Structure and Dynamics of DNA and RNA Double Helices Formed by d(CTG), d(GTC), r(CUG), and r(GUC) Trinucleotide Repeats and Associated DNA-RNA Hybrids.

Myotonic dystrophy type 1 is the most frequent form of muscular dystrophy in adults caused by an abnormal expansion of the CTG trinucleotide. Both the expanded DNA and the expanded CUG RNA transcript can fold into hairpins. Co-transcriptional formation of stable RNA·DNA hybrids can also enhance the instability of repeat tracts. We performed molecular dynamics simulations of homoduplexes associated with the disease, d(CTG)n and r(CUG)n, and their corresponding r(CAG)n:d(CTG)n and r(CUG)n:d(CAG)n hybrids that can form under bidirectional transcription and of non-pathological d(GTC)n and d(GUC)n homoduplexes. We characterized their conformations, stability, and dynamics and found that the U·U and T·T mismatches are dynamic, favoring anti-anti conformations inside the helical core, followed by anti-syn and syn-syn conformations. For DNA, the secondary minima in the non-expanding d(GTC)n helices are deeper, wider, and longer-lived than those in d(CTG)n, which constitutes another biophysical factor further differentiating the expanding and non-expanding sequences. The hybrid helices are closer to A-RNA, with the A-T and A-U pairs forming two stable Watson-Crick hydrogen bonds. The neutralizing ion distribution around the non-canonical pairs is also described.

Addressing the Embeddability Problem in Transition Rate Estimation.

Markov State Models (MSM) and related techniques have gained significant traction as a tool for analyzing and guiding molecular dynamics (MD) simulations due to their ability to extract structural, thermodynamic, and kinetic information on proteins using computationally feasible MD simulations. The MSM analysis often relies on spectral decomposition of empirically generated transition matrices. This work discusses an alternative approach for extracting the thermodynamic and kinetic information from the so-called rate/generator matrix rather than the transition matrix. Although the rate matrix itself is built from the empirical transition matrix, it provides an alternative approach for estimating both thermodynamic and kinetic quantities, particularly in diffusive processes. A fundamental issue with this approach is known as the embeddability problem. The key contribution of this work is the introduction of a novel method to address the embeddability problem as well as the collection and utilization of existing algorithms previously used in the literature. The algorithms are tested on data from a one-dimensional toy model to show the workings of these methods and discuss the robustness of each method in dependence of lag time and trajectory length.

RNA as a Major-Groove Ligand: RNA-RNA and RNA-DNA Triplexes Formed by GAA and UUC or TTC Sequences.

Friedreich's ataxia is associated with noncanonical nucleic acid structures that emerge when GAA:TTC repeats in the first intron of the FXN gene expand beyond a critical number of repeats. Specifically, the noncanonical repeats are associated with both triplexes and R-loops. Here, we present an in silico investigation of all possible triplexes that form by attaching a third RNA strand to an RNA:RNA or DNA:DNA duplex, complementing previous DNA-based triplex studies. For both new triplexes results are similar. For a pyridimine UUC+ third strand, the parallel orientation is stable while its antiparallel counterpart is unstable. For a neutral GAA third strand, the parallel conformation is stable. A protonated GA+A third strand is stable in both parallel and antiparallel orientations. We have also investigated Na+ and Mg2+ ion distributions around the triplexes. The presence of Mg2+ ions helps stabilize neutral, antiparallel GAA triplexes. These results (along with previous DNA-based studies) allow for the emergence of a complete picture of the stability and structural characteristics of triplexes based on the GAA and TTC/UUC sequences, thereby contributing to the field of trinucleotide repeats and the associated unusual structures that trigger expansion.

Novel eGZ-motif formed by regularly extruded guanine bases in a left-handed Z-DNA helix as a major motif behind CGG trinucleotide repeats.

The expansion of d(CGG) trinucleotide repeats (TRs) lies behind several important neurodegenerative diseases. Atypical DNA secondary structures have been shown to trigger TR expansion: their characterization is important for a molecular understanding of TR disease. CD spectroscopy experiments in the last decade have unequivocally demonstrated that CGG runs adopt a left-handed Z-DNA conformation, whose features remain uncertain because it entails accommodating GG mismatches. In order to find this missing motif, we have carried out molecular dynamics (MD) simulations to explore all the possible Z-DNA helices that potentially form after the transition from B- to Z-DNA. Such helices combine either CpG or GpC Watson-Crick steps in Z-DNA form with GG-mismatch conformations set as either intrahelical or extrahelical; and participating in BZ or ZZ junctions or in alternately extruded conformations. Characterization of the stability and structural features (especially overall left-handedness, higher-temperature and steered MD simulations) identified two novel Z-DNA helices: the most stable one displays alternately extruded Gs, and is followed by a helix with symmetrically extruded ZZ junctions. The G-extrusion favors a seamless stacking of the Watson-Crick base pairs; extruded Gs favor syn conformations and display hydrogen-bonding and stacking interactions. Such conformations could have the potential to hijack the MMR complex, thus triggering further expansion.

