctuate rapidly between open and closed states. The fraction of time a channel spends in the open state (open probability, P_o) determines the overall conductance and is regulated by voltage, ligands, mechanical forces, or other stimuli.

Selectivity vs. Throughput: Ion channels must balance two seemingly contradictory requirements: high selectivity (discriminating ions that differ in radius by <0.5 Å) and high throughput (conducting ~10⁷-10⁸ ions/second). This is achieved through precisely shaped selectivity filters that stabilize specific ions while allowing rapid conduction.

Molecular Recognition: The selectivity filter acts as a molecular sieve, using backbone carbonyl oxygens, charged side chains, or structured water molecules to create binding sites complementary in size and charge distribution to the permeant ion species.

The Three-Dimensional Structure of a Bacterial K⁺ Channel Shows How an Ion Channel Can Work

The 2003 Nobel Prize-winning work of Roderick MacKinnon and colleagues revealed the atomic structure of the bacterial K⁺ channel KcsA—a landmark achievement that provided the first detailed view of how ion channels achieve their remarkable selectivity and conductance properties.

Structural Features of the K⁺ Channel

Tetrameric Architecture: Four identical subunits symmetrically arranged around central pore
Transmembrane Helices: Each subunit contributes two α-helices (inner and outer) spanning the membrane
Pore Helix & Selectivity Filter: Between transmembrane helices, a pore helix and extended chain form the narrow selectivity filter
Water-Filled Cavity: A large central cavity (~10Å diameter) allows hydrated K⁺ ions to approach the selectivity filter from the intracellular side
Narrow Selectivity Filter: The 12Å-long filter region contains four K⁺ binding sites (S1-S4) formed by backbone carbonyl oxygens of the signature TVGYG sequence

The crystal structure revealed that the selectivity filter is lined by backbone carbonyl oxygens from the TVGYG motif, which precisely coordinate dehydrated K⁺ ions. This structure explained how the channel achieves exquisite selectivity: the carbonyl oxygens are positioned to exactly mimic the hydration shell of K⁺, but the cavity is too large to stabilize the smaller Na⁺ ion efficiently.

Filter Sequence: Highly conserved TVGYG motif forms the selectivity filter
Binding Sites: 4 binding sites (S1-S4) within the 12Å filter region
Coordination Geometry: 8 carbonyl oxygens coordinate each K⁺ ion
Snug Fit Hypothesis: Filter cavity optimized for K⁺ radius (1.33Å) vs. Na⁺ (0.95Å)
Knock-On Mechanism: K⁺ ions move in single file; incoming ion pushes outgoing ion

Energetic Balance: The dehydration cost for K⁺ (~75 kcal/mol) is exactly compensated by coordination with filter carbonyls. For Na⁺, the larger dehydration cost cannot be fully compensated, creating a ~3 kcal/mol barrier that explains >10,000:1 selectivity.

Sodium Channel Selectivity

Na_v channels face the opposite challenge: selecting Na⁺ (0.95Å) over K⁺ (1.33Å). The DEKA motif forms a narrower selectivity filter.

DEKA Locus: Aspartate, Glutamate, Lysine, Alanine residues from four domains
Smaller Pore: ~3-4Å diameter vs. ~12Å for K⁺ channels
Partial Hydration: Na⁺ retains partial hydration shell while passing through
Selectivity: ~10-100:1 for Na⁺ over K⁺

Calcium Channel Selectivity

Ca_v channels must select Ca²⁺ (1.00Å) over Na⁺ (0.95Å) and K⁺ (1.33Å) despite 1000-fold higher concentrations of monovalent ions.

EEEE/EEDD Locus: Ring of negatively charged glutamate residues
High-Field-Strength Site: Concentrated negative charge attracts divalent cations
Ion-Ion Repulsion: Two Ca²⁺ ions in filter; electrostatic repulsion speeds permeation
Selectivity: >1000:1 for Ca²⁺ over monovalent cations

4. Quantum Mechanical Aspects of Ion Permeation

While ion channel function is primarily understood through classical electrostatics and molecular dynamics, quantum mechanical effects contribute to selectivity, binding energetics, and potentially the dynamics of ion permeation.

Quantum Contributions to Selectivity

Electronic Structure: Ion-protein interactions involve charge transfer and polarization
Zero-Point Energy: Lighter ions (especially protons) have larger quantum fluctuations
Tunneling: Protons can tunnel through barriers in H₂O wires (water channels)
Basis Set Superposition Error: Accurate binding energies require quantum chemical corrections
Dispersion Interactions: van der Waals forces important for selectivity (DFT-D methods)

QM/MM Simulations of Ion Channels

Hybrid quantum mechanics/molecular mechanics (QM/MM) approaches treat the selectivity filter quantum mechanically while using classical force fields for the protein and solvent environment.

QM Region: Selectivity filter carbonyl oxygens, coordinating water, permeating ions
MM Region: Protein backbone, lipid bilayer, bulk solvent
Methods: DFT (B3LYP, PBE), post-Hartree-Fock (MP2, CCSD)
Insights: Polarization effects, charge transfer, accurate binding free energies
Challenges: Computational cost limits system size and sampling time

Proton Channels & Water Wires

Proton channels (aquaporins, M2 channel, bacterial porins) exhibit distinctive quantum behavior due to proton tunneling and delocalization in hydrogen-bonded networks.

Grotthuss Mechanism: Proton hopping via H₃O⁺ and H-bond rearrangements
Proton Tunneling: Quantum tunneling between adjacent water molecules
Nuclear Quantum Effects: Path integral molecular dynamics (PIMD) reveals delocalization
Kinetic Isotope Effects: H⁺ vs. D⁺ permeation rates differ due to tunneling

5. The Action Potential

The action potential is a rapid, transient reversal of membrane potential that propagates along axons and excitable membranes. It is the fundamental unit of electrical signaling in the nervous system.

The Function of a Nerve Cell Depends on Its Elongated Structure

Neurons are among the most structurally polarized cells in the body, with highly specialized compartments that enable long-distance electrical signaling. The elongated morphology of neurons is intimately linked to their function in transmitting information rapidly over long distances.

Cell Body (Soma)

Contains nucleus and most biosynthetic machinery. Integrates incoming synaptic signals from dendrites.

Dendrites

Highly branched input region. Covered with thousands of synapses receiving signals from other neurons.

Axon Hillock

Site of action potential initiation. High density of voltage-gated Na⁺ channels creates lowest threshold for firing.

Axon

Single long process (up to 1 meter in humans) conducting action potentials. Uniform diameter, few branches until terminal.

