Computing the Partition Function for Kinetically Trapped RNA Secondary Structures

An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in time and space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures – indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/

Multiscale Modeling of RNA Structures Using NMR Chemical Shifts

Structure determination is an important step in understanding the mechanisms of functional non-coding ribonucleic acids (ncRNAs). Experimental observables in solution-state nuclear magnetic resonance (NMR) spectroscopy provide valuable information about the structural and dynamic properties of RNAs. In particular, NMR-derived chemical shifts are considered structural "fingerprints" of RNA conformational state(s). In my thesis, I have developed computational tools to model RNA structures (mainly secondary structures) using structural information extracted from NMR chemical shifts. Inspired by methods that incorporate chemical-mapping data into RNA secondary structure prediction, I have developed a framework, CS-Fold, for using assigned chemical shift data to conditionally guide secondary structure folding algorithms. First, I developed neural network classifiers, CS2BPS (Chemical Shift to Base Pairing Status), that take assigned chemical shifts as input and output the predicted base pairing status of individual residues in an RNA. Then I used the base pairing status predictions as folding restraints to guide RNA secondary structure prediction. Extensive testing indicates that from assigned NMR chemical shifts, we could accurately predict the secondary structures of RNAs and map distinct conformational states of a single RNA. Another way to utilize experimental data like NMR chemical shifts in structure modeling is probabilistic modeling, that is, using experimental data to recover native-like structure from a structural ensemble that contains a set of low energy structure models. I first developed a model, SS2CS (Secondary Structure to Chemical Shift), that takes secondary structure as input and predicts chemical shifts with high accuracies. Using Bayesian/maximum entropy (BME), I was able to reweight secondary structure models based on the agreement between the measured and reweighted ensemble-averaged chemical shifts. Results indicate that BME could identify the native or near-native structure from a set of low energy structure models as well as recover some of the non-canonical interactions in tertiary structures. We could also probe the conformational landscape by studying the weight pattern assigned by BME. Finally, I explored RNA structural annotation using assigned NMR chemical shifts. Using multitask learning, eleven structural properties were annotated by classifying individual residues in terms of each structural property. The results indicate that our method, CS-Annotate, could predict the structural properties with reasonable accuracy. We believe that CS-Annotate could be used for assessing the quality of a structure model by comparing the structure derived structural properties with the CS-Annotate derived structural properties. One major limitation of the tools developed is that they require assigned chemical shifts. And to assign chemical shifts, a secondary structure model is typically assumed. However, with the recent advances in singly labeled RNA synthesis, chemical shifts could be assigned without the assumption about the secondary structure. We envision that using the chemical shifts derived from singly labeled NMR experiments, CS-Fold could be used for modeling the secondary structure of RNA. We also believe that unassigned chemical shifts could be used for selecting structure models. Native-like structures could be recovered by comparing optimally assigned chemical shifts with computed chemical shifts (generated by SS2CS). Overall, the results presented in this thesis indicate we could extract crucial structural information of the residues in an RNA based on its NMR chemical shifts. Moreover, with the tools like CS-Fold, SS2CS, and CS-Annotate, we could accurately predict the secondary structure, model conformational landscape, and study structural properties of an RNA.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163247/1/kexin_1.pd

An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids

It has been shown that minimum free energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold [7] has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble based approaches is the computational complexity of the partition function and base pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is $O(n^4)$ and the time complexity is $O(n^6)$ which are prohibitively large [4,12]. Our goal in this paper is to give a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is $O(MFE(n)\ell)$ for single RNA and $O(MFE(m, n)\ell)$ for RNA-RNA interaction in practice, in which $MFE$ is the running time of sparse folding and $\ell \leq n$ ($\ell \leq n + m$) is a sequence dependent parameter

PATTERNA: transcriptome-wide search for functional RNA elements via structural data signatures.

