Excitable Cells

Introduction to Excitable Cells

Excitable cells, such as neurons and muscle cells, are specialized for rapid electrical signaling. Their ability to generate and propagate electrical signals is fundamental to nervous system function and muscle contraction.

• Membrane potential (Vm): The voltage difference across a cell's plasma membrane due to unequal distribution of ions.

• Action potentials: Rapid, transient changes in membrane potential that serve as signals in excitable cells.

• Graded potentials: Local changes in membrane potential that vary in magnitude and can summate to trigger action potentials.

Electrical Principles in Biology

Membrane Potential and Ion Distribution

The membrane potential arises from the separation of opposite charges across the cell membrane, primarily due to the distribution of ions such as potassium (K+), sodium (Na+), and chloride (Cl-).

• Insulator: The lipid bilayer of the membrane prevents free passage of ions, maintaining charge separation.

• Conductor: Ion channels allow selective movement of ions, enabling changes in membrane potential.

• Active vs. Passive behaviors: Membrane can behave passively (like a capacitor) or actively (via opening/closing of ion channels).

Ion Channels

Types and Functions of Ion Channels

Ion channels are protein pores that facilitate the movement of specific ions across the membrane. Their activity is crucial for setting and changing membrane potentials.

• Ion selectivity: Channels may be selective for K+, Na+, Ca2+, etc.

• Gating mechanisms: Channels can be 'leak' (always open), voltage-gated (open in response to voltage changes), or ligand-gated (open in response to chemical signals).

• Activity patterns: Channels may be fast, delayed, transient, or long-lasting.

• K+ leak channels: Major contributors to the resting membrane potential.

Equilibrium Potentials: The Nernst Equation

Definition and Calculation

The Nernst potential (Eion) is the membrane voltage at which the net flux of a particular ion is zero, balancing diffusional and electrical forces.

• Equilibrium potential: The voltage at which an ion's movement due to concentration gradient is exactly opposed by the electrical gradient.

• Key variables: Ion concentrations inside and outside the cell, ion charge (z), temperature (T).

Nernst Equation:

• R: Universal gas constant (8.31 J/mol·K)

• T: Temperature in Kelvin (typically 310 K for 37°C)

• F: Faraday's constant (96,485 C/mol)

• z: Valence (charge) of the ion

Example: For K+ with [K+]outside = 4 mM, [K+]inside = 140 mM, z = +1, T = 310 K:

Practical Meaning of Nernst Potentials

• "Ceiling" and "Floor": The Nernst potentials for Na+ and K+ set the upper and lower boundaries for membrane potential changes.

• Depolarization: Membrane potential becomes less negative (moves toward Na+ Nernst potential).

• Hyperpolarization: Membrane potential becomes more negative (moves toward K+ Nernst potential).

Goldman-Hodgkin-Katz (GHK) Equation

Accounting for Multiple Ions

The GHK equation extends the Nernst equation to account for the relative permeabilities of multiple ions, providing a more accurate calculation of the membrane potential.

GHK Equation:

• Pion: Permeability of the membrane to each ion

• Concentration terms: [ion]in and [ion]out are the concentrations inside and outside the cell

Application: The GHK equation is used to calculate both resting and non-resting membrane potentials, depending on the permeabilities of the ions involved.

Terminology: Polarization States

Describing Membrane Potential Changes

• Polarized: Membrane potential is at rest, typically negative inside relative to outside.

• Depolarization: Membrane potential becomes less negative (moves toward zero or positive values).

• Hyperpolarization: Membrane potential becomes more negative than resting potential.

• Repolarization: Return of membrane potential to resting value after depolarization.

Ion Pumps and Maintenance of Gradients

Na+/K+ ATPase Pump

The sodium-potassium pump is an active transporter that maintains the concentration gradients of Na+ and K+ across the membrane, essential for excitable cell function.

• Active transport: Uses ATP to move 3 Na+ out and 2 K+ in against their concentration gradients.

• Maintains resting potential: Without this pump, ionic gradients would dissipate and cells would lose excitability.

Summary Table: Key Ion Concentrations and Potentials

The following table summarizes typical ion concentrations and their equilibrium potentials in neurons:

Additional info: Equilibrium potentials are calculated using the Nernst equation at physiological temperature (37°C).

Applications and Relevance

Significance in Neuronal Signaling

• Resting and action potentials are determined by the interplay of ion gradients, channel permeability, and active transport.

• Understanding Nernst and GHK equations is essential for interpreting neuronal excitability and synaptic transmission.

• Graded potentials and summation underlie complex neural processing and integration.