Foundational aspects of bioinformation and biocomputation

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（A -腺嘌呤，C -胞嘧啶，G -鸟嘌呤，T -胸腺嘧啶）来作为DNA链来记录遗传信息。在DNA上编码符号信息的可能性，以及生物化学过程（如DNA链的剪切和粘贴）已被证明能够执行算术和逻辑操作的事实，导致了DNA计算和分子编程领域的发展。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，与电子计算机中的被动数据相比，数据编码DNA链可以通过沃森-克里克互补性以可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。我的目标是开发和研究考虑到这些特定特征的生物信息和生物计算的数学模型，以及探索自然发生的DNA序列的数学特性及其应用。

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.