Multiscale Model of the Propagation of the Fertilization Wave in Sea Urchin Eggs

Abstract

We present a multiscale model describing blocking polyspermy during the fertilization in sea urchin eggs [1,2]. Our goal is to describe the processes controlling the formation of the vitelline envelope as a consequence of hyaline exocytosis. Our model combines two different levels of description: a) A reaction-diffusion scheme based on the CICR model [3], accounting for the initial propagation of the calcium wave, its duration and spatial distribution in the cell. b) The activation and dynamics of kinesin motors transporting vesicle clusters that contain hyaline, triggered due to calcium signaling. Our model incorporates a recent biochemical model [4] describing the kinetics of kinesin processivity in order to reproduce observed translational velocities, their duration and dependence on local ATP concentration. In addition, this dynamics is incorporated into a diffusion equation in the presence of external forces that accounts for the motions of vesicle clusters along the citoskeletal filaments of the egg [5]. Our model reproduces very well experimental data associated to the propagation velocities of the calcium wave, the kinesins and the vesicle clusters, as well as their duration and the kinetics of fluorescence used to indirectly quantify the cumulative exocytosis of hyaline at the plasmatic membrane.[1] D. J. Bonder, E. M. Fishkind, Actin-Membrane citoskeletal dynamics in early sea urchin development, in Citoskeletal mechanism during animal development, Ed. G. Capco (Academic Press Inc. 1995).[2] ALedesma-Duran, I. Santamaria-Holek, Multiscale model of the propagation of the fertilization wave in sea urchin eggs, in preparation.[3] J. P. Keener, J. Sneyd, Interdisciplinary mathematics 8, Springer, Berlin (1998).[4] N.J. Lopez Alamilla, I. Santamaria-Holek, Biophys. Chem. 167, 16-25 (2012).[5] F. F. de Miguel, I. Santamaria-Holek et al, Biophysics of active vesicle transport, accepted in PLoS ONE, August 2012.