Directional Signal Flow: Information flows from dendrites → soma → axon hillock → axon → synaptic terminals
Axonal Transport: Molecular motors transport proteins, organelles, and neurotransmitters along microtubules
Length Scales: Dendrites: tens of micrometers; Axons: millimeters to meters; Total distance: up to 1000× cell body diameter
Speed Requirements: To rapidly transmit signals over long distances, neurons evolved action potentials and myelination

Voltage-Gated Cation Channels Generate Action Potentials in Electrically Excitable Cells

The action potential is made possible by voltage-gated Na⁺ and K⁺ channels that open and close in response to changes in membrane potential, creating a regenerative, self-propagating electrical signal.

Voltage-Gated Sodium Channels (Na_v)

Activation Gate (m-gate): Opens rapidly (~1 ms) when membrane depolarizes past threshold (~-55 mV)
Inactivation Gate (h-gate): Closes more slowly (~1-2 ms) after activation, terminating Na⁺ influx
Three States: Closed (resting), Open (activated), Inactivated (refractory)
Recovery: Must repolarize to negative potentials to remove inactivation and return to closed state
Absolute Refractory Period: During inactivation, no stimulus can trigger another action potential

Voltage-Gated Potassium Channels (K_v)

Delayed Activation: Opens more slowly than Na⁺ channels (~2-5 ms after depolarization)
Sustained Opening: Remains open during depolarization, no fast inactivation
Repolarization Role: K⁺ efflux brings membrane back to negative potentials
Relative Refractory Period: Hyperpolarization after action potential requires stronger stimulus

The coordinated opening and closing of these voltage-gated channels creates the stereotyped waveform of the action potential: rapid depolarization (Na⁺ influx), brief reversal to positive potentials, rapid repolarization (K⁺ efflux), and hyperpolarization before return to rest.

Phases of the Action Potential

1. Resting Potential (-70 mV):

High K⁺ permeability (leak channels), Na⁺/K⁺-ATPase maintains gradients.

2. Depolarization (threshold → +40 mV):

Voltage-gated Na⁺ channels open, Na⁺ influx rapidly depolarizes membrane.

3. Repolarization (+40 → -70 mV):

Na⁺ channels inactivate, voltage-gated K⁺ channels open, K⁺ efflux repolarizes.

4. Hyperpolarization (undershoot):

K⁺ channels slow to close, membrane briefly more negative than resting.

5. Return to Resting:

Leak channels and Na⁺/K⁺-ATPase restore resting potential.

Hodgkin-Huxley Model

The 1952 Hodgkin-Huxley model (Nobel Prize 1963) mathematically describes action potential propagation using voltage-dependent conductances:

$$C_m\frac{dV}{dt} = -\bar{g}_{\text{Na}}m^3h(V-E_{\text{Na}}) - \bar{g}_K n^4(V-E_K) - g_L(V-E_L) + I_{\text{ext}}$$

m = Na⁺ activation gate, h = Na⁺ inactivation gate, n = K⁺ activation gate. Each gate follows first-order kinetics with voltage-dependent rate constants.

Predicts threshold behavior, all-or-none responses, refractory periods
Explains propagation velocity (1-100 m/s depending on axon diameter and myelination)
Foundation for modern computational neuroscience

Interactive Simulation: Hodgkin-Huxley Action Potential

Run the full Hodgkin-Huxley model below. A 10 µA/cm² current pulse (1–2 ms) triggers a single action potential. The 4-panel plot shows membrane voltage, gating variable dynamics (m, h, n), ionic currents (I_Na, I_K, I_L), and conductance changes over time. Try modifying the stimulus parameters or conductance values!

Python

hh_action_potential.py122 lines

#!/usr/bin/env python3
"""
Hodgkin-Huxley Action Potential Simulation
==========================================
Full HH model with Na+, K+, and leak channels.
A brief current pulse triggers a single action potential.
"""
import numpy as np
import matplotlib.pyplot as plt

# --- HH parameters ---
Cm = 1.0        # membrane capacitance (uF/cm^2)
gNa_max = 120.0 # max Na+ conductance (mS/cm^2)
gK_max = 36.0   # max K+ conductance (mS/cm^2)
gL = 0.3        # leak conductance (mS/cm^2)
ENa = 50.0      # Na+ reversal potential (mV)
EK = -77.0      # K+ reversal potential (mV)
EL = -54.4      # leak reversal potential (mV)

# --- Rate functions (V in mV) ---
def alpha_m(V): return 0.1 * (V + 40) / (1 - np.exp(-(V + 40) / 10))
def beta_m(V):  return 4.0 * np.exp(-(V + 65) / 18)
def alpha_h(V): return 0.07 * np.exp(-(V + 65) / 20)
def beta_h(V):  return 1.0 / (1 + np.exp(-(V + 35) / 10))
def alpha_n(V): return 0.01 * (V + 55) / (1 - np.exp(-(V + 55) / 10))
def beta_n(V):  return 0.125 * np.exp(-(V + 65) / 80)

# --- Simulation setup ---
dt = 0.01       # time step (ms)
T = 20.0        # total time (ms)
t = np.arange(0, T, dt)
N = len(t)

# External current: 10 uA/cm^2 pulse from t=1 to t=2 ms
I_ext = np.zeros(N)
I_ext[(t >= 1.0) & (t <= 2.0)] = 10.0

# Initial conditions (resting state at V = -65 mV)
V0 = -65.0
V = np.zeros(N); V[0] = V0
m = np.zeros(N); m[0] = alpha_m(V0) / (alpha_m(V0) + beta_m(V0))
h = np.zeros(N); h[0] = alpha_h(V0) / (alpha_h(V0) + beta_h(V0))
n = np.zeros(N); n[0] = alpha_n(V0) / (alpha_n(V0) + beta_n(V0))

# --- Forward Euler integration ---
for i in range(N - 1):
    gNa = gNa_max * m[i]**3 * h[i]
    gK = gK_max * n[i]**4
    INa = gNa * (V[i] - ENa)
    IK = gK * (V[i] - EK)
    IL = gL * (V[i] - EL)

dVdt = (I_ext[i] - INa - IK - IL) / Cm
    V[i+1] = V[i] + dVdt * dt
    m[i+1] = m[i] + (alpha_m(V[i]) * (1 - m[i]) - beta_m(V[i]) * m[i]) * dt
    h[i+1] = h[i] + (alpha_h(V[i]) * (1 - h[i]) - beta_h(V[i]) * h[i]) * dt
    n[i+1] = n[i] + (alpha_n(V[i]) * (1 - n[i]) - beta_n(V[i]) * n[i]) * dt

