Nano-mechanical measurements of protein-DNA interactions with a silicon nitride pulley

Proteins adhere to DNA at locations and with strengths that depend on the protein conformation, the underlying DNA sequence and the ionic content of the solution. A facile technique to probe the positions and strengths of protein-DNA binding would aid in understanding these important interactions. Here, we describe a ‘DNA pulley’ for position-resolved nano-mechanical measurements of protein-DNA interactions. A molecule of λ DNA is tethered by one end to a glass surface, and by the other end to a magnetic bead. The DNA is stretched horizontally by a magnet, and a nanoscale knife made of silicon nitride is manipulated to contact, bend and scan along the DNA. The mechanical profile of the DNA at the contact with the knife is probed via nanometer-precision optical tracking of the magnetic bead. This system enables detection of protein bumps on the DNA and localization of their binding sites. We study theoretically the technical requirements to detect mechanical heterogeneities in the DNA itself.


Fabrication of the silicon nitride knife
Nanofabrication of the silicon nitride blade 55 nm of low-stress silicon nitride was deposited on a 400 μm-thick (100) silicon wafer using low-pressure chemical vapor deposition ( Figure S1). The thickness of the nitride film was measured by ellipsometry. The nitride-coated wafer was hand-diced into 15 mm × 4 mm slivers, briefly rinsed with acetone, cleaned by air plasma for 10 min, and etched in 30% KOH at 75 °C for 20-30 min. A fresh blade was prepared before each experiment.
KOH etching along the straight (111) crystal plane is anisotropic and slow. However, we noticed that when the cleaved wafer had a somewhat curved edge, the etching proceeded much faster (~1 μm/min), possibly by bypassing (111) planes. The etch process left a 15-20 μm silicon nitride overhang. This procedure is robust down to membranes of thickness 30 nm. Below 30 nm, the membrane had a tendency to break upon drying due to surface tension forces. Figure S1. Fabrication of silicon nitride knife. Low-stress silicon nitride film was prepared on a silicon wafer by low-pressure chemical vapor deposition (LPCVD). Silicon under the nitride film was etched by 30% KOH, exposing the nitride blade. The curvature on the edges of the silicon sliver facilitated etching on the sides.

Attachment of magnet to the knife
A 1/16" cubic NdFeB magnet (K&J Magnetics, B111) was glued with epoxy on the back of the knife. The north pole of the magnet was oriented facing the front of the blade. The location of magnet determined the angle and strength of the magnetic force on the pulley, typically pulling the bead with ~1 pN of force at 45° relative to the flat surface of the blade. S4

Preparation of DNA construct
λ-DNA conjugation to bead and surface λ-DNA (48.5 kb, 16 μm, New England Biolabs) was prepared following a published protocol (1) ( Figure S2A) with slight modifications. Circular λ-DNA was dissolved at a concentration of 0.5 mg/mL (15.6 nM) in Tris-HCl buffer with 0.5 M NaCl. The molecule was linearized by heating to 90 °C for 10 min, followed by fast cooling in ice for 5 min. The linearized λ-DNA was then annealed with a 12-nt ssDNA oligo 5' labeled with digoxigenin (dig-12; Integrated DNA Technologies), and complementary to one terminal 12-nt ssDNA overhang (cos site). The dig-12 oligo was added at a concentration of 6 nM, selected to be the limiting reagent. The reaction was run for 1 h at room temperature. A second oligo, 5'-labeled with biotin, and complimentary to the other cos site, was then added at a concentration of 200 nM and incubated for 1 h at 4 °C. The hierarchy in relative concentrations enabled purification for doubly-labeled λ-DNA by antidigoxigenin-coated capillaries.

Surface attachment of λ-DNA and labeling by magnetic beads
The flat outer surface of square glass capillaries (1 mm I.D., Friedrich & Dimmock, BMC-1-15-50) was used as a substrate for the DNA pulley. These capillaries provided a convenient means to orient the pulley constructs in the focal plane of the microscope. The attachment of λ-DNA ( Figure S2B) was adapted from published protocols (2). The sequence of reactions is detailed in Table S1. The aldehyde modification and all subsequent reactions were carried out in PCR tubes (1 capillary per tube) at room temperature. Briefly, the glass surface was activated with glutaraldehyde, amino-modified with APTES, and coated with anti-digoxigenin. The antidigoxigenin-coated capillary was mixed with labeled λ-DNA. Streptavidin-coated magnetic beads (Dynabeads® MyOne™ Streptavidin C1, Life Technologies, 1 μm diameter, washed following manufacturer's protocol) were then coupled to the DNA on the capillary ( Figure S2C). Finally, ligase was added to repair the nicks in the construct (except when nicks were intentional-S5 ly introduced). Capillaries with attached beads were then transferred to the measurement chamber.

