Mathematical model of the evolution of statoconia

A mathematical model of the evolution of statoconia in statocysts of freshwater snails based on the analysis of experimental data [Wiederhold et al., 1990; Pedrozo et al., 1996; Gao et al., 1997; Gao and Wiederhold, 1997; Wiederhold et al., 1999] is proposed. The growth of statoconia is considered as the process of solution crystallization. The model proposed assumes that two main processes determine the evolution of statoconia in developing snails: the generation of new statoconia and the linear growth of statoconia sizes. The analytical solution of the model and qualitative comparison of theoretical results with the experimental data show: (1) there are at least three periods of statoconia evolution; (2) the generation of new statoconia mainly determines the first period of evolution when the shell diameter of snails D < 4 mm; (3) when D > 6 mm the size distribution of statoconia is determined by the growth of their sizes with a constant rate; (4) on the interval deltaD = 4-6 mm the transformation of size distribution with selective dissolution of statoconia takes place. The model agrees well with the experimental data and makes it possible to estimate some parameters of the statoconia kinetics. Additional experiments, which are necessary for further development of the model, and quantitative estimates of the mechanisms of statoconia evolution are formulated.