Ionic Basis of the Resting Membrane Potential: Study Guide

Ionic Basis of the Resting Membrane Potential

Introduction

The resting membrane potential is a fundamental property of all cells, especially neurons, and arises from the unequal distribution of ions across the cell membrane. This study guide explores the ionic gradients, membrane permeability, and the mathematical equations used to predict and explain membrane potentials.

Ions in Solution and Electrochemical Gradients

Water as the Solvent of Life

Water is the most abundant molecule in biological systems, serving as the medium for ion movement and biochemical reactions.

• Molecular Weight: 18 g/mol

• Density: ~1 kg/L

• Concentration: ~55 mol/L (much higher than any other solute)

• Role: Facilitates ion dissociation and transport

Ions in Water

Ions are atoms or molecules with a net electrical charge. Common biological ions include sodium (Na+), potassium (K+), chloride (Cl-), and calcium (Ca2+).

• Cations: Positively charged (e.g., Na+, K+)

• Anions: Negatively charged (e.g., Cl-)

• Dissociation: Ionic compounds like NaCl dissociate in water, allowing ions to move freely

Phospholipid Membranes and Ion Distribution

Phospholipid Bilayer Structure

Cell membranes are composed of a phospholipid bilayer, which acts as a barrier to most ions and polar molecules.

• Hydrophilic head: Faces water

• Hydrophobic tails: Face inward, away from water

• Function: Creates compartments and restricts ion movement

Selective Permeability

Membranes are selectively permeable, allowing certain ions to pass through via specific channels and transporters.

• Transporters and Pumps: Actively move ions against concentration gradients

• Ion Channels: Allow passive diffusion of ions down their concentration gradients

Ion Concentrations Inside and Outside Cells

Ions are unequally distributed across cell membranes, creating concentration gradients that drive passive diffusion.

Ion	Intracellular (mM)	Extracellular (mM)
Potassium (K+)	140	5
Sodium (Na+)	5–15	145
Chloride (Cl-)	4–30	110
Calcium (Ca2+)	0.0001	1–2

Membrane Potential and Electrical Signaling

Generation of Membrane Potential

The movement of ions across cell membranes generates electrical signals. Pumps and transporters maintain ionic gradients, resulting in a potential difference (membrane potential, Vm).

• Current (I): Flow of ions through open channels

• Membrane Potential (V): Difference in charge across the membrane

Two-Compartment Model

A simplified model illustrates how selective permeability and concentration gradients generate membrane potential.

• Equal KCl concentrations: No net flux, V = 0

• Higher KCl inside: K+ diffuses out, creating a positive charge outside

• Electrochemical equilibrium: Electrical gradient opposes further K+ movement

The Nernst Equation and Equilibrium Potential

Definition and Calculation

The equilibrium potential (EX) is the membrane potential at which the electrical and concentration gradients for a single ion are balanced. The Nernst equation calculates this potential.

• Variables: R (gas constant), T (temperature), F (Faraday's constant), z (valence), [X]out, [X]in

• Equation:

$E_X = \frac{RT}{zF} \ln \frac{[X]_{out}}{[X]_{in}}$

Simplified Nernst Equation for Monovalent Cations

At 18°C (291 K), for z = +1:

$E_X = 0.058 \log_{10} \frac{[X]_{out}}{[X]_{in}}$

Example Calculation

For K+ with [K]in = 10 mM, [K]out = 1 mM:

$E_K = 0.058 \log_{10} \frac{1}{10} = -0.058 \text{V} = -58 \text{mV}$

Driving Force and Ionic Flux

Electrochemical Equilibrium and Ion Flux

At equilibrium, the net movement of ions stops. Changing the membrane potential alters the direction and magnitude of ion flux.

• Driving Force: Difference between membrane potential (Vm) and equilibrium potential (EX)

• Equation: $I_X = g_X (V_m - E_X)$

Current-Voltage (IV) Relationship

IV Relationship for Cations and Anions

The IV relationship describes how current changes as a function of voltage. For cations, inward current is negative; for anions, current is opposite to ion flux.

• Cations: Negative current = inward flux, positive current = outward flux

• Anions: Current direction is opposite to ion flux

Typical Equilibrium Potentials in Neurons

Values for Major Ions

• EK: ~ -90 mV

• ECl: ~ -70 mV

• ENa: ~ +60 mV

• ECa: ~ +125 mV

Ohm’s Law and Driving Force

Ohm’s Law in Membrane Physiology

Ohm’s Law relates current, voltage, and resistance. In biological membranes, conductance (g) is the reciprocal of resistance (R).

• Equation: $I = gV$

• Driving Force: $I_X = g_X (V_m - E_X)$

Resting Membrane Potential and the Goldman Equation

Goldman-Hodgkin-Katz (GHK) Equation

The Goldman equation extends the Nernst equation to account for multiple ions and their relative permeabilities.

• PX: Permeability coefficient for each ion

• Vm: Determined by the weighted contributions of all permeant ions

Scenarios with Multiple Ions

• Membrane only permeable to K+: Vm = EK

• Membrane only permeable to Na+: Vm = ENa

• Membrane equally permeable to both: Vm = 0 mV

Summary Table: Extracellular and Intracellular Ion Concentrations

Ion	Intracellular (mM)	Extracellular (mM)
Potassium (K+)	140	5
Sodium (Na+)	5–15	145
Chloride (Cl-)	4–30	110
Calcium (Ca2+)	0.0001	1–2

Key Concepts and Applications

• Electrochemical equilibrium: Balance of electrical and concentration gradients

• Nernst equation: Predicts equilibrium potential for a single ion

• Goldman equation: Predicts membrane potential with multiple ions

• Driving force: Determines direction and magnitude of ion flux

• Resting membrane potential: Primarily determined by K+ permeability, but influenced by other ions

Example:

In a neuron, the resting membrane potential is typically around -70 mV, reflecting high permeability to K+ and lower permeability to Na+ and Cl-.

Additional info:

These notes expand on the original lecture content by providing definitions, equations, and context for the ionic basis of membrane potentials, suitable for exam preparation in anatomy and physiology courses.