Proving the Turing Universality of Oritatami Co-Transcriptional Folding (Full Text)

We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerize the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable and checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalized to other discrete dynamical systems, where proofs involve large case enumerations as well

Design and Characterization of RNA Nanotubes

RNA is a functionally rich and diverse biomaterial responsible for regulating several cellular processes. This functionality has been harnessed to build predominately small nanoscale structures for drug delivery and the treatment of disease. The understanding of design principles to build large RNA structures will allow for further control of stoichiometry and spatial arrangement drugs and ligands. We present the design and characterization of RNA nanotubes that self-assemble from programmable monomers, or tiles, formed by five distinct RNA strands. Tiles include double crossover junctions and assemble via single-stranded sticky-end domains. We find that nanotube formation is dependent on the intertile crossover distance. The average length observed for the annealed RNA nanotubes is ≈1.5 μm, with many nanotubes exceeding 10 μm, enabling the characterization of RNA nanotubes length distribution via fluorescence microscopy. Assembled tubes were observed to be stable for more than 24 h, however post-annealing growth under isothermal conditions does not occur. Nanotubes assemble also from RNA tiles modified to include a single-stranded overhang (toehold), suggesting that it may be possible to decorate these large RNA scaffolds with nanoparticles or other nucleic acid molecules

Design and Characterization of RNA Nanotubes

RNA is a functionally rich and diverse biomaterial responsible for regulating several cellular processes. This functionality has been harnessed to build predominately small nanoscale structures for drug delivery and the treatment of disease. The understanding of design principles to build large RNA structures will allow for further control of stoichiometry and spatial arrangement drugs and ligands. We present the design and characterization of RNA nanotubes that self-assemble from programmable monomers, or tiles, formed by five distinct RNA strands. Tiles include double crossover junctions and assemble via single-stranded sticky-end domains. We find that nanotube formation is dependent on the intertile crossover distance. The average length observed for the annealed RNA nanotubes is ≈1.5 μm, with many nanotubes exceeding 10 μm, enabling the characterization of RNA nanotubes length distribution via fluorescence microscopy. Assembled tubes were observed to be stable for more than 24 h, however post-annealing growth under isothermal conditions does not occur. Nanotubes assemble also from RNA tiles modified to include a single-stranded overhang (toehold), suggesting that it may be possible to decorate these large RNA scaffolds with nanoparticles or other nucleic acid molecules

Genus trace reveals the topological complexity and domain structure of biomolecules

The structure of bonds in biomolecules, such as base pairs in RNA chains or native interactions in proteins, can be presented in the form of a chord diagram. A given biomolecule is then characterized by the genus of an auxiliary two-dimensional surface associated to such a diagram. In this work we introduce the notion of the genus trace, which describes dependence of genus on the choice of a subchain of a given backbone chain. We find that the genus trace encodes interesting physical and biological information about a given biomolecule and its three dimensional structural complexity; in particular it gives a way to quantify how much more complicated a biomolecule is than its nested secondary structure alone would indicate. We illustrate this statement in many examples, involving both RNA and protein chains. First, we conduct a survey of all published RNA structures with better than 3 Å resolution in the PDB database, and find that the genus of natural structural RNAs has roughly linear dependence on their length. Then, we show that the genus trace captures properties of various types of base pairs in RNA, and enables the identification of the domain structure of a ribosome. Furthermore, we find that not only does the genus trace detect a domain structure, but it also predicts a cooperative folding pattern in multi-domain proteins. The genus trace turns out to be a useful and versatile tool, with many potential applications

Promoting RNA helical stacking via A-minor junctions

RNA molecules take advantage of prevalent structural motifs to fold and assemble into well-defined 3D architectures. The A-minor junction is a class of RNA motifs that specifically controls coaxial stacking of helices in natural RNAs. A sensitive self-assembling supra-molecular system was used as an assay to compare several natural and previously unidentified A-minor junctions by native polyacrylamide gel electrophoresis and atomic force microscopy. This class of modular motifs follows a topological rule that can accommodate a variety of interchangeable A-minor interactions with distinct local structural motifs. Overall, two different types of A-minor junctions can be distinguished based on their functional self-assembling behavior: one group makes use of triloops or GNRA and GNRA-like loops assembling with helices, while the other takes advantage of more complex tertiary receptors specific for the loop to gain higher stability. This study demonstrates how different structural motifs of RNA can contribute to the formation of topologically equivalent helical stacks. It also exemplifies the need of classifying RNA motifs based on their tertiary structural features rather than secondary structural features. The A-minor junction rule can be used to facilitate tertiary structure prediction of RNAs and rational design of RNA parts for nanobiotechnology and synthetic biology

