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DNA double helix, a tiny electromotor

Abstract

Flowing fluid past chiral objects has been used for centuries to power rotary motion in man-made machines. By contrast, rotary motion in nanoscale biological or chemical systems is produced by biasing Brownian motion through cyclic chemical reactions. Here we show that a chiral biological molecule, a DNA or RNA duplex rotates unidirectionally at billions of revolutions per minute when an electric field is applied along the duplex, with the rotation direction being determined by the chirality of the duplex. The rotation is found to be powered by the drag force of the electro-osmotic flow, realizing the operating principle of a macroscopic turbine at the nanoscale. The resulting torques are sufficient to power rotation of nanoscale beads and rods, offering an engineering principle for constructing nanoscale systems powered by electric field.

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Fig. 1: Unidirectional rotation of DNA and RNA molecules in external electric field.
Fig. 2: Torque generation mechanism.
Fig. 3: DNA-powered rotation of hydrodynamic loads.

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Data availability

Simulation trajectories corresponding to the main text figures are available via https://doi.org/10.13012/B2IDB-6770800_V1. The datasets supporting the plots generated during the current study are attached. Any other data and simulation trajectories are available upon request.

Code availability

All simulation and analysis code are available on reasonable request. Source Data are provided with this paper.

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Acknowledgements

C.M. and A.A. acknowledge the illuminating discussions with X. Shi, C. Dekker and H. Dietz. A.A. acknowledges A. Noy for suggesting a carbon nanotube system and A. Smolyanitsky for suggesting an energy conversion calculation. This work was supported by the National Science Foundation grants DMR-1827346 and PHY-1430124 (A.A.). The supercomputer time was provided through XSEDE allocation grant MCA05S028 (A.A.) and the Leadership Resource Allocation MCB20012 on Frontera of the Texas Advanced Computing Centre (A.A.).

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A.A. conceptualized and supervised the work, and performed project administration. A.A., C.M. and J.W. designed the methodology. C.M., L.Q. and J.W. performed the investigations and visualizations. A.A., C.M., L.Q. and J.W. acquired funding, and wrote the original draft, whereas A.A. and C.M. performed revisions.

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Correspondence to Aleksei Aksimentiev.

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Nature Nanotechnology thanks Derek Stein and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 All-atom simulations of DNA rotation using the TIP4P-D water model.

a, Rotation angle versus simulation time of a DNA duplex under 100 (red) and 10 (black) mV/nm electric field carried our using the TIP4P-D model of water. The simulation system was identical to the periodic TIP3P simulation system, Fig. 2a. The average rotation rate determined via a linear regression fit is −5.1 and −1.1 degrees/ns at 100 and 10 mV/nm, respectively. We attribute the non-linear scaling to a large statistical error of the 10 mV/nm simulation. For reference, the average rotation velocity observed in our TIP3P simulations under a 100 mV/nm field was −12.8 degrees/ns, Fig. 1c. b, Distribution of the effective torque values. The instantaneous torque values were sampled every 2.4 ps and averaged using 5 ns blocks. The vertical solid lines depict the mean values of the distributions: −0.74 and −0.11 pN nm for 100 and 10 mV/nm. For reference, the average magnitude of the effective torque measured using the TIP3P model of water is about 0.68 pN nm at electric field magnitude of 100 mV/nm, Fig. 2d. Thus, the torque values are insensitive to the water model used, indicating that the shear stress on DNA from the fluid does not depend on the fluid viscosity, as expected. c, Ionic current through a cubic volume of 1 M KCl electrolyte, 5.8 nm on each side, under a 10 mV/nm electric field obtained using the TIP3P, TIP4P-D and out custom implicit solvent models, averaged over 5-ns blocks. For reference, the expected experimental ionic current value is plotted as a dashed line, computed using the experimental 11.0 S/m conductivity of 1 M KCl. The bulk conductivity values computed from the currents are 16.2, 7.2, and 13.5 S/m for the TIP3P, TIP4P-D and our custom implicit solvent models, respectively. The lower than experimental conductivity of the TIP4P-D electrolyte suggests that the model may systematically underestimate the electro-kinetic effects because of the lower than expected electrophoretic mobility of ions.

