Parametric frequency analysis of oscillatory behavior of mouse Zona Pellucida spherical net model: cases of successful and of unsuccessful fertilization

Abstract

The current paper proposes a model for describing mechanical phenomena that occur during the process of mammal fertilization when spermatozoa impact the surface of Zona Pellucida. Zona pellucida (ZP) is a dynamical 3D matrix that surrounds the mammalian oocyte. In the process of fertilization, sperm cell has to penetrate this structure. To describe impact of sperm cells with velocities that are effective and those that are ineffective relative to the oscillatory behavior of ZP, the discreet continuum model in the form of spherical net model is used. Resultant trajectories of knot mass particles dynamics of mouse ZP spherical net model in the form of generalized Lussajous curves are presented. Using generalized Lussajous curves, parametric frequency analysis of oscillatory behavior of knot material particles in the mouse ZP spherical net model is conducted. The influence of impact angles of sperm cells on corresponding knot mass particle trajectory is discussed. Favorable and unfavorable trajectories of knot mass particle motions are discussed in the context of successful fertilization.

Influence of sperm impact angle on successful fertilization through mZP oscillatory spherical net model

“…In order to describe the oscillatory behavior of ZP structure and, inspired by the Wassermans' model of mouse ZP (mZP) [26], 3D structural changes of ZP in atomic force microscope (AFM) [27], and scanning electron microscope (SEM) analysis [28], we create an oscillatory spherical net model [22][23][24]29]. The molar ratio and masses of mZP glycoproteins were included in the model.…”

“…In this paper we extend the analysis presented in [22,23,24], by discussing a model that in comparison with the models used in the previously considered analyses, contains additional variables (sperm impact angle and sperm velocity).…”