CAREER: Coding Theoretic Problems in Genetic Data Acquisition, Modeling and Analysis

研究者研究了遗传数据采集、分析和建模过程中出现的三种新的编码理论范式。控制编码解决方案的系统的生物学原理是DNA和RNA序列杂交和自杂交。支持杂交的生物化学性质是单链DNA和RNA中的碱基与互补碱基形成氢键的亲和力，根据沃森-克里克规则定义。通过形成这样的键，成对的碱基产生由两条互补链或一条单链组成的平面或空间结构。结合结构增加了稳定性，但它们也在调节各种细胞功能中发挥重要作用，包括mrna前编辑或转录后基因沉默。在某些情况下，DNA序列中的特定自杂交模式代表序列断裂的前兆，并与遗传疾病（如癌症）密切相关。序列杂交过程除了具有化学和物理性质外，还具有明显的组合特征。研究者使用这些组合特征来建立一个严格的数学框架，在这个框架中分析基于序列杂交原理的技术和生物系统。在新的生物环境下，分析了几种经典的编码方案，包括叠加设计、平衡编码和行程长度约束编码。这些方案针对给定的应用进行了一般化、组合和优化。此外，还介绍了一些新的编码理论和算法问题，这些问题为代数编码理论带来了新的研究方向。概述的跨学科研究工作预计将对cDNA和适体微阵列的发展产生重大影响，也有望导致科罗拉多大学博尔德分校新的教育计划的创建。

The investigator studies three new coding-theoretic paradigms arising during the processes of genetic data acquisition, analysis, and modeling. The biological principles governing the systems for which coding solutions are sought are DNA and RNA sequence hybridization and self-hybridization. The bio-chemical property supporting hybridization is the affinity of bases in single DNA and RNA strands to form hydrogen bonds with their complementary bases, defined in terms of the Watson- Crick rule. By forming such bonds, paired bases generate planar or spatial structures that are comprised of two complementary strands or one single strand. Bonded structures have increased stability, but they also serve an important role in regulating various cellular functions, including pre-mRNA editing or post-transcriptional gene silencing. In certain cases, specific self-hybridization patterns in DNA sequences represent precursors to sequence breakage and are closely associated with genetic diseases such as cancer. Besides its chemical and physical properties, the process of sequence hybridization has distinctly combinatorial features. These combinatorial features are used by the investigator to establish a rigorous mathematical framework in which to analyze technological and biological systems operating on the principle of sequence hybridization. Several classical coding schemes are analyzed in new biological settings, including superimposed designs, balanced codes, and run-length constrained codes. Such schemes are generalized, combined, and optimized for a given application. Furthermore, some new coding-theoretic and algorithmic problems are introduced that lead to challenging and interesting new research directions in algebraic coding theory. The outlined interdisciplinary research efforts are expected to have significant impact on the development of cDNA and aptamer microarrays and are also expected to lead to the creation of a new educational program at the University of Colorado, Boulder.