9.1 Neurons, Resting Potential & Action Potentials

Functional Anatomy of the Neuron

The neuron is the fundamental structural and functional unit of the nervous system, specialized for receiving, integrating, and transmitting electrochemical signals. Neuronal morphology directly reflects its functional compartmentalization:

1. Dendrites: Highly branched cytoplasmic extensions projecting from the cell body that receive chemical signals from presynaptic axon terminals. Dendrites contain ligand-gated ion channels and metabotropic receptors, generating local, graded postsynaptic potentials.
2. Soma (Cell Body): Contains the cell nucleus, prominent nucleolus, and extensive rough endoplasmic reticulum (RER) organized into dense aggregates termed Nissl bodies. The soma synthesizes proteins, neurotransmitter precursors, and organelles required for neuronal homeostasis.
3. Axon Hillock: The funnel-shaped transition zone between the soma and the initial segment of the axon. Serves as the trigger zone for action potential generation. The axon hillock integrates incoming Excitatory Postsynaptic Potentials (EPSPs) and Inhibitory Postsynaptic Potentials (IPSPs) via spatial and temporal summation due to its exceptionally high concentration of voltage-gated $\text{Na}^+$ channels.
4. Axon: A single, elongated cylindrical projection that conducts action potentials away from the soma toward target cells. Axons maintain a specialized axoplasm and axolemma but lack ribosomes, relying on anterograde axonal transport (mediated by kinesin motor proteins along microtubules) to receive materials from the soma.
5. Myelin Sheath: A multilayered lipid-rich insulating membrane wrapped concentrically around the axon. In the Central Nervous System (CNS), myelin is synthesized by oligodendrocytes, which can myelinate segments of up to 50 distinct axons. In the Peripheral Nervous System (PNS), myelin is produced by Schwann cells, where a single Schwann cell wraps around only one axonal segment.
6. Nodes of Ranvier: Uninsulated gaps in the myelin sheath occurring at regular intervals (~1 mm). Voltage-gated $\text{Na}^+$ channels are heavily concentrated at these nodes (up to 10,000 channels/$\mu\text{m}^2$), permitting saltatory conduction.
7. Axon Terminal (Presynaptic Bouton): The distal termination of the axon that forms synapses with postsynaptic cells. Contains abundant mitochondria and synaptic vesicles filled with chemical neurotransmitters.

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Electrochemical Basis of Resting Membrane Potential

All living cells maintain an electrical potential difference across their plasma membrane, but neurons are specialized to utilize this potential for rapid signaling. In a resting neuron, the interior of the cell is negatively charged relative to the extracellular fluid, yielding a resting membrane potential ($V_m$) of approximately $-70\text{ mV}$.

This resting potential is established and maintained by two primary mechanisms:

1. Active Ion Transport via $\text{Na}^+/\text{K}^+$ ATPase

The primary active transporter $\text{Na}^+/\text{K}^+$ ATPase (sodium-potassium pump) utilizes the hydrolysis of one molecule of ATP to pump 3 $\text{Na}^+$ ions out of the cell and 2 $\text{K}^+$ ions into the cell against their respective electrochemical gradients. This maintains steep concentration gradients:

• High intracellular $[\text{K}^+]$ ($140\text{ mM}$) relative to extracellular $[\text{K}^+]$ ($4\text{ mM}$).
• High extracellular $[\text{Na}^+]$ ($145\text{ mM}$) relative to intracellular $[\text{Na}^+]$ ($12\text{ mM}$).

Because the pump transfers a net positive charge outward (3 positive charges out for every 2 positive charges in), it is electrogenic, directly contributing approximately $-3\text{ mV}$ to $-5\text{ mV}$ to the resting membrane potential.

