Comprehensive Study Guide: Action Potentials and Ionic Conductance Electrolytes and Electrophysiology

General Features of Action Potentials

• Definition of Action Potentials: A transient all-or-none reversal of the membrane potential produced by a regenerative inward current in excitable membranes. They are also colloquially referred to as "spikes" or "impulses."
• Regenerative Nature: Regenerative means self-reinforcing, utilizing positive feedback, and autocatalyzing.
• Major Functions:     * Rapid Transmission: Facilitates the movement of information over long distances within nerve and muscle fibers.     * Control of Effector Responses: Regulates biological actions such as muscle contraction or the release of neurotransmitters.
• Spike Transduction: This is the process of translating neural activity from a graded amplitude code (varying in size) to a spike frequency code (varying in rate).
• Key Timing and Frequency Definitions:     * Spike Frequency: Calculated as $\text{Spike Frequency} = \frac{1}{\text{interspike interval}}$.     * Absolute Refractory Period: The period immediately following an action potential during which a stimulus, regardless of its strength, cannot elicit a second action potential. This period limits the maximum spike frequency of the cell.     * Relative Refractory Period: The period after an action potential when the threshold for initiating a second action potential is increased. A stronger-than-normal stimulus is required during this time.
• Fundamental Properties:     * All-or-None: Once triggered, the action potential (AP) is an explosive, regenerative event. It has a specific voltage threshold; once initiated, its amplitude and duration are independent of the triggering event's characteristics.     * Propagation Without Decrement: The amplitude of the AP does not decline with distance as it travels along the fiber, distinguishing it from electrotonic (passive) potentials.

Biological Diversity of Electrical Excitability

• Tissues Exhibiting Excitability: While primarily associated with nerves and muscles, electrical excitability is found in various tissues:     * Pancreatic Islets: Rhythmic burst-firing occurs in pancreatic islets or single $\beta$ cells, specifically observed when exposed to $11.1\,mmol\,dm^{-3}$ glucose.     * Egg Cells: Action potentials have been recorded in the egg cells of sea urchins, tunicates, and mice.     * Plants: The Venus flytrap (Dionaea muscipula) utilizes action potentials, as documented by Kinard et al. (1999) in the Biophysical Journal (76: 1423–1435).

Historical Foundations of the Ionic Basis of the Action Potential

• Julius Bernstein (1912): Suggested the "membrane breakdown hypothesis," proposing that all ionic "gates" open during an AP, causing a total breakdown of membrane resistance. If true, the membrane potential ($E_m$) should reach precisely $0\,mV$ during the spike.
• Cole and Curtis (1939): Conducted experiments on the squid giant axon using a $20\,kHz$ oscillating current and a Wheatstone Bridge circuit.     * Findings: They observed that membrane impedance decreased (and conductance increased) during the AP. A widening of the trace in their frequency figures indicated the membrane became more electrically "leaky," which was consistent with Bernstein’s hypothesis of resistance breakdown.
• The Hodgkin and Huxley "Overshoot" (1939): Working independently but alongside Cole and Curtis (1940) on the squid giant axon, they discovered that the membrane potential actually goes positive (reverses polarity) during the AP. This "overshoot" contradicted Bernstein’s prediction of reaching only $0\,mV$.

The Sodium Hypothesis

• Hodgkin and Katz (1949): Investigated the dependence of APs on extracellular $Na^+$ ions.     * Experiment: They gradually replaced extracellular $Na^+$ with choline, a positive ion that cannot cross the membrane.     * Result: The amplitude of the AP in the squid giant axon decreased proportionally to the reduction in $Na^+$.     * Conclusion: During the AP, there is a selective and transient increase in membrane permeability to $Na^+$.
• Numerical Examples of $E_{Na}$ Shifts:     * $100\%\,Na^+$ ($140\,mmol\,dm^{-3}$): $E_{Na} = +55\,mV$.     * $50\%\,Na^+$ ($70\,mmol\,dm^{-3}$): $E_{Na} = +39\,mV$.     * $10\%\,Na^+$ ($14\,mmol\,dm^{-3}$): $E_{Na} = 0\,mV$.
• Richard D. Keynes (1951): Used radioisotopes ($^{42}K$ and $^{24}Na$) to track ion movements across the membranes of crab and cuttlefish giant axons, providing further evidence for ionic flux during excitation.

