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.