Topology

Topology has a number of interesting applications, including molecular biology and synthesizing new chemical compounds to help in gene therapy. For example, strands of DNA (deoxyribonucleic acid, which contains the genetic code that defines life) often become knotted. Researchers need to know if the knotted mass of DNA is just one strand of DNA that has wound back upon itself, or if it is several strands of DNA which have become entangled. Topology, especially knot theory, helps molecular biologists solve such problems of equivalency.

Topology also has applications in synthesizing new molecules, called dendrimers, which may be used in gene therapy. Dendrimers are branching, tree-like polymers (strings of smaller molecules) synthesized in laboratories by chemically attaching the polymers to a core molecule. Dendrimers are approximately the same size as many naturally occurring molecules, including DNA and proteins. In gene therapy, new genetic material needs to be transported to the nucleus of a cell to replace damaged or defective genes in human cells. Then the repaired cells can reproduce more healthy cells. However, there must be a way to transport the healthy DNA into cells, which is where dendrimers come in. Normally, DNA wraps itself around clusters of proteins called histones. Gene therapists can fool the immune system of the human body by substituting dendrimers for naturally occurring clusters of histones and thus transport healthy DNA into damaged cells. Topology is useful in this process, because its purpose is to decide mathematically which shapes are equivalent. The closer that synthetic dendrimers mimic the naturally-occurring histones, then the greater are the chances that the DNA will be transported to create healthy cells.