Electrical Signaling in Neurons (4C) - Chem & Physics

SECTION 1

Historical Context & Motivation

The quest to understand how nerves transmit signals spans more than two centuries and sits at the intersection of physics, chemistry, and biology. Early natural philosophers debated whether nervous impulses were hydraulic, mechanical, or electrical in nature. The resolution of this debate fundamentally shaped our understanding of physiology and laid the groundwork for modern neuroscience. For the MCAT, grasping this history illuminates why electrochemical principles — not merely electrical ones — are central to neuronal signaling. Each experimental advance refined the biophysical model that describes how neurons encode and relay information at speeds exceeding 100 m/s.

1791 • Galvani's 'Animal Electricity'

Luigi Galvani demonstrated that frog legs twitched when contacted by dissimilar metals, proposing that animal electricity was intrinsic to living tissue, not merely an external stimulus. This was the first evidence that biological systems generate electrical signals.

1902 • Bernstein's Membrane Hypothesis

Julius Bernstein proposed that the resting membrane potential arises from selective permeability to potassium ions, and that excitation involves a transient breakdown of this selective permeability — a remarkably prescient model that anticipated the ionic basis of the action potential.

1952 • Hodgkin & Huxley Model

Alan Hodgkin and Andrew Huxley used the giant squid axon and voltage-clamp techniques to derive the quantitative model of the action potential, describing conductance changes for Na⁺ and K⁺ as voltage- and time-dependent parameters. Their work earned the 1963 Nobel Prize in Physiology or Medicine.

1976 • Neher & Sakmann — Patch Clamp

Erwin Neher and Bert Sakmann developed patch-clamp electrophysiology, enabling the recording of currents through single ion channels. This technique confirmed the stochastic opening and closing of discrete channel proteins and earned the 1991 Nobel Prize.

2003 • MacKinnon — Crystal Structure of K⁺ Channel

Roderick MacKinnon resolved the crystal structure of the KcsA potassium channel, revealing the structural basis of ion selectivity at the selectivity filter — a breakthrough recognized with the 2003 Nobel Prize in Chemistry.

The central question that this body of work addresses is deceptively simple: how does a neuron convert a chemical or mechanical stimulus into a rapid, all-or-none electrical impulse that can propagate over long distances without decrement? Answering this requires an integration of thermodynamics, electrostatics, membrane biophysics, and protein biochemistry — precisely the interdisciplinary reasoning the MCAT expects.

SECTION 2

Core Principles & Definitions

Electrical signaling in neurons rests on a set of foundational biophysical principles. The neuronal membrane is a lipid bilayer that acts as a capacitor, separating charges and establishing a voltage difference. Embedded within this membrane are ion channels and ion pumps that selectively regulate the flow of Na⁺, K⁺, Cl⁻, and Ca²⁺ across the membrane. The interplay between the chemical concentration gradient and the electrical potential gradient for each ion species defines the electrochemical gradient, which is the thermodynamic driving force for ion movement.

Resting Membrane Potential

The steady-state voltage across the neuronal membrane, typically about −70 mV, established primarily by the differential permeability to K⁺ and maintained by the Na⁺/K⁺-ATPase pump (3 Na⁺ out, 2 K⁺ in per ATP hydrolyzed).

Equilibrium Potential (E_ion)

The voltage at which the electrical driving force on a particular ion exactly balances its concentration gradient, yielding zero net flux. Calculated by the Nernst equation for each ion species independently.

Action Potential

A rapid, transient, all-or-none depolarization-repolarization cycle caused by sequential activation and inactivation of voltage-gated Na⁺ channels followed by voltage-gated K⁺ channels. It is the fundamental unit of neuronal information transfer.

Saltatory Conduction

In myelinated neurons, action potentials jump between nodes of Ranvier, dramatically increasing conduction velocity while reducing metabolic cost by limiting active ion flux to small unmyelinated gaps.

Graded Potentials

Local, decremental changes in membrane potential (EPSPs and IPSPs) that are proportional to stimulus strength. These undergo temporal and spatial summation at the axon hillock to determine whether threshold is reached.

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KEY TAKEAWAY

Think of the neuronal membrane as a dam across a river. The concentration gradient is the water pressure behind the dam, the electrical gradient is the height of the water on each side, and ion channels are sluice gates. Opening a specific gate doesn't just let water through — it changes the water levels on both sides, which in turn changes the pressure on neighboring gates. The action potential is a cascading sequence of gate openings that propagates as a wave along the river bank, analogous to how voltage-gated channels open sequentially along the axon.

