Biopolymers and cell. 1988. Volume 4. № 1. 35 - 40

V. A. Markel, M. 1. Stokman

CRITICAL (PERCOLATION) BEHAVIOUR AND FRACTAL DIMENSION OF AGGREGATES IN IMMUNOLOGICAL AGGLUTINATION REACTION

Summary

    Equilibrium and kinetic properties of the immunological agglutination reaction are theoretically considered. A percolation model of agglutination is suggested which predicts critical behaviour of the reaction in a serum concentration. The appearance of an infinite cluster of agglutinated particles (bacteria) is shown to be similar to the phase second-order transition. The fraction of particles which are bound to the infinite cluster (precipitate) plays the role of the order parameter. The kinetics of an early stage of the agglutination reaction, previously studied, is in agreement with predictions of the dynamic scaling. It permits finding the fractal dimension of the bacterial clusters which has proved to be nontrivial, i. e. distinct from the dimension of the space. Magnitudes of the fractal dimension are compared to predicl'ons of theoretical models.