Resting membrane potential

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Resting Membrane Potential

Definition

The resting membrane potential (RMP) is the electrical potential difference across the membrane of an excitable cell (nerve, muscle) when it is not generating a signal. By convention, the intracellular potential is expressed relative to the extracellular fluid (which is set to 0 mV). The inside of the cell is negative relative to the outside.

Typical values:

Neurons: -65 to -70 mV (commonly cited as -70 mV)
Skeletal/cardiac muscle fibers: -70 to -90 mV

This is what it looks like when measured with a microelectrode:

Measuring the resting membrane potential - microelectrode inserted into neuron shows -65 mV on voltmeter, with negative charges on inside and positive on outside of membrane

Measuring the resting membrane potential. A voltmeter measures the difference in electrical potential between the tip of a microelectrode inside the cell and a reference wire in extracellular fluid. The inside is about -65 mV relative to outside. - Neuroscience: Exploring the Brain, 5th Ed.

Ionic Basis: The Three Pillars

1. Ion Concentration Gradients (set by the Na⁺-K⁺ ATPase)

The Na⁺-K⁺ pump continuously maintains steep concentration gradients:

Ion	Intracellular	Extracellular
Na⁺	14 mEq/L	142 mEq/L
K⁺	140 mEq/L	4 mEq/L

These gradients mean K⁺ wants to leave the cell (high inside → low outside) and Na⁺ wants to enter (high outside → low inside). - Guyton & Hall Medical Physiology

2. Differential Membrane Permeability

At rest, the membrane is far more permeable to K⁺ and Cl⁻ than to Na⁺ and Ca²⁺. This is the single most important factor.

K⁺ "leak" channels (tandem pore domain / TREK channels) are open at rest
The membrane is about 100 times more permeable to K⁺ than to Na⁺ at rest

Because K⁺ leaks out down its concentration gradient, positive charges are lost from inside, making the interior negative. This negative charge then creates an electrical force pulling K⁺ back in - an equilibrium is reached at the K⁺ equilibrium potential (calculated by the Nernst equation: approximately -94 mV).

The small inward Na⁺ leak (through those same K⁺ leak channels) partially offsets this, bringing the actual resting potential up to about -86 mV by diffusion alone (Goldman equation result). - Guyton & Hall Medical Physiology

3. The Na⁺-K⁺ ATPase (Electrogenic Contribution)

The pump has two roles:

Role	Mechanism	Magnitude
Indirect (major)	Maintains K⁺ and Na⁺ gradients that power the diffusion potentials	Most of the -86 mV
Direct (minor)	Pumps 3 Na⁺ out for only 2 K⁺ in → net outward positive charge	~-4 mV additional

The net result: approximately -90 mV in a large nerve fiber.

Na+-K+ pump and K+ leak channels - pump moves 3Na+ out and 2K+ in using ATP; K+ leak channels allow K+ to flow out via selectivity filter

The Na⁺-K⁺ pump (left) and K⁺ "leak" channels (right). The pump's 3:2 stoichiometry makes it electrogenic. - Guyton & Hall Medical Physiology

Step-by-Step Build-Up (Guyton's Three Conditions)

Three diagrams showing resting membrane potential establishment: A) K+ diffusion alone = -94 mV; B) K+ + Na+ diffusion = -86 mV; C) K+ + Na+ diffusion + Na-K pump = -90 mV

Guyton & Hall Medical Physiology - Establishment of resting membrane potential under three conditions.

(A) K⁺ diffusion only: K⁺ inside/outside ratio = 35:1 → Nernst potential = -94 mV
(B) K⁺ + Na⁺ diffusion: Na⁺ leak partially depolarizes → Goldman equation gives -86 mV
(C) All factors including the Na⁺-K⁺ pump: Electrogenic pump adds ~-4 mV → net -90 mV

The Nernst and Goldman Equations

Nernst Equation - calculates the equilibrium potential for a single ion:

$$E_{ion} = \frac{61}{z} \log \frac{[ion]{outside}}{[ion]{inside}}$$

Where z = valence. For K⁺ (z = +1): E_K = 61 × log(4/140) ≈ -94 mV For Na⁺ (z = +1): E_Na = 61 × log(142/14) ≈ +61 mV

Goldman (Constant Field) Equation - accounts for multiple ions and their relative permeabilities (P):

$$V_m = 61 \log \frac{P_{K^+}[K^+]o + P{Na^+}[Na^+]o + P{Cl^-}[Cl^-]i}{P{K^+}[K^+]i + P{Na^+}[Na^+]i + P{Cl^-}[Cl^-]_o}$$

Chord Conductance Equation - weights each ion's equilibrium potential by its relative conductance:

$$E_m = \frac{G_{K^+}}{G_T}E_{K^+} + \frac{G_{Na^+}}{G_T}E_{Na^+} + \frac{G_{Cl^-}}{G_T}E_{Cl^-} + \frac{G_{Ca^{2+}}}{G_T}E_{Ca^{2+}}$$

Ions with the highest conductance pull the membrane potential toward their own equilibrium potential. At rest, K⁺ conductance dominates, so RMP ≈ E_K. - Costanzo Physiology, 7th Ed.