Extended Data Fig. 2 Effective force of the electric field on DNA and RNA molecules.

a, Simulation system containing a 21 bp DNA helix (blue and red strands; orange phosphorus atoms) submerged in a volume of 1 M KCl electrolyte (not shown). The insets schematically illustrate how the phosphorus atoms of the molecule are harmonically restrained to their initial coordinates. Equilibrium displacement of the atoms from their initial coordinates along the nanopore axis multiplied by the spring constant of the harmonic restraint equals by magnitude the effective axial force experienced by the molecule. b, Axial component of the module of the effective force, per base pair, on a DNA (black) or an RNA (blue) duplex as a function of the applied electric field.

Extended Data Fig. 3 Rotational diffusion of DNA and RNA molecules.

Mean squared angular displacement (MSAD) of a 16-bp DNA (black) and a 16-bp RNA (blue) duplex is plotted versus the lag time. The MSAD values were determined from the analysis of the 500 ns angular displacement traces obtained under zero applied electric field conditions; the traces are shown in Fig. 1a. Dividing the slopes of the MSAD curves by a factor of two yields the rotational diffusion constants, D, of DNA and RNA duplexes at 288 and 273 deg2 ns–1, respectively. The corresponding rotational mobilities, μ=D/kBT, where kBT is the thermal energy, are μDNA=1.24 deg ns–1 pN–1 nm–1 and μRNA=1.17 deg ns–1 pN–1 nm–1.

Extended Data Fig. 4 Directly observed versus computed rate of rotation of a finite 16-bp duplex.

The rate of rotation observed in the applied electric field simulations, Fig. 1c of the main text, is plotted versus the rotation rate calculated using two estimates of the angular mobility μ and the direct measurement of the torque under electric field, Fig. 2d. The torque per base pair was estimated from the applied field strength using the linear regression fit to the data, Fig. 2d. The rotation rate ω was calculated from the definition of mobility, μ = ω/τ, where τ is the torque on the duplex. Two strategies were used to determine the mobility: using the slope of the mean squared angular displacement as a function of lag time, Extended Data Fig. 3, and directly using the mobility determined from a linear regression fit to rotation rate due to a constant applied torque, Fig. 2e. We attribute slight deviations of the data from perfect agreement (dashed gray line) to a statistical error in determining the effective torque per base pair from Fig. 2d.

Extended Data Fig. 5 Flow of ions around nucleic acid molecules.

a, Schematic of the simulation system where the DNA was made effectively infinite by connecting its stands over the periodic boundary. A similar system was constructed for RNA. b, Average K+ ion velocity along duplex axis versus distance from the axis. Data were averaged over multiple trajectories at ±50 mV/nm electric field or ±12.7 bar/nm pressure gradient using 5 Å radial bins. c, Density of water molecules versus distance from the duplex axis. For the DNA system, the electric field and solvent flow data overlap almost exactly. d, Average tangential velocity of a K+ ion versus radial distance from the central axis of the DNA or RNA duplex. Data were computed as described in panel b. e–g, Same as in panels b–d but for a Cl ion. h, Average tangential solvent momentum due to motion of water molecules within a cylindrical volume centred on the DNA or RNA duplex. At each radial value, the momentum of each solvent species was computed from the product of the average density, the average tangential velocity of the solvent species, the mass of that species and the radius. For all plots, the shaded regions depicts the magnitude of the difference between data obtained at opposite directions of the electric field; the solid lines depict the average over the two directions.

Extended Data Fig. 6 Implicit solvent simulations of DNA rotation.

a, Simulation system consisting of a rigid body representation of a DNA duplex surrounded by point-like particles representing potassium (red) and chloride (teal) ions. Two grid-based potentials prescribe the interactions between the DNA duplex and the ions, a 1 kcal mol–1 iso-surface for DNA–potassium potential is shown in grey. The DNA duplex is effectively infinite under the periodic boundary conditions. The centre of mass of the duplex is harmonically restrained to prevent translation. A 100 mV/nm electric field is applied to the ions. b, Rotation angle as a function of simulations time for implicit solvent and all-atom simulations of DNA rotation under a 100 mV/nm electric field. The all-atom trace is from Fig. 1b. c, Average rotation rate versus electric field strength obtained from implicit solvent and all-atom simulations. The all-atom data are from Fig. 1c. d, Distributions of instantaneous torques, sampled every 2.4 ps and averaged over 5 ns blocks. A vertical solid line depicts the mean of each distribution. The effective torque was measured by preventing DNA rotation using a harmonic dihedral angle potential. The all-atom data are from Fig. 2c.