Measurement setup Sample chamber and stages
A capillary with DNA pulley was mounted in a custom Teflon/aluminum chamber with a glass bottom for imaging ( Figure 1F in the main text). The chamber was loaded with 500 μL of sample solution and mounted on a nanopositioning piezo stage (Mad City Labs, Nano-LP100). The piezo stage was mounted on a manual micropositioning stage (Mad City Labs, MicroStage) for coarse positioning. The silicon nitride knife was clamped on a separate xyz-micromanipulator (Newport) and was aligned relative to the capillary. The knife-edge was aligned orthogonal to the x-y plane to avoid out-of-plane movements in the bead during the scanning.
The entire setup including the microscope was enclosed in a box to block air currents and supported on a vibration-isolation optical table. Shielding of air currents was essential to obtaining low drift: without the shield, drift was ~10 nm/min, and with the shield, drift was ~1 nm/min.

Optical setup
Measurements were performed on an inverted microscope (Olympus IX71). The sample was illuminated from above with a white LED. The image of the magnetic bead, silicon nitride knife, and capillary was collected with a 40× air objective (Olympus, N.A. 0.60), passed through a 3× beam expander, and recorded with an EMCCD camera (Andor DU-897-UV, 16-μm pixels), operated without electron-multiplying gain. Frame rates were selected between 2 and 200 Hz depending on the measurement.

Composition of sample buffer
For all DNA pulley experiments, we used the following Tris-HCl buffer. 1 mM of CaCl 2 was added for experiments with EcoRI/EcoRV.

Localization of fixed beads Bead-to-bead distance measurements
To estimate the precision of bead localization we imaged two beads fixed on a glass coverslip. The beads were tightly fixed on the surface, so apparent fluctuations in bead-to-bead distance arose purely from measurement error. The position of the coverslip was advanced in 5 nm steps and imaged with an exposure time of 20 ms. Movies were averaged over 1 s and the bead coordinates were extracted by a radial symmetry-based algorithm on 15×15 pixels region of interest. (3) Regardless of the underlying movement of the piezo stage, the measured distance between the two beads was nearly constant, showing tight correlation in the movements ( Figure S3). The fluctuation in the inter-bead distance, , measured at 1 Hz was 1.9 Å. The measurement of inter-bead separation involves two measurements of position, each associated with the same measurement error, so the precision of localization for a single bead is 1.9/√2 = 1.3 Å in a 1 Hz bandwidth.

Calibration of piezoelectric stage
The precision of the piezoelectric stage (Mad City Labs, Nano-LP100) was measured by following 5 nm steps over a total displacement of 1 μm. As shown in Figure S4, the motion of piezo stage introduced 2-nm r.m.s. mechanical noise in an 1 Hz bandwidth.

Long-term drift
The level of mechanical drift was checked by tracking a bead over many hours. As shown in Figure S5, the length-scale of mechanical drift was ~1 nm in 1 min, and ~10 nm in 1 h. Characterization of noise by Allan variance (4) showed a gradual increase of deviation over long timescales due to the drift ( Figure S5D).

