Optical Voltage Sensing Using DNA Origami

We explore the potential of DNA nanotechnology for developing novel optical voltage sensing nanodevices that convert a local change of electric potential into optical signals. As a proof-of-concept of the sensing mechanism, we assembled voltage responsive DNA origami structures labeled with a single pair of FRET dyes. The DNA structures were reversibly immobilized on a nanocapillary tip and underwent controlled structural changes upon application of an electric field. The applied field was monitored through a change in FRET efficiency. By exchanging the position of a single dye, we could tune the voltage sensitivity of our DNA origami structure, demonstrating the flexibility and versatility of our approach. The experimental studies were complemented by coarse-grained simulations that characterized voltage-dependent elastic deformation of the DNA nanostructures and the associated change in the distance between the FRET pair. Our work opens a novel pathway for determining the mechanical properties of DNA origami structures and highlights potential applications of dynamic DNA nanostructures as voltage sensors.


Description of the model construction protocol and the model parameters.
Simulations were performed under various applied bias potentials. For each voltage, a spatially varying electrostatic potential was obtained from a continuum COMSOL multiphysics model that solved coupled equations for incompressible Stokes flow, electrostatics, and Fick's diffusion of ions. The COMSOL model is described in detail below.
The resulting electrostatic potential was exported in a three-dimensional grid used to apply forces to the DNA using an effective charge of 0.25 e per nucleotide, where e is the fundamental charge of an electron. This scaling factor is consistent with experimental measurements of the effective force due to an applied bias on a DNA molecule in a nanopore of similar geometry to the nanocapillary. 1 Simulations were performed using a cut-off of 40 Å and integration timesteps of 200 and 50 fs for low-and high-resolution models, respectively. The diffusion coefficient of each bead was set to 150 Å 2 /ns and the temperature was set to 291 K.

Continuum model of a nanocapillary.
A continuum model of the nanocapillary was constructed using the COMSOL multiphysics software package. Specifically, the modules "Creeping flow", "Transport of diluted species", and "Electrostatics" were used to model the electric potential in and around the pore. The outer diameter of the capillary was set to 2.5 times the inner diameter. At the aperture, the inner diameter was 10-nm. Between the aperture and a 100 nm distance along the capillary axis, the inner diameter increased with a 5.2° slope from the axis. Between 100 nm and 5000 nm, the slope decreased to 2.7° from the axis. Boundary conditions were set that prevented flow outside the nanocapillary between 500 and 1000 nm along the capillary axis as measured from the aperture. The overall system dimensions were 15000 nm along the capillary axis, and 2000 nm across. The bulk concentration of KCl solution was set to 1 M. The steady state solution to the coupled system S6 of equations was solved numerically at 1 atm and 298.15 K using the azimuthally-symmetric 2D projection of cylindrical coordinates.
The equations for incompressible Stokes flow were solved with solvent density of 1 g/cm 3 , and viscosity of 8.9 × 10 -4 Pa s, with no slip boundary conditions on all walls except the surfaces representing the entrance and exit of the chambers above and below the capillary, where the pressure was set to zero. A volumetric force was applied to the fluid with -F (c +c -) V, where F is the Faraday constant, c ± is the local concentration of ions, and V is the local electrostatic potential. The electrostatic potential was calculated according to the Poisson equation given a distribution of ions with a relative permittivity of 80, no charge boundary condition on the walls of the cis and trans chambers, a surface charge of -0.01 C/m 2 on the glass capillary, and variable voltage difference across the chambers. Finally, the ion concentration was determined by a system of equations that allowed convection coupling to the solvent flow, diffusion using D = 1.9579 × 10 -5 and 2.032 × 10 -5 cm 2 /s, and the electrostatic force on the charged particles, using a mobility µ = D/k B T.
The resulting electric potential was rotated azimuthally and exported in a regular 240 × 240 × 950 voxel grid at a resolution of 0.5 nm in the directions normal to the capillary axis, and 0.2 nm along the capillary axis. The exported region contained 40 nm beyond the aperture of the capillary and 150 nm of the capillary. The potential within the nanocapillary walls was set to 20 kcal/mol providing a steric barrier. The potential map was then smoothed by convolution with a 1-nm wide three-dimensional Gaussian kernel.

