Free-Energy Landscape of RNA Hairpins Constructed via Dihedral Angle Principal Component Analysis

Abstract

To systematically construct a low-dimensional free-energy landscape of RNA systems from a classical molecular dynamics simulation, various versions of the principal component analysis (PCA) are compared: the cPCA using the Cartesian coordinates of all atoms, the dPCA using the sine/cosine-transformed six backbone dihedral angles as well as the glycosidic torsional angle chi and the pseudorotational angle P, the aPCA which ignores the circularity of the 6 + 2 dihedral angles of the RNA, and the dPCA(etatheta), which approximates the 6 backbone dihedral angles by 2 pseudotorsional angles eta and theta. As representative examples, a 10-nucleotide UUCG hairpin and the 36-nucleotide segment SL1 of the Psi site of HIV-1 are studied by classical molecular dynamics simulation, using the Amber all-atom force field and explicit solvent. It is shown that the conformational heterogeneity of the RNA hairpins can only be resolved by an angular PCA such as the dPCA but not by the cPCA using Cartesian coordinates. Apart from possible artifacts due to the coupling of overall and internal motion, this is because the details of hydrogen bonding and stacking interactions but also of global structural rearrangements of the RNA are better discriminated by dihedral angles. In line with recent experiments, it is found that the free energy landscape of RNA hairpins is quite rugged and contains various metastable conformational states which may serve as an intermediate for unfolding.

Order parameters for macromolecules: Application to multiscale simulation

“…The methodology stresses on the large dimensionality of the model essential for timescale separation. 17 Similar ideas arise from our multiscale analysis developed in Sec. III and other papers.…”

“…In this way, they capture key pathways for structural transitions and associated energy barriers. Earlier choices for OP-like variables include principal component analysis (PCA) modes to identify collective behaviors in macromolecular systems, [13][14][15] dihedral angles, 16,17 curvilinear coordinates to characterize macromolecular folding and coiling, 18 bead models wherein a peptide or nucleotide is represented by a bead which interacts with others via a phenomenological force, and spatial coarse-grained models. [19][20][21] These approaches suffer from one or more of the following difficulties: (1) characteristic variables are not slowly varying in time; (2) macromolecular twist is not readily accounted for; (3) their internal dynamics, and hence inelasticity of their collisions is neglected; and (4) the forces involved must be calibrated for most new applications.…”

Free-energy landscape of a hyperstable RNA tetraloop

“…As an alternative determination of the folded free-energy landscape, we performed a principal component analysis of the dihedral angles (dPCA) (30,31) of the configurational ensembles in the lowest temperatures. The first two principal components provided an optimal separation of conformations and effectively described the entire free-energy ensemble in six general configurations (Fig.…”

“…Additional corrections will be necessary in future modifications to the AMBER force field. Characterizing the free-energy landscapes of RNA tetraloops has long been a goal for RNA molecular simulations and has been the subject of multiple studies on different loop systems using a variety of molecular dynamics techniques (25,26,31,42,49,50). In this study, we have determined that the free-energy landscape of an RNA tetraloop can be rigorously characterized through extensive REMD simulations and that analysis of multiple global and internal degrees of freedom can describe a plethora of configurations associated with these landscapes.…”

“…To characterize the different minima of the folding free-energy landscape and identify the barriers between native and nonnative tetraloop configurations, we use dPCA (30,31) of RNA-specific backbone and sugar nucleobase dihedral angles (α, β, γ, δ, e, ζ, and χ). Individual peaks are analyzed with the aforementioned clustering methods, and the first centroid is used to identify individual basins.…”