Theoretical aspects of biocomputing

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In the same way we use letters of the alphabet to write text, and bits 0 and 1 to write computer machine code, the four basic DNA units(adenine,guanine,cytosine,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 can be used to perform arithmetic and logic operations,led to the development of the field of DNA computing. The primary goal of my research is to analyze this new way of storing and manipulating data on DNA strands. Indeed, 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 the electronic computer, data-encoding DNA strands can interact with each other in un-programmed ways. Third, each data encoding DNA strand is usually present in  millions of identical copies and the bio-operations operate according to statistical laws.This proposal addresses a) the issue of data encoding on DNA by studying  properties that ensure that biocomputations proceed error-free, and  b) lies the foundation of a "theory of bioinformation" by studying the algebraic properties of the new concepts defined in a). Another of the proposed research topics is  an investigation into the mathematical properties of genomic bioinformation by  i)  exploring the use of Chaos Game Representation as a  genomic signature, and ii) searching for the optimal tool to measure the complexity of genomes, both of which could lead to methods of quantifying and comparing genomes of various organisms. The last aspect of the proposed research is an exploration in the theory of self-assembly of small components into complex structures as a computational tool, which  could provide insights in the way nature stores and processes information, as well as have implications for   nanoscience and nanotechnology.