In this chapter, we sample some of the potential applications of topology to problems in disparate scientific domains. Some of these questions motivated the theoretical concepts in this book to begin with, so it is reasonable to scrutinize the applicability of the work by revisiting the questions. I am not an expert in any of these domains. Rather, my objective is to demonstrate the utility of the theory, algorithms, and software by giving a few illustrative examples. My hope is that researchers in the fields will find these examples instructive and inspiring, and utilize the tools I have developed for scientific inquiry. Applied work is an on-going process by nature, so I present both current and future work in this chapter, including nonapplied future directions.

Computational Structural Biology

The field of computational structural biology explores the structural properties of molecules using combinatorial and numerical algorithms on computers. The initial impetus for the work in this book was understanding the topologies of proteins through homology. In this section, I look at three applications of my work to structural biology: feature detection, knot detection, and structure determination.

Topological Feature Detection

In Chapter 6, the small protein gramicidin A motivated our study of persistence, as we were incapable of differentiating between noise and feature in the data captured by homology.