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# Demonstrating sub-electron noise performance in Single electron Sensitive
Readout (SiSeRO) devices

Tanmoy Chattopadhyay  Kavli Institute of Astrophysics and Cosmology, Stanford
University, 452 Lomita Mall, Stanford, CA 94305, USA  Sven Herrmann  Kavli
Institute of Astrophysics and Cosmology, Stanford University, 452 Lomita Mall,
Stanford, CA 94305, USA  Peter Orel  Kavli Institute of Astrophysics and
Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA
Kevan Donlon  MIT Lincoln Laboratory, Lexington, MA, USA  Steven W. Allen
Kavli Institute of Astrophysics and Cosmology, Stanford University, 452 Lomita
Mall, Stanford, CA 94305, USA  SLAC National Accelerator Laboratory, 2575 Sand
Hill Road, Menlo Park, CA 94025, USA  Department of Physics, Stanford
University, 382 Via Pueblo Mall, Stanford CA 94305, USA  Marshall W. Bautz
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA, USA  Brianna Cantrall  Kavli Institute of
Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA
94305, USA  Michael Cooper  MIT Lincoln Laboratory, Lexington, MA, USA
Beverly LaMarr  Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA, USA  Chris Leitz  MIT
Lincoln Laboratory, Lexington, MA, USA  Eric Miller  Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA, USA  R. Glenn Morris  Kavli Institute of Astrophysics and
Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA
Abigail Y. Pan  Kavli Institute of Astrophysics and Cosmology, Stanford
University, 452 Lomita Mall, Stanford, CA 94305, USA  Department of Physics,
Stanford University, 382 Via Pueblo Mall, Stanford CA 94305, USA  Gregory
Prigozhin  Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA, USA  Ilya Prigozhin  MIT Lincoln
Laboratory, Lexington, MA, USA  Haley R. Stueber  Kavli Institute of
Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA
94305, USA  Department of Physics, Stanford University, 382 Via Pueblo Mall,
Stanford CA 94305, USA  Daniel R. Wilkins  Kavli Institute of Astrophysics and
Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA

###### Abstract

Single electron Sensitive Read Out (SiSeRO) is a novel on-chip charge
detection technology that can, in principle, provide significantly greater
responsivity and improved noise performance than traditional charge coupled
device (CCD) readout circuitry. The SiSeRO, developed by MIT Lincoln
Laboratory, uses a p-MOSFET transistor with a depleted back-gate region under
the transistor channel; as charge is transferred into the back gate region,
the transistor current is modulated. With our first generation SiSeRO devices,
we previously achieved a responsivity of around 800 pA per electron, an
equivalent noise charge (ENC) of 4.5 electrons root mean square (RMS), and a
full width at half maximum (FWHM) spectral resolution of 130 eV at 5.9 keV, at
a readout speed of 625 Kpixel/s and for a detector temperature of 250 K.
Importantly, since the charge signal remains unaffected by the SiSeRO readout
process, we have also been able to implement Repetitive Non-Destructive
Readout (RNDR), achieving an improved ENC performance. In this paper, we
demonstrate sub-electron noise sensitivity with these devices, utilizing an
enhanced test setup optimized for RNDR measurements, with excellent
temperature control, improved readout circuitry, and advanced digital
filtering techniques. We are currently fabricating new SiSeRO detectors with
more sensitive and RNDR-optimized amplifier designs, which will help mature
the SiSeRO technology in the future and eventually lead to the pathway to
develop active pixel sensor (APS) arrays using sensitive SiSeRO amplifiers on
each pixel. Active pixel devices with sub-electron sensitivity and fast
readout present an exciting option for next generation, large area
astronomical X-ray telescopes requiring fast, low-noise megapixel imagers.

###### keywords:

Single electron Sensitive Read Out (SiSeRO), X-ray detectors, X-ray charge-
coupled devices, repetitive non-destructive readout (RNDR), readout
electronics, instrumentation

##  1 INTRODUCTION

X-ray Charge Coupled Devices (CCDs) [1, 2, 3] have been the workhorses of
X-ray astronomical instrumentation for more than three decades. With recent
technological progress and the development of sensitive readout electronics,
current generation X-ray CCDs provide significantly improved readout speeds
($\sim$2 MHz) and noise performance [4, 5, 6, 7, 8, 9, 10, 11]. However, to
enable next generation flagship missions in X-ray astronomy (e.g.
Lynxiiihttps://www.lynxobservatory.com/), future X-ray detectors will require
much faster readout rates and very low read noise, ideally in the sub-electron
regime. With such low noise, the full discovery potential at soft X-ray
energies (E $<0.5$ keV) can be achieved, together with unprecedented gain
calibration [12]. Precise gain calibration at low X-ray energies is also
helpful in characterizing the low energy response of instruments accurately.