# Compute full conductance and current arrays for plotting
gNa_t = gNa_max * m**3 * h
gK_t = gK_max * n**4
INa_t = gNa_t * (V - ENa)
IK_t = gK_t * (V - EK)
IL_t = gL * (V - EL)

# --- Plotting (dark theme, 2x2) ---
fig, axes = plt.subplots(2, 2, figsize=(13, 9))
fig.patch.set_facecolor('#0f172a')
fig.suptitle('Hodgkin-Huxley Action Potential', color='white', fontsize=14, fontweight='bold', y=0.97)

for ax in axes.flat:
    ax.set_facecolor('#1e293b')
    ax.tick_params(colors='#cbd5e1', labelsize=9)
    for spine in ax.spines.values():
        spine.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.4, linewidth=0.5)

axes[0,0].plot(t, V, color='#06b6d4', linewidth=1.5)
axes[0,0].set_title('Membrane Potential', color='white', fontsize=11)
axes[0,0].set_xlabel('Time (ms)', color='#94a3b8', fontsize=10)
axes[0,0].set_ylabel('V (mV)', color='#94a3b8', fontsize=10)

axes[0,1].plot(t, m, color='#ef4444', linewidth=1.3, label='m (Na act.)')
axes[0,1].plot(t, h, color='#3b82f6', linewidth=1.3, label='h (Na inact.)')
axes[0,1].plot(t, n, color='#22c55e', linewidth=1.3, label='n (K act.)')
axes[0,1].set_title('Gating Variables', color='white', fontsize=11)
axes[0,1].set_xlabel('Time (ms)', color='#94a3b8', fontsize=10)
axes[0,1].set_ylabel('Probability', color='#94a3b8', fontsize=10)
axes[0,1].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white', loc='center right')

axes[1,0].plot(t, INa_t, color='#ef4444', linewidth=1.3, label='I_Na')
axes[1,0].plot(t, IK_t, color='#22c55e', linewidth=1.3, label='I_K')
axes[1,0].plot(t, IL_t, color='#a855f7', linewidth=1.3, label='I_L')
axes[1,0].set_title('Ionic Currents', color='white', fontsize=11)
axes[1,0].set_xlabel('Time (ms)', color='#94a3b8', fontsize=10)
axes[1,0].set_ylabel('Current (uA/cm^2)', color='#94a3b8', fontsize=10)
axes[1,0].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

axes[1,1].plot(t, gNa_t, color='#ef4444', linewidth=1.3, label='gNa = gNa_max * m^3 * h')
axes[1,1].plot(t, gK_t, color='#22c55e', linewidth=1.3, label='gK = gK_max * n^4')
axes[1,1].set_title('Conductances', color='white', fontsize=11)
axes[1,1].set_xlabel('Time (ms)', color='#94a3b8', fontsize=10)
axes[1,1].set_ylabel('g (mS/cm^2)', color='#94a3b8', fontsize=10)
axes[1,1].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

plt.tight_layout(rect=[0, 0, 1, 0.94])
plt.savefig('hh_action_potential.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())

peak_V = np.max(V)
rest_V = V[0]
peak_gNa = np.max(gNa_t)
peak_gK = np.max(gK_t)
print("=" * 55)
print("Hodgkin-Huxley Action Potential Simulation")
print("=" * 55)
print(f"  Resting potential:   {rest_V:.1f} mV")
print(f"  Peak depolarization: {peak_V:.1f} mV")
print(f"  AP amplitude:        {peak_V - rest_V:.1f} mV")
print(f"  Peak gNa:            {peak_gNa:.1f} mS/cm^2")
print(f"  Peak gK:             {peak_gK:.1f} mS/cm^2")
print(f"  Stimulus: 10 uA/cm^2 for 1 ms (t = 1-2 ms)")
print(f"  Time step: {dt} ms, Total: {T} ms")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Interactive Visualization: Gating Kinetics

Explore how steady-state activation/inactivation curves, time constants, and window conductances vary with membrane potential. The Na⁺ “window current” region (where m_∞³·h_∞ > 0) plays a critical role in threshold behavior and pacemaker activity.

Python

gating_kinetics.py90 lines

#!/usr/bin/env python3
"""
Ion Channel Gating Kinetics
============================
Voltage-dependent steady-state activation/inactivation, time constants,
and window currents for Hodgkin-Huxley Na+ and K+ channels.
"""
import numpy as np
import matplotlib.pyplot as plt

# --- HH rate functions (V in mV) ---
def alpha_m(V): return 0.1 * (V + 40) / (1 - np.exp(-(V + 40) / 10))
def beta_m(V):  return 4.0 * np.exp(-(V + 65) / 18)
def alpha_h(V): return 0.07 * np.exp(-(V + 65) / 20)
def beta_h(V):  return 1.0 / (1 + np.exp(-(V + 35) / 10))
def alpha_n(V): return 0.01 * (V + 55) / (1 - np.exp(-(V + 55) / 10))
def beta_n(V):  return 0.125 * np.exp(-(V + 65) / 80)

def x_inf(alpha, beta): return alpha / (alpha + beta)
def tau_x(alpha, beta): return 1.0 / (alpha + beta)

V = np.linspace(-100, 60, 500)

m_inf = x_inf(alpha_m(V), beta_m(V))
h_inf = x_inf(alpha_h(V), beta_h(V))
n_inf = x_inf(alpha_n(V), beta_n(V))
tau_m = tau_x(alpha_m(V), beta_m(V))
tau_h = tau_x(alpha_h(V), beta_h(V))
tau_n = tau_x(alpha_n(V), beta_n(V))

gNa_max, gK_max = 120.0, 36.0
na_window = gNa_max * m_inf**3 * h_inf
k_window = gK_max * n_inf**4

