Statistics and Thermodynamics in the Growth of Antigen-Antibody Complexes

Ping Zhang ； Hai-Jun Wang

《Chinese Journal of Physics》 48卷2期 (2010/04) Pp. 277-293

並列摘要

For the system consisting of multivalent antigen (Ag) and antibody (Ab) molecules, the branched growth process of antigen-antibody complexes is theoretically investigated by the methods of statistical mechanics and thermodynamics. A main attempt is made to consider the statistical and thermodynamic properties concerning the formation of Ag-Ab complexes. Specifically, starting with two kinds of partition functions constructed from two different statistical viewpoints, the equilibrium free energy and the law of mass action as well as the equilibrium size distribution of the Ag-Ab complexes are derived. The aggregation process resulting from Ag-Ab binding is studied by considering it as a sol-gel transition process. Then the gelation condition, the gelation region associated with the valences of Ag and Ab, and the composition are obtained, which enable one to find the proper conditions that the precipitation or agglutination takes place. For describing the sol-gel transition in the system of interest, the scaling behaviors of the k-th moment and the gel fraction near the critical point are investigated to give the corresponding scaling laws. Furthermore, as an application, the isothermal compressibility is obtained, which can characterize the connectivity induced by binding pairs.