2. Passive Ion Permeability & Leak Channels

The resting plasma membrane contains numerous open potassium leak channels but very few active sodium leak channels. At rest, the membrane permeability to $\text{K}^+$ ($P_{\text{K}}$) is approximately 25 to 30 times greater than its permeability to $\text{Na}^+$ ($P_{\text{Na}}$). $\text{K}^+$ ions diffuse down their chemical concentration gradient out of the cell through leak channels. As positively charged $\text{K}^+$ leaves, it leaves behind uncompensated intracellular organic anions (proteins, organic phosphates, $\text{ATP}^{4-}$), accumulating a net negative charge along the inner surface of the plasma membrane.

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Equilibrium Potentials & Mathematical Modeling

The Nernst Equation

The equilibrium potential ($E_{\text{ion}}$) is the membrane potential at which the electrical force driving an ion across the membrane precisely balances its chemical concentration gradient, resulting in zero net flux of that ion across the membrane. It is calculated using the Nernst equation:

$E_{\text{ion}} = \frac{RT}{zF} \ln\left(\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}\right)$

At physiological body temperature ($37^\circ\text{C} = 310\text{ K}$), converting to base-10 logarithms yields the simplified Nernst equation:

$E_{\text{ion}} = \frac{61.5}{z} \log_{10}\left(\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}\right)$

Where:

• $z$ is the valence (charge) of the ion ($+1$ for $\text{K}^+$ and $\text{Na}^+$, $+2$ for $\text{Ca}^{2+}$, $-1$ for $\text{Cl}^-$).
• $[\text{ion}]{\text{out}}$ and $[\text{ion}]{\text{in}}$ are the extracellular and intracellular ion concentrations.

Using standard mammalian physiological values:

• Potassium Equilibrium Potential ($E_{\text{K}}$): $E_{\text{K}} = \frac{61.5}{+1} \log_{10}\left(\frac{4}{140}\right) = 61.5 \times \log_{10}(0.02857) \approx -95\text{ mV to }-90\text{ mV}$
• Sodium Equilibrium Potential ($E_{\text{Na}}$): $E_{\text{Na}} = \frac{61.5}{+1} \log_{10}\left(\frac{145}{12}\right) = 61.5 \times \log_{10}(12.08) \approx +60\text{ mV to }+65\text{ mV}$

AAMC MCAT Trap: Notice that the resting membrane potential ($-70\text{ mV}$) is much closer to $E_{\text{K}}$ ($-90\text{ mV}$) than to $E_{\text{Na}}$ ($+60\text{ mV}$). This occurs because the resting membrane permeability to $\text{K}^+$ is dramatically higher than to $\text{Na}^+$. If $\text{K}^+$ permeability increases further, $V_m$ hyperpolarizes toward $-90\text{ mV}$. If $\text{Na}^+$ permeability increases, $V_m$ depolarizes toward $+60\text{ mV}$.

The Goldman-Hodgkin-Katz (GHK) Equation

Because multiple ions contribute to the actual membrane potential, the overall resting membrane potential ($V_m$) is calculated by the Goldman-Hodgkin-Katz (GHK) voltage equation, which accounts for the concentrations and relative membrane permeabilities ($P$) of $\text{K}^+$, $\text{Na}^+$, and $\text{Cl}^-$:

$V_m = \frac{RT}{F} \ln\left(\frac{P_{\text{K}}[\text{K}^+]_{\text{out}} + P_{\text{Na}}[\text{Na}^+]_{\text{out}} + P_{\text{Cl}}[\text{Cl}^-]_{\text{in}}}{P_{\text{K}}[\text{K}^+]_{\text{in}} + P_{\text{Na}}[\text{Na}^+]_{\text{in}} + P_{\text{Cl}}[\text{Cl}^-]_{\text{out}}}\right)$

Notice that for chloride ($\text{Cl}^-$), the intracellular concentration is in the numerator and extracellular in the denominator because chloride carries a negative valence ($z = -1$).

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Phases of the Action Potential & Voltage-Gated Conductances

An action potential is an all-or-none, rapid, transient reversal of membrane potential that propagates along an axon. It occurs when graded potentials summate at the axon hillock to reach the threshold potential (approximately $-55\text{ mV}$).

