Week 2 ELM 5: Electrochemical Gradients

Diffusion

Simple Diffusion

• Diffusion is the movement of molecules down a concentration gradient, from areas of high concentration to areas of low concentration.
• Consider a drop of concentrated calcium ions (Ca++) added to water. The ions will spontaneously move from the high concentration area to the low concentration area until the concentration is uniform.
• The concentration gradient dissipates over time as the molecules spread out.
• This process increases entropy (disorder), in accordance with the 2nd Law of Thermodynamics.

Diffusion Across Membranes

• Ions cannot cross lipid bilayers due to the hydrophobic nature of the membrane.
• Ionic concentrations can differ significantly on either side of a membrane, creating a concentration gradient.
• If a "hole" is introduced into the membrane (e.g., by a protein channel), ions will flow down their concentration gradient until equilibrium is reached.
• Molecules that create these "holes" facilitate diffusion.

Types of Transporters

• Pumps (Primary Transporters): Use energy (e.g., ATP) to move ions against their concentration gradient (e.g., sodium pump).
• Carriers (Secondary Transporters): Use the electrochemical gradient of one ion to move another ion (e.g., sodium-calcium exchanger).
• Ion Channels: Provide a pathway for ions to flow down their electrochemical gradient (e.g., potassium channels, nicotinic acetylcholine receptors).
  • Ion channels can be opened by voltage changes or ligand binding.

Molecular Motion and Diffusion

• Molecules in liquids are in constant motion due to thermal agitation.
• Water molecules have an average center-to-center distance (r) of about 2.8 Ångströms.
• Molecules move short distances (Ångströms) for short times (picoseconds) before colliding with each other.

Fick's Law of Diffusion

• Adolf Fick (at age 26) showed that the number of molecules (N) moving across an interface is proportional to:
  • The area of the interface (A).
  • The concentration gradient.
• Mathematically, this is expressed as: -dN/dt = D \cdot A \cdot dc/dx
  • Where: -dN/dt is the rate of transfer.
    • dc/dx is the concentration gradient.
    • D is the diffusion coefficient, a proportionality constant.
• The key idea is that the rate of diffusion is proportional to both the area and the concentration gradient.

Einstein and Diffusion

• Albert Einstein (in 1906, also at age 26) showed that diffusion results from the random walk of molecules.
• The distance a diffusing molecule travels from its starting point depends on the dimensionality of the diffusion:
  • One dimension: t = d^2 / 2D
  • Two dimensions: t = d^2 / 4D
  • Three dimensions: t = d^2 / 6D
    • Where: d is the root mean square distance (cm).
      • t is time in seconds.
      • D is the diffusion coefficient in cm²/sec.

Implications of Diffusion for Biology

• Basic diffusion laws significantly impact biological processes.
  • 1D diffusion: Movement along DNA.
  • 2D diffusion: Movement within a membrane.
  • 3D diffusion: Movement in liquid (cytosol, extracellular fluid).
• Molecules diffuse further in three dimensions because the chances of colliding with other molecules are lower.
• In contrast, molecules moving in two dimensions are more likely to collide.
• Analogy: Planes at Heathrow airport (more congestion in 2D).

Further Implications of Diffusion

• Catalysts work by providing a surface (2D) that allows molecules to collide more easily.
• Signaling molecules in membranes (2D) have a higher chance of interacting (e.g., GPCRs).
• Signaling molecules have longer ranges when they are not bound to membranes (3D).

Electrophoretic Movement

Introduction to Electrophoretic Movement

• Electrophoretic movement considers the influence of an electric field on ion movement.
• In a sodium chloride (NaCl) solution, ions will move under the influence of an electric field.

The Electrochemical Gradient

• Ion movement under the influence of an electric field is called electrophoretic movement.
• Electrophoretic movement can either add to or subtract from diffusion, depending on the charge of the ion and the direction of the electric field.
• The total gradient is called the electrochemical gradient, and it is the sum of:
  • The gradient caused by diffusion.
  • The gradient caused by electrophoretic movement.

Strength of Electrochemical Gradient

• The electrochemical gradient can be weak or strong, depending on the relative contributions of the concentration gradient and the electrical gradient.
• Cells are typically negative inside, which influences the movement of ions across the membrane.

Ohm's Law

Factors Influencing Ion Movement

• Ions move through ion channels, and their direction is determined by the electrochemical gradient (into or out of the cell).
• The rate at which ions move across the membrane depends on four key factors:
  • The size of the electrochemical gradient.
  • The nature of the ion.
  • The number of open ion channels.
  • The properties of the ion channel.

Basic Electrical Concepts

• Current (I): The flow of ions (many ions flowing per second = big current; few ions flowing per second = small current).
• Voltage (V): The potential difference between two points (big potential difference = high voltage; no potential difference = no voltage; no ion flow without a potential difference).
• Resistance (R): The opposition to the flow of ions (low resistance = big current; high resistance = small current).

Ohm's Law Explained

• Ohm's Law describes the relationship between current, voltage, and resistance:
  • Current (I) = Volts (V) / Resistance (R)
• Electrophysiologists often use a rearranged equation that involves conductance:
  • Current (I) = Volts (V) \times Conductance
    • Where conductance is the inverse of resistance (Conductance = 1/R).

Influences on Movement of Ions (Recap)

• The size of the electrochemical gradient.
• The nature of the ion.
• Number of open ion channels.
• The properties of the ion channel.

Effect of Electrochemical Gradient Size

• A weak electrochemical gradient results in less ion flow, while a strong electrochemical gradient results in greater ion flow.

Effect of the Nature of the Ion

• Charge: Positive or negative charge affects direction of movement in an electrical field.
• Number of Charges: E.g., +1 or +2 affects the strength of the electrical force.
• The Nernst equation (covered later) takes these factors into account.
  • Example:
    • Sodium ions (Na+) with a high electrochemical gradient.
    • Chloride ions (Cl-) with a high concentration gradient but electrical gradient in the opposite direction result in low electrochemical gradient.

Effect of Number of Open Ion Channels

• More open ion channels lead to greater ion flow.

Effect of Properties of the Ion Channel

• Selectivity: Some channels are selective for specific ions (e.g., a sodium-selective channel).
• Permeability: Some channels allow ions to pass through more easily than others (i.e., more permeable ion channel).