We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the algorithm is complex, which led us to adopt a useful graphical representation (Feynman diagrams) borrowed from quantum field theory. We present an implementation of the algorithm that generates the optimal minimum energy structure for a single RNA sequence, using standard RNA folding thermodynamic parameters augmented by a few parameters describing the thermodynamic stability of pseudoknots. We demonstrate the properties of the algorithm by using it to predict structures for several small pseudoknotted and non-pseudoknotted RNAs. Although the time and memory demands of the algorithm are steep, we believe this is the first algorithm to be able to fold optimal (minimum energy) pseudoknotted RNAs with the accepted RNA thermodynamic model.
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU -base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse…
Unraveling the Mechanism of Drug Binding to SARS-CoV-2 RNA Pseudoknot with Thermodynamics-Driven Machine Learning
Platform of Inter/Transdisciplinary Energy Research, Kyushu University（interdisciplinary 能源研究平台，九州大学）；Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University（物理研究所，物理、天文学与信息学学院，尼古拉库普林大学）
Monovalent ions modulate the flux through multiple folding pathways of an RNA pseudoknot
RNA假结（PKs）是核糖核酸（ribozyme）和核糖核蛋白（ribonucleoprotein）复合物的最小三级结构基序，其功能由其结构、稳定性和动力学决定。因此，重要的是要阐明其热力学/折叠机制的一般原则。在这里，我们结合实验和模拟来研究VPK假结的折叠/展开途径，VPK假结是参与核糖体移码的小鼠乳腺肿瘤病毒（MMTV）PK的变体。荧光核苷酸类似物（2-氨基嘌呤和pyrrolocytidine）放置在不同的茎/环的PK位置，激光温度跳跃的方法作为本地探针，使我们能够监测组装的顺序VPK与两个螺旋具有不同的内在稳定性。实验和分子模拟表明，在50 mM KCl的优势折叠途径人口只有更稳定的部分折叠的发夹。随着盐浓度的增加，平行折叠途径出现，涉及不太稳定的发夹结构作为替代中间体。值得注意的是，通道之间的通量由离子强度调制。这些发现支持了PK结构形成的顺序由发夹的相对稳定性决定的原理，发夹的相对稳定性可以通过序列变异或盐浓度来改变。我们的研究不仅明确地表明，PK折叠的平行途径，但也建立了定量描述的RNA自组装需要一个协同的实验和模拟相结合。
Theory for RNA folding, stretching, and melting including loops and salt
核酸二级结构的形成强烈地依赖于盐浓度和温度。我们开发了一个理论，RNA折叠，正确地占序列的影响，熵的贡献与环的形成，和盐的影响。使用迭代表达式的配分函数，忽略伪结，我们计算折叠自由能和最小自由能配置的基础上实验得出的碱基配对自由能。环形成的构型熵由渐近表达式-c ln m建模，其中m是环的长度，c是环指数，其是可调节的常数。盐的影响进入两种方式：第一，我们得到盐诱导的修改的自由能参数描述碱基配对，第二，我们包括静电自由能环的形成。这两种效应都是在Debye-Hueckel水平上模拟的，包括对流冷凝。我们验证了我们的理论为两个不同的RNA序列：对于tRNA-phe，在不同的盐浓度下的热变性的热容量曲线准确地再现实验结果。对于P5 ab RNA发夹，我们推导出的全球相图在三维空间跨越的温度，拉伸力，和盐浓度，并获得良好的协议与实验确定的临界展开力。我们表明，一个适当的描述RNA的熔化和拉伸，盐和环熵效应是必要的。
