FIG. 11 Representation of the slope T [Eq. (11)] of the reduced mass distribution in the domain I (see Fig. 10) of the aggregation process as a function of the square root of the HCG concentration expressed in IU/g antibody-coated latex.

HCG molecules and the two types of sensitized latexes. The transition from domains I to II occurs at the same time in all of these experiments.

C. Coagulation Involving One Latex Bearing the Antibody Specific for the «HCG Determinant, a Second Latex Bearing the Antibody Specific for the pHCG Determinant, and the Solubilized HCG Protein at the Concentration of 33 IU/g Latex

The three constituents were mixed simultaneously and left at rest to allow the onset of perikinetic aggregation. Experiments were carried out using different proportions (20%, 50%, and 80%) of a given sensitized latex, and the corresponding variations of S(t) and N(t) as a function of time (log-log scale) are shown in Fig. 13. Under these conditions, the kinetics and extent of aggregation were determined to be functions of the composition of the system [10-13]. When the two latexes are present in equal proportions, the average masses S(t) (curve c) and N(t) (curve d) increase at their most rapid rate to values of S(t) = 13 and N(t) = 5, after which aggregation abruptly slows. One notes that the masses increase faster than in the previous experiments of heterocoagulation [curves a and b in Fig. 13, for the system complex A (or B) and the other

FIG. 12 Representation of the average masses S(t) (curves a and c) and N(t) (curves b and d) as a function of aggregation time (log-log scale). The HCG concentration is 33 IU/g latex. Curves a and b: Heterocoagulation in a mixture containing equal proportions of one latex bearing the complex [antibody-antigen] and a second latex bearing only the antibody: (•, ■), complex [anti-aHCG + HCG] and the [anti-PHCG]; (O, □), complex [anti-PHCG + HCG] and the [anti-aHCG]; curves c and d correspond to experiments containing initially equal proportions of latex bearing the [anti-PHCG] and the [anti-aHCG] and HCG at the concentration of 33 IU/g latex (see Fig. 10).

FIG. 12 Representation of the average masses S(t) (curves a and c) and N(t) (curves b and d) as a function of aggregation time (log-log scale). The HCG concentration is 33 IU/g latex. Curves a and b: Heterocoagulation in a mixture containing equal proportions of one latex bearing the complex [antibody-antigen] and a second latex bearing only the antibody: (•, ■), complex [anti-aHCG + HCG] and the [anti-PHCG]; (O, □), complex [anti-PHCG + HCG] and the [anti-aHCG]; curves c and d correspond to experiments containing initially equal proportions of latex bearing the [anti-PHCG] and the [anti-aHCG] and HCG at the concentration of 33 IU/g latex (see Fig. 10).

sensitized latex present in equal proportions]. As noted further, the aggregation rate did not depend on the nature of the complex A or B present in the system.

For the dissymmetrical systems, the aggregation rate is expected to not depend on the nature of the [latex + anti-aHCG] or [latex + anti-PHCG] present in great excess in the system insofar as it was assumed that the HCG molecules were distributed over the surface of the two sensitized latex particles in proportion to the developed areas. This assumption is not valid since the system 20% anti-aHCG + 80% anti-PHCG aggregates faster than does the system 80% anti-aHCG + 20% anti-PHCG. Moreover, the transition from domain I to II at 200

FIG. 13 Aggregation in a mixture containing the two types of sensitized latex particles and the solubilized HCG protein at a concentration of 33 IU/g latex. Representation of the weight S(t) (circle) and number N(t) average masses (square) as a function of time for experiment carried out in the presence of 33 IU HCG/g latex and different mixtures of sensitized latex particles: (O, □) [80% anti-aHCG + 20% anti-PHCG]; (•, ■) [20% anti-aHCG + 80% anti-PHCG]; curves c [S(t)] and d [N(t)] correspond to [50% anti-aHCG + 50% anti-PHCG]. Curves a and b refer to aggregation of complexes A or B (no free HCG molecules) in the presence of the second sensitized latex particles at the same latex concentration.

FIG. 13 Aggregation in a mixture containing the two types of sensitized latex particles and the solubilized HCG protein at a concentration of 33 IU/g latex. Representation of the weight S(t) (circle) and number N(t) average masses (square) as a function of time for experiment carried out in the presence of 33 IU HCG/g latex and different mixtures of sensitized latex particles: (O, □) [80% anti-aHCG + 20% anti-PHCG]; (•, ■) [20% anti-aHCG + 80% anti-PHCG]; curves c [S(t)] and d [N(t)] correspond to [50% anti-aHCG + 50% anti-PHCG]. Curves a and b refer to aggregation of complexes A or B (no free HCG molecules) in the presence of the second sensitized latex particles at the same latex concentration.

min appears to be delayed to 900 min (transition from domain II to III) for the latter system. Therefore, the anti-PHCG-coated latex, which controls the extent of aggregation insofar as it is present at the low concentration of 20% in one experiment, gives rise to the complex B, which has longer activity toward aggregation. Conversely, the anti-aHCG-coated latex, which controls the aggregation in the second experiment, gives rise to the complex A, which is more efficient toward aggregation because the average aggregate masses increase faster. Since we have no theoretical or numerical support to interpret the prolonged activity of the complex B, the higher efficiency of complex A may be analyzed taking into account results of the numerical study of Meakin and Djordjevic addressed to cluster-cluster aggregation in two-monomer systems of different functionalities [10]. This study led us to conclude the following: when two sensitized latex particles are suspended in equal portions in a solution containing a small amount of HCG proteins (full coating of the sensitized latex particles is not allowed), the solute HCG molecules do not adsorb evenly on the two sensitized latexes but preferentially adsorb on the anti-aHCG sites. The former analysis based on the electrophoretic mobility of the complexes A and B (Fig. 3) erroneously led us to the inverse conclusion in Ref. 8.

This result deserves a supplementary comment. The uneven distribution of HCG molecules between the two sensitized latexes cannot result from a different covering of the bare latex particles with anti-aHCG or anti-PHCG molecules since the surface density of the two antibodies was determined to be identical and equal to 2.37 mg/m2. On the other hand, the different aggregation rates observed for the dissymmetrical systems cannot result from differences in the affinity of the two determinants for the a and P moieties of the HCG molecules since the reactivity of complex A (or B) toward the other sensitized latex was determined to be measured by the same value of the exponent t. Therefore, our conclusion initially derived from the extension of the La Mer model [21] and finally based on the studies of Meakin and Djordjevic [10] of the existence of an uneven adsorption of HCG molecules on the two sensitized latexes is thus confirmed.

Finally, the effect of the slow rotation that is applied in the slide test has been ignored in the present study, but we imagine that the process may increase the absolute aggregation rate and slightly affect the fragmentation mechanism of the aggregate [42]. One may imagine that slight agitation will disrupt aggregates of low internal cohesion and preserve aggregates comprising highly linked particles. This effect has been investigated recently to interpret the internal cohesion of aggregates resulting from orthokinetic or perikinetic processes [43].

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