Establishing a link between RNA structure and function remains a great challenge in RNA biology. The emergence of high-throughput structure profiling experiments is revolutionizing our ability to decipher structure, yet principled approaches for extracting information on structural elements directly from these data sets are lacking. We present PATTERNA, an unsupervised pattern recognition algorithm that rapidly mines RNA structure motifs from profiling data. We demonstrate that PATTERNA detects motifs with an accuracy comparable to commonly used thermodynamic models and highlight its utility in automating data-directed structure modeling from large data sets. PATTERNA is versatile and compatible with diverse profiling techniques and experimental conditions

A Statistical Analysis of RNA Folding Algorithms Through Thermodynamic Parameter Perturbation

Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction algorithms are to changes in these parameters. We find that already for changes corresponding to the actual experimental error to which these parameters have been determined 30% of the structure are falsly predicted and the ground state structure is preserved under parameter perturbation in only 5% of all cases. We establish that base pairing probabilities calculated in a thermal ensemble are a viable though not perfect measure for the reliability of the prediction of individual structure elements. A new measure of stability using parameter perturbation is proposed, and its limitations discussed.Comment: 6 pages, 3 figures, 1 table submitted to Nucleic Acids Researc

RNA secondary sturcture prediction using a combined method of thermodynamics and kinetics

Nowadays, RNA is extensively acknowledged an important role in the functions of information transfer, structural components, gene regulation and etc. The secondary structure of RNA becomes a key to understand structure-function relationship. Computational prediction of RNA secondary structure does not only provide possible structures, but also elucidates the mechanism of RNA folding. Conventional prediction programs are either derived from evolutionary perspective, or aimed to achieve minimum free energy. In vivo, RNA folds during transcription, which indicates that native RNA structure is a result from both thermodynamics and kinetics. In this thesis, I first reviewed the current leading kinetic folding programs and demonstrate that these programs are not able to predict secondary structure accurately. Upon that, I proposed a new sequential folding program called GTkinetics. Given an RNA sequence, GTkinetics predicts a secondary structure and a series of RNA folding trajectories. It treats the RNA as a growing chain, and adds stable local structures sequentially. It is featured with a Z-score to evaluate stability of local structures, which is able to locate native local structures with high confidence. Since all stable local structures are captured in GTkinetics, it results in some false positives, which prevents the native structure to form as the chain grows. This suggests a refolding model to melt the false positive hairpins, probable intermediate structures, and to fold the RNA into a new structure with reliable long-range helices. By analyzing suboptimal ensemble along the folding pathway, I suggested a refolding mechanism, with which refolding can be evaluated whether or not to take place. Another way to favor local structures over long-distance structures, we introduced a distance penalty function into the free energy calculation. I used a sigmoidal function to compute the energy penalty according to the distance in the primary sequence between two nucleotides of a base pair. For both the training dataset and the test dataset, the distance function improves the prediction to some extent. In order to characterize the differences between local and long-range helices, I carried out analysis of standardized local nucleotide composition and base pair composition according to the two groups. The results show that adenine accumulates on the 5' side of local structure, but not on that of long-range helices. GU base pairs occur significantly more frequent in the local helices than that in the long-range helices. These indicate that the mechanisms to form local and long range helices are different, which is encoded in the sequence itself. Based on all the results, I will draw conclusions and suggest future directions to enhance the current sequential folding program.MSCommittee Chair: Stephen Harvey; Committee Member: Heitsch, Christine; Committee Member: Hud, Nick; Committee Member: Wartell, Roger; Committee Member: Weitz, Joshu

Statistical modeling of RNA structure profiling experiments enables parsimonious reconstruction of structure landscapes.

RNA plays key regulatory roles in diverse cellular processes, where its functionality often derives from folding into and converting between structures. Many RNAs further rely on co-existence of alternative structures, which govern their response to cellular signals. However, characterizing heterogeneous landscapes is difficult, both experimentally and computationally. Recently, structure profiling experiments have emerged as powerful and affordable structure characterization methods, which improve computational structure prediction. To date, efforts have centered on predicting one optimal structure, with much less progress made on multiple-structure prediction. Here, we report a probabilistic modeling approach that predicts a parsimonious set of co-existing structures and estimates their abundances from structure profiling data. We demonstrate robust landscape reconstruction and quantitative insights into structural dynamics by analyzing numerous data sets. This work establishes a framework for data-directed characterization of structure landscapes to aid experimentalists in performing structure-function studies