The Single electron Sensitive Read Out (SiSeRO) technology developed by MIT
Lincoln Laboratory (MIT-LL) is a novel charge detection approach for X-ray
CCDs [13]. SiSeROs replace the doped implant at the sense node of the CCD
output stage with an internal gate under a p-type metal-oxide-semiconductor
field-effect transistor (p-MOSFET). The internal gate minimizes the parasitic
capacitance on the sense node, providing higher gain and improved low noise
performance. Perhaps the most interesting feature of SiSeRO devices is that
the signal charge can be transferred in and out of the internal gate without
destroying the charge $-$ a technique popularly known as repetitive non-
destructive readout (RNDR). Utilizing RNDR, read noise can be reduced
significantly. The RNDR technique has previously been demonstrated and shown
to provide sub-electron noise yield in DEPFET devices [14, 15], Skipper CCDs
[16, 12, 17] and in a prototype Complementary Metal-Oxide-Semiconductor (CMOS)
imaging sensor (CIS) [18, 19].

In Chattopadhyay et al. 2024[20], we presented the first demonstration of the
RNDR technique in a SiSeRO prototype device. That study implemented nine RNDR
cycles, where each cycle was $\sim$1.0 $\mu$s CDS (correlated double sampling)
long, achieving an equivalent noise charge (ENC) of 2.06
$\mathrm{e}^{-}_{\mathrm{RMS}}$ at the end of the ninth cycle (a factor of 3
improvement in noise). In this paper, we report RNDR measurements for a larger
number of cycles. The new tests were performed using an improved experimental
setup, which provides enhanced cooling of the detectors. With around 1 $\mu$s
CDS per cycle, and 57 RNDR cycles, we achieved a readout noise of 0.51
$\mathrm{e}^{-}_{\mathrm{RMS}}$. While the current SiSeRO prototypes are in
the CCD format, the technology also has the potential to be incorporated into
active pixel sensor (APS) arrays, in which each pixel includes a SiSeRO. This
should enable extremely low noise performance at high readout speeds. A
prototype SiSeRO APS device is currently being fabricated at MIT-LL and will
be tested early next year. In parallel, in order to test new sensitive SiSeRO
amplifier designs, we are fabricating new SiSeRO based CCD devices with 16
different SiSeRO variants at the output. Along with that, an RNDR optimized
SiSeRO CCD variant is also under fabrication offering sixteen SiSeRO
amplifiers in series at the output stage. Such devices should immediately
provide a factor of four improvement in noise performance at the same readout
rate.

In the next sections, we give a brief description of the SiSeRO devices and
the RNDR technique, the experimental setup, and the new RNDR results. We
summarize the work in section 5 and outline our future plans.

##  2 An overview of the SiSeRO devices and the RNDR technique

Figure 1: Left: Schematic of a SiSeRO output stage, utilizing a p-MOSFET
transistor (S: Source, D: Drain, G: Gate) with an internal gate beneath the
p-MOSFET. The internal gate is emptied using the reset transistor (RG) and
reset drain (RD). Charge transferred across the output gate (OG) from the last
serial gate (summing well or SW) to the internal gate modulates the drain
current of the p-MOSFET. Right: A simple demonstration of RNDR technique. The
signal charge is moved between the internal gate and SW for repeated
measurements.

The current SiSeRO detectors, fabricated at MIT-LL, consist of a CCD pixel
array with a SiSeRO amplifier (p-MOSFET) at the output stage. Figure 1 (left)
shows a simplified 3D schematic of the SiSeRO output stage. When a charge
packet is transferred from summing well (SW, the last serial register gate) to
the internal gate via OG (output gate), it modulates the transistor drain
current, which is then readout by the readout electronics [13, 21]. There is a
trough on the internal gate that helps confine the charge packet under the
MOSFET to maximize the change in the transitor current. An advantage of
SiSeROs over conventional voltage follower-based CCD output stages is that the
internal gate minimizes parasitic capacitance on the sense node, resulting in
a high conversion gain and minimized noise.

