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Current Research

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.

See also Polymer.



Ball, W.W. Rouse. A Short Account of the History of Mathematics. London: Sterling Publications, 2002.

Kline, Morris. Mathematical Thought: From Ancient to Modern Times. 3 vols. New York: Oxford University Press, 1972.

Peterson, Ivars. The Mathematical Tourist: Snapshots of Modern Mathematics. New York: W. H. Freeman,1988.


Tomalia, Donald A. "Dendrimer Molecules." Scientific American 272 (May 1995): 62-66.

Patrick Moore


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Dendrimer molecules

—Branching, treelike polymers synthesized in laboratories by attaching the polymers to a core molecule.


—Deoxyribonucleic acid, a thin, ladderlike molecular structure which contains the genetic code that defines life.

Euclidean geometry

—Geometry based upon the postulates of the Greek educator, Euclid who lived roughly 300 B.C. Euclid's parallel postulate that only one line may be drawn through a given point such that it is parallel to another line, was overthrown in the nineteenth century and gave way to the nonEuclidean geometries created by Gauss and Riemann.


—The area of mathematics that deals with deductions concerning the measurements and relationships between points, lines, angles, and figures in physical space.


—Strings of smaller molecules.

Additional topics

Science EncyclopediaScience & Philosophy: Thallophyta to ToxicologyTopology - Topological Equivalency, Famous Topologists, Classifications, Current Research