Calibration of magnetic force on the pulley Fluctuation measurement
A bead on a spring undergoes thermal fluctuations of mean square amplitude along each axis: where k is the spring constant, is Boltzmann's constant and T is the absolute temperature. These fluctuations decay with a correlation time: where γ is the drag constant, η is the dynamic viscosity of the medium, a is the radius of the bead. The effective spring constants along the r-and w-axes are in turn related to the magnetic force. Along the r-axis, the force and extension are related by the modified Marko-Siggia formula for a WLC (5) : where F is the force; x is the extension; = 45 nm is the persistence length; = 16.2 μm is the contour length; and = 1000 pN is the elastic modulus (6). The effective spring constant is: The magnetic force on the bead was measured from thermal fluctuation of the bead, in situ before scanning experiments ( Figure S6). The bead fluctuation with all stages at rest and with the blade withdrawn was recorded at 200 Hz.
To quantify the bias induced by the finite exposure time of the camera, we ran a simple numerical simulation of a Brownian particle in a harmonic potential with a 10 ms relaxation time. We used 0.1 ms time-steps and produced a trajectory of 10 6 steps. We then simulated the effect of the finite exposure time of the camera by averaging the trajectory in 5 ms discrete intervals. The autocorrelation functions of the raw and discretely sampled trajectories are shown in Figure  S6D. Discrete sampling led to an underestimate of the variance in particle position by 17%, but a negligible influence on the autocorrelation function at non-zero lag. For motion of a particle with a correlation time of 70 ms, discrete sampling with 5 ms integration times led to an underestimate of position variance of only 2.5%.
To fit the autocorrelation functions, we discarded the data point at zero lag (on account of the bias from finite camera exposure). We then fit the remaining data to a function of the form A exp(-t/) + B. The purpose of the constant offset, B, was to accommodate slow drift in the measured bead position, which led to a plateau in the autocorrelation function at timescales long com-S10 pared to the relaxation time. Typical time scales of fluctuations were  r ~10 ms along r, and  w ~70 ms along w ( Figure S6B and C).

Localization of protein-DNA complexes Incubation with restriction enzymes
The DNA pulley was first incubated with 50 nM EcoRI-HF or EcoRV-HF (New England Biolabs, R3101 and R3195) in a scanning buffer (Table S2) containing 1 mM CaCl 2 (10 mM Tris-HCl, 100 mM NaCl, 0.1% polyvinylpyrrolidone, 0.1% Tween-20), for 1 h. After incubation, the number of pulley constructs on capillary was not reduced substantially, confirming that the catalytic activity of the restriction enzymes was lost.
The EcoRI-incubated DNA pulley constructs were studied by applying the same scanning condition as in the simple trajectory mapping. The scanning speed was 1 μm/s with a 100 Hz camera frame rate.

Geometry of the DNA pulley
We solved the geometry of the pulley system to parameterize the bead motion. We then mapped the measured bead coordinate, r, onto the location in the DNA sequence of the DNAblade contact.
The analysis of the pulley geometry is greatly simplified if the blade edge is aligned parallel to the z-axis. Before experiments, the microscope focus was moved along the z-axis and the blade edge was aligned to be vertical. However, the angle of the magnetic force vector is not precisely controlled due to the need to manually position the magnet prior to gluing. Furthermore, the similar scale of the magnet size (1/16") and the distance between the magnet and the bead implies that the magnetic field contour at the bead location is not simple to compute. The angle of the magnetic force in the x-y plane is trivially determined by noting the direction of DNA stretching; but the azimuthal angle, , relative to the z-axis must be included as a fitting parameter. When the z-component of the magnetic force vector is not zero, the bead is pulled out of the x-y plane, and therefore the z-coordinates of the three points B (bead), O (pivot or origin), and S (surface attachment) can be different ( Figure S9). The focus of the microscope is adjusted so that only B is located in the image plane. Translation of the capillary (and hence S) along the y-axis does not change the z-coordinate of B, i.e. the bead remains in the focal plane during the scanning process, regardless of a vertical offset in the stretching force.
From Figure S9B, we can relate the observed bead coordinate, r, to the piezo coordinate, p. Let d be the distance between the capillary and the knife, and let S 0 be the position on the capillary closest to the knife edge. The DNA-capillary attachment is inferred to cross when the DNA appears maximally extended along r. This piezo coordinate is defined as p = 0.
From the right triangle , we get .
(5) Therefore, the extension of the DNA between O and B, r, is given by (6) where is the total extension of DNA projected onto the x-y plane. Note that is always shorter than the total contour length L 0 (16.2 μm) because: (a) the DNA is not fully extended by the stretching force, and (b) the z-component of magnetic force might be nonzero, pulling the molecule slightly out of the x-y plane.