Our first generation SiSeRO test devices have an active area of $\sim$4 mm
$\times$ 4 mm with a 512 $\times$ 512 array of 8 $\mu$m pixels. They come in
two primary variants $-$ surface channel and buried channel p-MOSFET
transistors, along with sub-variants that adjust the location and size of the
trough. Unsurprisingly, the surface channel MOSFET variants (CCID-85 family)
were found to have relatively large readout noise [13]. For variants with a
buried-channel SiSeRO (CCID-93 family), we initially achieved an ENC of 6
$\mathrm{e}^{-}_{\mathrm{RMS}}$ at 625 KHz readout speed (1 $\mu$s CDS). This
was further improved to 4.5 $\mathrm{e}^{-}_{\mathrm{RMS}}$ by applying
digital filtering techniques to minimize the 1/f noise [22]. We measured a
gain or responsivity of 800 pico-ampere (pA) per electron for this device. The
spectral resolution at the energy of the 5.9 keV Mn Kα line was measured to be
$\sim$ 132 eV (FWHM).

As noted above, one of the most interesting features of SiSeRO devices is that
the charge packet in the internal gate remains unaffected during the readout
process, which offers the possibility of repetitive measurements of the same
charge signal by moving the charge in and out of the internal gate multiple
times. By averaging over a large number of multiple independent measurements
of the same charge, the final noise can be reduced significantly, potentially
into the sub-electron regime. In Fig. 1 (right), we show a simplified
schematic of how RNDR is implemented in our setup. In the absence of dedicated
transfer gates in the current prototype devices, we employed clocking to the
output gate (OG) and summing well (SW) to pull the charge back from the
internal gate. In Chattopadhyay et al. 2024[20], we reported RNDR measurements
for nine repetitive readout cycles with 1 $\mu$s CDS per cycle integration.
With nine RNDR cycles on a CCID-93 device, we obtained an ENC performance of
2.06 $\mathrm{e^{-}_{RMS}}$ at the end of the ninth cycle [20]. In this study,
we perform a larger number of cycles (57) on a different SiSeRO detector from
the same CCID-93 family.

##  3 Experimental setup

Our most recent SiSeRO measurements were carried out in the newly-commissioned
2.5 meter XOC X-ray Beamline at Stanford [23] (hereafter beamline) shown in
Fig. 2.

Figure 2: Left: The 2.5 meter XOC X-ray Beamline[23] used for RNDR
experimentation. Right: A CCID-93 SiSeRO device mounted inside the detector
chamber on the chamber door.

The beamline can be used for the testing and characterization of a broad range
of X-ray detectors of different types and sizes. The detector under test is
mounted directly on the inside of the detector chamber door (Fig. 2 right).
The beamline employs a cryo-cooler to cool down the detector to -100∘C. A
Proportional-Integral-Derivative (PID) algorithm controls the detector
temperature with better than 0.2∘C accuracy. An 55Fe radioactive source is
mounted within the detector chamber, and an X-ray fluorescence (XRF) source
module is mounted at the other end of the beamline. The XRF source can provide
mono-energetic lines spanning the 0.3$-$10 keV range at suitable flux levels.
Details of the beamline mechanical design, detector cooling, and source module
can be found in Stueber et al. 2024[23].

As mentioned earlier, for this experiment, we used a CCID-93 detector with a
buried-channel SiSeRO at the output stage. The readout electronics [13, 20]
consist of a custom preamplifier board (the detector and the circuit board are
shown in Fig. 2 right) and a commercial Archon controller [24] (the black box
in the left picture). The preamplifier uses a drain current readout, where an
I2V amplifier first converts and amplifies the SiSeRO output and a
differential driver (at the second stage) converts the output to a fully
differential signal. The Archon, procured from Semiconductor Technology
Associates, Inc (STAiiiiiihttp://www.sta-inc.net/archon/), provides the
required bias and clock signals, and digitization of the output signal. A
custom flex cable [25] is used to connect the detector board to the controller
which is kept outside the detector chamber. We have also developed an
8-channel Application-Specific Integrated Circuit (ASIC) based readout
electronics (known as Multi-Channel Readout Chip or MCRC ASIC[9, 11]) for the
SiSeROs. The results presented in this paper were obtained from the discrete
electronics readout module.

