AE

Electrical Activity & The Action Potential - Video Notes (Ch 6 & 7)

The Nervous System: Cells and Potentials

  • Neuron components: Dendrites, cell body, axon, nerve terminal.
  • Within a neuron: Action potential (AP) is all-or-none.
  • Between neurons: Synaptic potentials are graded.
  • The nervous system uses electrical activity to propagate signals and chemical signals at synapses.

The Action Potential & Resting Potential

  • Membrane potential (Vm) is the voltage difference across the cell membrane.
  • Resting potential is typically negative; an AP is an abrupt, transient deviation from rest, triggered by a stimulus.
  • Classic depiction: Resting potential precedes the AP; AP is all-or-none; stimulus duration (e.g., 2 ms) influences initiation but not amplitude once threshold is reached.

Membrane Potential: Baseline Values

  • Resting Vm ranges in different cell types:
    • Neurons and skeletal muscle: typically around -60 to -90 mV
    • Smooth muscle: around -55 mV
    • Erythrocytes (red blood cells): around -9 mV
  • The resting Vm is set by ion gradients and membrane permeability to major ions.

Ion Gradients and Nernst Potentials

  • Membrane potential is generated by ion concentration gradients stored as potential energy in the gradients themselves.
  • Nernst potentials (for ions) describe the equilibrium potential for a given concentration gradient across the membrane. Ranges:
    • K+: around -100 mV
    • Ca2+: around +100 mV
  • General form of the Nernst equation:
    E{ion} = \frac{RT}{zF} \ln\left(\frac{[ion]{out}}{[ion]_{in}}\right)
  • At 37°C, monovalent ions can be approximated with a base-10 form:
    E{ion} \approx \text{61.5 mV} \cdot \log{10}\left(\frac{[ion]{out}}{[ion]{in}}\right)
  • The membrane potential at any moment depends on which ions have permeant channels open (K+, Na+, Cl−, Ca2+, etc.). If only K+, Na+, Cl− were permeable, the total current would be:
    I{Total} = IK + I{Na} + I{Cl}

Electrical Model of the Cell Membrane

  • Ohm’s law relates voltage (V) and current (I) through resistance (R) or conductance (G):
    V = IR
    \quad \text{or} \quad V = \frac{I}{G} (S units)
  • The lipid bilayer behaves as a capacitor in parallel with ion channels (conductances).

Currents, Conductances, and Driving Force

  • Current through an ion is the product of its conductance and its driving force:
    I = G \cdot (Vm - E{ion})
  • Key dynamic: conductances are voltage- and time-dependent.
  • During the action potential, conductances for different ions change dramatically:
    • Sodium conductance increases several thousand-fold in the early phase (rapid depolarization).
    • Potassium conductance increases ~30-fold later during the AP for a short period (repolarization).
  • Specific currents (examples):
    • IK = GK \cdot (Vm - EK)
    • I{Na} = G{Na} \cdot (Vm - E{Na})

Patch Clamp and Channel Studies

  • Patch-clamp techniques:
    • Voltage-clamp: deduces properties of ion channels by controlling Vm.
    • Patch-clamp (single-channel) studies observe individual channel behavior.
  • Applications include:
    • Drug-channel interactions
    • Receptor-mediated processes
    • Biochemical regulatory mechanisms

Channel Gating: Opening and Closing

  • Gating: the process by which a channel opens or closes; characterized by probabilities of being open vs closed.
  • Opening rate constant and closing rate constant describe the kinetics of gating.

What Makes a Channel Open? Gate Types

  • Voltage-dependent gating:
    • Associated with action potentials; changes within the cell; long-distance signaling; all-or-none behavior.
  • Ligand-gated gating:
    • Associated with synaptic potentials; local signaling between cells; graded responses.

Voltage-Gated vs Ligand-Gated Channels: Conceptual View

  • Ligand-gated channels: respond to chemical signals (e.g., neurotransmitters) and mediate local, graded potentials.
  • Voltage-gated channels: respond to changes in membrane potential and underlie action potentials; include Na+ and K+ channels.

