Biopolym. Cell. 1988; 4(1):35-40.
Structure and Function of Biopolymers
Critical (percolation) behaviour and fractal dimension of aggregates in immunological agglutination reaction
1Markel V. A., 2Stokman M. I.
  1. Institute of Automatics and Electrometry, Siberian Branch, Academy of Sciences of the USSR
    Novosibirsk, USSR
  2. Novosibirsk State University
    Novosibirsk, USSR


Equilibrium and kinetic properties of the immunological agglutination reaction are theoretically considered. A percolation model of agglutination is suggested which predicts critical behavior 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 predictions of theoretical models.


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