##  4 Results

Figure 3: SiSeRO digital waveform for one pixel over 57 repetitive readout
cycles showing the baseline and signal measurements for each cycle. The zoom-
in view shows the OG clock, baseline and signal for a single RNDR cycle.

Figure 3 shows waveform of the SiSeRO for one pixel over 57 RNDR cycles. As
noted above, for the RNDR measurements, we clock OG and SW gates (OGhigh 5.5
V, OGlow 1.0 V; SWhigh 3.0 V, SWlow -1.5 V). The individual baselines are
introduced when OG settles down to OGLow (see the insert plot in Fig. 3). Note
that the OG clock pulses in the waveform result from some capacitive coupling
between OG and the MOSFET. The corresponding individual signal regions are
introduced when the charge packet is moved back to the internal gate by
changing the SW potential to SWLow (as shown in the insert plot). After the
final cycle, the charge packet is drained to RD using the reset gate (RG)
clock.

For our tests, we used a titanium (Ti) target in the XRF source, providing Kα
and Kβ lines at 4.5 and 4.9 keV respectively.

Figure 4: Spectrum obtained at -100∘C at the beginning (1st RNDR cycle) (left)
and at the end of the 57th RNDR cycle (right) showing the Ti Kα (4.5 keV) and
Kβ (4.9 keV) lines. The spectra were generated using the single-pixel (grade
0) events. The FWHM energy resolutions at 4.5 keV are 134 eV and 129 eV and
the corresponding read noises 3.8 and 0.51 $\mathrm{e}^{-}_{\mathrm{RMS}}$,
respectively.

For each RNDR cycle, we generate single-pixel (grade 0) spectra of the Kα and
Kβ lines and fit the 4.5 keV line with a Gaussian model to calculate the
centroid and FWHM of the line. We also calculate the read noise for each cycle
by measuring the width of distribution of charge (in ADU or analog to digital
unit) in the overscan region [20]. Because of minimal thermal leakage
contamination, the noise measured from the overscan region supposedly
represents the noise due to the output stage and the following readout
circuitry. The measured gains are then used to normalize and measure the read
noise in number of electrons.

Figure 5: Left: Measured centroid in analog to digital unit (ADU) for 4.5 keV
as a function of RNDR cycles (representing gain). Both the individual (blue
circles) and averaged gains (red circles) remain constant, implying no charge
loss during the repetitive transfer of charge. Right: Measured FWHM at 4.5 keV
as a function of RNDR cycles. Both the individual and the averaged
measurements lie well within the $\sim$1$\sigma$ error bar of each other.

As an example, the spectra along with the Gaussian fits, obtained for the 1st
and 57th RNDR cycles are shown in the left and right panel of Fig. 4
respectively. The 4.5 keV line centroids (representation of gain of the
system), measured in this way for all the individual RNDR cycles, are shown by
the red circles in the left plot of Fig. 5. The blue circles show the averaged
measurements of the same. The centroid values are found to be well within the
error bar of each other which implies that there is no charge loss during the
fifty seven repetitive transfers of charge. Using the fitted centroid values,
we also calculate the responsivity of the device to be around 830 pA /
electron.

The measured FWHM values of the 4.5 keV line are shown as a function of the
RNDR cycles in the right plot of Fig. 5. The individual measurements (blue
circles) all lie within the $\sim$1$\sigma$ error bar of each other at aroud
134 eV. The averaged measurements, shown by the blue cirles in the same plot,
show a slight improvement in the spectral resolution at around 129 eV.

The read noise measurements are demonstrated in Fig. 6, where we show the
individual and averaged measurements in red and blue circles respectively. As
seen in the figure, the individual cycles yield similar noise measurements
around 3.8 $\mathrm{e}^{-}_{\mathrm{RMS}}$. This is cross-verified by fitting
the values with a power law, which results in a flat line (shown by the red
dashed line). This further suggests that the transfer of charge in and out of
the internal gate is efficient. The averaged measurements show that the noise
follows a nearly 1/$\mathrm{\sqrt{N}}$ trend, as shown by the fitted power law
line (blue dashed line). A slight deviation from the 1/$\mathrm{\sqrt{N}}$
trend is expected due to the presence of 1/f noise in these detectors [26,
27]. Starting with an ENC of 3.8 $\mathrm{e}^{-}_{\mathrm{RMS}}$, we achieved
an ENC of 0.51 $\mathrm{e}^{-}_{\mathrm{RMS}}$ at the end of the 57th RNDR
cycle.