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
fig.patch.set_facecolor('#0f172a')
fig.suptitle('Ion Channel Gating Kinetics (Hodgkin-Huxley)', color='white',
             fontsize=13, fontweight='bold', y=1.0)

for ax in axes:
    ax.set_facecolor('#1e293b')
    ax.tick_params(colors='#cbd5e1', labelsize=9)
    for spine in ax.spines.values():
        spine.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.4, linewidth=0.5)
    ax.set_xlabel('Membrane Potential (mV)', color='#94a3b8', fontsize=10)

axes[0].plot(V, m_inf, color='#ef4444', linewidth=2, label='m_inf (Na+ act.)')
axes[0].plot(V, h_inf, color='#3b82f6', linewidth=2, label='h_inf (Na+ inact.)')
axes[0].plot(V, n_inf, color='#22c55e', linewidth=2, label='n_inf (K+ act.)')
axes[0].plot(V, m_inf**3 * h_inf, color='#f59e0b', linewidth=1.5, linestyle='--',
             label='m_inf^3 * h_inf')
axes[0].set_ylabel('Probability', color='#94a3b8', fontsize=10)
axes[0].set_title('Steady-State Activation / Inactivation', color='white', fontsize=11)
axes[0].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white',
               loc='center right')
axes[0].set_ylim(-0.02, 1.05)

axes[1].plot(V, tau_m, color='#ef4444', linewidth=2, label='tau_m')
axes[1].plot(V, tau_h, color='#3b82f6', linewidth=2, label='tau_h')
axes[1].plot(V, tau_n, color='#22c55e', linewidth=2, label='tau_n')
axes[1].set_ylabel('Time Constant (ms)', color='#94a3b8', fontsize=10)
axes[1].set_title('Gating Time Constants', color='white', fontsize=11)
axes[1].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')
axes[1].set_ylim(bottom=0)

axes[2].fill_between(V, 0, na_window, color='#ef4444', alpha=0.25)
axes[2].plot(V, na_window, color='#ef4444', linewidth=2, label='Na+ window')
axes[2].fill_between(V, 0, k_window, color='#22c55e', alpha=0.15)
axes[2].plot(V, k_window, color='#22c55e', linewidth=2, label='K+ steady-state')
axes[2].set_ylabel('Conductance (mS/cm^2)', color='#94a3b8', fontsize=10)
axes[2].set_title('Window / Steady-State Conductance', color='white', fontsize=11)
axes[2].legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

plt.tight_layout()
plt.savefig('gating_kinetics.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())

V_half_m = V[np.argmin(np.abs(m_inf - 0.5))]
V_half_h = V[np.argmin(np.abs(h_inf - 0.5))]
V_half_n = V[np.argmin(np.abs(n_inf - 0.5))]
print("=" * 55)
print("Ion Channel Gating Kinetics Summary")
print("=" * 55)
print(f"  Half-activation V_1/2(m):   {V_half_m:.1f} mV")
print(f"  Half-inactivation V_1/2(h): {V_half_h:.1f} mV")
print(f"  Half-activation V_1/2(n):   {V_half_n:.1f} mV")
print(f"  Peak tau_m: {np.max(tau_m):.3f} ms at V = {V[np.argmax(tau_m)]:.1f} mV")
print(f"  Peak tau_h: {np.max(tau_h):.2f} ms at V = {V[np.argmax(tau_h)]:.1f} mV")
print(f"  Peak tau_n: {np.max(tau_n):.2f} ms at V = {V[np.argmax(tau_n)]:.1f} mV")
print(f"  Na+ window peak: {np.max(na_window):.2f} mS/cm^2 at {V[np.argmax(na_window)]:.1f} mV")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Cable Theory & Propagation

Action potential propagation along axons is described by cable equation:

$$\lambda^2\frac{\partial^2 V}{\partial x^2} = \tau\frac{\partial V}{\partial t} + V$$

λ = length constant (space clamp), τ = time constant. Myelination increases λ by insulating axon, allowing saltatory conduction between nodes of Ranvier.

🎥 Video Lectures: Action Potentials & Hodgkin-Huxley Model

🎥 MIT 9.40: Hodgkin-Huxley Model I

MIT OCW — Introduction to Neural Computation (Spring 2018) — Voltage clamp technique, K⁺ current analysis, and the quantitative description of voltage-gated conductances

🎥 MIT 9.40: Hodgkin-Huxley Model II

MIT OCW — Introduction to Neural Computation (Spring 2018) — Na⁺/K⁺ conductance dynamics, inactivation gating, and the complete action potential model

🎥 Alila Medical Media: Action Potential in Neurons

Beautifully animated walkthrough of resting potential, threshold, Na⁺ channel activation/inactivation, K⁺ channel delayed rectification, and the full action potential cycle

🎥 CrashCourse: Action! Potential!

CrashCourse Anatomy & Physiology — Engaging overview of Na⁺/K⁺ pump, resting potential, threshold, depolarization, repolarization, and how AP frequency encodes stimulus intensity

Interactive Axon Cable Model

The cable model represents an axon as a series of RC circuits. Current injected at one point spreads passively along the axon, decaying with distance (length constant λ) and time (time constant τ).

Membrane Resistance (r_m): 10 kΩ·cm²

Higher r_m → longer λ (signal travels farther)

Axial Resistance (r_i): 100 Ω·cm

Lower r_i → longer λ (wider axons conduct better)

Membrane Capacitance (c_m): 1 µF/cm²

Lower c_m → faster τ (quicker response)

Injection Point: x = 0

Myelinated:

Cable Parameters:

λ (length constant) = 0.32 cm

τ (time constant) = 10.00 ms

λ = √(r_m/r_i), τ = r_m × c_m

Cable Equation

$$\lambda^2 \frac{\partial^2 V}{\partial x^2} - \tau_m \frac{\partial V}{\partial t} = V$$

Steady-State Solution

$$V(x) = V_0 \, e^{-|x|/\lambda}$$

Myelination Increases the Speed and Efficiency of Action Potential Propagation in Nerve Cells

In vertebrates, many axons are wrapped in myelin, a lipid-rich insulating sheath produced by glial cells (oligodendrocytes in CNS, Schwann cells in PNS). Myelination dramatically increases conduction velocity while reducing energy costs.

Structural Features

Multiple wraps (up to 100 layers) of glial membrane
Myelin sheaths 1-2 mm long separated by ~1 μm gaps
Nodes of Ranvier: unmyelinated gaps with high Na_v density
Paranodal junctions: seal between myelin and axon

Functional Benefits

Increased membrane resistance (R_m)
Decreased membrane capacitance (C_m)
Increased length constant λ (~100× increase)
Decreased time constant τ (faster passive spread)

Saltatory Conduction: Action potentials "jump" from node to node rather than propagating continuously, increasing speed from ~1 m/s (unmyelinated) to >100 m/s (myelinated)
Energy Efficiency: Fewer Na⁺ and K⁺ ions cross membrane (only at nodes), reducing ATP consumption by Na⁺/K⁺-ATPase by ~100-fold
Space Efficiency: Myelinated axons conduct faster than unmyelinated axons of same diameter; achieving same speed without myelin would require ~100× larger diameter
Disease Relevance: Demyelinating diseases (Multiple Sclerosis, Guillain-Barré syndrome) cause severe neurological deficits due to slowed/blocked conduction

6. Patch-Clamp Electrophysiology

Patch-clamp recording, developed by Neher and Sakmann (Nobel Prize 1991), allows measurement of ionic currents through single ion channels with pA (picoampere) resolution and sub-millisecond time resolution.