Summary Table

Factor	Direction of influence	Magnitude of contribution
K⁺ leak out (diffusion)	Hyperpolarizes (more negative)	Major (~-86 mV from diffusion)
Na⁺ leak in (diffusion)	Depolarizes (less negative)	Small offset
Cl⁻ distribution	Near equilibrium at RMP	Minor
Na⁺-K⁺ pump (electrogenic)	Hyperpolarizes	~-4 mV
Intracellular anions (proteins)	Stabilize negativity inside	Passive contribution

Clinical Relevance

Hyperkalemia (high extracellular K⁺): reduces the K⁺ concentration gradient → RMP becomes less negative (depolarized) → cells become more excitable initially, then inexcitable (inactivation of Na⁺ channels). This explains muscle weakness and cardiac arrhythmias in hyperkalemia.
Hypokalemia (low extracellular K⁺): increases the K⁺ gradient → RMP becomes more negative (hyperpolarized) → cells are harder to excite → muscle weakness, paralysis, arrhythmias.
Local anesthetics block Na⁺ channels, preventing depolarization from reaching threshold from the RMP.

As Costanzo Physiology notes: the Na⁺-K⁺ ATPase is necessary both to create/maintain the K⁺ concentration gradient (and thus the RMP) AND to maintain the Na⁺ gradient (needed for the action potential upstroke).

Action potential in general physiology

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Action Potential - General Physiology

Definition

An action potential (AP) is a brief, rapid, self-propagating reversal of membrane potential that occurs in excitable cells (neurons, skeletal muscle, cardiac muscle). It is the fundamental electrical signal used by the nervous system to transmit information and by muscle to initiate contraction. - Costanzo Physiology, 7th Ed.

Starting point: RMP ≈ -70 mV (inside negative relative to outside).

Key Terminology

Term	Definition
Depolarization	Membrane potential becomes less negative (inward positive current)
Hyperpolarization	Membrane potential becomes more negative (outward positive current)
Threshold potential	The critical voltage (~-55 mV) at which AP becomes inevitable; net inward current exceeds net outward current
Overshoot	Phase where the membrane potential becomes positive (cell interior briefly positive)
Undershoot (after-hyperpolarization)	Post-AP phase where Vm is more negative than RMP
Refractory period	Period during which another AP cannot be normally elicited

Phases of the Action Potential

The AP of nerve and skeletal muscle proceeds through distinct, sequential phases:

$Action potential with Na+ and K+ conductance curves showing all phases including overshoot, hyperpolarization, absolute and relative refractory periods plotted against time in milliseconds$

Time course of voltage and conductance changes during the action potential of nerve. - Costanzo Physiology, 7th Ed.

Phase 1 - Resting State (-70 mV)

Membrane is polarized: inside negative, outside positive
K⁺ leak channels open; membrane highly permeable to K⁺
Voltage-gated Na⁺ channels are closed but available (activation gate closed, inactivation gate open)
Voltage-gated K⁺ channels closed

Phase 2 - Upstroke (Depolarization) to threshold → ~+30 mV

A stimulus depolarizes the membrane from -70 mV to threshold (~-55 mV, i.e., about 15-30 mV above RMP)
At threshold, a positive feedback cycle is triggered: membrane depolarizes → voltage-gated Na⁺ channels open → Na⁺ rushes in → more depolarization → more Na⁺ channels open
Na⁺ conductance increases up to 500-5000-fold
Na⁺ floods in down its electrochemical gradient (E_Na = +61 mV), driving Vm toward E_Na
In large fibers, Vm overshoots beyond 0 mV to approximately +30 to +40 mV
The K⁺ conductance is still low at this point

Phase 3 - Repolarization

Two simultaneous events end the upstroke and restore the negative Vm:

Na⁺ channel inactivation: The inactivation gate (slow gate) closes a few ten-thousandths of a second after opening. Na⁺ channels enter an inactivated (closed) state. Na⁺ conductance rapidly falls.
Voltage-gated K⁺ channel activation: Delayed opening (slower than Na⁺ channels) increases K⁺ conductance ~30-fold. K⁺ rushes out of the cell, restoring negativity.