Figure 6: Read noise from the RNDR analysis. The red circles show the
individual read noise measurements from the 57 individual measurements while
the blue filled circles are obtained after averaging over the measurements.
The measurements follow the expected 1/$\mathrm{\sqrt{N}}$ trend, shown by the
dashed blue line. The read noise for the first cycle is measured to be 3.8
$\mathrm{e}^{-}_{\mathrm{RMS}}$, while at the end of fifty seventh cycle, the
read noise has improved to 0.51 $\mathrm{e}^{-}_{\mathrm{RMS}}$.

##  5 Summary and future plans

Single electron Sensitive Read Out (SiSeRO) is a novel on-chip charge
detection technology that can provide improved responsivity and noise
performance than traditional readout circuitry. Developed by MIT-LL, the
current SiSeRO prototype devices are in the CCD format with each output stage
having a SiSeRO amplifier. In this paper, we demonstrated sub-electron noise
performance for a CCID-93 SiSeRO prototype by implementing 57 RNDR cycles. The
noise evolution across the cycles show a nearly $\mathrm{1/\sqrt{N}}$ trend,
with a final noise of 0.51 $\mathrm{e^{-}_{RMS}}$ at an operating temperature
-100∘C and an impressive readout rate of 1 $\mu$s of CDS integration per
cycle.

In order to mature the SiSeRO technology, we are currently fabricating three
novel SiSeRO detectors at MIT-LL based on more optimized and improved SiSeRO
amplifier designs [28]. The first detector variant will have 16 parallel
SiSeROs at the output, with variations in the geometry of the internal gate,
location of the trough, and isolation of the MOSFET from the surrounding
gates. This will allow us to optimize the technology further for better noise
and gain performance. Another SiSeRO variant, aimed towards optimizing the
RNDR method, will have 16 SiSeRO amplifiers in series at the output, with
dedicated transfer gates between each pair of the SiSeRO amplifiers. This will
allow 16 measurements of the same signal charge, resulting in a reduction of
noise by a factor of four while maintaining the same frame rate. The noise can
be reduced further by introducing RNDR sampling between each pair of the
SiSeRO amplifiers. Both these detector types are expected to be fabricated by
the end of the current year. We plan to utilize the MCRC ASIC to readout these
detectors.

Our long-term goal is to build a SiSeRO active pixel sensor (APS) following
the concept used in RNDR optimized DEPFET detectors [14]. The first prototype
SiSeRO matrix is currently under fabrication and will be available for testing
soon. Based upon the test results, we later plan to develop a larger matrix
array based on this concept. Such a detector will provide a pathway to develop
an extremely low noise, fast readout mega-pixel spectro-imager for future
X-ray astronomical missions.

###### Acknowledgements.

This work has been supported by NASA grants APRA 80NSSC19K0499 “Development of
Integrated Readout Electronics for Next Generation X-ray CCDs” and SAT
80NSSC20K0401 “Toward Fast, Low-Noise, Radiation-Tolerant X-ray Imaging Arrays
for Lynx: Raising Technology Readiness Further.”

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# Hairygami: Analysis of DNA Nanostructures’ Conformational Change Driven by
Functionalizable Overhangs

Matthew Sample  School for Engineering of Matter, Transport, and Energy,
Arizona State University, Tempe, AZ 85287, USA  School of Molecular Sciences
and Center for Molecular Design and Biomimetics, The Biodesign Institute,
Arizona State University, 1001 South McAllister Avenue, Tempe, Arizona 85281,
USA  Hao Liu  School of Molecular Sciences and Center for Molecular Design and
Biomimetics, The Biodesign Institute, Arizona State University, 1001 South
McAllister Avenue, Tempe, Arizona 85281, USA  Michael Matthies  School of
Molecular Sciences and Center for Molecular Design and Biomimetics, The
Biodesign Institute, Arizona State University, 1001 South McAllister Avenue,
Tempe, Arizona 85281, USA  Petr Šulc  School of Molecular Sciences and Center
for Molecular Design and Biomimetics, The Biodesign Institute, Arizona State
University, 1001 South McAllister Avenue, Tempe, Arizona 85281, USA

