Foundational aspects of bioinformation and biocomputation

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In the same way we use the letters of the alphabet to write text, and bits 0 and 1 to write computer machine code, the four basic DNA units (A - adenine, C - cytosine, G - guanine, T - thymine) are used by Nature to write genetic information as DNA strands. The possibility of encoding symbolic information on DNA, and the fact that biochemical processes such as cut-and-paste of DNA strands have been proved to be able to perform arithmetic and logic operations, led to the development of the field of DNA computing and molecular programming. Bioinformation and biocomputation are different from their electronic counterparts in several aspects. First, biodata is not associated to a memory location but consists of infinitesimal DNA strands free-floating in solution. Second, in contrast to data in an electronic computer, which is passive, data-encoding DNA strands can interact with each other in programmable ways due to their Watson-Crick complementarity. Third, each data encoding DNA strand is usually present in millions of identical copies, and the bio-operations operate according to statistical laws. I aim to develop and investigate mathematical models of bioinformation and biocomputation that take into account such specific characteristics, as well as explore mathematical properties of naturally occurring DNA sequences, and their applications.