The Folding Kinetics of RNA

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

The Folding Kinetics of RNA

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

The Folding Kinetics of RNA

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

Tractable RNA–ligand interaction kinetics

Abstract Background The binding of small ligands to RNA elements can cause substantial changes in the RNA structure. This constitutes an important, fast-acting mechanism of ligand-controlled transcriptional and translational gene regulation implemented by a wide variety of riboswitches. The associated refolding processes often cannot be explained by thermodynamic effects alone. Instead, they are governed by the kinetics of RNA folding. While the computational analysis of RNA folding can make use of well-established models of the thermodynamics of RNA structures formation, RNA–RNA interaction, and RNA–ligand interaction, kinetic effects pose fundamentally more challenging problems due to the enormous size of the conformation space. The analysis of the combined process of ligand binding and structure formation even for small RNAs is plagued by intractably large state spaces. Moreover, the interaction is concentration-dependent and thus is intrinsically non-linear. This precludes the direct transfer of the strategies previously used for the analysis of RNA folding kinetics. Results In our novel, computationally tractable approach to RNA–ligand kinetics, we overcome the two main difficulties by applying a gradient-based coarse graining to RNA–ligand systems and solving the process in a pseudo-first order approximation. The latter is well-justified for the most common case of ligand excess in RNA–ligand systems. We present the approach rigorously and discuss the parametrization of the model based on empirical data. The method supports the kinetic study of RNA–ligand systems, in particular at different ligand concentrations. As an example, we apply our approach to analyze the concentration dependence of the ligand response of the rationally designed, artificial theophylline riboswitch RS3. Conclusion This work demonstrates the tractability of the computational analysis of RNA–ligand interaction. Naturally, the model will profit as more accurate measurements of folding and binding parameters become available. Due to this work, computational analysis is available to support tasks like the design of riboswitches; our analysis of RS3 suggests strong co-transcriptional effects for this riboswitch. The method used in this study is available online, cf. Section “Availability of data and materials”

Tractable RNA–ligand interaction kinetics

Background: The binding of small ligands to RNA elements can cause substantial changes in the RNA structure. This constitutes an important, fast-acting mechanism of ligand-controlled transcriptional and translational gene regulation implemented by a wide variety of riboswitches. The associated refolding processes often cannot be explained by thermodynamic effects alone. Instead, they are governed by the kinetics of RNA folding. While the computational analysis of RNA folding can make use of well-established models of the thermodynamics of RNA structures formation, RNA–RNA interaction, and RNA–ligand interaction, kinetic effects pose fundamentally more challenging problems due to the enormous size of the conformation space. The analysis of the combined process of ligand binding and structure formation even for small RNAs is plagued by intractably large state spaces. Moreover, the interaction is concentration-dependent and thus is intrinsically non-linear. This precludes the direct transfer of the strategies previously used for the analysis of RNA folding kinetics. Results: In our novel, computationally tractable approach to RNA–ligand kinetics, we overcome the two main difficulties by applying a gradient-based coarse graining to RNA–ligand systems and solving the process in a pseudo-first order approximation. The latter is well-justified for the most common case of ligand excess in RNA–ligand systems. We present the approach rigorously and discuss the parametrization of the model based on empirical data. The method supports the kinetic study of RNA–ligand systems, in particular at different ligand concentrations. As an example, we apply our approach to analyze the concentration dependence of the ligand response of the rationally designed, artificial theophylline riboswitch RS3. Conclusion: This work demonstrates the tractability of the computational analysis of RNA–ligand interaction. Naturally, the model will profit as more accurate measurements of folding and binding parameters become available. Due to this work, computational analysis is available to support tasks like the design of riboswitches; our analysis of RS3 suggests strong co-transcriptional effects for this riboswitch. The method used in this study is available online, cf. Section “Availability of data and materials”.© The Author(s) 201