Order and interactions in DNA arrays: Multiscale molecular dynamics simulation

Abstract

While densely packed DNA arrays are known to exhibit hexagonal and orthorhombic local packings, the detailed mechanism governing the associated phase transition remains rather elusive. Furthermore, at high densities the atomistic resolution is paramount to properly account for fine details, encompassing the DNA molecular order, the contingent ordering of counterions and the induced molecular ordering of the bathing solvent, bringing together electrostatic, steric, thermal and direct hydrogen-bonding interactions, resulting in the observed osmotic equation of state. We perform a multiscale simulation of dense DNA arrays by enclosing a set of 16 atomistically resolved DNA molecules within a semi-permeable membrane, allowing the passage of water and salt ions, and thus mimicking the behavior of DNA arrays subjected to external osmotic stress in a bathing solution of monovalent salt and multivalent counterions. By varying the DNA density, local packing symmetry, and counterion type, we obtain osmotic equation of state together with the hexagonal-orthorhombic phase transition, and full structural characterization of the DNA subphase in terms of its positional and angular orientational fluctuations, counterion distributions, and the solvent local dielectric response profile with its order parameters that allow us to identify the hydration force as the primary interaction mechanism at high DNA densities.

Molecular Dynamics Simulation of High Density DNA Arrays

“…Only recently it became feasible to set up an all-atom MD simulation for a larger set of DNA molecules [51,53] characterized by a single packing geometry with only a partial characterization of the DNA countercharge and solvent ordering. This approach has been later extended by the applications of the multiscale MD technique AdResS (Adaptive Resolution Scheme) [54][55][56][57][58][59][60][61][62][63][64][65][66][67], which has been already successfully applied to various biological systems [68][69][70][71][72][73][74][75][76][77], enabling a concurrent and consistent coupling between the atomistic (AT) and the coarse-grained (CG) representations with a key feature of allowing molecules to freely move not only in real space but also in the resolution space across different regions and change their resolution on the fly according to their position in the computational domain.…”

“…The pertaining EoS phenomenology was investigated for a finite orientationally ordered array of 64 vs. 16 explicit atom-resolved DNAs within a solution-permeable membrane, modeled as a confining cylinder [51] or as a confining polygon allowing for hexagonal and/or orthorhombic packing symmetries [73]. In the latter case, the modeling of the semipermeable membrane allows for comparison of the osmotic pressure for two high density phases with different packing symmetries.…”

“…The EoS is obtained from multiple simulations with varied DNA-DNA densities corresponding to different average interaxial spacings for each bathing solution composition, either at lower densities [51] or high DNA densities [73] that are relevant for the H-OR phase transition. To conduct the simulations efficiently, the multiscale AdResS was adapted to the simulated system [73]; see the next sections.…”

“…In the two most recent simulations, the parametrizations were chosen such as to be close to experimental conditions in the osmotic stress experiments [4,23], with either 250 mM or 1 M pure NaCl [73], or with 200/50 mM NaCl-MgCl 2 ionic mixture [51], leading in both cases to the pronounced screening of the electrostatic interactions. On the other hand, the strongly coupled ions were simulated either as a combination of 1 M NaCl and spermidine Spd 3+ , where 6 Spd 3+ molecules are used per each DNA molecule [73] or sub-mM concentration of Sm 4+ and 200 mM NaCl [51]. In both cases, the system was neutralized by pure Na counterions or a combination of pure Na counterions and multivalent cations.…”

“…In addition to an implementation of the osmotic isobaric ensemble, simulation of a full array composed of as large a number of DNAs as possible is, therefore, a requirement. Applying the large water reservoir simulation methodology in order to implement the osmotic isobaric ensemble, the DNA subphase can then be segregated from the large water reservoir by way of either a cylindrical [51] or a combined orthorhombic-hexagonal semipermeable boundary [73]. Changing the symmetry of the boundary confining the DNA subphase is a convinient approach to capture the phase transitions with a change of packing symmetry, such as the cholesteric (Ch) → line hexatic (LH) (or hexagonal columnar H) and/or the line hexatic → orthorhombic (OR) phase transitions [3,11,15,18].…”