Free Ion Activity Model

The Free Ion Activity Model (FIAM) is the most commonly used model to describe biouptake fluxes outside of the cell.  The model employs the following assumptions:
  1. The plasma membrane of the cell is the primary site for metal interactions with living organisms.
  2. Interaction with the plasma membrane can be described as a surface complexation reaction.
  3. Metal transport towards the membrane in solution and surface complexation reaction occur rapidly, such that pseudo-equilibrium is established between metal species in the bulk solution and at the biological surface.
  4. The biological response is strictly dependent on the concentration of MXcell surface complex.
  5. In the range of metal concentrations of toxicological interest, the concentration of free sites remains virtually constant and variations in {MXcell} follow variations in [Mz+].
  6. During exposure to the metal of interest, the nature of the biological surface remains constant.
These assumptions limit the applicability of the model to certain systems, but the results of the model are consistent with experimental results for systems involving divalent trace metals, inorganic media or filtered seawater, a fixed pH, and a known ligand concentration.

The FIAM uses three equations to model any metal-organism system:

    1.  Metal Ion in Solution
        K1[M]=[ML]/[M]
        where Mz+ is the free metal ion, L is the ligand, and ML is the metal complex.  The metal complex is a metal ion bonded to a ligand.

    2.  Metal Ion Surface Reaction
        {MXcell} = K2*{Xcell}*[M]
        where {-Xcell} and {MXcell} are the concentrations of the surface site and metal-surface complex, respectively
    3.  Metal-Ligand Complex Surface Reaction
        {MXcell} = K1*K3*{Xcell}*[M]

These equations show that the concentration of metal bound to special surface sites only depends on the concentration of metal ions in solution and doesn't depend on the concentration of ligand or available surface sites (see assumption 5).  Therefore, the graph below predicts the concentration of metal bound to special surface sites for any system modeled by FIAM:

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Information from: Campbell, Peter G. C. "Interactions Between Trace Metals and Aquatic Organisms: A Critique of the Free Ion Activity Model." Metal Speciation and Bioavailability in Aquatic Systems. Ed. Andre Tessier and David R. Turner. Vol. 3. New York: John Wiley & Sons, Incorporated, 1996. 45-102.