DNA computing: Arrival of biological mathematics

Abstract

The field usually referred to as mathematical biology is a highly interdisciplinary area that lies at the intersection of mathematics and biology. Classical illustrations include the development of stochastic processes and statistical methods to solve problems in genetics and epidemiology. As the name used to describe work in this field indicates, with “biology” the noun, and “mathematical” the modifying adjective, the relationship between mathematics and biology has so far been one–way. Typically, mathematical results have emerged from or have been used to solve biological problems (see [34] for a comprehensive survey). In contrast, Leonard Adleman, [1], succeeded in solving an instance of the directed Hamiltonian path problem solely by manipulating DNA strings. This marks the first instance of the connection being reversed: a mathematical problem is the end toward which the tools of biology are used. To be semantically correct, instead of categorizing the research in DNA computing as belonging to mathematical biology, we should be employing the mirror–image term biological mathematics for the field born in November 1994. Despite the complexity of the technology involved, the idea behind biological mathematics is the simple observation that the following two processes, one biological and one mathematical, are analogous: (a) the very complex structure of a living being is the result of applying simple operations (copying, splicing, etc.) to initial information encoded in a DNA sequence, (b) the result f(w) of applying a computable function to an argument w can be obtained by applying a combination of basic simple functions to w (see Section 4 or [65] for details). If noticing this analogy were the only ingredient necessary to cook a computing DNA soup, we would have been playing computer games on our DNA