Lecture #11

Membrane Potentials

Introduction to Membrane Potentials

Membrane potentials are fundamental electrical properties of living cells, resulting from the separation of charge across the plasma membrane. These potentials are essential for the function of excitable cells such as neurons and muscle cells.

• Definition: A membrane potential is the voltage difference between the inside and outside of a cell, created by the unequal distribution of ions.

• Importance: Membrane potentials enable cells to transmit electrical signals, regulate ion transport, and initiate cellular responses such as muscle contraction and neurotransmitter release.

• Example: Neurons use changes in membrane potential to generate action potentials for communication.

What is Electricity?

Electricity in biological systems refers to the separation or manipulation of electric charge, which is essential for cellular function.

• Definition: Electricity is the movement or separation of electric charge, resulting in electrical phenomena.

• Biological Context: Living organisms (cells, tissues, organs) generate electrical phenomena through ion movement.

• Transmembrane Electrical Potential: Every living cell maintains a voltage across its plasma membrane due to charge separation.

• Example: The voltage across a neuron’s membrane is crucial for nerve impulse transmission.

Electricity in Fluids

In biological fluids, electricity is carried by ions rather than electrons, and the voltage represents stored potential energy.

• Charge Carriers: In cells, charge is carried by electrolytes such as Na+, K+, Cl-, Ca2+, not by electrons.

• Voltage (Electric Potential): The electrical potential difference is expressed in volts and represents stored energy due to charge separation.

• Example: The difference in ion concentration across a membrane creates a voltage, as illustrated by the water tank analogy (potential difference).

Voltage and Electric Fields

Voltage creates an electric field that exerts force on charged particles, influencing their movement across membranes.

• Force on Charge: Opposite charges attract, like charges repel. The force (F) on a charge (q) in an electric field (E) is given by:

$F = q \cdot E$

• Electric Field Lines: These lines represent the direction and strength of the electric field, guiding the movement of ions such as Cl- and Na+.

• Example: In neurons, electric fields drive the movement of ions during signal transmission.

Resting Membrane Potential

Definition and Importance

The resting membrane potential (RMP) is the voltage difference across the plasma membrane of a cell at rest, typically with the inside being more negative than the outside.

• Definition: Resting membrane potential is the electrical potential difference between the inside and outside of a resting cell, usually measured in millivolts (mV).

• Typical Value: For neurons, the RMP is approximately -70 mV.

• Significance: RMP is essential for the excitability of neurons and muscle cells, setting the stage for action potentials.

Establishment of Resting Membrane Potential

The RMP is established by differences in ion concentrations and selective permeability of the plasma membrane, primarily involving potassium (K+) and sodium (Na+).

• Ion Concentration Differences: The inside of the cell has higher K+ and lower Na+ compared to the outside.

• Selective Permeability: The membrane is more permeable to K+ at rest, allowing it to diffuse out and making the inside more negative.

• Sodium-Potassium Pump: The Na+/K+ ATPase actively transports 3 Na+ out and 2 K+ in, contributing to the negative charge inside.

• Electrogenic Effect: The pump results in a net loss of positive charge, further driving the interior negative.

• Example: Some heart medications modulate the pump to affect membrane potential.

Equilibrium Potentials and the Nernst Equation

Each ion has an equilibrium potential, calculated using the Nernst equation, which predicts the voltage at which there is no net movement of that ion across the membrane.

• Nernst Equation: For a given ion, the equilibrium potential (Eion) is:

$E_{ion} = \frac{RT}{zF} \ln \left( \frac{[ion]_{outside}}{[ion]_{inside}} \right)$

• Simplified for K+ at 37°C:

$E_K = 61.5 \log \left( \frac{[K^+]_{outside}}{[K^+]_{inside}} \right)$

• Example: For K+, with typical concentrations, $E_K \approx -90$ mV.

Goldman-Hodgkin-Katz Equation

The overall membrane potential is determined by the relative permeabilities and concentrations of multiple ions, described by the Goldman-Hodgkin-Katz (GHK) equation.

• GHK Equation:

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

• Relative Conductance: The ease with which ions cross the membrane affects the membrane potential.

Depolarization and Hyperpolarization

Changes in membrane potential can trigger cellular responses. Depolarization makes the membrane potential more positive, while hyperpolarization makes it more negative.

• Depolarization: Caused by influx of Na+ or Ca2+, leading to cellular activation (e.g., neurotransmitter release, muscle contraction).

• Hyperpolarization: Caused by efflux of K+ or influx of Cl-, making the cell less likely to fire an action potential.

• Example: Depolarization in neurons triggers exocytosis of neurotransmitters.

Summary Table: Major Ions and Their Roles in Membrane Potential

Ion	Inside Cell	Outside Cell	Equilibrium Potential (mV)	Effect on Membrane Potential
K+	High	Low	-90	Drives inside negative
Na+	Low	High	+61	Drives inside positive
Cl-	Low	High	-70	Stabilizes membrane potential
Ca2+	Very Low	Low	+120	Triggers exocytosis, contraction

Additional info: The notes have been expanded to include full definitions, equations, and context for the major concepts in membrane potentials and resting membrane potential, suitable for college-level Anatomy & Physiology students.