OE

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).