The UA_handle: a versatile submotif in stable RNA architectures†

Stable RNAs are modular and hierarchical 3D architectures taking advantage of recurrent structural motifs to form extensive non-covalent tertiary interactions. Sequence and atomic structure analysis has revealed a novel submotif involving a minimal set of five nucleotides, termed the UA_handle motif (5′XU/ANnX3′). It consists of a U:A Watson–Crick: Hoogsteen trans base pair stacked over a classic Watson–Crick base pair, and a bulge of one or more nucleotides that can act as a handle for making different types of long-range interactions. This motif is one of the most versatile building blocks identified in stable RNAs. It enters into the composition of numerous recurrent motifs of greater structural complexity such as the T-loop, the 11-nt receptor, the UAA/GAN and the G-ribo motifs. Several structural principles pertaining to RNA motifs are derived from our analysis. A limited set of basic submotifs can account for the formation of most structural motifs uncovered in ribosomal and stable RNAs. Structural motifs can act as structural scaffoldings and be functionally and topologically equivalent despite sequence and structural differences. The sequence network resulting from the structural relationships shared by these RNA motifs can be used as a proto-language for assisting prediction and rational design of RNA tertiary structures

Comprehensive features of natural and in vitro selected GNRA tetraloop-binding receptors

Specific recognitions of GNRA tetraloops by small helical receptors are among the most widespread long-range packing interactions in large ribozymes. However, in contrast to GYRA and GAAA tetraloops, very few GNRA/receptor interactions have yet been identified to involve GGAA tetraloops in nature. A novel in vitro selection scheme based on a rigid self-assembling tectoRNA scaffold designed for isolation of intermolecular interactions with A-minor motifs has yielded new GGAA tetraloop-binding receptors with affinity in the nanomolar range. One of the selected receptors is a novel 12 nt RNA motif, (CCUGUG … AUCUGG), that recognizes GGAA tetraloop hairpin with a remarkable specificity and affinity. Its physical and chemical characteristics are comparable to those of the well-studied ‘11nt’ GAAA tetraloop receptor motif. A second less specific motif (CCCAGCCC … GAUAGGG) binds GGRA tetraloops and appears to be related to group IC3 tetraloop receptors. Mutational, thermodynamic and comparative structural analysis suggests that natural and in vitro selected GNRA receptors can essentially be grouped in two major classes of GNRA binders. New insights about the evolution, recognition and structural modularity of GNRA and A-minor RNA–RNA interactions are proposed

A protolanguage describing RNA tertiary folds

One of the great challenges for emerging fields in nanobiotechnology and synthetic biology is to be able to control the three-dimensional structures of biomolecular components with a high degree of precision. The simplest way to accomplish this is by studying and understanding the way that nature has already solved these problems for biomolecular assembly. Stable RNAs are modular three-dimensional architectures that take advantage of recurrent structural motifs to form extensive networks of non-covalent tertiary interactions. A limited set of basic structural components can account for the formation of most structural motifs uncovered in ribosomal and stable RNAs. The sequence networks resulting from the structural relationships shared by these RNA motifs can be used as a protolanguage for assisting the prediction and rational design of RNA tertiary structures. Experimental methods for comparing and characterizing structural RNA motifs that define helical stacking, bending and branching or/and long-range assembly are presented. In vitro selection is used to generate new classes of RNA loop/receptor interaction. Using RNA protolanguage, new varieties of multi-helix RNA junctions that fold in a single stacking conformer are designed. The synthesis of well-defined polyhedral RNA nanoparticles defined by tertiary structure with full control over composition stoichiometry and spatial addressability is demonstrated. This work establishes that RNA tertiary structure can be used as a full-edged protolanguage to program RNA sequences to fold into any arbitrary shapes with self-assembling and ligand-responsive behavior, and lays part of the foundation for a general method of RNA design and construction