SECTION 3

Visual Explanation — The Action Potential

The following diagram illustrates the phases of a typical action potential as recorded from an intracellular electrode, along with the corresponding conductance changes for sodium and potassium. Understanding this waveform — and correlating each phase with the underlying channel states — is essential for the MCAT.

The action potential waveform showing all six phases: ① resting state at −70 mV, ② depolarization as voltage-gated Na⁺ channels open, ③ overshoot past 0 mV toward +40 mV, ④ repolarization as Na⁺ channels inactivate and K⁺ channels open, ⑤ hyperpolarization (undershoot) below resting potential, and ⑥ restoration to resting potential as K⁺ channels close. The dashed lines indicate threshold (−55 mV) and resting potential (−70 mV).

Note that the entire action potential unfolds in approximately 1–2 milliseconds. The threshold potential near −55 mV represents the critical voltage at which the positive feedback loop of Na⁺ influx becomes self-sustaining: enough voltage-gated Na⁺ channels open to depolarize the membrane further, which opens more Na⁺ channels. This regenerative mechanism is what gives the action potential its all-or-none character. Once threshold is crossed, the action potential proceeds to completion with a stereotyped amplitude and time course, regardless of the magnitude of the suprathreshold stimulus.

SECTION 4

Mathematical Framework

The quantitative description of neuronal electrical signaling centers on two key equations that relate ion concentrations and permeabilities to membrane voltage. Mastery of these equations — their derivations, assumptions, and clinical relevance — is a high-yield MCAT objective.

NERNST EQUATION

E_ion = (RT / zF) × ln([ion]_outside / [ion]_inside)

Where E_ion = equilibrium potential for the ion (V), R = gas constant (8.314 J·mol⁻¹·K⁻¹), T = temperature in Kelvin, z = valence of the ion (e.g., +1 for Na⁺, +2 for Ca²⁺), F = Faraday's constant (96,485 C·mol⁻¹). At 37 °C (310 K), RT/F ≈ 26.7 mV. Converted to log₁₀ with the factor 2.303, this yields the commonly used form: E = (61.5 mV / z) × log₁₀([ion]_out / [ion]_in).

GOLDMAN-HODGKIN-KATZ (GHK) EQUATION

V_m = (RT/F) × ln( (P_Na[Na⁺]_o + P_K[K⁺]_o + P_Cl[Cl⁻]_i) / (P_Na[Na⁺]_i + P_K[K⁺]_i + P_Cl[Cl⁻]_o) )

Where V_m = membrane potential, and P_Na, P_K, P_Cl = membrane permeabilities for each ion. Note that Cl⁻ is a monovalent anion, so its concentration terms are inverted (inside in numerator, outside in denominator) to account for the negative charge. The GHK equation extends the Nernst equation by considering multiple ions simultaneously and weighting each by its relative permeability.

MEMBRANE AS AN RC CIRCUIT

τ = R_m × C_m

Where τ = membrane time constant, R_m = membrane resistance (inversely related to the number of open ion channels), C_m = membrane capacitance (~1 μF/cm²). The time constant determines how quickly the membrane potential changes in response to a current injection. A larger τ means slower voltage changes. Myelination reduces C_m and increases R_m, which increases the length constant (λ) and facilitates saltatory conduction.

LENGTH CONSTANT

λ = √(r_m / r_i)

Where λ = length constant (distance over which a graded potential decays to 37% of its original value), r_m = membrane resistance per unit length, r_i = internal (axoplasmic) resistance per unit length. Larger diameter axons have lower r_i and thus a longer length constant, improving passive signal propagation.

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MCAT Integration Point

The MCAT frequently tests the Nernst equation and GHK equation in the context of altered ion concentrations (e.g., hyperkalemia, channelopathies). Be prepared to predict how changes in extracellular K⁺ concentration shift the resting potential and affect neuronal excitability. A rise in [K⁺]_out depolarizes the membrane (makes E_K less negative), increasing excitability at moderate levels but potentially causing depolarization block at extreme levels.

SECTION 5

Ion Channel Classification & Channel States

Ion channels are the molecular effectors of neuronal electrical signaling, and the MCAT expects you to understand their classification, gating mechanisms, and functional states. Channels can be categorized by their gating stimulus, ion selectivity, and pharmacological sensitivity. The diagram below illustrates the three conformational states of a voltage-gated Na⁺ channel that are critical for understanding the action potential's refractory periods.

Voltage-gated Na⁺ channels cycle through three states during the action potential. In the closed (resting) state (green), the activation gate (m) is shut but the inactivation gate (h) is open — the channel is ready to open. In the open (active) state (cyan), both gates are open and Na⁺ floods inward. In the inactivated state (red), the h gate has swung shut while m remains open — the channel cannot conduct and cannot be reopened until the membrane repolarizes and the channel returns to the closed state.

