Mathematical models for mechanically induced morphogenetic pattern formation

Nesenberend, D.N. (2026)

Doctoral Thesis

During the development of the (human) body from a single fertilized egg, organs and structures must form. The development and growth of biological forms is called morphogenesis. In morphogenesis, cells collaborate by communicating through signaling molecules and mechanical signals. The question of how a specific biological structure develops precisely is difficult to answer. There are often countless cells that all need to move to the right place and become the correct cell type for a biological structure to function optimally. In this thesis, we use mathematical modeling to increase the understanding of morphogenetic processes. Firstly, we study a general model in which evolution equations are used to investigate whether an interaction between an activating signal molecule and the curvature of a tissue is sufficient to create spatial structures. Here we use geometric singular perturbation theory to prove the existence of periodic patterns that qualitatively vary depending on the interaction strength between the activating molecule and the curvature. Secondly, we use a hybrid Cellular Potts and finite element computational model to explore cell behavior observed in vitro. In these in vitro experiments, cells are embedded in a synthetic hydrogel and exhibit elongation and radial alignment. The model predicts that the hydrogel needs the property of strain stiffening and that the behavior of the cells is induced collectively. Lastly, we study a protein called Septin that can bind to the cell membrane and respond to and induce membrane curvature. We derive evolution equations from an energy functional to describe the local Septin orientation given a particular membrane geometry. Using numerical simulations of the evolution equations, we predict Septin orientation profiles on a number of membranes and energetically favorable geometries.

• Morphogenesis
• Mathematical modeling
• Partial differential equations
• Geometric Singular Perturbation Theory
• Cellular Potts Model
• Curvature
• Strain stiffening

• All authors: Nesenberend, D.N.
• Supervisor: Doelman, A.; Merks, R.M.H.
• Co-supervisor: Veerman, F.W.J.
• Committee: Derks, G.L.A.; Hupkes, H.J.; Marciniak-Czochra , A.; Maini, P.K.; Hille, S.C.; Krause, A.L.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2026-03-11
• DOI: doi:10.60602/1887-4297199