European Biophysics Journal

, Volume 34, Issue 7, pp 899–911 | Cite as

Anticooperativity in diffusion-controlled reactions with pairs of anisotropic domains: a model for the antigen–antibody encounter

  • F. PiazzaEmail author
  • P. De Los Rios
  • D. Fanelli
  • L. Bongini
  • U. Skoglund


The encounter between anisotropic agents in diffusion-controlled reactions is a topic of very general relevance in chemistry and biology. Here we introduce a simplified model of encounter of an isotropic molecule with a pair of partially reacting agents and apply it to the encounter reaction between an antibody and its antigen. We reduce the problem to the solution of dual series relations, which can be solved iteratively, yielding the exact solution for the encounter rate constant at any desired order of accuracy. We quantify the encounter effectiveness by means of a simple indicator and show that the two binding centers systematically behave in an anticooperative fashion. However, we demonstrate that a reduction of the binding active sites allows the composite molecule to recover binding effectiveness, in spite of the overall reduction of the rate constant. In addition, we provide a simple formula that enables one to calculate the anticooperativity as a function of the size of the binding site for any values of the separation between the two active lobes and of the antigen size. Finally, some biological implications of our results are discussed.


Diffusion-controlled reactions Encounter rate constant Anisotropic reactants Anticooperativity Antibodies 



We wish to thank three anonymous referees for their useful comments.


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Copyright information

© EBSA 2005

Authors and Affiliations

  • F. Piazza
    • 1
    Email author
  • P. De Los Rios
    • 1
  • D. Fanelli
    • 2
    • 3
  • L. Bongini
    • 3
  • U. Skoglund
    • 3
  1. 1.Laboratoire de Biophysique Statistique, SB–ITPEcole Politechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Dipartimento di Energetica “S. Stecco”Università di FirenzeFlorenceItaly
  3. 3.Department of Cell and Molecular BiologyKarolinska InstitutetStockholmSweden

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