Patch-Clamp Configurations

Cell-Attached: Seal on intact cell; minimal disruption
Inside-Out: Patch excised; cytoplasmic face accessible
Outside-Out: Patch re-sealed; extracellular face accessible
Whole-Cell: Break patch; measure total membrane current
Perforated Patch: Amphotericin pores; preserve cytoplasm

Measured Parameters

Single-Channel Conductance: γ = i/V (typically 1-100 pS)
Open Probability: P_o (fraction of time open)
Gating Kinetics: Opening/closing rates, dwell times
I-V Relationship: Voltage-dependent current amplitudes
Reversal Potential: E_rev for ion identification

Applications & Insights

Channel Pharmacology: Drug effects on single channels (blockers, modulators, toxins)
Gating Mechanisms: Markov models fit to single-channel kinetics reveal conformational states
Disease Mechanisms: Channelopathy mutations alter gating, conductance, or trafficking
Structure-Function: Correlate structural features with electrophysiological properties
High-Throughput Screening: Automated patch-clamp for drug discovery

🎥 Patch Clamp Technique Animation

Animated explanation of the patch clamp technique: gigaohm seal formation, cell-attached/inside-out/outside-out/whole-cell configurations, and recording single-channel currents (Neher & Sakmann, Nobel Prize 1991)

Patch-Clamp Recording Indicates That Individual Gated Channels Open in an All-or-Nothing Fashion

One of the most striking discoveries from patch-clamp recordings was that individual ion channels do not gradually increase their conductance—they open and close in discrete, all-or-nothing transitions between fully open and fully closed states.

Single-Channel Observations

Channel current switches between discrete levels (0 pA vs. ~2 pA)
No intermediate conductance states during transitions
Transition time <10 μs (limited by recording bandwidth)
Open and closed dwell times vary stochastically

Macroscopic Currents

Smooth macroscopic current = sum of many stochastic openings
Graded response arises from probability, not gradual opening
Voltage changes P_o, not single-channel conductance
Ensemble averaging reveals kinetic schemes

Molecular Interpretation: All-or-nothing gating reflects discrete conformational states of the channel protein—the open state has a defined, stable pore geometry
Stochastic Gating: Individual channels open and close randomly, but statistical properties (mean open time, P_o) are determined by voltage, ligands, and other factors
Two-State Approximation: Simplest model: closed ⇌ open. More complex channels have multiple closed states, open states, and inactivated states
Single-Molecule Biophysics: Ion channels were among the first membrane proteins studied at the single-molecule level, paving the way for single-molecule FRET, optical tweezers, and other techniques

7. Channelopathies & Disease

Mutations in ion channel genes cause a diverse spectrum of "channelopathies" affecting the nervous system, heart, muscle, kidney, and other organs. Over 60 human diseases are linked to ion channel dysfunction.

Neurological Channelopathies

Epilepsy: SCN1A (Na_v1.1), KCNQ2/3 (K_v7.2/3)
Migraine: CACNA1A (Ca_v2.1), SCN1A
Ataxia: KCNA1 (K_v1.1), CACNA1A
Peripheral Neuropathy: SCN9A (Na_v1.7) - pain insensitivity
Myasthenia: CHRNA1, CHRNB1 (nicotinic AChR)

Cardiac Channelopathies

Long QT Syndrome (LQTS): KCNQ1, KCNH2, SCN5A - arrhythmia, sudden death
Brugada Syndrome: SCN5A - ventricular fibrillation
Catecholaminergic Polymorphic VT: RYR2 (Ca²⁺ release channel)
Short QT Syndrome: KCNH2, KCNQ1, KCNJ2

Muscle Channelopathies

Hyperkalemic Periodic Paralysis: SCN4A (skeletal muscle Na_v1.4)
Hypokalemic Periodic Paralysis: CACNA1S (Ca_v1.1)
Myotonia Congenita: CLCN1 (muscle Cl⁻ channel)
Malignant Hyperthermia: RYR1 (sarcoplasmic reticulum Ca²⁺ channel)

Other Channelopathies

Cystic Fibrosis: CFTR (chloride channel) - lung, pancreas
Bartter Syndrome: KCNJ1 (kidney K⁺ channel) - salt wasting
Polycystic Kidney Disease: PKD1, PKD2 (TRP channels)
Retinitis Pigmentosa: CNGA1 (retinal cation channel) - blindness

🎥 Video Lectures: Cardiac Ion Channels & Channelopathies

🎥 Ninja Nerd: Cardiac Conduction System

Detailed 48-minute lecture on cardiac electrical impulses: SA/AV nodes, His-Purkinje system, voltage-gated Na⁺, L-type Ca²⁺, and K⁺ channels in cardiac myocytes, and the cardiac action potential phases

🎥 Armando Hasudungan: Cardiac Action Potential

Illustrated lecture on cardiac myocyte membrane potential, the 5 phases (0–4) of the cardiac action potential, and the distinct roles of Na⁺, Ca²⁺, and K⁺ channels in each phase

🎥 Armando Hasudungan: Neuromuscular Junction

ACh release, nicotinic AChR (ligand-gated Na⁺/K⁺ channels) at the motor end plate, end-plate potential generation, and excitation-contraction coupling

🎥 Ninja Nerd: Antiarrhythmic Drugs & Channelopathies

How ion channel mutations cause cardiac arrhythmias: Long QT syndrome, Brugada syndrome, and how Na⁺, K⁺, and Ca²⁺ channel blockers are used therapeutically

Therapeutic Targeting of Ion Channels

Ion channels are among the most successful drug targets, with >13% of approved drugs modulating channel function.

Local Anesthetics: Lidocaine, novocaine block Na_v channels
Anticonvulsants: Carbamazepine, lamotrigine (Na_v), gabapentin (Ca_vα2δ)
Cardiac Antiarrhythmics: Quinidine, flecainide block cardiac Na⁺ and K⁺ channels
Calcium Channel Blockers: Amlodipine, verapamil for hypertension, angina
Sulfonylureas: Glibenclamide blocks K_ATP channels for diabetes
Benzodiazepines: Diazepam, alprazolam potentiate GABA_A receptors

7B. Ion Channels in Synaptic Transmission

Synaptic transmission is the fundamental process by which neurons communicate. It requires the precisely coordinated activity of multiple ion channel types—voltage-gated channels to propagate the action potential and trigger neurotransmitter release, and ligand-gated channels to transduce the chemical signal back into an electrical response in the postsynaptic cell.

