Understanding Multivalency (aka Avidity)

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Making a Ligand or Drug multivalent is a common method to try to improve the potency or EC50 of that drug from that predicted by the Hill Equation. Below we summarize the full spectrum of multivalent enhancement for the n = 2 case (n being the degree of multivalency) but these rules are easily extendable to the n-valent case aswell.

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The minumum multivalent enhancement is observed when only one “binder” can bind one target at a time. This often occurs if the linker between the binding moeities is too short. In these, cases the EC50 is only improved by a statistical factor of 2 (or n in the n-valent case).

The maximum multivalent enhancement is observed when both “binders” must bind two targets simultaneously. This can occur if the linker between the binding moeities is rigid and is a geometric match for the multivalent target. These situations are very rare in biological contexts but can be observed in the context of supramolecular assembly (where precise geometric engineering is possible). In this case the EC50 is equal to the Kd raised to the a power of 2 (or n in the n-valent case).

Generally, most multivalent-enhancement occurs in between these extremes where “both binders” can bind simultaneously. Here, the concept of “effective concentration” comes into play and defined as the molarity of the receptor (one divided by Avogadro’s number) divided by the search volume space that the linker can explore (often assumed to be the volume of a sphere). Here the EC50 equation is equal to the Kd raised to a power of 2 and divided by the effective concentration.

 

REFERENCES: 

  1. Crothers, D. Metzger, H. The influence of polyvalency on the binding properties of antibodies. Immunochemistry, 1972, 9, 341-357.
  2. Kramer, R.; Lehn, J.M.; Marquis-Rigault, A.; Self-recognition in helicate self-assembly: Spontaneous formation of helical metal complexes from mixtures of ligands and metal ions. PNAS, 1993, 90, 5394-5398.
  3. Mammen, M.; Choi, S. K.; Whitesides, G. M. Polyvalent interactions in biological systems: implications for design and use of multivalent ligands and inhibitors Angew. Chem. Int. Ed. 1998, 37, 2754-2794.
  4. Lauffenburger, D.A. Receptors: Models for Binding, Trafficking and Signalling, Oxford University Press 1993.
  5. Ercolani, G. Phsysical Basis of Self-Assembly Macroclyclizations. J. Phys. Chem. B. 1998, 102, 5699-5703.
  6. Ercolani, G.; Piguet, C.; Borkovec, M.; Hamacek, J. Symmetry numbers and statistical factors in self-assembly and multivalency. J. Phys. Chem. B. 2007, 111, 12195-12203.

 

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This work by Eugene Douglass and Chad Miller is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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