###### Abstract

DNA origami is a widely used method to construct nanostructures by self-
assembling designed DNA strands. These structures are often used as
”breadboards” for templated assembly of proteins, gold nanoparticles,
aptamers, and other molecules, with applications ranging from therapeutics and
diagnostics to plasmonics and photonics. Imaging these structures using AFM or
TEM is not capable to capture their full conformation ensemble as they only
show their structure flattened on a surface. However, certain conformations of
the nanostructure can position guest molecules into distances unaccounted for
in their intended design, thus leading to spurious interactions between guest
molecules that are designed to be separated. Here, we use molecular dynamics
simulations to capture conformational ensemble of 2D DNA origami tiles and
show that introducing single-stranded overhangs, which are typically used for
functionalization of the origami with guest molecules, induces a curvature of
the tile structure in the bulk. We show that the shape deformation is of
entropic origin, with implications for design of robust DNA origami
breadboards as well as potential approach to modulate structure shape by
introducing overhangs. We then verify experimentally that the overhangs
introduce curvature into the DNA origami tiles.

##  I Introduction

The emerging fields of DNA and RNA nanotechnology use DNA or RNA strands to
self-assemble nanoscale structures and devices. The fields have multiple
promising applications that include therapeutics, diagnostics, molecular
computing, biotemplatemplated assembly for nanophotonics and optical
computing, nano-electronics, and synthetic biology [1, 2, 3, 4, 5]. Currently,
the most popular construct in DNA nanotechnology is the DNA origami [6]. It
typically consists of a single-stranded DNA scaffold strand taken from M$13$
bacteriophage ($7249$ bases long), and short staple strands that are
complementary to different regions of the scaffold strand that then self-
assemble a structure of a desired shape. Originally, DNA origami were designed
as 2D structures, and later work has extended this concept to $3$D [7]. The
origami designs have been very quickly adopted by the broad bionanotechnology
research community because DNA strands can be functionalized e.g. by attaching
gold nanoparticles, proteins, small molecules, quantum dots and aptamers [8,
9, 10, 11]. Given the fact that we know where each nucleotide is going to be
positioned with respect to the rest of the structure in the final assembled
shape, the DNA origami technique effectively provides nanoscale precision for
positioning objects with respect to each other. A common strategy to introduce
these functional moieties to DNA origamis is to extend the strands comprising
the structure with single-stranded overhangs. However, it has not been
previously explored how such modifications can affect the structure of the
origami, and therefore potentially its function as well.

Typically, DNA origami structures are characterized by surface-based
techniques like atomic force microscopy (AFM) and transmission electron
microscopy (TEM). During this analysis the structure is adhered to a charged
surface, limiting the number of conformations that can be observed. While this
is not playing a role for applications in molecular electronics, molecular
medicine and diagnostics assays often rely on the interactions of the
structures in solution, and hence the images produced by AFM and TEM imaging
techniques are not necessarily representative of the conformations that the
structures sample in solution. $3$D nanostructures have also been
characterized by cryo-EM techniques [12, 13]. However, the image processing
and reconstruction of $3$D DNA nanostructures in high resolution remains a
challenging process, which relies on automated construction of an ensemble
average, and hence it can still miss some conformations. Flexible DNA
structures sample in the bulk highly deformed conformations [14], potentially
impacting their function such as when different functionalized regions that
are not supposed to interact with each other might appear in close proximity,
or when the attached particles are not at the distances intended in the
design.