Presynaptic Terminal: From Action Potential to Vesicle Fusion

Step 1: Action Potential Invasion

The action potential propagates along the axon via sequential activation of Na_v channels and arrives at the presynaptic bouton. The depolarization wavefront (+30 to +40 mV) activates voltage-gated Ca²⁺ channels concentrated at “active zones”—specialized membrane regions directly apposed to synaptic vesicle docking sites.

Step 2: Ca²⁺ Channel Opening & Ca²⁺ Influx

Ca_v2.1 (P/Q-type) predominates at most central synapses; Ca_v2.2 (N-type) predominates at many peripheral synapses
Channels are physically tethered to the release machinery by direct interactions with SNARE proteins and RIM
The “nanodomain” (~20–50 nm) coupling means Ca²⁺ sensors on vesicles experience very high local [Ca²⁺] (>100 µM) despite low bulk cytoplasmic [Ca²⁺] (~0.1 µM at rest)
Ca²⁺ influx duration: ~0.5–1 ms per action potential; ~10,000–25,000 Ca²⁺ ions enter per active zone

Step 3: SNARE-Mediated Vesicle Fusion

Ca²⁺ binds to synaptotagmin-1 (C2A and C2B domains), requiring 5 Ca²⁺ ions for full activation
Ca²⁺-bound synaptotagmin pulls on the assembled SNARE complex (syntaxin-1 + SNAP-25 + synaptobrevin/VAMP-2)
SNARE zippering generates mechanical force to overcome the ~40 kT energy barrier for membrane fusion
Total latency from Ca²⁺ influx to vesicle fusion: <200 µs (synaptic delay: ~0.5–1 ms total)

The Synaptic Cleft: Neurotransmitter Dynamics

Diffusion & Binding

Neurotransmitter traverses the cleft (~20–40 nm) in ~1–5 µs by free diffusion
Peak cleft concentration: ~1 mM glutamate, ~1–5 mM ACh (transient, ~1 ms pulse)
Lateral diffusion and spillover to perisynaptic receptors contributes to volume transmission

Enzymatic Degradation

Acetylcholinesterase (AChE): Hydrolyzes ACh in <1 ms; catalytic efficiency near diffusion limit
AChE inhibitors (neostigmine, donepezil) prolong ACh action; used in myasthenia gravis and Alzheimer’s
Nerve agents (sarin, VX) irreversibly inhibit AChE → cholinergic crisis

Reuptake Transporters

Glutamate: EAAT1–5; primarily in astrocytes
GABA: GAT-1 (target of tiagabine)
Serotonin: SERT (target of SSRIs: fluoxetine, sertraline)
Dopamine: DAT (target of cocaine, methylphenidate)
Norepinephrine: NET (target of TCAs, SNRIs)

Postsynaptic Responses: EPSPs, IPSPs, and Integration

Excitatory Postsynaptic Potentials (EPSPs)

Fast EPSP: Mediated primarily by AMPA receptors (Na⁺/K⁺ flux, E_rev ≈ 0 mV); rise time ~0.5 ms, decay ~5–10 ms
NMDA component: Slower, longer-lasting; contributes at depolarized potentials after Mg²⁺ unblock; provides Ca²⁺ for plasticity
Nicotinic EPSPs: At NMJ (~40 mV depolarization, suprathreshold) and CNS (~1–5 mV subthreshold)
A single cortical EPSP: ~0.5–2 mV (subthreshold); ~40–50 EPSPs needed for threshold

Inhibitory Postsynaptic Potentials (IPSPs)

GABA_A-mediated: Cl− influx; fast IPSPs with decay ~10–30 ms
Glycine-mediated: Cl− influx; fast IPSPs predominant in spinal cord and brainstem
Shunting inhibition: Even when E_Cl ≈ V_rest, increased Cl− conductance “short-circuits” incoming EPSPs
GABA_B-mediated: Metabotropic; activates GIRK channels via Gβγ; slow IPSPs lasting 100–300 ms

Synaptic Integration

Spatial summation: Simultaneous EPSPs from multiple synapses on different dendrites sum at the soma/axon hillock
Temporal summation: Rapidly successive EPSPs at the same synapse summate before the membrane time constant (τ_m ≈ 10–30 ms) allows decay
Axon initial segment (AIS): Dense concentration of Na_v1.6 channels; lowest threshold for AP initiation
E/I balance: ~80% excitatory / ~20% inhibitory synapses; disruption implicated in epilepsy, schizophrenia, and autism

Quantal Release: The Fundamental Unit

Katz’s Quantal Hypothesis

Each vesicle contains ~5,000–10,000 neurotransmitter molecules
Miniature EPSPs (mEPSPs): Spontaneous single-vesicle fusion produces ~0.4 mV depolarizations at NMJ
Evoked EPSPs are integer multiples of mEPSP amplitude: EPSP = n × q
Quantal content (m): m = np (n = release-ready vesicles, p = release probability per AP)
NMJ: m ≈ 200–300 (reliable); central synapses: m ≈ 1–10 (probabilistic)

Vesicle Pools & Release Probability

Readily releasable pool (RRP): ~5–10 docked vesicles per active zone; released within 10–20 ms
Recycling pool: ~20–50 vesicles; replenishes RRP during moderate activity
Reserve pool: ~100–200 vesicles; mobilized only during intense stimulation
Release probability varies: ~0.05–0.1 (hippocampal) to ~0.9 (climbing fiber–Purkinje)

Synaptic Plasticity: NMDA Receptors and Long-Term Potentiation

Long-Term Potentiation (LTP)

Induction: High-frequency stimulation (100 Hz, 1 s) or theta-burst depolarizes postsynaptic neuron sufficiently to relieve Mg²⁺ block
NMDAR activation: Coincident glutamate + depolarization → Ca²⁺ influx into dendritic spine
CaMKII activation: Ca²⁺/calmodulin activates CaMKII; autophosphorylation at Thr286 creates persistent kinase activity (“molecular memory switch”)
Expression: Phosphorylation of existing AMPARs + exocytosis of new GluA1-containing AMPARs → increased synaptic strength
Late LTP: Requires CREB-dependent gene transcription and local protein synthesis

Long-Term Depression (LTD)