  Membrane Potential (mV)
   +40 |              /
       |             /  \ Repolarization
   +20 |  Depolarization 
     0 |           /      \
   -20 |          /        \
   -40 |         /          \
   -55 |-------/ Threshold   \
   -70 |======/               \____________ Resting Potential (-70 mV)
   -80 |                       \__________/ Hyperpolarization
       +------------------------------------
         0    1    2    3    4    5    6  Time (ms)

Detailed Molecular Phases

1. Resting Phase ($-70\text{ mV}$): Voltage-gated $\text{Na}^+$ channels are in their closed (resting) state. Voltage-gated $\text{K}^+$ channels are closed.
2. Threshold Stimulus ($-55\text{ mV}$): Summation of EPSPs depolarizes the axon hillock from $-70\text{ mV}$ to $-55\text{ mV}$. This threshold depolarization causes voltage-sensing domain shifts that trigger the rapid opening of activation gates on voltage-gated $\text{Na}^+$ channels.
3. Depolarization Phase ($-55\text{ mV}$ to $+35\text{ mV}$): Opening of voltage-gated $\text{Na}^+$ channels dramatically increases $P_{\text{Na}}$, causing a massive influx of $\text{Na}^+$ down both its concentration and electrical gradients. This positive feedback loop (Hodgkin cycle) rapidly shoots membrane potential upward toward $E_{\text{Na}}$, peaking at approximately $+35\text{ mV}$.
4. Inactivation & Repolarization Phase ($+35\text{ mV}$ to $-70\text{ mV}$): At peak depolarization ($+35\text{ mV}$), two critical events occur simultaneously:
   • $\text{Na}^+$ Channel Inactivation: The intracellular inactivation gate (ball-and-chain mechanism) of the voltage-gated $\text{Na}^+$ channel closes, halting $\text{Na}^+$ influx. Inactivated channels cannot be opened by any stimulus.
   • $\text{K}^+$ Channel Activation: Voltage-gated $\text{K}^+$ channels, which opened slowly in response to initial threshold depolarization, reach full conductance. Driven by both concentration gradient and electrical repulsion at $+35\text{ mV}$, $\text{K}^+$ rapidly effluxes out of the cell, repolarizing $V_m$ back toward negative values.
5. Hyperpolarization Phase ($-70\text{ mV}$ to $-80\text{ mV}$): Voltage-gated $\text{K}^+$ channels are slow to close. As a result, $\text{K}^+$ efflux continues past the resting potential, driving $V_m$ close to $E_{\text{K}}$ ($-80\text{ mV}$ to $-85\text{ mV}$). Once voltage-gated $\text{K}^+$ channels fully close, passive leak channels and the $\text{Na}^+/\text{K}^+$ ATPase restore the resting potential to $-70\text{ mV}$.

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Refractory Periods

Refractory periods ensure unidirectional action potential propagation along the axon and set an upper limit on firing frequency.

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Conduction Velocity & Cable Properties

The speed at which an action potential propagates along an axon is governed by axial resistance and membrane electrical properties:

1. Axon Diameter: Larger diameter axons have a larger cross-sectional area, which significantly decreases internal axial resistance ($R_i$) to ionic current flow. Lower $R_i$ allows local current to spread further and faster along the interior of the axon.
2. Myelination & Saltatory Conduction: Myelin wraps the axon with multiple insulating phospholipid bilayers, altering two key cable parameters:
   • Increases Membrane Resistance ($R_m$): Prevents charge leakage out of the axoplasm across the membrane.
   • Decreases Membrane Capacitance ($C_m$): Reduces the amount of charge stored on the membrane, allowing local potential changes to charge the membrane much faster.

In myelinated axons, ionic currents flow rapidly through the low-resistance axoplasm from one Node of Ranvier to the next. Action potentials do not continuous-scan along every micrometer of membrane; instead, they regenerate exclusively at the nodes in a jumping pattern termed saltatory conduction, increasing conduction velocity up to 100-fold (up to $120\text{ m/s}$).