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.

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.

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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.

We have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of collective variable based molecular dynamics simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of the mean force, minimum free energy path, the diffusion constant, and the transition rate remain invariant under coordinate transformation due to the Riemannian treatment of the collective variable space.Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along a minimum free energy path. *