Extended Data Fig. 7 Water flow-induced rotation of a DNA molecule.

a, Simulation system containing a 21 bp DNA helix (light grey; green backbone) submerged in a volume of 1 M KCl electrolyte (semi-transparent molecular surface); only a fraction of ions is shown explicitly, for clarity. The DNA molecule is made effectively infinite by connecting each of its strands to itself over the periodic boundary of the simulation unit cell. For illustration, partial periodic images of the DNA molecule are shown in grey. The water flow is produced by applying a small, constant force to each water molecule parallel to the axis of the DNA molecule (see Methods). Phosphorus atoms of the DNA are harmonically restrained to the surface of a cylinder such that the DNA is free to rotate about its axis; additional restrains prevent the molecules from drifting in the direction of the flow. b, Angular displacement of the DNA molecule as a function of simulation time. The sign of displacement is prescribed by the right-hand rule with respect to the positive direction of the force applied to the water molecules, as indicated in panel a. c, Average angular velocity of the DNA helix versus pressure gradient due to force applied to each water molecule. Each data point was determined by averaging a ~60–200 ns MD trajectory. The line shows a linear regression fit to the data. The right axis displays the rotational velocity of the DNA in units of revolutions per minute (RPM).

Extended Data Fig. 8 Stochastic displacement of DNA pressed against a graphene surface.

a, Side view of a simulation system consisting of a DNA duplex placed in contact with a layer of carbon atoms and 1 M KCl electrolyte solution, which is not shown for clarity. A 10 pN force is applied to the DNA centre of mass (CoM), pushing it towards the graphene. b, Sequence of snapshots illustrating spontaneous displacement of DNA along the graphene surface during a 150 ns MD simulation. A trace of the DNA CoM position is shown alongside the DNA (red to blue line). c, Mean squared displacement (MSD) of the CoM position of the DNA duplex. The CoM was projected into the plane of the graphene for MSD calculation. Dashed line depicts a linear regression fit to the data. The effective diffusion coefficient of the DNA was extracted from the slope of the fit as \(\left\langle {\Delta x^2} \right\rangle = 4D\Delta t\). The diffusion coefficient was converted into a friction coefficient as \(\gamma = k_BT/D\). d, MSD of the rotation angle of the DNA duplex. The rotation angle was obtained after projecting the duplex axis vectors into the plane of the graphene. The effective rotational diffusion coefficient was extracted from the slope of the fit as \(\left\langle {\Delta \theta ^2} \right\rangle = 2D_{{{{\mathrm{rot}}}}}\Delta t\). The rotational diffusion coefficient was converted into a rotational friction coefficient as \(\gamma _{{{{\mathrm{rot}}}}} = k_BT/D_{{{{\mathrm{rot}}}}}\).

Extended Data Fig. 9 Schematic of the T-bar DNA construct.

The construct consists of a 20 bp dumbbell connected to a 30 bp DNA duplex via a three-way stacked DNA junction. The two DNA strands are coloured in green and blue.

Extended Data Fig. 10 Scaling of the rotational friction coefficient with the size of the rotating object.

Left, centre and right panels show theoretical dependences of the rotational drag coefficients of a sphere, of a rod and of a DNA molecule rotating about its axis, respectively. Theoretical expressions for the spherical and rod-like objects are provided in Methods. For a DNA load, the drag coefficient per basepair was taken to be 1.23 degrees ns–1 pN–1 nm–1, a value extracted from the all-atom MD simulations presented in Fig. 2d. The purple star in the middle panel depicts the friction coefficient extracted from our all-atom MD simulation of a DNA duplex pressed against a graphene surface (see Extended Data Fig. 7 for details) after accounting for the difference between the simulated and experimental viscosity values.

Supplementary information

Supplementary Video 1

Rotation of a DNA duplex driven by a 100 mV nm–1 electric field applied along the duplex axis in the upward direction. The 16 bp duplex is shown using van der Waals (vdW) spheres coloured in light grey (bases) and green (backbone). For clarity, the volume occupied by 1 M KCl electrolyte is not shown. Phosphorus atoms of the duplex are harmonically restrained to the surface of a cylinder such that the DNA is free to rotate about its axis without drifting in the applied field. The video illustrates a 60 ns excerpt of a 200 ns molecular dynamics trajectory.