Induction: Low-frequency stimulation (1–5 Hz for 10–15 min) produces modest NMDAR activation
Lower [Ca²⁺]: Preferentially activates calcineurin (PP2B) and PP1
BCM theory: Sliding threshold determines whether activity induces LTP (high Ca²⁺) or LTD (moderate Ca²⁺)
AMPAR endocytosis: Dephosphorylation of GluA1 Ser845 promotes clathrin-mediated AMPAR removal

The CaMKII “Molecular Switch”

CaMKII is a dodecameric holoenzyme (12 subunits in two stacked hexameric rings) constituting ~1–2% of total brain protein. Upon Ca²⁺/CaM binding, neighboring subunits transphosphorylate at Thr286, rendering the kinase constitutively active even after Ca²⁺ returns to baseline. Autophosphorylated CaMKII translocates to the PSD where it binds GluN2B subunits, anchoring itself at the activated synapse. It then phosphorylates GluA1 Ser831, TARP γ-8, and PSD scaffolding proteins to enhance synaptic strength. Genetic knockout or pharmacological inhibition of CaMKII abolishes LTP and severely impairs spatial learning, confirming its essential role in synaptic plasticity and memory formation.

7A. Voltage-Gated Cation Channels Are Evolutionarily and Structurally Related

Despite their distinct ion selectivities and physiological roles, voltage-gated Na⁺, K⁺, and Ca²⁺ channels share a common evolutionary origin and remarkable structural similarity. This superfamily of voltage-gated cation channels arose through gene duplication and divergence, with variations in selectivity filters and regulatory domains producing specialized functions.

Conserved Structural Architecture

All voltage-gated cation channels share core structural features that define the superfamily:

Voltage Sensor Domain (VSD): Four transmembrane helices (S1-S4) with positively charged residues (mostly arginines) in S4 that sense voltage changes
Pore Domain (PD): S5-S6 helices with intervening P-loop forming the ion conduction pathway
Tetrameric Assembly: Four subunits/domains arranged symmetrically around central pore
Six-Transmembrane Topology: Each functional unit has 6 transmembrane segments (S1-S6)
Voltage Coupling: Conformational changes in VSD (S1-S4) mechanically coupled to pore opening/closing (S5-S6)

K_v Channels (Shaker Family)

Architecture: Four separate subunits, each with 6TM (S1-S6)
Selectivity: TVGYG signature sequence in P-loop
Function: Membrane repolarization, spike frequency adaptation
Evolution: Ancestral form; simplest voltage-gated architecture
Diversity: 40+ genes in mammals (K_v1-12 subfamilies)

Na_v Channels

Architecture: Single polypeptide with 4 homologous domains (I-IV), each 6TM
Selectivity: DEKA locus (Asp-Glu-Lys-Ala from domains I-IV)
Function: Rapid depolarization in action potentials
Evolution: Arose by gene duplication/fusion of ancestral K_v-like gene
Fast Inactivation: IFM motif (Ile-Phe-Met) in III-IV linker acts as inactivation gate

Ca_v Channels

Architecture: Single polypeptide with 4 domains (I-IV), each 6TM (like Na_v)
Selectivity: EEEE or EEDD locus (Glu residues from all 4 domains)
Function: Ca²⁺ influx for signaling, neurotransmitter release
Evolution: Closely related to Na_v; diverged ~600 million years ago
Auxiliary Subunits: β, α2δ, γ subunits modulate gating and trafficking

HCN Channels (Related Family)

Architecture: Four subunits, 6TM each, plus cyclic nucleotide-binding domain
Function: Hyperpolarization-activated (opposite voltage dependence)
Role: Pacemaker currents (I_h) in heart and neurons
Evolution: Diverged early from K_v lineage

Evolutionary Timeline & Key Innovations

~2 billion years ago (Bacteria/Archaea)

Ancestral K⁺-selective channels appear (KcsA-like); tetrameric 2TM architecture

~1.5 billion years ago (Early Eukaryotes)

Fusion of 2TM + voltage sensor → 6TM K_v channels with voltage sensitivity

~600-800 million years ago (Metazoans)

Gene duplication/fusion creates 4-domain Na_v and Ca_v channels; enables fast electrical signaling in early nervous systems

~500 million years ago (Vertebrates)

Diversification into specialized subtypes (Na_v1.1-1.9, Ca_v1-3 families); myelination and saltatory conduction emerge

Sequence and Structural Homology

S4 Helix Conservation: The voltage-sensing S4 helix contains conserved Arg residues (R1-R4) at every third position across all voltage-gated channels
Pore Loop Homology: Despite different selectivity, the P-loop architecture (pore helix + selectivity filter) is conserved in topology
Sequence Identity: Na_v and Ca_v share ~30-40% sequence identity; both share ~20-30% with K_v channels
Functional Interconversion: Mutagenesis studies show that changing a few selectivity filter residues can interconvert selectivity (e.g., EEEE → DEKA converts Ca_v → Na_v-like)

8. Computational Modeling of Ion Channels

Computational approaches spanning quantum mechanics to network-level simulations provide insights into channel structure, dynamics, and function that complement experimental methods.

Molecular Dynamics Simulations

All-Atom MD: Explicit lipids, water, ions; timescales up to microseconds
Coarse-Grained MD: Reduced representation for longer timescales (milliseconds)
Enhanced Sampling: Umbrella sampling, metadynamics for free energy landscapes
Applications: Gating mechanisms, ion permeation pathways, drug binding
Software: GROMACS, AMBER, NAMD, CHARMM, Desmond

Continuum Electrostatics (Poisson-Boltzmann)

Poisson-Boltzmann Equation: Electrostatic potential in dielectric continuum
Applications: pK_a calculations, binding free energies, ion distributions
Software: APBS, DelPhi, MEAD
Advantage: Computationally efficient for large systems
Limitation: Neglects atomic detail and explicit solvent structure

Brownian Dynamics & PNP Simulations

Poisson-Nernst-Planck (PNP): Continuum description of ion fluxes
Brownian Dynamics (BD): Stochastic trajectories of ions in electrostatic field
Applications: Current-voltage relationships, ion flux rates, selectivity
Advantage: Bridge between atomic detail and macroscopic currents

Machine Learning Approaches

AlphaFold: Protein structure prediction including ion channels
Neural Network Potentials: ML force fields for faster MD simulations
Graph Neural Networks: Predict drug-channel interactions
Transfer Learning: Predict channelopathy effects from sequence
Automated Analysis: ML for analyzing patch-clamp data, detecting events

9. Future Directions

Emerging Research Areas

Cryo-EM Revolution: Near-atomic resolution structures of channels in multiple states
Optogenetics: Light-activated channels (channelrhodopsins) for circuit manipulation
Synthetic Biology: Designer channels with novel selectivity and gating properties
Nanopore Sequencing: Biological and solid-state pores for DNA/RNA sequencing
Quantum Biology: Probing quantum effects in ion selectivity and gating
Single-Molecule FRET: Real-time conformational dynamics during gating

Therapeutic Opportunities

Precision Medicine: Genotype-guided therapy for channelopathies
Pain Management: Selective Na_v1.7 blockers for chronic pain
Gene Therapy: AAV-mediated delivery of functional channel genes
Small Molecule Modulators: State-dependent channel modulators with improved specificity
Biologics: Antibodies and peptides targeting extracellular channel domains

📺 Comprehensive Video Lecture Library

A curated collection of the best video lectures on ion channels, membrane electrophysiology, and neuronal signaling from leading universities and educators. Videos are organized by topic for systematic study.

