414/514 Immunology Principles 415/515 Immunology Principles and Practice

Affinity and Avidity

• Affinity - strength of binding between a single epitope and paratope
  • determined by the equilibrium constant (Ka) of the association reaction between antibody (Ab) and antigen, represented by hapten (H)

    Ab + H = AbH
    	according to	the law of mass action
    Ka = [AbH]/[Ab][H]	where:
    	[Ab] =	concentration of free Ab binding sites, and
    	[H] =	concentration of free hapten at equilibrium

    • at [Hc], the free hapten concentration at which half the Ab binding sites are filled

      [AbH] = [Ab] and Ka =1/[Hc]

    • the higher the affinity, the lower the [Hc] when this occurs, therefore the higher the Ka (in units of L/mole)
    • this can be expressed in terms of the force of interaction as a difference in free energy, as:
      • delta G = -RT ln Ka
      • where:
        • G = Gibbs free energy
        • R = universal gas constant
        • T = absolute temperature
        • ln = natural logarithm
    • mathematical rearrangement yields the equation:
      • r/[H] = nk - rk
      • where:
        • r = the average number of H bound to each Ab
        • n = valence of Ab
    • Scatchard plot is generated by plotting r/[H] vs. r
      • monoclonal antibodies give a straight line, whereas polyclonal antibodies give a concave line
      • X-intercept = valence of the antibody
      • Y-axis value = affinity at the point on the plot that corresponds to [Hc]
• Avidity
  • Functional affinity - strength of the interaction of antigen molecules with multiple epitopes with antibodies with more than one paratope

  n Ab + m Ag = Abn Agn

  • Multiple epitope-paratope interactions are involved, so the factors contributing to avidity are complicated (consider the extreme case of a bacterium with multiple non-identical epitopes interacting with an IgM antibody with ten paratopes)
  • Multivalency of antigen and antibody lead to a "bonus" effect due to cooperative interactivity of the molecules in AgAb complexes
    • the probability that all AgAb interactions will dissociate simultaneously is exceedingly small
    • therefore, if one interaction is dissociated, the others will remain associated, thus enhancing the probability that those dissociated will reassociate
  • The bonus effect is that avidity is a multiple of the affinities of the individual interactants (not a simple sum of their affinities); therefore:

  deltaG1 = -RT ln Ka1 + deltaG2 = -RT ln Ka2

  deltaG = deltaG1 + deltaG2 = -RT ln Ka1 + -RT ln Ka2

  -RT ln Kavid = -RT (lnKa1 + lnKa2) = -RT ln(Ka1 x Ka2)

= Kavid = Ka1 x Ka2