Theoretical aspects of biocomputing

就像我们用字母表中的字母来写文本，用0和1来写计算机机器代码一样，自然界用四个基本的DNA单元（腺嘌呤、鸟嘌呤、胞嘧啶、胸腺嘧啶）来写DNA链的遗传信息。在DNA上编码符号信息的可能性，以及DNA链的剪切和粘贴等生物化学过程可以用来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在DNA链上存储和操作数据的新方法。事实上，生物信息和生物计算在几个方面与电子对应物不同。首先，生物数据不与存储位置相关联，而是由在溶液中自由漂浮的无限小的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，每一个编码DNA链的数据通常存在于数百万个相同的拷贝中，并且生物运算按照统计规律进行。这个提议解决了a）通过研究确保生物计算无差错进行的属性来解决DNA上的数据编码问题，以及B）通过研究a）中定义的新概念的代数属性来奠定“生物信息理论”的基础。另一个拟议的研究课题是通过i）探索使用混沌游戏表示作为基因组签名，以及ii）寻找测量基因组复杂性的最佳工具，对基因组生物信息的数学特性进行调查，这两种方法都可以导致量化和比较各种生物体的基因组的方法。拟议研究的最后一个方面是探索作为计算工具的小组件自组装成复杂结构的理论，这可以提供自然存储和处理信息的方式的见解，并对 纳米科学和纳米技术。

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.