The combined effect: K⁺ conductance >> Na⁺ conductance → rapid repolarization back toward -70 mV.

Phase 4 - After-Hyperpolarization (Undershoot)

Voltage-gated K⁺ channels remain open slightly longer than needed
Vm is transiently driven below RMP, toward E_K (-85 to -94 mV)
K⁺ channels gradually close → Vm returns to -70 mV (RMP)

The Voltage-Gated Na⁺ Channel - Three States

The Na⁺ channel has two gates: a fast activation gate (outer, opens quickly with depolarization) and a slow inactivation gate (inner, closes slowly with depolarization).

Na+ channel in three states: (1) Closed but available - activation gate closed, inactivation gate open; (2) Open - both gates open, Na+ flows in; (3) Inactivated - activation gate open but inactivation gate closed, no Na+ flow

States of activation and inactivation gates on the nerve Na⁺ channel. - Costanzo Physiology, 7th Ed.

State	Activation Gate	Inactivation Gate	Na⁺ flow	When
Closed, available	Closed	Open	No	At rest
Open	Open	Open	Yes (inward)	Upstroke
Inactivated	Open	Closed	No	Peak of AP

Recovery from inactivation requires repolarization back to near RMP - this is the basis of the absolute refractory period.
Blocked by tetrodotoxin (TTX) from puffer fish and local anesthetics (lidocaine, bupivacaine). - Costanzo Physiology, 7th Ed.

Na⁺/K⁺ Conductance Changes - The Full Picture

Action potential and conductance graph showing Na+ conductance spikes sharply early, K+ conductance rises later and more slowly, ratio of conductances plot, and all phases of the AP including overshoot and hyperpolarization

Changes in Na⁺ and K⁺ conductance during the action potential. Na⁺ conductance increases several thousand-fold during the early stages; K⁺ conductance increases ~30-fold during the latter stages. - Guyton & Hall Medical Physiology

Key sequence:

Na⁺ conductance: spikes sharply at AP onset (>>K⁺), then rapidly falls as inactivation closes channels
K⁺ conductance: rises slowly, peaks after Na⁺ channels are mostly inactivated, persists slightly into after-hyperpolarization
Na⁺:K⁺ conductance ratio: >1000:1 at upstroke (driving depolarization) → reverses sharply during repolarization

Three Cardinal Characteristics of Action Potentials

1. Stereotypical Size and Shape

Each AP for a given cell looks identical: same peak voltage, same duration. The shape does not vary with stimulus strength.

2. All-or-None Response

Either the AP fires fully (threshold is reached) or it does not fire at all. A sub-threshold stimulus produces only a graded, decremental local potential that fades out. There is no "partial" AP.

3. Nondecremental Propagation

Each AP regenerates itself at each adjacent point on the membrane at full amplitude. It does not diminish as it travels. - Costanzo Physiology, 7th Ed.

Propagation of the Action Potential

When an AP fires at one point, local currents flow from the active (depolarized) site to adjacent resting membrane. These currents depolarize the adjacent segment to threshold, triggering a new AP there. This repeats continuously along the fiber.

Why does the AP travel in only one direction? The region behind the AP is in its absolute refractory period (Na⁺ channels inactivated), so it cannot fire again. Propagation therefore moves exclusively forward.

Conduction velocity is influenced by:

Fiber diameter - larger fibers = faster conduction (less internal resistance)
Myelination - saltatory conduction in myelinated fibers (AP jumps node to node) is far faster than continuous conduction in unmyelinated fibers

Refractory Periods

Absolute Refractory Period (ARP)

Corresponds to the upstroke + most of repolarization
No stimulus, however large, can trigger another AP
Mechanism: Na⁺ channel inactivation gates are closed; channels cannot reopen until repolarization returns them to the "closed but available" state
Sets the maximum firing frequency of a neuron

Relative Refractory Period (RRP)

Follows ARP; coincides with the after-hyperpolarization
An AP can be triggered, but requires a stronger-than-normal stimulus
Mechanism: K⁺ conductance is still elevated; Vm is more negative than RMP; more inward current needed to reach threshold

Initiation of the AP - Positive Feedback Loop

The AP initiation is an explosive, self-sustaining positive feedback cycle:

Depolarization to threshold → Na⁺ channels open → Na⁺ influx → further depolarization → more Na⁺ channels open → ... (until all channels open)

