Thesis advisor: Peter Clote / RNA molecules play important roles in living organisms, such as protein translation, gene regulation, and RNA processing. It is known that RNA secondary structure is a scaffold for tertiary structure leading to extensive amount of interest in RNA secondary structure. This thesis is primarily focused on the development of novel algorithms for the analysis of RNA secondary structure evolution and folding kinetics. We describe a software RNAsampleCDS to generate mRNA sequences coding user-specified peptides overlapping in up to six open reading frames. Sampled mRNAs are then analyzed with other tools to provide an estimate of their secondary structure properties. We investigate homology of RNAs with respect to both sequence and secondary structure information as well. RNAmountAlign an efficient software package for multiple global, local, and semiglobal alignment of RNAs using a weighted combination of sequence and structural similarity with statistical support is presented. Furthermore, we approach RNA folding kinetics from a novel network perspective, presenting algorithms for the shortest path and expected degree of nodes in the network of all secondary structures of an RNA. In these algorithms we consider move set MS2 , allowing addition, removal and shift of base pairs used by several widely-used RNA secondary structure folding kinetics software that implement Gillespie’s algorithm. We describe MS2distance software to compute the shortest MS2 folding trajectory between any two given RNA secondary structures. Moreover, RNAdegree software implements the first algorithm to efficiently compute the expected degree of an RNA MS2 network of secondary structures. The source code for all the software and webservers for RNAmountAlign, MS2distance, and RNAdegree are publicly available at http://bioinformatics.bc.edu/clotelab/. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Biology.

The primary objective was to study the kinetics of folding of RNase Sa. Wild-type RNase Sa does not contain tryptophan. A tryptophan was substituted at residue 81 (WT*) to allow fluorescence spectroscopy to be used to monitor folding. This tryptophan mutation did not change the stability. An analysis of the folding kinetics of RNase Sa showed two folding phases, indicating the presence of an intermediate and consistent with the following mechanism: D ↔ I ↔ N. Both refolding limbs of the chevron plot (abcissa = final conc. of denaturant and ordinate = kinetic rate) had non-zero slopes suggesting that proline isomerization was not rate-limiting. The conformational stability of a charge-reversed variant, WT*(D17R), of a surface exposed residue on RNase Sa has been studied by equilibrium techniques. This mutant with a single amino acid charge reversal of a surface exposed residue resulted in decreased stability. Calculations using Coulomb’s Law suggested that favorable electrostatic interactions in the denatured state were the cause for the decreased stability for the charge-reversed variant. Folding and unfolding kinetic studies were designed and conducted to study the charge-reversal effect. Unfolding kinetics showed a 10-fold increase in the unfolding rate constant for WT*(D17R) over WT* and no difference in the rate of refolding. Kinetics experiments were also conducted at pH 3 where protonation of Asp17 (charge reversal site) would be expected to negate the observed kinetic effect. At pH 3 the kinetics of unfolding of WT* RNase Sa and the WT*(D17R) mutant were more similar. These kinetic results indicate that a single-site charge reversal lowered the free energy of the denatured state as suspected. Additionally, the results showed that the transition state was stabilized as well. These results show that a specific Coulombic interaction lowered the free energy in the denatured and transition state of the charge-reversal mutant, more than in WT*. To our knowledge, this is the first demonstration that a favorable electrostatic interaction in the denatured state ensemble has been shown to influence the unfolding kinetics of a protein.

Protein folding is considered to be one of the grand challenge problems in biology. Protein folding refers to how a protein's amino acid sequence, under certain physiological conditions, folds into a stable close-packed three-dimensional structure known as the native state. There are two major problems in protein folding. One, usually called protein structure prediction, is to predict the structure of the protein's native state given only the amino acid sequence. Another important and strongly related problem, often called protein folding, is to study how the amino acid sequence dynamically transitions from an unstructured state to the native state. In this dissertation, we concentrate on the second problem. There are several approaches that have been applied to the protein folding problem, including molecular dynamics, Monte Carlo methods, statistical mechanical models, and lattice models. However, most of these approaches suffer from either overly-detailed simulations, requiring impractical computation times, or overly-simplified models, resulting in unrealistic solutions. In this work, we present a novel motion planning based framework for studying protein folding. We describe how it can be used to approximately map a protein's energy landscape, and then discuss how to find approximate folding pathways and kinetics on this approximate energy landscape. In particular, our technique can produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap. The roadmap can be computed in a few hours on a desktop PC using a coarse potential energy function. In addition, our motion planning based approach is the first simulation method that enables the study of protein folding kinetics at a level of detail that is appropriate (i.e., not too detailed or too coarse) for capturing possible 2-state and 3-state folding kinetics that may coexist in one protein. Indeed, the unique ability of our method to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics that are not available to other theoretical techniques.

RNAs are biomolecules ubiquitous in all living cells. Usually, they fold into complex molecular structures, which often mediate their biological function. In this work, models of RNA folding have been studied in detail. One can distinguish two fundamentally different approaches to RNA folding. The first one is the thermodynamic approach, which yields information about the distribution of structures in the ensemble in its equilibrium. The second approach, which is required to study the dynamics of folding during the course of time, is the kinetic folding analysis. It is much more computationally expensive, but allows to incorporate changing environmental parameters as well as time-dependent effects into the analysis. Building on these methods, the BarMap framework (Hofacker, Flamm, et al., 2010) allows to chain several pre-computed models and thus simulate folding reactions in a dynamically changing environment, e. g., to model co- transcriptional folding. However, there is no obvious way to identify spurious output, let alone assessing the quality of the simulation results. As a remedy, BarMap-QA, a semi-automatic software pipeline for the analysis of cotranscriptional folding, has been developed. For a given input sequence, it automatically generates the models for every step of the RNA elongation, applies BarMap to link them together, and runs the simulation. Post-processing scripts, visualizations, and an integrated viewer are provided to facilitate the evaluation of the unwieldy BarMap output. Three novel, complementary quality measures are computed on-the-fly, allowing the analyst to evaluate the coverage of the computed models, the exactness of the computed mapping between the individual states of each model, and the fraction of correctly mapped population during the simulation run. In case of deficiencies, the output is automatically re-rendered after parameter adjustment. Statistical evidence is presented that, even when coarse graining the ensemble, kinetic simulations quickly become infeasible for longer RNAs. However, within the individual gradient basins, most high-energy structures only have a marginal probability and could safely be excluded from the analysis. To tell relevant and irrelevant structures apart, a precise knowledge of the distribution of probability mass within a basin is necessary. Both a theoretical result concerning the shape of its density, and possible applications like the prediction of a basin’s partition function are given. To demonstrate the applicability of computational folding simulations to a real-world task of the life sciences, we conducted an in silico design process for a synthetic, transcriptional riboswitch responding to the ligand neomycin. The designed constructs were then transfected into the bacterium Escherichia coli by a collaborative partner and could successfully regulate a fluorescent reporter gene depending on the presence of its ligand. Additionally, it was shown that the sequence context of the riboswitch could have detrimental effects on its functionality, but also that RNA folding simulations are often capable to predict these interactions and provide solutions in the form of decoupling spacer elements. Taken together, this thesis offers the reader deep insights into the world of RNA folding and its models, and how these can be applied to design novel biomolecules.