Featured: Membrane Transport & Electrical Properties

A comprehensive lecture covering the fundamental principles of membrane transport and electrical properties of biological membranes: ion gradients, Nernst equation, membrane potential, passive and active transport, ion channels, pumps, and molecular mechanisms underlying electrical signaling.

Neuroscience & Electrophysiology

🎥 Armando Hasudungan: Neurophysiology Overview

Action potentials, neurotransmission, synaptic integration, EPSPs, IPSPs, and information processing in neural circuits

🎥 CrashCourse: Action! Potential!

Na⁺/K⁺ pump, resting potential, threshold, depolarization, repolarization, refractory periods, and stimulus encoding

MIT OpenCourseWare: Advanced Electrophysiology

🎥 MIT 9.40: Hodgkin-Huxley Model I

MIT OCW — Neural Computation — Voltage clamp, K⁺ current analysis, and the quantitative description of voltage-gated conductances

🎥 MIT 9.40: Hodgkin-Huxley Model II

MIT OCW — Neural Computation — Na⁺/K⁺ conductance dynamics, inactivation gating, and the complete action potential model

Cardiac Electrophysiology & Synaptic Transmission

🎥 Ninja Nerd: Cardiac Conduction System

SA/AV nodes, His-Purkinje system, cardiac action potential phases, and Na⁺/Ca²⁺/K⁺ channels in cardiac myocytes

🎥 Armando Hasudungan: Neuromuscular Junction

ACh release, nicotinic AChR activation, end-plate potential, and excitation-contraction coupling at the motor end plate

Ion Channels & Electrical Properties of Membranes

Introduction to Membrane Biophysics

Key Features of Ion Channels

1. Membrane Potential & Electrochemical Gradients

The Nernst Equation

Typical Ion Concentrations (mM)

Calculated Nernst Potentials (37°C)

The Goldman-Hodgkin-Katz (GHK) Equation

Video Lecture Series: The Goldman-Hodgkin-Katz Equation

Part 1: Introduction & Derivation

Part 2: Multiple Ion Species

Part 3: Applications to Membrane Potential

Part 4: Worked Examples & Problem Solving

The Membrane Potential in Animal Cells Depends Mainly on K⁺ Leak Channels and the K⁺ Gradient

The Resting Potential Decays Only Slowly When the Na⁺-K⁺ Pump Is Stopped

🎥 Video Lectures: Membrane Potential

🎥 Armando Hasudungan: Resting Membrane Potential

🎥 Armando Hasudungan: Membrane Transport

Interactive Membrane Equivalent Circuit

Calculated Values:

Try This:

2. Classes of Ion Channels

Voltage-Gated Channels

Voltage-Gated Ion Channel Architecture & Mechanism

Voltage-Gated Sodium Channels (Nav1.1–1.9)

Voltage-Gated Potassium Channels (Kv1–12)

Voltage-Gated Calcium Channels (Cav1–3)

The Voltage-Sensing Mechanism: A Unified View

Ligand-Gated Channels (Ionotropic Receptors)

Mechanosensitive Channels

Other Channel Types

Detailed Ligand-Gated Ion Channel Pharmacology & Structure

Nicotinic Acetylcholine Receptors (nAChR)

GABAA Receptors

AMPA Receptors (GluA1–4)

NMDA Receptors (GluN1/GluN2A–D)

Kainate Receptors (GluK1–5)

5-HT3 Receptor

Glycine Receptor (GlyR)

P2X Receptors (Trimeric)

Key Structural Comparison

🎥 Video Lectures: Ion Channel Structure & Function

🎥 Ninja Nerd: Cell Membrane Structure & Function

🎥 Armando Hasudungan: The Neuron

3. Ion Selectivity Mechanisms

Ion Channels Are Ion-Selective and Fluctuate Between Open and Closed States

The Three-Dimensional Structure of a Bacterial K⁺ Channel Shows How an Ion Channel Can Work

Structural Features of the K⁺ Channel

Sodium Channel Selectivity

Calcium Channel Selectivity

4. Quantum Mechanical Aspects of Ion Permeation

Quantum Contributions to Selectivity

QM/MM Simulations of Ion Channels

Proton Channels & Water Wires

5. The Action Potential

The Function of a Nerve Cell Depends on Its Elongated Structure

Cell Body (Soma)

Dendrites

Axon Hillock

Axon

Voltage-Gated Cation Channels Generate Action Potentials in Electrically Excitable Cells

Voltage-Gated Sodium Channels (Nav)

Voltage-Gated Potassium Channels (Kv)

Phases of the Action Potential

Hodgkin-Huxley Model

Interactive Simulation: Hodgkin-Huxley Action Potential

Interactive Visualization: Gating Kinetics

Cable Theory & Propagation

🎥 Video Lectures: Action Potentials & Hodgkin-Huxley Model

🎥 MIT 9.40: Hodgkin-Huxley Model I

🎥 MIT 9.40: Hodgkin-Huxley Model II

🎥 Alila Medical Media: Action Potential in Neurons

🎥 CrashCourse: Action! Potential!

Interactive Axon Cable Model

Cable Parameters:

Cable Equation

Steady-State Solution

Myelination Increases the Speed and Efficiency of Action Potential Propagation in Nerve Cells

Structural Features

Functional Benefits

Voltage-Gated Sodium Channels (Na_v1.1–1.9)

Voltage-Gated Potassium Channels (K_v1–12)

Voltage-Gated Calcium Channels (Ca_v1–3)

GABA_A Receptors

5-HT₃ Receptor

Voltage-Gated Sodium Channels (Na_v)

Voltage-Gated Potassium Channels (K_v)

K_v Channels (Shaker Family)

Na_v Channels

Ca_v Channels