This only becomes self-sustaining when Na⁺ influx > K⁺ efflux. Below threshold, K⁺ efflux wins and the membrane repolarizes without firing. - Guyton & Hall Medical Physiology

Role of Ca²⁺

Ca²⁺ stabilizes Na⁺ channel gating by binding to the external surface of the channel protein
Hypocalcemia removes this stabilizing effect → Na⁺ channels activate at lower voltages → membrane becomes hyperexcitable → spontaneous discharge → tetany
Voltage-gated Ca²⁺ channels ("slow channels") also contribute to depolarization in some cells (e.g., sinoatrial node, smooth muscle) - Guyton & Hall Medical Physiology

Pharmacological Blockers (Summary)

Drug/Toxin	Target	Effect
Tetrodotoxin (TTX)	Voltage-gated Na⁺ channels	Blocks upstroke; prevents AP
Local anesthetics (lidocaine, bupivacaine)	Voltage-gated Na⁺ channels	Blocks upstroke; nerve block
Tetraethylammonium (TEA)	Voltage-gated K⁺ channels	Blocks repolarization

Quick Comparison: Nerve AP vs. Cardiac AP

Feature	Nerve / Skeletal Muscle	Cardiac Ventricular
RMP	~-70 mV	~-90 mV
Duration	~1-2 ms	~200-400 ms
Plateau phase	Absent	Present (Phase 2, Ca²⁺ channels)
ARP	Short	Very long (prevents tetany)
Pacemaker	No	SA node (spontaneous)

Ficks law of diffusion

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Fick's Law of Diffusion

Background

Adolf Fick (1829-1901) was a German physiologist who in 1855 formulated the quantitative laws governing the passive movement of molecules down a concentration gradient. These laws are fundamental to physiology, pharmacology, and respiratory medicine.

Diffusion is the net movement of molecules from a region of high concentration to a region of low concentration, driven entirely by random thermal motion - no energy (ATP) is required.

Fick's First Law (Steady-State Diffusion)

Fick's First Law describes diffusion under steady-state conditions (when the concentration gradient is not changing over time):

$$\boxed{J = -D \cdot \frac{\Delta C}{\Delta x}}$$

Or in the physiological membrane form:

$$\boxed{\dot{V}_x = \frac{D \cdot A \cdot \Delta P}{\Delta x}}$$

Symbol	Meaning	Units
J	Flux (net diffusion rate)	mol/cm²/s
D	Diffusion coefficient	cm²/s
ΔC	Concentration difference (C₁ - C₂)	mol/L
Δx	Thickness of the membrane/diffusion path	cm
A	Surface area available for diffusion	cm²
ΔP	Partial pressure difference (for gases)	mmHg
−	Negative sign indicates flow is down the gradient

The negative sign indicates net flux occurs in the direction of decreasing concentration. Net flux is zero when ΔC = 0 (equilibrium). - Fitzpatrick's Dermatology

Fick's Second Law (Non-Steady-State Diffusion)

Fick's Second Law predicts flux when the concentration gradient is changing over time:

$$\frac{\partial C}{\partial t} = D \cdot \frac{\partial^2 C}{\partial x^2}$$

It also gives the relationship between time and distance of diffusion:

$$\Delta t = \frac{x^2}{2D}$$

This has a profound physiological implication: diffusion time scales with the square of distance.

Distance	Time (water molecule, D = 2.5 × 10⁻⁵ cm²/s)
10 μm (width of stratum corneum)	~0.4 ms - very fast
100 μm	~40 ms - much slower
1 mm	~4 seconds
1 cm	~400 seconds

This is why diffusion is effective across short distances (cell membranes, alveolar walls) but completely impractical over long distances - which is why the circulatory system exists. - Fitzpatrick's Dermatology

The Diffusion Coefficient (D)

D reflects how easily a molecule moves through a particular medium. It depends on:

Factor	Effect on D	Rationale
Temperature ↑	D ↑	Greater thermal kinetic energy
Molecular weight ↑	D ↓	Larger/heavier molecules move slower (D ∝ 1/√MW)
Viscosity of medium ↑	D ↓	More resistance to movement
Lipid solubility ↑	D ↑ (for membranes)	Easier entry into lipid bilayer

For gases, D is also multiplied by solubility in the medium (not just size). This is critical:

CO₂ diffusion coefficient across biological membranes is ~20 times higher than O₂
Despite being a larger molecule, CO₂ is far more soluble in water/tissue
For the same partial pressure gradient, CO₂ diffuses 20× faster than O₂ - Costanzo Physiology, 7th Ed.; Miller's Anesthesia, 10th Ed.