Construction of the coarse-grained model.
A low-resolution model of the object was constructed using a python script that directly queried caDNAno data structures. A coarsegrained bead was first placed at every crossover and at the ends of each ssDNA or dsDNA segment. Within each caDNAno helix, additional beads were placed at evenly spaced positions between adjacent pairs of the crossover or terminal beads so that fewer than seven S7 base pairs or four ssDNA nucleotides would be located between any pair of beads. Harmonic intrahelical bond potentials were placed between the dsDNA beads with a rest length of 0.34 × N b nm/bp or 0.5 N b nm/nt and with k spring = 10/N b or 1/N b kcal mol -1 nm -2 for dsDNA and ssDNA, respectively, where N b is the number of base pairs or nucleotides between the beads.
A harmonic potential was placed on the angle between every three consecutive beads within a helix with rest angle of 180° and ݇ ୱ୮୰୧୬ = ଵ.ହ ଵି షಿ /ಿ k B T radian -2 , where N a is the number of base pairs or nucleotides between the first and third bead and N p is the persistence length expressed in base pairs or nucleotides, 147 and 3 for dsDNA and ssDNA, respectively. Crossover bonds were defined by harmonic potentials having the rest length of 1.85 nm and k spring = 4 kcal mol -1 nm -2 , matching observations from simulations. 2 A harmonic potential was also applied to the angle between the connected crossover beads and each adjacent crossover bead on the same double-helical segment. The potential was assigned a rest angle of 90° and ݇ ୱ୮୰୧୬ = .ହ ଵି షಿ ౙ /ಿ k B T radian -2 , where N c is the number of basepairs between the crossovers. Another harmonic potential was applied to the dihedral angle between each set of four beads forming adjacent crossovers within a double helical segment with rest angle of 34.2°/bp offset by ±120° if the crossovers occur between strands with opposing sense. The spring constant for the dihedral angle potential was determined using a least squares fit so where N tw = 265 is the twist persistence length expressed in terms of base pairs.
We extracted the potential of mean force per turn between parallel, effectively infinite DNA helices from all-atom umbrella sampling simulations as previously described, except the electrolyte contained 100 mM MgCl 2.
3 This potential was used as a target for refinement of the non-bonded interactions between the coarse-grained beads. Two parallel, idealized S8 helices were constructed, allowing the per-turn coarse-grained interaction potential to be calculated by integrating a trial bead-bead interaction potential over the lengths of DNA.
With the value of the bead-bead potential at each 0.1 nm from 0 to 5 nm taken as a variable, the coarse-grained helix interaction was optimized against the all-atom potential of mean force using a least-squares protocol. This process was repeated for all pairs of coarse-grained bead sizes, where the size of each bead was taken to be half of its intrahelical bond lengths when express in terms of nucleotides. Pairs of beads connected by fewer than seven intrahelical bonds were excluded from nonbonded interaction calculations. Also excluded were nonbonded interactions between each crossover bead and the partner crossover bead in the adjacent helix and the two nearest neighbour beads of the partner bead.
The high-resolution model was constructed in the same manner as the low-resolution model described above, except that beads were placed at a density of 1 bead/bp. In addition, a dummy azimuthal orientation bead was added to each dsDNA bead, connected through a stiff harmonic bond with rest length of 1 Å and k spring = 30 kcal mol -1 Å -2 . Each adjacent pair of dsDNA beads had harmonic potentials placed on the angle between each orientation bead and the two dsDNA beads with rest angle of 90° and ݇ ୱ୮୰୧୬ = .ହ ଵି షಿ ౘ /ಿ k B T radian -2 . Finally, a dihedral angle potential was placed between the orientation bead, its parent dsDNA bead, the adjacent dsDNA bead and its orientation bead with a rest angle of 34.2°/bp and k spring = 110 k B T/radian 2 . Hence the orientation bead provided a measure of the local twist of the DNA and interacted with the rest of the system only through the above bonded terms.
The initial coordinates of the high-resolution model were obtained by mapping onto the coordinates of the low-resolution model as follows. Each high-resolution non-orientation bead was placed by interpolating the position of the two nearest intrahelical low-resolution beads at the end of the simulation. The orientation beads were placed with 1-Å offset, normal to the axis of interpolation and with a 34.2°/bp twist. Specifically, the azimuthal angle for the S9 orientation bead was obtained from a quaternion-based interpolation of the rotation matrices minimizing the mean square deviation between initial and final coordinates of the neighbourhoods around the adjacent low-resolution beads in the same helix. The neighbourhood for each bead of the low-resolution model was taken to be all beads within 5 nm and beads in the same helix within 10 nm of the bead. The low-resolution model of the DNA origami plate was placed about 10 nm above the nanocapillary with the leash initially compacted and facing the capillary aperture. For each applied bias, a 40 µs simulation was performed, during which capture of the plate occurred.
Capture occurred quickly at all applied biases, except in the 100 mV case. The capture simulation was therefore extended for another 40 µs for 100 mV.
The conformation of the system every 2 µs during the last 10 µs of the capture simulation was used to construct a series of high-resolution models for each applied bias. For each configuration, a 2 µs simulation yielded the distance between base pairs that had fluorescent dyes attached, providing an estimate for the distance between the FRET dye pairs. were partially taken from the Component Library by Alexander Franzen.

