An implicit divalent counterion force field for RNA molecular dynamics

Nucleic acid folding simulations using a physics-based atomistic free energy model

Performing full-resolution atomistic simulations of nucleic acid folding has remained a challenge for biomolecular modeling. Understanding how nucleic acids fold and how they transition between different folded structures as they unfold and refold has important implications for biology. This paper reports a theoretical model and computer simulation of the ab initio folding of DNA inverted repeat sequences. The formulation is based on an all-atom conformational model of the sugar-phosphate backbone via chain closure, and it incorporates three major molecular-level driving forces-base stacking, counterion-induced backbone self-interactions, and base pairing-via separate analytical theories designed to capture and reproduce the effects of the solvent without requiring explicit water and ions in the simulation. To accelerate computational throughput, a mixed numerical/analytical algorithm for the calculation of the backbone conformational volume is incorporated into the Monte Carlo simulation, and special stochastic sampling techniques were employed to achieve the computational efficiency needed to fold nucleic acids from scratch. This paper describes implementation details, benchmark results, and the advantages and technical challenges with this approach.

A Deep Dive into DNA Base Pairing Interactions Under Water

Base pairing plays a pivotal role in DNA functions and replication fidelity. But while the complementarity between Watson-Crick matched bases is generally believed to arise from the different number of hydrogen bonds in G|C pairs versus A|T, the energetics of these interactions are heavily renormalized by the aqueous solvent. Employing large-scale Monte Carlo simulations, we have extracted the solvent contribution to the free energy for canonical and some noncanonical and stacked base pairs. For all of them, the solvent's contribution to the base pairing free energy is exclusively destabilizing. While the direct hydrogen bonding interactions in the G|C pair is much stronger than A|T, the thermodynamic resistance produced by the solvent also pushes back much stronger against G|C compared to A|T, generating an only ∼1 kcal/mol free energy difference between them. We have profiled the density of water molecules in the solvent adjacent to the bases and observed a "freezing" behavior where waters are recruited into the gap between the bases to compensate for the unsatisfied hydrogen bonds between them. A very small number of water molecules that are associated with the Watson-Crick donor/acceptor atoms turn out to be responsible for the majority of the solvent's thermodynamic resistance to base pairing. The absence or presence of these near-field waters can be used to enhance fidelity during DNA replication.

Visualizing Disordered Single-Stranded RNA: Connecting Sequence, Structure, and Electrostatics

Disordered homopolymeric regions of single-stranded RNA, such as U or A tracts, are found within functional RNAs where they play distinct roles in defining molecular structure and facilitating recognition by partners. Despite this prominence, details of conformational and biophysical properties of these regions have not yet been resolved. We apply a number of experimental techniques to investigate the conformations of these biologically important motifs and provide quantitative measurements of their ion atmospheres. Single strands of RNA display pronounced sequence-dependent conformations that relate to the unique ion atmospheres each attracts. Chains of rU bases are relatively unstructured under all conditions, while chains of rA bases display distinct ordering through stacking or clustering motifs, depending on the composition of the surrounding solution. These dramatic structural differences are consistent with the measured disparity in ion composition and atmospheres around each homopolymer, revealing a complex interplay of base, ion, and single-strand ordering. The unique structural and ionic signatures of homopolymer ssRNAs explains their role(s) in folding structured RNAs and may explain their distinct recognition by protein partners.

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.

Theoretical Model for Solvent-Induced Base Stacking Interactions in Solvent-Free DNA Simulations

Ultrahigh-throughput conformational sampling of biopolymers like nucleic acids are most effectively carried out without explicit solvents, but the physical origins of almost all inter- and intramolecular interactions controlling nucleic acid structures are rooted in water. Single-stranded (ss) DNAs or RNAs in water are characterized by ensembles of diverse conformations. To properly capture solvent-induced nucleobase stacking interactions in an otherwise solvent-free Monte Carlo algorithm, theoretical models are developed here to describe the solvent entropy and dispersion terms in base stacking free energies. To validate these models, equilibrium ensembles of ss (dA) _n and (dT) _n sequences ( n = 30, 40, and 50) were simulated, and they quantitatively reproduced experimental small-angle X-ray scattering (SAXS) data. Simulated dA ensembles show substantial stacking. While less prevalent, stacking in dT chains is not negligible. Analysis of SAXS profiles suggests that excess features between wavevector 0.03 and 0.18 Å^-1 correlate with stacking, and stacking in dA versus dT chains is chain length-dependent, where (dT)₃₀ and (dA)₃₀ chains have more similar structures, but longer dA chains show more stacking over dT. The average stack length in ss-dA chains is 5-10 nucleotides, yielding an estimate for the overall A|A stacking free energy at ∼1 kcal/mol.

Unraveling Mg2+-RNA binding with atomistic molecular dynamics

Interaction with divalent cations is of paramount importance for RNA structural stability and function. We report here a detailed molecular dynamics study of all the possible binding sites for Mg2+ on an RNA duplex, including both direct (inner sphere) and indirect (outer sphere) binding. In order to tackle sampling issues, we develop a modified version of bias-exchange metadynamics, which allows us to simultaneously compute affinities with previously unreported statistical accuracy. Results correctly reproduce trends observed in crystallographic databases. Based on this, we simulate a carefully chosen set of models that allows us to quantify the effects of competition with monovalent cations, RNA flexibility, and RNA hybridization. Our simulations reproduce the decrease and increase of Mg2+ affinity due to ion competition and hybridization, respectively, and predict that RNA flexibility has a site-dependent effect. This suggests a nontrivial interplay between RNA conformational entropy and divalent cation binding.