Channel Type	Gating Stimulus	Key Examples	Functional Role
Voltage-gated	Change in membrane potential	Na_v1.1–1.9, K_v, Ca_v	Action potential generation, repolarization, neurotransmitter release
Ligand-gated	Neurotransmitter or ligand binding	nAChR, GABA_A, NMDA, AMPA	Synaptic transmission, EPSPs and IPSPs
Mechanically-gated	Physical deformation / stretch	Piezo1/2, hair cell channels	Sensory transduction (touch, hearing, proprioception)
Leak channels	Constitutively open	K⁺ leak (KCNK, K_2P)	Setting resting membrane potential

Major ion channel families in neuronal signaling

SECTION 6

Worked Example — Nernst & GHK Calculations

A neuron has the following ion concentrations and permeabilities at 37 °C (body temperature). Calculate the equilibrium potential for K⁺, the equilibrium potential for Na⁺, and the resting membrane potential using the Goldman equation. Given: [K⁺]_out = 5 mM, [K⁺]_in = 140 mM, [Na⁺]_out = 145 mM, [Na⁺]_in = 12 mM, P_K : P_Na = 1 : 0.04 at rest. Ignore Cl⁻ contribution for simplicity.

Calculating Equilibrium and Resting Potentials

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Step 1 — Set Up the Nernst Equation for K⁺

At 37 °C, the simplified Nernst equation is E = (61.5 mV / z) × log₁₀([ion]_out / [ion]_in). For K⁺ (z = +1): E_K = (61.5 / 1) × log₁₀(5 / 140).

E_K = 61.5 × log₁₀(0.0357) = 61.5 × (−1.447) ≈ −89.0 mV
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Step 2 — Set Up the Nernst Equation for Na⁺

For Na⁺ (z = +1): E_Na = (61.5 / 1) × log₁₀(145 / 12).

E_Na = 61.5 × log₁₀(12.08) = 61.5 × 1.082 ≈ +66.6 mV
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Step 3 — Apply the Simplified GHK Equation

Ignoring Cl⁻, the GHK equation simplifies to: V_m = 61.5 × log₁₀( (P_K[K⁺]_out + P_Na[Na⁺]_out) / (P_K[K⁺]_in + P_Na[Na⁺]_in) ). Let P_K = 1 and P_Na = 0.04. Numerator: (1)(5) + (0.04)(145) = 5 + 5.8 = 10.8. Denominator: (1)(140) + (0.04)(12) = 140 + 0.48 = 140.48.

V_m = 61.5 × log₁₀(10.8 / 140.48) = 61.5 × log₁₀(0.0769) = 61.5 × (−1.114) ≈ −68.5 mV
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Step 4 — Interpret the Results

The calculated resting membrane potential of −68.5 mV is close to E_K (−89 mV) but not identical, because the small Na⁺ permeability pulls V_m slightly positive. At rest, the membrane is far from E_Na (+66.6 mV), so there is a large driving force for Na⁺ entry whenever Na⁺ channels open — this is the energy that powers the rapid depolarization phase of the action potential.

V_m,rest ≈ −68.5 mV, consistent with the typical range of −60 to −80 mV for mammalian neurons.

SECTION 7

Graded Potentials vs. Action Potentials

One of the most frequently tested distinctions on the MCAT is the difference between graded potentials and action potentials. While both are changes in membrane potential, they differ fundamentally in mechanism, propagation, and information coding. The table below provides a systematic comparison of their properties.

Property	Graded Potentials	Action Potentials
Amplitude	Variable — proportional to stimulus strength	Fixed — all-or-none (~100 mV swing)
Propagation	Decremental — decays with distance (passive spread)	Non-decremental — regenerated at each point along axon
Direction	Bidirectional from point of origin	Unidirectional (refractory period prevents backpropagation)
Summation	Temporal and spatial summation possible	No summation — obeys all-or-none law
Refractory Period	None — can be generated continuously	Absolute (~1 ms) and relative (~2–3 ms)
Channel types	Ligand-gated or mechanically-gated	Voltage-gated Na⁺ and K⁺ channels
Location	Dendrites, cell body, sensory receptors	Axon hillock → along the axon
Information coding	Analog — graded amplitude encodes stimulus intensity	Digital — frequency coding (more intense → higher firing rate)

Systematic comparison of graded and action potentials

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KEY TAKEAWAY

Graded potentials and action potentials serve complementary roles, analogous to an analog-to-digital converter in engineering. Sensory inputs and synaptic signals produce analog graded potentials of variable amplitude. At the axon hillock, if the summed graded potentials exceed threshold, they trigger a digital action potential — an all-or-none pulse that propagates without information loss. Stimulus intensity is then encoded in the frequency of action potentials (rate coding), not their amplitude. This analog-to-digital conversion is fundamental to how the nervous system processes information.