Voltage-Gated Channels and Hypothesized Mechanisms

• The Hypothesis:     * Rising Phase (Depolarization): Opening of voltage-gated $Na^+$ channels allowing $Na^+$ to move down its concentration gradient into the cell.     * Falling Phase (Repolarization): Closing (inactivation) of $Na^+$ channels and the opening of voltage-gated $K^+$ channels.
• The Challenge of Testing: Testing this requires varying $E_m$ systematically to measure conductance. However, depolarizing to open $Na^+$ channels normally triggers a positive feedback loop leading to a full action potential, making measurement difficult.

The Voltage Clamp Technique

• Invention: Kenneth S. Cole (1949) invented the "voltage clamp." Hodgkin and Huxley used it in the early 1950s to describe ionic conductances.
• Function: The voltage clamp prevents ionic currents from altering the membrane potential ($E_m$) by using a feedback amplifier.     * Feedback Amplifier: Generates a current equal and opposite to the ionic current flowing through the channels to keep the potential at a "command potential."
• Significance of Constant Voltage:     * When voltage changes, current is split between ion channels and charging the membrane capacitor ($I_{cap} = C \times \frac{dV}{dt}$).     * By clamping the voltage to a stable level, the large capacitive current ends almost instantly, allowing researchers to measure the pure ionic current flowing through channels.     * Gating Currents: The outward movement of approximately $54$ positive charges during depolarization represents the gating current ($I_{gating}$).
• Observed Currents: Voltage-clamp recordings in the squid giant axon revealed two currents:     1. An early inward current (carried by $Na^+$).     2. A late outward current (carried by $K^+$).

Investigating and Separating Ionic Currents

• Methods to Determine Ion Responsibility:     1. I/V Curve Construction: Conducted by Hodgkin, Huxley, and Katz (1952).     2. Ion Substitution: Replacing external $Na^+$ with choline. Replacing $90\%\,[Na^+]<em>o$ shifts $E</em>{Na}$ from $+55\,mV$ to $-9\,mV$.     3. Pharmacological Blockers:         * TTX (Tetrodotoxin): Selectively blocks voltage-gated $Na^+$ channels (Narahashi, Moore, & Scott, 1964).         * TEA (Tetraethylammonium): Selectively blocks voltage-gated $K^+$ channels (Armstrong & Hille, 1972). Note: In squid giant axons, TEA must be applied intracellularly to be effective.
• Dynamics of Inward $Na^+$ Current: The early inward current first increases as $G_{Na}$ increases, then decreases as the membrane potential approaches $E_{Na}$ (decreasing driving force: $V_m - E_{Na}$).
• Dynamics of Outward $K^+$ Current: The late outward current increases due to both increasing $G_K$ and increasing driving force ($V_m - E_K$).

Sodium Channel Inactivation and the Ball-and-Chain Model

• Inactivation vs. Activation:     * $Na^+$ Channels: Activate rapidly in response to depolarization and then inactivate (close) even if the membrane remains depolarized.     * $K^+$ Channels: Activate slowly in response to depolarization and (in the squid giant axon) do not inactivate.
• Pronase Experiment: Intracellular injection of the enzyme Pronase blocks $Na^+$ channel inactivation. This demonstrated that activation and inactivation are separate processes handled by different parts of the channel.
• Voltage Dependence: Both activation and inactivation are voltage-dependent, but inactivation is slower (delayed relative to activation).
• Ball-and-Chain Model (Armstrong and Bezanilla, 1977):     1. Closed: Activation gate is closed.     2. Open: Activation gate opens due to depolarization, allowing $Na^+$ flux. This creates a "receptor" site at the inner mouth of the pore.     3. Inactivated: An inactivation gate (the "ball," likely a hairpin loop) hangs in the cytoplasm and binds to the receptor at the inner mouth of the pore, occluding it.     4. Repolarization: Repolarization removes the inactivation ball and re-closes the activation gate.

