Conformational entropy of the RNA phosphate backbone and its contribution to the folding free energy

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 Base Stacking Driving Forces in DNA

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.

Atomistic Free Energy Model for Nucleic Acids: Simulations of Single-Stranded DNA and the Entropy Landscape of RNA Stem-Loop Structures

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 ∼10(6) 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.