Journal of Applied Mathematics & Bioinformatics

Oscillatory Spherical Net Model of Mouse Zona Pellucida

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• Abstract

  Zona pellucida (ZP), acellular mantel of mammalian oocyte, changes its thickness and elastic properties before and after fertilization. To describe changes in mechanical properties of ZP, the oscillatory spherical net Model of mouse ZP is developed. Using the method of discrete continuum, ZP is modeled as a discreet spherical net with nonlinear elastic and visco-elastic connections. Elements in this discrete spherical net correspond to ZP proteins. A mathematical model of nonlinear free and forced vibrations is presented. This ZP model could explain its nonlinear oscillatory behavior: material particles in the net move in three orthogonal directions and in each of the directions multi-frequency vibrations are asynchronous, and the resultant of nonlinear dynamics is space trajectory in the form of the generalized Lissajus curves. Favorable and unfavorable kinetic states of oscillations of oscillatory spherical net ZP model are discussed as well. It is possible that a different type of multi-frequency regime of oscillations appears in ZP before fertilization: from pure periodic to pure chaotic-like regimes. Synchronized regimes of the knot’s mass particle motion in the sphere ZP net are favorable kinetic states while chaotic-like motions represent an unfavorable kinetic state for possible successful penetration of spermatozoid trough ZP and consequent fertilization.