Collaborative Research: CIF: Small: Coded String Reconstruction Problems in Molecular Storage

由于目前的DNA和蛋白质测序平台无法读取表示蛋白质/基因序列的长字符串的内容，因此从它们的片段或大量片段中重建文本字符串的问题在计算生物学中是一个非常重要的问题。字符串重建的一个典型例子出现在DNA组装中：在DNA组装中，一个人创建同一长字符串的多个副本，然后切割副本以读出重叠的短子字符串，这些子字符串可以通过匹配它们的前缀和后缀来组合在一起。由于碎片和匹配过程中的错误，重建的字符串可能不是原始字符串的完美副本。此外，对于许多字符串来说，惟一的重构本质上是不可能的。这代表了用于基础生物学研究的下一代测序技术的一个主要问题，因为在这种情况下，不可能确保明确的结果。本项目所追求的成功代码设计可以解决阻碍新兴分子计算和存储范式实现的可靠性和内容检索问题。这个项目是关于开发新的编码方法，用于基于其组成子字符串，子序列和子字符串组成的字符串或字符串池的唯一重建。所采用的技术代表了新的图论、组合优化和信息论方法的结合。特别是，该项目将研究平衡部分de Bruijn字符串用于基于子字符串的重建，加泰罗尼亚式路径用于多集组合重建，以及涉及删除纠正码和叠加码的专门修改的编码多迹重建方法。这些编码方案将在伊利诺伊大学开发的基于dna和基于合成聚合物的数据存储平台上进行测试。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The problem of reconstructing text strings from their fragments or masses of fragments is of focal importance in computational biology as current DNA and protein sequencing platforms are unable to read the content of long strings that denote protein/gene sequences. One prototypical example of string reconstruction arises in DNA assembly: there, one creates multiple copies of the same long string and cuts the copies to read out short overlapping substrings that can be put together by matching their prefixes and suffixes. The reconstructed string may not be a perfect replica of the original string due to errors in the fragmentation and matching processes. Furthermore, for many strings unique reconstruction is inherently impossible. This represents a major issue for next generation sequencing technologies used in fundamental biological research, since in this setting it is impossible to ensure unambiguous results. The successful code designs pursued in this project can resolve reliability and content retrieval issues impeding implementations of emerging molecular computing and storage paradigms. This project is concerned with developing novel coding methods for unique reconstruction of strings or pools of strings based on their constituent substrings, subsequences and substring compositions. The techniques employed represent a combination of new graph-theoretic, combinatorial optimization and information theory approaches. In particular, the project will investigate the use of balanced partial de Bruijn strings for substring-based reconstruction, Catalan-like paths for multiset composition reconstruction as well as coded multi-trace reconstruction methods involving specialized modifications of deletion-correcting codes and superposition codes. The coding schemes will be tested on DNA-based and synthetic polymer-based data storage platforms under the development at the University of Illinois.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.