Theoretical aspects of biocomputing

就像我们用字母表中的字母来写文字，用0和1位来写计算机机器代码一样，大自然用四个基本的DNA单位（腺嘌呤、鸟嘌呤、胞嘧啶、胸腺嘧啶）来作为DNA链来书写遗传信息。在DNA上编码符号信息的可能性，以及诸如DNA链的剪切和粘贴等生化过程可用于执行算术和逻辑运算的事实，导致了DNA计算领域的发展。我研究的主要目标是分析这种存储和操作DNA链数据的新方法。事实上，生物信息和生物计算在几个方面与电子计算不同。首先，生物数据与存储位置无关，而是由在溶液中自由漂浮的无穷小的DNA链组成。其次，与电子计算机不同，编码数据的DNA链可以以非编程的方式相互作用。第三，每个编码DNA链的数据通常有数百万个相同的副本，生物操作根据统计规律进行。该提案解决了a)通过研究确保生物计算无错误进行的特性来解决DNA数据编码问题，b)通过研究a)中定义的新概念的代数特性奠定了“生物信息理论”的基础。另一个提议的研究课题是通过i)探索使用混沌博弈表示作为基因组特征，以及ii)寻找测量基因组复杂性的最佳工具来研究基因组生物信息的数学特性，这两者都可能导致量化和比较各种生物体基因组的方法。该研究的最后一个方面是探索小部件自组装成复杂结构作为计算工具的理论，这可以为自然存储和处理信息的方式提供见解，以及对纳米科学和纳米技术的影响。

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.