SECTION 8

Connections to Synaptic Transmission & Clinical Pathology

Electrical signaling in individual neurons is the foundation upon which synaptic transmission, neural circuits, and ultimately cognition are built. The action potential arriving at the axon terminal opens voltage-gated Ca²⁺ channels, triggering vesicle fusion and neurotransmitter release via the SNARE complex machinery — linking the electrical signal to a chemical one. The MCAT expects you to understand this electrochemical coupling and its clinical disruptions.

Concept	Basic Neuronal Signaling (This Lesson)	Advanced / Clinical Extension
Ion selectivity	Na⁺ and K⁺ channels have distinct selectivity filters	Channelopathies (e.g., SCN1A mutations in epilepsy) alter selectivity or gating kinetics
Myelination	Increases conduction velocity via saltatory conduction	Demyelinating diseases (Multiple Sclerosis, Guillain-Barré) slow/block conduction
Refractory periods	Limit maximum firing frequency and enforce unidirectional propagation	Local anesthetics (lidocaine) bind inactivated Na⁺ channels, prolonging the refractory period
Electrochemical gradients	Nernst and GHK equations predict V_m	Hyperkalemia depolarizes cells → arrhythmias; hypokalemia hyperpolarizes → muscle weakness
Neurotransmitter release	AP triggers Ca²⁺ influx at terminal	Botulinum toxin cleaves SNARE proteins; tetanus toxin blocks inhibitory neurotransmitter release

Basic vs. advanced/clinical extensions of neuronal signaling concepts

Looking forward, the principles of electrical signaling extend into cardiac electrophysiology (the cardiac action potential uses the same fundamental ion channel gating but with different channel subtypes and much longer plateau phases), smooth muscle physiology, and even non-excitable cell signaling. Understanding the biophysical framework established in this lesson provides the scaffolding for these more complex systems. On the MCAT, passage-based questions may require you to apply Nernst calculations to novel cell types or predict the effect of a pharmacological agent that modifies channel gating — tasks that require a deep, principle-based understanding rather than rote memorization.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

During the rising phase of the action potential, the membrane potential moves toward E_Na but never quite reaches it. Explain why the peak of the action potential is typically around +30 to +40 mV rather than the full E_Na of approximately +60 mV.

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The peak action potential falls short of E_Na because two concurrent processes prevent the membrane from ever fully equilibrating to E_Na. First, voltage-gated Na⁺ channels begin to inactivate (the h gate closes) within ~1 ms of opening, progressively reducing Na⁺ conductance before V_m can equilibrate to E_Na. Second, voltage-gated K⁺ channels (delayed rectifiers) activate with a slight delay, increasing outward K⁺ current that opposes further depolarization. The peak voltage is reached at the moment when net membrane current transitions from inward to outward — that is, when sufficiently reduced Na⁺ conductance and sufficiently increased K⁺ conductance together cause outward current to overtake inward current. At that instant, depolarization ceases and repolarization begins. This is not a simple current balance between two equal currents, nor a weighted average of equilibrium potentials; rather, it is the voltage at which the net ionic current reverses sign, which occurs well below E_Na (~+60 mV) because Na⁺ channel inactivation and K⁺ channel activation both act to curtail the depolarizing drive before that equilibrium potential is reached, producing a typical peak of +30 to +40 mV.

Question 2: BASIC CALCULATION

Using the Nernst equation at 37 °C, calculate the equilibrium potential for Ca²⁺ given [Ca²⁺]_out = 2.0 mM and [Ca²⁺]_in = 0.0001 mM (100 nM). Remember that z = +2 for calcium.

Show answer

Using E = (61.5 mV / z) × log₁₀([Ca²⁺]_out / [Ca²⁺]_in): E_Ca = (61.5 / 2) × log₁₀(2.0 / 0.0001) = 30.75 × log₁₀(20,000) = 30.75 × 4.301 ≈ +132.3 mV. This extremely positive equilibrium potential explains why Ca²⁺ has a very strong inward driving force at resting membrane potential (−70 mV) and why even a small increase in Ca²⁺ permeability produces significant Ca²⁺ influx, which is critical for neurotransmitter release and intracellular signaling.