Voltage-Dependent Gating: Illustrative Schemas

  • A representative voltage gating schematic shows transitions among Closed, Open, and Inactivated states depending on voltage.
  • At hyperpolarized voltages: channels tend to be closed; depolarization promotes opening; subsequent inactivation gates may close despite depolarization.

K+ and Na+ Channels: Single-Channel and Gating Kinetics

  • K+ channel: typically has a single activation gate with multiple subunits; activation leads to channel opening.
  • Na+ channel: has a fast activation gate (m) and inactivation gate (h); opening requires depolarization, and inactivation contributes to the peak and termination of the AP.
  • Single-channel traces show voltage-dependent opening and closing and the kinetics differ between K+ and Na+ channels.

Hodgkin–Huxley Model: Conductances and Gating Variables

  • The HH model formalizes how Na+ and K+ conductances produce action potentials in squid axon (classic model):
  • Na+ conductance: g{Na} = g{Na,max} \cdot m^3 \cdot h
  • K+ conductance: g{K} = g{K,max} \cdot n^4
  • Gating variables m, h, n are voltage- and time-dependent, obeying first-order kinetics: the probability that a gate is open is defined by the product of its corresponding gates (e.g., m^3h for Na+; n^4 for K+).
  • Na+ channel features: fast activation (m) and fast inactivation (h).
  • K+ channel features: slower activation; single activation gate; contributes to repolarization.
  • Illustrative HH conductance traces show how gNa and gK vary with voltage and time, driving the AP waveform.

Action Potential: Feedback Cycles

  • Positive feedback loop: depolarization opens Na+ channels → more depolarization → more Na+ channels open.
  • Negative feedback: depolarization also triggers K+ channel opening → K+ efflux → repolarization.
  • The balance of these feedbacks shapes the AP.

Action Potential: Threshold, Rest, and Propagation

  • Threshold: the membrane potential at which an AP is triggered; below threshold, stimuli fail to elicit an AP.
  • Resting potential is stable until a stimulus pushes Vm to threshold.
  • Propagation: APs travel along axons; the electrotonic potential decays with distance, but the AP maintains constant amplitude and shape as it propagates along the membrane.
  • Delay between stimulus and response increases with distance from the stimulus site.

Propagation: Axon Size and Myelination

  • Radius (diameter) effects:
    • Increasing radius increases membrane area and decreases internal resistance, facilitating current flow down the axon.
    • Larger axons support faster propagation.
  • Myelination dramatically increases propagation speed via saltatory conduction:
    • Myelinated segments (internodes) have high membrane resistance and low capacitance, forcing APs to jump between nodes of Ranvier.
    • Unmyelinated axons have slower conduction.

Length Constant and Time Constant in Signal Propagation

  • Length constant (λ): how far a passive potential change travels before decaying significantly.
    • λ increases with higher membrane resistance (Rm) and larger axon diameter; decreases with higher internal resistance (Ri).
  • Time constant (τ): how quickly Vm changes at a site in response to a current input.
    • τ = Rm × Cm where Cm is membrane capacitance.
    • Faster signaling corresponds to smaller τ (shorter time constant).
  • Consequences:
    • Longer λ and shorter τ favor faster and distance-spanning signaling, especially with myelination.

Refractory Periods

  • Absolute refractory period: no AP can be elicited, regardless of stimulus strength; h gates are closed.
  • Relative refractory period: a stronger-than-normal stimulus may elicit an AP; h gates are recovering.
  • The refractory periods contribute to unidirectional propagation and spike timing.

Diversity of Ion Channels

  • Resting potential and AP properties vary across cell types due to differences in ion channels.
  • The resting potential and AP peak/duration differ among neurons, cardiac cells, muscle cells, etc.

