Collaborartive Research: Monte Carlo Study of Pseudoknotted RNA Molecules: Motifs, Structure and Folding

RNA分子是细胞机器的重要组成部分。现在已知它们对于许多生物过程是必不可少的，包括蛋白质合成、转录调节、染色体复制、病毒感染和RNA干扰。然而，我们对RNA分子的了解仍然有限。该研究项目通过引入新的分子模型和有效的计算工具填补了当前RNA研究的重要空白。具体而言，研究小组的目标是在研究伪结RNA结构并了解其性质的主题下解决以下问题：（1）RNA分子关键二级元件的熵估计;（2）从RNA序列中鉴定稳定的伪结基序并开发RNA家族的伪结基序库;（3）从RNA序列中识别稳定的伪结基序并开发RNA家族的伪结基序库。（3）预测假结RNA分子的三维系综，并表征其折叠机制。 所有这些问题都涉及探索非常大的状态空间的概率分布，必须开发新的数学和统计工具。具体而言，研究小组研究和开发了几种技术，包括有效的约束顺序蒙特卡罗（SMC）方法，有效的马尔可夫链蒙特卡罗（MCMC）方法和混合速率加速方案及其组合。方法学的发展为解决潜在的生物学问题提供了坚实的基础。反过来，这些问题又成为新的统计思想和程序的试验场和灵感来源。这种交叉受精对于生物科学和统计科学的重大进步都是理想的。它为数学/统计学和生物学跨学科领域的下一代科学家和研究人员提供了完美的教育和培训环境。在博士后、研究生和本科生层面开展综合教育和研究活动。本项目旨在提高我们对RNA的理解，RNA是一类重要的生物分子，也是细胞机器的重要组成部分。现在已知它们对许多生物过程是必不可少的。深入了解RNA及其动力学和功能，将提高我们开发新药物和诊断程序的能力，并推动进一步的技术进步，从而有益于人类社会。开发创新的统计工具来解决根本问题。这些工具也可以用于许多其他应用中。该项目是统计科学与生物信息学，计算生物学和生物物理学之间的交叉施肥。它为数学/统计学和生物学跨学科领域的下一代科学家和研究人员提供了完美的教育和培训环境。 在博士后，研究生和本科生层面开展综合教育和研究活动，并特别注意吸引妇女和少数民族学生进入数学生物学领域的精彩研究生涯。一组公共和免费的软件开发用于实现所开发的算法。它能够使生物学家和生物信息学研究人员在自己的研究和发现中使用新的算法和软件。

RNA molecules are an important component of the cellular machinery. They are now known to be essential for numerous biological processes, including protein synthesis, transcription regulation, chromosome replication, viral infection, and RNA interference. However, our knowledge of RNA molecules is still limited. This research project fills important gaps in current RNA studies by introducing novel molecular models and efficient computational tools. Specifically, the research team aims to solve the following problems under a coherent theme of studying pseudoknotted RNA structure and understanding their properties: (1) Estimation of entropy of key secondary elements of RNA molecules; (2) Identification of stable pseudoknot motifs from RNA sequences and developing libraries of pseudoknot motifs for RNA families; (3) Prediction of three dimensional ensemble of pseudoknotted RNA molecules and characterize their folding mechanism. All these problems involve exploration of probability distributions on very large state spaces where novel mathematical and statistical tools must be developed. Specifically, the research team studies and develops several techniques including efficient constrained Sequential Monte Carlo (SMC) methods, efficient Markov Chain Monte Carlo (MCMC) methods and mixing rate acceleration schemes and their combinations. The methodological development provides a solid foundation for solving the underlying biological problems. In return, those problems serve as the testing ground and inspiration of new statistical ideas and procedures. The cross-fertilization is ideal for significant advances in both biological and statistical sciences. It provides a perfect environment of education and training of the next generation of scientists and researchers in the interdisciplinary field of mathematics/ statistics and biology. Integrated education and research activities at post-doc, graduate and undergraduate levels are conducted. A set of free software are produced for implementing the developed algorithms.This project intends to improve our understanding of RNA, an important class of biomolecules and an important component of the cellular machinery. They are now known to be essential for numerous biological processes. A deeper understanding of RNA, its dynamics and functionality, will increase our ability to develop new medicines and diagnostic procedure and propel further technological advancement, hence beneficial to the human society. Innovative statistical tools are developed to solve the underlying problems. Such tools can also be used in many other applications. The project is a cross-fertilization between statistical science and bioinformatics, computational biology, and biophysics. It provides a perfect environment of education and training of the next generation of scientists and researchers in the interdisciplinary field of mathematics/statistics and biology. Integrated education and research activities at post-doc, graduate and undergraduate levels are conducted and special attentions are paid to attract women and minority students into the wonderful research career in the field of math-biology. A set of public and free software are developed for implementing the developed algorithms. It is able to empower biologists and bioinformatics researchers with new algorithms and software in their own research and discovery.