Supplementary Video 2

Rotation of an l-DNA duplex driven by a 100 mV nm–1 electric field applied along the duplex axis in the upward direction. The 16 bp duplex is shown using vdW spheres coloured in light grey (bases) and green (backbone). For clarity, the volume occupied by 1 M KCl electrolyte is not shown. Phosphorus atoms of the duplex are harmonically restrained to the surface of a cylinder such that the DNA is free to rotate about its axis without drifting in the applied field. The video illustrates a 60 ns excerpt of a 188 ns molecular dynamics trajectory.

Supplementary Video 3

Rotation of an RNA duplex driven by a 100 mV nm–1 electric field applied along the duplex axis in the upward direction. The 16 bp duplex is shown using vdW spheres coloured in light grey (bases) and green (backbone). For clarity, the volume occupied by 1 M KCl electrolyte is not shown. Phosphorus atoms of the duplex are harmonically restrained to the surface of a cylinder such that the RNA is free to rotate about its axis without drifting in the applied field. The video illustrates a 60 ns excerpt of a 199 ns molecular dynamics trajectory.

Supplementary Video 4

Streamlines representing the average flow of fluid past a periodic DNA duplex when a 100 mV nm–1 electric field is applied along the duplex’ axis in the upward direction. Streamlines are coloured from white to red or blue in proportion to the speed with which the fluid moves. The colour signifies whether the streamline winds in a left- (blue) or right-handed (red) direction around the duplex. Streamlines were generated by binning the water oxygen atoms into a roughly 1 Å resolution 3D grid and measuring the displacement of each water molecule after a 240 fs interval, taking the mean in each bin over the entire 100 ns trajectory. The resulting grids of water velocities and local densities were passed into the streamline algorithm of the yt Python package (Astrophys. J., Suppl. Ser. 192:9), and a custom script was used to write commands for visualization using VMD.

Supplementary Video 5

Streamlines representing the average flow of fluid past a periodic RNA duplex when a 100 mV nm–1 electric field is applied along the duplex’ axis in the upward direction. Streamlines are coloured from white to red or blue in proportion to the speed with which the fluid moves. The colour signifies whether the streamline winds in a left- (blue) or right-handed (red) direction around the duplex. Streamlines were generated by binning the water oxygen atoms into a roughly 1 Å resolution 3D grid and measuring the displacement of each water molecule after a 240 fs interval, taking the mean in each bin over the entire 100 ns trajectory. The resulting grid of water velocities and local densities were passed into the streamline algorithm of the yt Python package, and a custom script was used to write commands for visualization using VMD.

Supplementary Video 6

Rotation of a DNA duplex under a solvent flow produced by a 12.7 bar nm–1 hydrostatic pressure gradient. The 21 bp duplex is shown using vdW spheres coloured in light grey (bases) and green (backbone). The two strands of the duplex are connected to themselves across the periodic boundary of the simulation unit cell (not shown), making the duplex effectively infinite in the direction of the pressure gradient. For clarity, the volume occupied by 1 M KCl electrolyte and the ions is not shown. Phosphorus atoms of the duplex are harmonically restrained to the surface of a cylinder such that the DNA is free to rotate about its axis without drifting in the solvent flow. The video illustrates a 60 ns excerpt of a 120 ns molecular dynamics trajectory.

Supplementary Video 7

DNA rotation in a carbon nanopore under a 197 mV transmembrane potential. The DNA phosphorus atoms were restrained to the surface of a cylinder, depicted as a semi-transparent surface. The video illustrates a 58 ns excerpt of one of the trajectories presented in Fig. 3b.

Supplementary Video 8

Spontaneous diffusion of a 38-bp DNA duplex along a graphene layer. A constant 10 pN force distributed among the phosphorus atoms of the DNA pushes the duplex towards the graphene. The centre of mass position of the duplex is traced using a red-to-white-to-blue line. The video illustrate the entire 160 ns duration of the simulation.

Supplementary Video 9

Rotation of a DNA T-bar construct in a carbon nanopore driven by a 394 mV transmembrane potential. The top and side views of the system are shown simultaneous in the two panels. In contrast to previous simulations, no external restrains were applied to the DNA construct. The animation depicts the entirety of one of the trajectories presented in Fig. 3d.

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Maffeo, C., Quednau, L., Wilson, J. et al. DNA double helix, a tiny electromotor. Nat. Nanotechnol. 18, 238–242 (2023). https://doi.org/10.1038/s41565-022-01285-z

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