The tissue as self-assembly of notochord with sequential linear programming

Abstract

Zebrafish serves as a model organism in morphogenesis studies in cell biology. One of the main difficulties of modeling a specific morphogenetic process come from the proper identification of its key features. To study the influence of geometric constraint in morphogenesis, here this article models the notochord as hard spheres assemble in an elliptical cylinder and optimize the packing density. This article implements linear approximation on the hard sphere constraints and find the optimal packing configuration by the sequential linear programming (SLP) method. During the process, this article modifies the SLP scheme into expanding the spheres in a fixed cylindrical confinement. This article finds the staircase and similar structures becomes predominant as increasing the ellipticity of the confinement. Our study deepens the understanding of the notochord morphogenesis, and also provides methodological guidance on related modeling studies involving geometric constraints.