Atomic hydrodynamics of DNA: Coil-uncoil-coil transitions in a wall-bounded shear flow

Extensive experimental work on the response of DNA molecules to externally applied forces and on the dynamics of DNA molecules flowing in microchannels and nanochannels has been carried out over the past two decades, however, there has not been available, until now, any atomic-scale means of analyzing nonequilibrium DNA response dynamics. There has not therefore been any way to investigate how the backbone and side-chain atoms along the length of a DNA molecule interact with the molecules and ions of the flowing solvent and with the atoms of passing boundary surfaces. We report here on the application of the nonequilibrium biomolecular dynamics simulation method that we developed [G. M. Wang and W. C. Sandberg, Nanotechnology 18, 4819 (2007)] to analyze, at the atomic interaction force level, the conformational dynamics of short-chain single-stranded DNA molecules in a shear flow near a surface. This is a direct atomic computational analysis of the hydrodynamic interaction between a biomolecule and a flowing solvent. The DNA molecules are observed to exhibit conformational behaviors including coils, hairpin loops, and figure-eight shapes that have neither been previously measured experimentally nor observed computationally, as far as we know. We relate the conformational dynamics to the atomic interaction forces experienced throughout the length of a molecule as it moves in the flowing solvent past the surface boundary. We show that the DNA conformational dynamics is related to the asymmetry in the molecular environment induced by the motion of the surrounding molecules and the atoms of the passing surface. We also show that while the asymmetry in the environment is necessary, it is not sufficient to produce the observed conformational dynamics. A time variation in the asymmetry, due in our case to a shear flow, must also exist. In order to contrast these results with the usual experimental situation of purely diffusive motion in thermal equilibrium we have also carried out computations with a zero shear rate. We show that in thermal equilibrium there is asymmetry and an atomic hydrodynamic coupling between DNA molecules and the solvent molecules but there is no coil-uncoil transition.

Figure 1

(Color) Geometry of atomic Au nanochannel walls and initial position and orientation of the six DNA molecules surrounded by water molecules and ions.

Figure 2

(Color) Instantaneous molecular configurations of, and comparisons between, DNA molecule 6 (upper) and DNA molecule 1 (lower). Atomic representation shows the actual relative atomic positions while the ribbons show the backbone structures and blue dots are the attached bases. For clarity the water molecules and ions are not shown. (a) $t=0\mathrm{ps}$. Molecule 1 (left) is across the channel centerplane and molecule 6 (right) is adjacent to the wall. Both molecules had the same initially minimized, thermally equilibrated length. (b) $t=29\mathrm{ps}$. Molecule 1 has been rotated and stretched as it aligned with the flow. Molecule 6 has coiled into a hairpinlike configuration as it also aligned with the flow. (c) $t=53\mathrm{ps}$. Molecule 1 has remained in an extended configuration as it remains aligned with the flow direction. Molecule 6 has gone from a tightly coiled hairpinlike state to a figure-eight loop configuration, also remaining aligned with the flow direction. (d) $t=124\mathrm{ps}$. Molecule 1 has shortened slightly with some kinks but still is primarily aligned with the flow direction. Molecule 6 has compressed its length but retains the figure-eight configuration with a twist.

Figure 3

(a) End-to-end length $\left(L_{\mathrm{ee}}\right)$ and radius of gyration $\left(R_{\mathrm{g}}\right)$ time variation of molecules 1 and 6 in a wall-bounded shear flow. Solid curves show $L_{\mathrm{ee}}$ variations of DNA molecules 1 and 6 and dotted curves show $R_g$ variations. (b) End-to-end length $\left(L_{\mathrm{ee}}\right)$ and radius of gyration $\left(R_g\right)$ time variation of molecules 1 and 6 in thermal equilibrium. Solid curves show $L_{\mathrm{ee}}$ variations of DNA molecules 1 and 6 and dotted curves show $R_g$ variations.

Figure 4

(a) Total hydrodynamic force components on DNA molecules 1 and 6 as a function of time at a flow shear rate of $48\mathrm{ps}$. (b) Total hydrodynamic force components on DNA molecules 1 and 6 as a function of time in an equilibrium solvent.

Figure 5

(a) Total hydrodynamic torque components with respect to the center of mass of DNA molecules 1 and 6 as a function of time. (b) Total hydrodynamic torque components with respect to the center of mass of DNA molecules 1 and 6 as a function of time for the equilibrium case.

Figure 6

(Color online) Internal bonding forces as a function of time in a shear flow for (a) DNA molecule 1 and (b) DNA molecule 6. B1 and B12 correspond to the first (end) and 12th (middle) backbone O–P bonds; S1 and S12 are the first and 12th (middle) sidechain-backbone bonds. Insets: Dark (black online version) curves are 20 backbone bonds and light (purple online) curves are side-chain bonds connecting them to the molecule backbone. (a) DNA molecule 1 bond force time-histories. (b) DNA molecule 6 bond force time histories.

Figure 7

(Color) Equilibrium MD simulation without walls for DNA molecules 1 and 6.

Figure 8

(Color online) Total hydrodynamic force on only DNA molecules 1 and 6 as a function of time from equilibrium MD simulations without walls.

Figure 9

(Color) Equilibrium MD simulation for six DNA molecules in a box without solid walls.

Figure 10

(a) Total hydrodynamic force and (b) torque components of DNA molecules 1 and 6 as a function of time from equilibrium MD simulations without walls.

Figure 11

(Color) NEBD simulation box with moving walls and the same initial locations and configurations of DNA molecules 1 and 6 as in Fig. 1.

Figure 12

Radius of gyration and end-to-end length of DNA molecules 1 and 6 as a function of time from NEBD simulations at a shear rate $0.48∕\mathrm{ps}$ with walls.

Figure 13

(Color online) Total hydrodynamic force components on DNA molecules 1 and 6 as a function of time from NEBD simulations with walls at a shear rate of $0.48∕\mathrm{ps}$.