Threshold Determination and Feedback Loops

• Standard Threshold: Typically between $-50\,mV$ and $-55\,mV$. It varies based on recent cellular activity.
• Negative Feedback Loop ($K^+$): Depolarization increases $P_K$ (potassium permeability), which brings $V_m$ closer to $E_K$, opposing the depolarization.
• Positive Feedback Loop ($Na^+$): Depolarization increases $P_{Na}$, which further depolarizes the membrane toward $E_{Na}$.
• Threshold Definition: The point where the positive feedback mechanism ($Na^+$) overcomes the negative feedback mechanism ($K^+$).
• Factors Raising Threshold: Any factor enhancing $G_K$ or reducing $Na^+$ availability (like inactivation) will raise the threshold (e.g., during the refractory period or accommodation).

Mathematical Modeling: The Hodgkin-Huxley Equations

• Ohm's Law Application: Conductance ($G$), measured in Siemens ($S$), is the inverse of resistance ($R = 1/G$).     * $G_{Na} = \frac{I_{Na}}{V_m - E_{Na}}$     * $G_K = \frac{I_K}{V_m - E_K}$
• The Hodgkin-Huxley Model (1952): Used time- and voltage-dependent coefficients to reconstruct the AP voltage changes:     * $n$: $K^+$ activation coefficient ($0 \rightarrow 1$).     * $m$: $Na^+$ activation coefficient ($0 \rightarrow 1$).     * $h$: $Na^+$ inactivation coefficient ($1 \rightarrow 0$).
• Calculation Method: Andrew Huxley reconstructed the AP for $10\,\mu s$ intervals using a Brunsviga 20 mechanical calculator. Calculating a $5\,ms$ action potential took $8\,hours$ by hand.
• Nobel Prize: Alan Hodgkin (1914–1998) and Andrew Huxley (1917–2012) were awarded the Nobel Prize in 1963 for this work.

Calcium Ions and Membrane Excitability

• The Stabilizing Effect: High extracellular calcium ($[Ca^{2+}]_o$) stabilizes membranes, decreasing excitability. Low $[Ca^{2+}]_o$ (hypocalcemia) makes membranes hyperexcitable.
• Homeostasis Regulators:     * Parathyroid Hormone (PTH): Secreted by the parathyroid gland to increase blood $[Ca^{2+}]_o$.     * Calcitonin: Produced by the thyroid gland to decrease blood $[Ca^{2+}]_o$.
• Clinical Symptomatology:     * Hypercalcemia (High $Ca^{2+}$): Symptoms include fatigue, depression, confusion, cardiac arrhythmias, coma, and death. Often caused by hyperparathyroidism or hypothyroidism.     * Hypocalcemia (Low $Ca^{2+}$): Symptoms include cardiac arrhythmias, cramps, tingling, spasms of the larynx/bronchi (interrupted breathing), and seizures. Often caused by hypoparathyroidism or hyperthyroidism.
• Surface Potential Theory: Suggested by A.F. Huxley; $Ca^{2+}$ ions adsorb to the outer edge of the membrane, creating an electric field inside the membrane that adds to the resting potential.
• Experimental Evidence: A fivefold reduction in extracellular calcium resulted in a $10\,mV$ to $15\,mV$ reduction in the depolarization required to reach AP threshold.

Impulse Propagation and Compartmentalization

• Unmyelinated Axon Propagation: Driven by continuous regeneration and refractory periods.     * Absolute Refractory Period: Driven by $Na^+$ channel inactivation.     * Relative Refractory Period: Driven by increased $K^+$ conductance.
• Myelinated Axon (Saltatory Conduction):     * Action potentials are generated only at the Nodes of Ranvier.     * Between nodes, there is passive (electrotonic) spread of potential.     * Nodes are typically no more than $2\,mm$ apart to ensure threshold is reached at the next node ($\Delta V_m(x) = \Delta V_0 \times e^{-\frac{x}{\lambda}}$).     * Channel Distribution:         * Nodes of Ranvier: High clustering of voltage-gated $Na^+$ channels.         * Juxtaparanodal Regions: Concentration of voltage-gated $K^+$ channels and some $Ca^{2+}$ channels.