Construction of DNA/RNA Triplex Helices Based on GAA/TTC Trinucleotide Repeats.

Atypical DNA and RNA secondary structures play a crucial role in simple sequence repeat (SSR) diseases, which are associated with a class of neurological and neuromuscular disorders known as "anticipation diseases," where the age of disease onset decreases and the severity of the disease is increased as the intergenerational expansion of the SSR increases. While the mechanisms underlying these diseases are complex and remain elusive, there is a consensus that stable, non-B-DNA atypical secondary structures play an important - if not causative - role. These structures include single-stranded DNA loops and hairpins, G-quartets, Z-DNA, triplex nucleic acid structures, and others. While all of these structures are of interest, structures based on nucleic acid triplexes have recently garnered increased attention as they have been implicated in gene regulation, gene repair, and gene engineering. Our work here focuses on the construction of DNA triplexes and RNA/DNA hybrids formed from GAA/TTC trinucleotide repeats, which underlie Friedreich's ataxia. While there is some software, such as the Discovery Studio Visualizer, that can aid in the initial construction of DNA triple helices, the only option for the triple helix is constrained to be that of an antiparallel pyrimidine for the third strand. In this protocol, we illustrate how to build up more generalized DNA triplexes and DNA/RNA mixed hybrids. We make use of both the Discovery Studio Visualizer and the AMBER simulation package to construct the initial triplexes. Using the steps outlined here, one can - in principle - build up any triple nucleic acid helix with a desired sequence for large-scale molecular dynamics simulation studies.

Atypical structures of GAA/TTC trinucleotide repeats underlying Friedreich's ataxia: DNA triplexes and RNA/DNA hybrids.

Expansion of the GAA/TTC repeats in the first intron of the FXN gene causes Friedreich's ataxia. Non-canonical structures are linked to this expansion. DNA triplexes and R-loops are believed to arrest transcription, which results in frataxin deficiency and eventual neurodegeneration. We present a systematic in silico characterization of the possible DNA triplexes that could be assembled with GAA and TTC strands; the two hybrid duplexes [r(GAA):d(TTC) and d(GAA):r(UUC)] in an R-loop; and three hybrid triplexes that could form during bidirectional transcription when the non-template DNA strand bonds with the hybrid duplex (collapsed R-loops, where the two DNA strands remain antiparallel). For both Y·R:Y and R·R:Y DNA triplexes, the parallel third strand orientation is more stable; both parallel and antiparallel protonated d(GA+A)·d(GAA):d(TTC) triplexes are stable. Apparent contradictions in the literature about the R·R:Y triplex stability is probably due to lack of molecular resolution, since shifting the third strand by a single nucleotide alters the stability ranking. In the collapsed R-loops, antiparallel d(TTC+)·d(GAA):r(UUC) is unstable, while parallel d(GAA)·r(GAA):d(TTC) and d(GA+A)·r(GAA):d(TTC) are stable. In addition to providing new structural perspectives for specific therapeutic aims, our results contribute to a systematic structural basis for the emerging field of quantitative R-loop biology.

Effective Riemannian Diffusion Model for Conformational Dynamics of Biomolecular Systems.

We present a Riemannian formalism for effective diffusion of biomolecules in collective variable spaces that provides a robust framework for conformational free energy calculation methods. Unlike their Euclidean counterparts, the Riemannian potential of mean force (PMF) and minimum free energy path (MFEP) are invariant under coordinate transformations. The presented formalism can be readily employed to modify the collective variable based enhanced sampling techniques, such as umbrella sampling (US) commonly used in biomolecular simulations, to take into account the role of intrinsic geometry of collective variable space. Although our model is mathematically equivalent to a Euclidean diffusion with a position-dependent diffusion tensor, the Riemannian formulation provides a more convenient framework for free energy calculation methods and path-finding algorithms aimed at characterizing the effective conformational dynamics of biomolecules. A simple three-dimensional toy model and a pentapeptide (met-enkephalin) simulated in an explicit solvent environment are used to illustrate the workings of the formalism and its implementation.