Ratiometric measurements of length and molecular coordinate
The relation of the observed contour length projected into the x-y plane, l 0 , and the total extension in 3-D, L 0 , is sin (7) where is the azimuthal angle of the magnetic force vector. In our measurements, the two variables, and sin do not have to be separated. Hence we regard as a single fitting parameter, acknowledging that we do not know and sin independently. The progression of the blade relative to the molecule in the image plane, / , is the same as the one in 3-D space, / . Therefore, knowledge of the ratio / is sufficient to infer the absolute position, i.e., the sequence coordinate of the DNA-blade contact.

Deviations from pure pulley motion due to protein bumps on the DNA
When a DNA-bound protein catches on the blade edge, the measured location of the bead deviates from the predicted location, and therefore the point of contact between the DNA and blade as inferred from bead tracking deviates from the point of contact predicted from piezo motion. From Eq. (6), the predicted location of blade, , is: The blade position inferred from bead tracking is: In the absence of bumps along the DNA, the measured position of the blade will be the same as prediction, . By comparing to , deviation from regular trajectory can be followed as a function of sequence. S15

Measurement of DNA bending around a single-stranded nick
The capillary with appended DNA and beads was incubated with Nb.BbvCI at 37 °C for 1 h for nicking. The capillary was then washed with WB (Table S2) to remove nicking enzymes. The sample was then incubated with EcoRI, as in Section 6.

Simulation of DNA bending using theory of elastica
A sharp kink, i.e. a region of perfect flexibility, constitutes the largest mechanical signal one might hope to detect in DNA, and could arise e.g. from a single-stranded nick, a bubble, or possibly from covalent damage to the DNA. We thus sought to estimate the deviation in bead coordinate that would be induced by a running a point of perfect flexibility over the blade, assuming a perfectly sharp blade.
We compare the bead position under two scenarios: (1) the DNA bends smoothly around the edge of the (assumed perfectly sharp) blade, following the contour set by the applied tension and the continuum elasticity of the DNA; and (2) the DNA adopts a sharp kink at the blade and then extends in a straight line along the magnetic force. This calculation constitutes an upper bound on the signal. The blades used in our experiments were not sharp (55 nm diameter of curvature) compared to the persistence length, so our experiments would yield signals smaller than the estimates below.
For radii of curvature much smaller than the persistence length, the contour of a homogeneous linear elastic rod is described by a set of curves called the elastica. We modeled DNA as a simple elastic rod experiencing an external force on the ends. Due to the two-fold mirror symmetry of the force in the DNA pulley, we only consider the half with a magnetic bead. The bending of DNA pivoted on the nitride blade can be thought of as a rod with one end clamped ( Figure S11). Consider a segment of the tethered DNA with a length L, smaller than the persistence length (50 nm). The distal end of this DNA segment is pulled along the direction of magnetic tension. The angle between the tangent to the rod and the y-axis () is related to the force and the rod length by (7): where is the bending modulus and F | | is the applied force. The direction of magnetic force sets a boundary condition for the slope of curve. We solve for an elastica that asymptotes to the force angle ( /2 ). Substituting into the Eq. (10) gives a length scale, * , over which the DNA transitions from a bent to a linear shape. The complete shape of the elastica regime ( Figure S12, solid curves) is parametrically given by : 2 /F , / 2F cos cos cos / . (11) As depicted in Figure S12A and B, the signal we are looking for is the difference in the bead position, resulting from a change in the local structure. If the DNA behaves as a perfect WLC, it will follow the solid curves. If the curvature introduced in the DNA is relieved by a localized kink, it follows a free-joint curve shown in dashed lines. To estimate the signal, the coordinates of the end of the DNA segment are compared for the two models.
A large force angle or a weak force is expected to give a large difference between the smoothly bent and the kinked state. The amplitude of the lateral displacement, dw is generally larger than the radial displacement, dr ( Figure S12C and D).
One must compare the amplitudes of the displacements to the amplitudes and timescales of the thermal fluctuations in bead position. Thermal fluctuations are larger and slower for a weak force than for a strong force; and are larger and slower for measuring dw than for measuring dr. To detect kinks or other intrinsic mechanical heterogeneities in DNA will require (a) a sharper blade than we used, and (b) better long-term stability of the apparatus to permit averaging the bead coordinate over many relaxation time constants to achieve better tracking accuracy.