Base stacking is a key determinant of nucleic acid structures, but the precise origin of the thermodynamic driving force behind the stacking of nucleobases remains open. The rather mild stacking free energy measured experimentally, roughly a kcal/mol depending on the identity of the bases, is physiologically significant because while base stacking confers stability to the genome in its double helix form, the duplex also has to be unwound in order to be replicated or transcribed. A stacking free energy that is either too high or too low will over- or understabilize the genome, impacting the storage of genetic information and also its retrieval. While the molecular origin of stacking driving force has been attributed to many different sources including dispersion, electrostatics, and solvent hydrogen bonding, here we show via a systematic decomposition of the stacking free energy using large-scale computer simulations that the dominant driving force stabilizing base stacking is nonhydrophobic solvent entropy. Counteracting this is the conformational entropic penalty on the sugar–phosphate backbone against stacking, while solvent hydrogen-bonding, charge–charge interactions, and dispersive forces produce only secondary perturbations. Solvent entropic forces and DNA backbone conformational strains therefore work against each other, leading to a very mild composite stacking free energy in agreement with experiments.

Polyaromatic dye molecules employed in photovoltaic and electronic applications are often processed in organic solvents. The aggregation of these dyes is key to their applications, but a fundamental molecular understanding of how the solvent environment controls the stacking of polyaromatics is unclear. This study reports initial results from Monte Carlo simulations of how various acene molecule dimers stack when they are dissolved in different solvents. Free energies computed using full dispersion interactions versus those with sterics only suggest that solvent entropy alone accounts for the majority of the stacking free energy in solvents with compact molecular geometries such as carbon tetrachloride. However, in contrast with carbon tetrachloride, we also observe significant variations in the stacking free energies of naphthalene, anthracene, and tetracene across other solvents such as toluene and cyclohexane. The weak attractive dispersion interactions between the acene solutes and planar and near-planar solvent molecules enable them to intercalate between the acene monomers, inducing extra stability beyond what solvent entropic driving force alone could predict. In all three solvents studied (carbon tetrachloride, cyclohexane, toluene) the solvent environment helps facilitate stacking of all three acenes studied (naphthalene, anthracene, tetracene), inducing a significant stabilization free energy between −4 and −8 kcal/mol. Extensive free energy umbrella sampling along the other orthogonal directions allows us to accurately calculate the dimerization equilibrium constants of all three acenes, which vary over several orders of magnitude in a way that depends intricately on the solvent they are in. Given the prevalence of solution-based processing techniques for organic electronic and photonic devices, these results provide useful insights into the critical role that solvent structure and characteristics play in the solution-based aggregation of organic dyes.

A nucleic acid folds according to its free energy, but persistent residual conformational fluctuations remain along its sugar–phosphate backbone even after secondary and tertiary structures have been assembled, and these residual conformational entropies provide a rigorous lower bound for the folding free energy. We extend a recently reported algorithm to calculate the residual backbone entropy along a RNA or DNA given configuration of its bases and apply it to the crystallographic structures of the 23S ribosomal subunit and DNAs in the nucleosome core particle. In the 23S rRNAs, higher entropic strains are concentrated in helices and certain tertiary interaction platforms while residues with high surface accessibility and those not involved in base pairing generally have lower strains. Upon folding, residual backbone entropy in the 23S subunit accounts for an average free energy penalty of +0.47 (kcal/mol)/nt (nt = nucleotide) at 310 K. In nucleosomal DNAs, backbone entropies show periodic oscillations with sequence position correlating with the superhelical twist and shifts in the base-pair-step geometries, and nucleosome positioning on the bound DNA exerts strong influence over where entropic strains are located. In contrast to rRNAs, residual backbone entropies account for a free energy penalty of only +0.09 (kcal/mol)/nt in duplex relative to single-stranded DNAs.

While single-stranded (ss) segments of DNAs and RNAs are ubiquitous in biology, details about their structures have only recently begun to emerge. To study ssDNA and RNAs, we have developed a new Monte Carlo (MC) simulation using a free energy model for nucleic acids that has the atomisitic accuracy to capture fine molecular details of the sugar–phosphate backbone. Formulated on the basis of a first-principle calculation of the conformational entropy of the nucleic acid chain, this free energy model correctly reproduced both the long and short length-scale structural properties of ssDNA and RNAs in a rigorous comparison against recent data from fluorescence resonance energy transfer, small-angle X-ray scattering, force spectroscopy and fluorescence correlation transport measurements on sequences up to ∼100 nucleotides long. With this new MC algorithm, we conducted a comprehensive investigation of the entropy landscape of small RNA stem–loop structures. From a simulated ensemble of ∼106 equilibrium conformations, the entropy for the initiation of different size RNA hairpin loops was computed and compared against thermodynamic measurements. Starting from seeded hairpin loops, constrained MC simulations were then used to estimate the entropic costs associated with propagation of the stem. The numerical results provide new direct molecular insights into thermodynaimc measurement from macroscopic calorimetry and melting experiments.

We present an implicit ion model fo the calculation of the electrostatic free energies of RNA conformations in the presence of divalent counterions such as Mg2+. The model was applied to the native and several non-native structures of the hammerhead ribozyme and the group I intron in Tetrahymena to study the stability of candidate unfolding intermediates. Based on a rigorous statistical mechanical treatment of the counterions that are closely associated with the RNA while handling the rest of the ions in the solution via a mean field theory in the Grand Canonical ensemble, the implicit ion model accurately reproduces the ordering of their free energies, correctly identifying the native fold as the most stable structure out of the other alternatives. For RNA concentrations in the range below 0.1 μM, divalent concentrations of ∼0.5 mM or above, and over a wide range of solvent dielectric constants, the equilibrium number of divalent ions associated with the RNA remains close to what is needed to exactly neutralize the phosphate negative charges, but the stability of compact RNA folds can be reversed when the divalent ion concentration is lower than ∼0.1 mM, causing the number of associated ions to underneutralize the RNA. In addition to calculating counterion-mediated free energies, the model is also able to identify potential high-affinity electronegative ion binding pockets on the RNA. The model can be easily integrated into an all-atom Monte Carlo RNA simulation as an implicit counterion model.

In this paper, we describe how the inverse kinematic solution to the loop closure problem may be generalized to reclose a RNA segment of arbitrary length containing any number of nucleotides without disturbing the atomic positions of the rest of the molecule. This generalization is made possible by representing the boundary conditions of the closure in terms of a set of virtual coordinates called RETO, allowing the inverse kinematics to be reduced from the original six-variable/six-constraint problem to a four-variable/four-constraint problem. Based on this generalized closure solution, a new Monte Carlo algorithm has been formulated and implemented in a fully atomistic RNA simulation capable of moving loops of arbitrary lengths using torsion angle updates exclusively. Combined with other conventional Monte Carlo moves, this new algorithm is able to sample large-scale RNA chain conformations much more efficiently. The utility of this new class of Monte Carlo moves in generating large-loop conformational rearrangements is demonstrated in the simulated unfolding of the full-length hammerhead ribozyme with a bound substrate.