Tractable RNA–ligand interaction kinetics

Felix Kühnl, Peter F. Stadler, Sebastian Will

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. 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. 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".