Bulk fluorescence emission spectra of DNA origami structures.
The bulk fluorescence properties of the DNA origami designs A 1 and A 2 , each labelled with a FRET pair (ATTO532 and ATTO647N) were determined by steady-state fluorescence emission measurements in solution ( Figure S4). We excited the donor dye ATTO532 at a wavelength of 500 nm and the acceptor dye ATTO647 at a wavelength of 600 nm. Upon donor excitation, the emission in the wavelength range 530-600 nm (I D (D * )) can be attributed to the donor while emission in the spectral window 635-700nm (I A (D * )) corresponds to acceptor emission due to FRET. For acceptor excitation, we measure direct acceptor emission in the spectral window 635-700 nm (I A (A * )).
We can use these fluorescence intensities to obtain the proximity ratio E ens *  Stable trappings of the origami structures occurred at voltages between 100 mV and 400 mV. The capillaries that showed stable trappings over this entire voltage range were found to have a bare capillary resistance lying within 31-40 MΩ.
A summary of the voltage-dependent properties of DNA origami plates with pore and a 260 nm long double-stranded leash is shown in Figure S5. Representative histograms of the relative conductance change ∆G at voltages ranging from 100 mV to 300 mV are shown in Figure S5A      We used N tot = 185 traces from 8 capillaries in design A 1 and N tot = 241 traces from 6 capillaries in design A 2 . The error bars correspond to the standard error of the mean. Taking an average over all the voltages, the proximity ratio E sm * is considerably higher in design A 1 (E sm * = 0.53±0.08 (SD)) than in design A 2 (E sm * = 0.22±0.01 (SD)). This is consistent with the theoretical inter-dye distances, which are shorter in design A 1 (R 1 = ~3 nm) than in design A 2 (R 2 = ~5.

Estimated force required to stretch the dsDNA leash.
The elastic behaviour of dsDNA has been extensively characterised, 6 giving rise to three broad force-extension regimes: Entropic elasticity at low forces (~0.1-10 pN), intrinsic elasticity at intermediate forces (~5-50 pN) and overstretching at high forces (>65 pN). 7,8 As the persistence length of dsDNA is l p ≈ 50 nm, 8 a leash section of length 6 nm will be straight at room temperature.
Within our voltage range of 100-400 mV, we estimate an upper force limit of roughly 16 pN per DNA molecule (assuming the electric force normalised by the voltage applied on a DNA molecule in a nanopore is κ ≈ 0.04 pN/mV). 5,6,9 We will thus consider the intrinsic elasticity regime to estimate what force F is needed to stretch a 17 bp long dsDNA polymer such that its end-to-end distance x exceeds its theoretical B-form contour length L. Based on the approximation 7

S F Fl
and using a stretch modulus S = 1000 pN, 7 we obtain F > 40 pN for x/L >1 at room temperature.
Hence, the range of electric forces applied in our experiment are all far below the minimum force required to induce a linear elastic response of the stiff leash section connecting the FRET pair in Below is the staple list of the DNA sequences for all unfunctionalised staples. The staples contributing to the leash are marked in red and the staples with biotins attached to the 5' end for surface measurements are highlighted in yellow.  11 we carefully analysed the intrinsic variability in absolute fluorescence intensities among different capture events and capillaries including the plastic deformation of DNA origami structures with a leash.

Start
We performed the following experiment to prove single capture of DNA origami structures: DNA origami plates were assembled that are labelled with a single dye, either with a donor (ATTO532) or acceptor (ATTO647N), using the predefined dye positions in design A 1 . After folding and filtering, the two samples were mixed in an equimolar ratio and the measurements were The occurrence of aggregates forming during the folding and purification process (i.e. before mixing of the two species) is low at 7%, as estimated from the relative band intensities using agarose gel electrophoresis ( Figure S13).  Figure S13. Agarose gel electrophoresis. Lane 1: 1 kb ladder. Lane 2: DNA origami plate with monomer (93%) and dimer band (7%) as measured by intensity.