Question 3: INTERMEDIATE

A patient presents with hyperkalemia, raising extracellular [K⁺] from 5 mM to 8 mM while intracellular [K⁺] remains 140 mM. Calculate the new E_K at 37 °C and predict how this shift affects the neuron's resting membrane potential and excitability.

Show answer

E_K = (61.5 / 1) × log₁₀(8 / 140) = 61.5 × log₁₀(0.0571) = 61.5 × (−1.243) ≈ −76.4 mV. Compared to the normal E_K of −89 mV, this is roughly 13 mV more positive. Because the resting potential is dominated by K⁺ permeability, V_m will also shift positive (depolarize), moving closer to threshold. At moderate hyperkalemia, neurons become more excitable (closer to threshold). However, at extreme levels, persistent depolarization can cause Na⁺ channel inactivation (depolarization block), paradoxically reducing excitability and leading to muscle weakness or cardiac arrhythmias.

Question 4: APPLIED

Lidocaine is a local anesthetic that preferentially binds to the inactivated state of voltage-gated Na⁺ channels (use-dependent block). Explain why lidocaine is more effective at blocking rapidly firing neurons than quiescent neurons, and predict the effect on action potential generation.

Show answer

Lidocaine exhibits use-dependent (frequency-dependent) block because its binding site is more accessible when the Na⁺ channel is in the inactivated conformation. In rapidly firing neurons, channels cycle through the open and inactivated states more frequently, spending a greater fraction of time in the inactivated state. Lidocaine binds preferentially during inactivation and dissociates slowly, so with each successive action potential, more channels become drug-bound and unable to return to the closed (resting) state that is required for reopening. In quiescent neurons, channels spend most of their time in the closed state, from which lidocaine has lower affinity and faster dissociation. The clinical result is selective blockade of pain-transmitting C-fibers (which fire at high frequency during nociception) while sparing motor neurons (which fire at lower rates), providing analgesia without complete paralysis.

Question 5: CRITICAL THINKING

In a hypothetical neuron, the membrane's permeability to Na⁺ is genetically increased such that P_Na / P_K at rest shifts from 0.04 to 0.20. Using the concentrations from the worked example ([K⁺]_out = 5 mM, [K⁺]_in = 140 mM, [Na⁺]_out = 145 mM, [Na⁺]_in = 12 mM), calculate the new resting V_m and discuss the downstream consequences for action potential initiation, the Na⁺/K⁺-ATPase workload, and long-term neuronal viability.

Show answer

Using the simplified GHK: numerator = (1)(5) + (0.20)(145) = 5 + 29 = 34; denominator = (1)(140) + (0.20)(12) = 140 + 2.4 = 142.4. V_m = 61.5 × log₁₀(34 / 142.4) = 61.5 × log₁₀(0.2388) = 61.5 × (−0.622) ≈ −38.3 mV. This resting potential of −38 mV is above the typical threshold of −55 mV, meaning the neuron would be in a state of persistent depolarization. Several consequences follow: (1) voltage-gated Na⁺ channels will be largely inactivated at this resting potential, resulting in depolarization block — the neuron would actually be less excitable, not more, as it cannot generate normal action potentials. (2) The Na⁺/K⁺-ATPase must work much harder to counteract the increased passive Na⁺ influx, dramatically increasing ATP consumption and O₂ demand. (3) Chronically, the elevated intracellular Na⁺ could reverse the Na⁺/Ca²⁺ exchanger (NCX), raising intracellular Ca²⁺ and triggering excitotoxic cell death. This scenario parallels gain-of-function Na⁺ channelopathies associated with epilepsy and neuropathic pain syndromes.

SUMMARY

Lesson Summary

Summary

Neuronal electrical signaling depends on the electrochemical gradient maintained by the Na⁺/K⁺-ATPase and selective ion channel permeability. The Nernst equation calculates the equilibrium potential for a single ion species, while the Goldman-Hodgkin-Katz equation integrates multiple ion permeabilities to predict the resting membrane potential (typically −60 to −80 mV). Graded potentials provide analog, decremental signals at dendrites and the soma, while action potentials are all-or-none, regenerative signals that propagate along the axon via sequential activation of voltage-gated Na⁺ and K⁺ channels.

The three conformational states of voltage-gated Na⁺ channels — closed, open, and inactivated — underlie the absolute and relative refractory periods, which enforce unidirectional propagation and set the maximum firing frequency. Myelination increases conduction velocity through saltatory conduction by reducing membrane capacitance and increasing the length constant. For the MCAT, be prepared to apply the Nernst and GHK equations quantitatively, predict the effects of altered ion concentrations and pharmacological agents on neuronal excitability, and distinguish between graded and action potential properties in passage-based reasoning.