A Differential Equations Model of Insulin Spherulite Growth and a Surprising Connection to Algebraic Topology

Evan Heidtmann


A certain type of aggregate of biological protein called a spherulite can occur naturally in humans under some disease conditions. This paper describes research on amyloid spherulites of bovine insulin protein as a model system for studying spherulite growth. Following a survey of the current state of knowledge in this subfield, a simple force-based computer model of spherulite growth is developed and analyzed for its agreement with experimental data. The Hairy Ball Theorem from algebraic topology is introduced, developed, proven, and applied to improve the understanding of the currently unexplained amorphous core that occurs in insulin spherulites. Promising avenues of future research are given for both the computer model and the implications of the mathematical theorem.