Undersampling and the inference of coevolution in proteins

Protein structure, function, and evolution depend on local and collective epistatic interactions between amino acids. A powerful approach to defining these interactions is to construct models of couplings between amino acids that reproduce the empirical statistics (frequencies and correlations) observed in sequences comprising a protein family. The top couplings are then interpreted. Here, we show that as currently implemented, this inference is always biased, a problem that fundamentally arises from the distinct scales at which epistasis occurs in proteins in the context of limited sampling. We show that these issues explain the ability of current approaches to predict tertiary contacts between amino acids and the inability to obviously expose larger networks of functionally-relevant, collectively evolving residues called sectors. This work provides a necessary foundation for more deeply understanding and improving evolution-based models of proteins.

The kink-turn in the structural biology of RNA

The kink-turn (k-turn) is a widespread structural motif found in functional RNA species. It typically comprises a three-nucleotide bulge followed by tandem trans sugar edge-Hoogsteen G:A base pairs. It introduces a sharp kink into the axis of duplex RNA, juxtaposing the minor grooves. Cross-strand H-bonds form at the interface, accepted by the conserved adenine nucleobases of the G:A basepairs. Alternative acceptors for one of these divides the k-turns into two conformational classes N3 and N1. The base pair that follows the G:A pairs (3b:3n) determines which conformation is adopted by a given k-turn. k-turns often mediate tertiary contacts in folded RNA species and frequently bind proteins. Common k-turn binding proteins include members of the L7Ae family, such as the human 15·5k protein. A recognition helix within these proteins binds in the widened major groove on the outside of the k-turn, that makes specific H-bonds with the conserved guanine nucleobases of the G:A pairs. L7Ae binds with extremely high affinity, and single-molecule data are consistent with folding by conformational selection. The standard, simple k-turn can be elaborated in a variety of ways, that include the complex k-turns and the k-junctions. In free solution in the absence of added metal ions or protein k-turns do not adopt the tightly-kinked conformation. They undergo folding by the binding of proteins, by the formation of tertiary contacts, and some (but not all) will fold on the addition of metal ions. Whether or not folding occurs in the presence of metal ions depends on local sequence, including the 3b:3n position, and the −1b:−1n position (5′ to the bulge). In most cases −1b:−1n = C:G, so that the 3b:3n position is critical since it determines both folding properties and conformation. In general, the selection of these sequence matches a given k-turn to its biological requirements. The k-turn structure is now very well understood, to the point at which they can be used as a building block for the formation of RNA nano-objects, including triangles and squares.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity—that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔGalign, the probability of aligning tertiary contact partners, and ΔGtert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔGHJH) or from changes in the electrostatic environment (ΔG+/−) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔGtert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔGtert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

3D RNA from evolutionary couplings

Non-protein-coding RNAs are ubiquitous in cell physiology, with a diverse repertoire of known functions. In fact, the majority of the eukaryotic genome does not code for proteins, and thousands of conserved long non-protein-coding RNAs of currently unkown function have been identified. When available, knowledge of their 3D structure is very helpful in elucidating the function of these RNAs. However, despite some outstanding structure elucidation of RNAs using X-ray crystallography, NMR and cryoEM, learning RNA 3D structures remains low-throughput. RNA structure prediction in silico is a promising alternative approach and works well for double-helical stems, but full 3D structure determination requires tertiary contacts outside of secondary structures that are difficult to infer from sequence information. Here, based only on information from RNA multiple sequence alignments, we use a global statistical sequence probability model of co-variation in a pairs of nucleotide positions to detect 3D contacts, in analogy to recently developed breakthrough methods for computational protein folding. In blinded tests on 22 known RNA structures ranging in size from 65 to 1800 nucleotides, the predicted contacts matched physical nucleotide interactions with 65-95% true positive prediction accuracy. Importantly, we infer many long-range tertiary contacts, including non-Watson-Crick interactions, where secondary structure elements assemble in 3D. When used as restraints in molecular dynamics simulations, the inferred contacts improve RNA 3D structure prediction to a coordinate error as low as 6 to 10 angstrom rmsd deviation in atom positions, with potential for further refinement by molecular dynamics. These contacts include functionally important interactions, such as those that distinguish the active and inactive conformations of four riboswitches. In blind prediction mode, we present evolutionary couplings suitable for folding simulations for 180 RNAs of unknown structure, available at https://marks.hms.harvard.edu/ev_rna/. We anticipate that this approach can help shed light on the structure and function of non-protein-coding RNAs as well as 3D-structured mRNAs.