Ion Currents, Genes, and Currents by Channel Type

  • Ion categories and representative channel types include:
    • K+ channels: Kv (neuronal delayed rectifier), Eag (cardiac fast delayed rectifier), KCNQ (M-current; cardiac slow delayed rectifier), Slo (BK, high conductance Ca2+- and voltage-dependent), Kir (inward rectifiers), 2P (two-pore leak channels).
    • Na+ channels: TTX-sensitive (neurons, adult skeletal muscle, glia); TTX-resistant (cardiac muscle, some sensory neurons).
    • Ca2+ channels: L-type (high voltage-activated), N/P/Q/R-types (high voltage-activated T-type (low voltage-activated) for some cells).
    • CNG channels, transient receptor potential (Trp) channels, and pacemaker currents.
  • This diversity underlies the wide variety of excitability profiles seen across cell types.

Transmembrane Topology of Ion Channels

  • K+ channels and many others have multiple membrane-spanning domains with defined topology.
  • Hydropathy plots and membrane-spanning models show S1–S6 segments with P-loop pore.
  • Voltage sensor: S4 segment contains positively charged residues and moves in response to changes in membrane potential, driving opening/closing.
  • Structure includes extracellular vestibules and cytosolic domains that regulate gating and ion selectivity.

Channel Modulation and Accessory Subunits

  • Channel function is regulated by:
    • Expression level and localization (how many channels and where they are expressed).
    • Accessory subunits and protein-protein interactions affecting kinetics and trafficking.
    • Signaling through G protein-coupled receptors (GPCRs).
    • Post-translational modifications (e.g., phosphorylation).
    • Interactions with membrane lipids (e.g., PIP2) that modulate activity.

Accessory Subunits and Channel Complexes

  • Channels can associate with auxiliary subunits that modify gating, conductance, and pharmacology.
  • Examples include auxiliary B subunits and other regulatory partners that influence current amplitude and kinetics.
  • Phosphorylation and other modifications can alter channel behavior and response to signals.

Notable Concepts and Connections

  • The resting potential is a weighted average influenced by the relative permeability of the membrane to K+, Na+, and Cl−, with the ion most permeable at rest dominating Vm.
  • The action potential is a coordinated, transient event driven by voltage-dependent gating of Na+ and K+ channels, described quantitatively by the Hodgkin–Huxley framework.
  • Propagation speed is governed by axon diameter, myelination, and the cable properties of the membrane (λ and τ).
  • Real neurons show a diversity of channels and regulatory mechanisms, enabling a spectrum of excitability and signaling styles.
  • Experimental tools like patch-clamp allow dissection of single-channel properties and pharmacology, linking channel function to cellular behavior.

Key Formulas (Summary)

  • Nernst equation for ion i: Ei = \frac{RT}{zi F} \ln\left(\frac{[i]{out}}{[i]{in}}\right)
    • For 37°C (base-10 form):
      Ei \approx 61.5\,\text{mV} \cdot \log{10}\left(\frac{[i]{out}}{[i]{in}}\right)
  • Resting membrane potential and ion permeabilities depend on permeant ions; example relationships using monovalent ions:
    • Vm \approx -92\ \,\text{mV} \text{ when } [K^+]{out}/[K^+]_{in}=5/150
    • Vm \approx +67\ \,\text{mV} ext{ for Na+ with } [Na^+]{out}/[Na^+]_{in}=5/150
    • Vm \approx -86\ \,\text{mV} ext{ for Cl- with } [Cl^-]{out}/[Cl^-]_{in}=5/150
  • Driving force and current:
    I = G \cdot (Vm - E{ion})
  • Hodgkin–Huxley conductances:
    g{Na} = g{Na,max} \cdot m^3 \cdot h \ g{K} = g{K,max} \cdot n^4
  • Time constant and length constant (conceptual):
    \tau = Rm Cm \quad\text{and}\quad \lambda = \sqrt{\frac{Rm}{Ri}} \times \text{(geometry factors)}
  • Action potential dynamics: positive Na+ feedback and negative K+ feedback drive the AP, with opening of Na+ channels and subsequent K+ channel activation.