Full Physiological Form of Fick's Law

For membrane transport (as used clinically):

$$\dot{V}_x = \frac{D \cdot A \cdot \Delta P}{\Delta x}$$

Rate of diffusion is:

Directly proportional to: diffusion coefficient (D), surface area (A), concentration/partial pressure gradient (ΔP or ΔC)
Inversely proportional to: membrane thickness (Δx)

Application to Pulmonary Gas Exchange

Gas exchange in the lung showing O2 diffusing from alveolar space into red blood cells through the respiratory membrane (capillary wall + alveolar wall), and CO2 diffusing in the opposite direction

O₂ and CO₂ move across the alveolar-capillary membrane via Fick's laws of diffusion. - Frameworks for Internal Medicine

For O₂ across the alveolar-capillary membrane:

$$\dot{V}{O_2} = \frac{D \cdot A \cdot (P{A_{O_2}} - P_{c_{O_2}})}{\Delta x}$$

Where:

P_AO₂ = alveolar PO₂ (~100 mmHg)
P_cO₂ = pulmonary capillary PO₂ (~40 mmHg in mixed venous)
Driving force = 60 mmHg for O₂

Lung Diffusing Capacity (D_L)

The terms D, A, and Δx can be combined into a single measurable parameter:

$$D_L = \frac{D \cdot A}{\Delta x}$$

So the equation simplifies to:

$$\dot{V}_x = D_L \cdot \Delta P$$

D_LCO (diffusing capacity for carbon monoxide) is the clinical measurement of lung diffusion capacity, because CO transfer is entirely diffusion-limited. - Costanzo Physiology, 7th Ed.

Factors That Change D_L (Clinical Relevance)

Condition	Change in D_L	Mechanism
Emphysema	↓	Destruction of alveoli → ↓ surface area (A)
Pulmonary fibrosis	↓	Thickening of alveolar-capillary membrane → ↑ Δx
Pulmonary edema	↓	Increased diffusion distance → ↑ Δx
Anemia	↓	Less Hb to bind O₂ (reduces protein-binding component)
Exercise	↑	Recruitment of additional capillaries → ↑ A
Polycythemia	↑	More Hb available

Why does impaired diffusion cause hypoxemia but NOT hypercapnia?

CO₂ is ~20× more soluble in water than O₂ → its effective diffusion coefficient is far higher
Even a thickened membrane transfers CO₂ adequately
Hypoxemia often triggers hyperventilation, which further lowers PaCO₂
Frameworks for Internal Medicine

Application to Drug Pharmacokinetics (Katzung)

Fick's Law in pharmacology:

$$\text{Flux} = \frac{\text{Area} \times \text{Permeability coefficient} \times (C_1 - C_2)}{\text{Thickness}}$$

Lipid diffusion is the most important rate-limiting step for most drugs
The lipid:aqueous partition coefficient determines how readily a drug enters lipid membranes
Ionized drugs cannot diffuse well (charged molecules attract water, are lipid-insoluble)
Henderson-Hasselbalch equation predicts the ionized fraction and therefore the diffusibility of weak acids/bases - Katzung's Basic & Clinical Pharmacology, 16th Ed.

Types of Diffusion in Physiology

Type	Mechanism	Examples
Simple (passive) diffusion	Down concentration gradient, no carrier, no energy	O₂, CO₂, lipid-soluble drugs, ethanol
Facilitated diffusion	Carrier-mediated, down gradient, no energy	Glucose (GLUT transporters), amino acids
Aqueous diffusion	Through pores/channels, down gradient	Water (aquaporins), small ions
Active transport	Against gradient, requires ATP	Na⁺-K⁺ ATPase, drug efflux pumps (P-gp)

Only simple/facilitated diffusion and aqueous diffusion follow Fick's law directly. Active transport does not, as it moves molecules against their concentration gradient.

Summary

$$\boxed{\text{Rate of diffusion} \propto \frac{D \times A \times \Delta C}{\Delta x}}$$

The key relationships to remember:

More surface area → faster diffusion (lungs have ~70 m² for this reason)
Thicker membrane → slower diffusion (fibrosis impairs gas exchange)
Larger gradient → faster diffusion (breathing high-FiO₂ increases PAO₂ and thus the gradient)
Higher D → faster diffusion (CO₂ >> O₂ per unit gradient)
Diffusion is only efficient over micrometers - the capillary system brings blood to within 20-50 μm of every metabolizing cell

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