Currently, there is no experimental technique available that would allow for
easy, reliable and high-precision characterization of the conformational
ensemble of DNA origami nanostructures. Super-resolution imaging-based
approaches, such as DNA-PAINT [15], or small angle X-ray scattering (SAXS) can
provide information about conformations in the bulk [16], but ideally need to
be accompanied by a model that can inform the measurements for improvement of
signal to noise ratio in analysis. Here, we show how computational modeling
can provide crucial insight into the flexibility and motion of $2$D DNA
origami structures, and in particular focus on conformational ensemble changes
induced by DNA overhangs attached to the nanostructure. Modeling of DNA
origami can present significant challenges, however, given the sizes of the
DNA origamis of over $14\,000$ nucleotides. Atomistic resolution modeling is
limited to at most microseconds timescales, and hence over the past several
years coarse-grained models [17, 18, 19, 20] and finite-element based
predictions approaches have been developed to computationally sample DNA
origami mean shape [21, 22, 23, 24, 25]. In this study, we use the nucleotide-
level coarse-grained model oxDNA [17, 18, 26, 27], as it has been shown to
accurately capture both single-stranded and double-stranded DNA biophysics
[28, 29]. It is parameterized to reproduce thermodynamic, mechanical and
structural properties of both single-stranded and double-stranded DNA [17].
The model has been used to study a range of DNA nanotechnology systems, and
where available, good agreement with experimental results has been found [28].

Figure 1: The addition of overhangs causes a $2$D DNA origami tile $(a)$ to
adopt a curved shape $(b)$. The origin of the curvature is mainly due to the
entropic penalty of the overhang sequences on a flat surface $(c)$, compared
to a curved surface $(d)$ (shown schematically as a side view of an overhang).
The overhangs on the curved surface have more accessible conformational space
(shown in red) than they do on the flat surface.

We use the oxDNA model to study the effects of $2$D DNA origami deformation
induced by the presence of single-stranded and double-stranded overhangs. An
enhanced sampling method was utilized to sample the conformational space of
the structure. We show that bent conformations are significantly enhanced as
longer or denser overhangs are attached to the origami (Fig. 1). We show that
the effect is of entropic origin, with the highly bent conformation being more
favorable for structures with longer and denser overhangs. The results have
implications both for DNA origami designs used for cargo delivery or surface-
bound strand displacement based computation [30, 31], as the attached
overhangs can have unintended effects on the structures’ conformational
ensemble. At the same time, the mechanism of entropy-induced curvature of DNA
origami tiles can be exploited to impose certain preferred shapes to DNA
structures for example as a design feature that is intended to distinguish
between inside and outside in a bent structure, e.g. in the case of nanotubes
[32]. We study here the effects of overhang length and density at different
temperatures and salt concentrations, and show how the distribution of
different shapes of the DNA tile is affected by their presence.

##  II Results and Discussion

###  II.1 Studied Systems

Figure 2:  $(a)$ Mean structure of twist-corrected rectangular origami with
$169$ overhang extensions comprised of twenty nucleotide bases. The arrows
indicate the measured end-to-end distance order parameter ($R_{\rm ee}$) used
to model the curvature of the structures. Low $R_{\rm ee}$ values correspond
to high curvatures and high $R_{\rm ee}$’s to low curvatures. $(b)$ Mean
structures of umbrella simulation windows equilibrated around $0.62$ nm, $31$
nm, and $62$ nm respectively. Figure 3: Effect of overhang length on
structural curvature. $(a)$ Free energy profiles as a function of the end-to-
end distance of the twist-corrected rectangular tile origami. The dots
indicate the location of the weighted average value. $(b)$ oxView
visualization of mean structures and corresponding weighted average values. We
compared structures with no overhangs, $3$nt, $9$nt, and $20$nt overhangs. The
free energy profiles show that structures with a greater number of nucleotides
in the overhangs, effectively longer overhang length, exhibit higher
probabilities to be in states with higher magnitudes of curvature.

The primary model system we chose to study the structural impact of DNA
origami functionalization though extending staple strands was the twist-
corrected rectangular DNA origami from Ref. [33] (shown on the left in Fig.
1$a$). The DNA origami rectangles of this type have been utilized in various
applications as a molecular canvas for nanometer scale positioning due to the
$\sim 5$ nm resolution of the site specific addressable DNA overhangs [33]. We
extended DNA overhangs from the $5^{\prime}$ ends of the origami’s staple
strands, using a multitude of overhang conditions including single-strands,
double-strands ($169$ overhangs, $85$ overhangs), as well as varying their
length. To model experimentally realized systems, we initially created
structures with nine nucleotide ($9$nt) and twenty nucleotide ($20$nt) long
overhang extensions. The $9$nt overhang structure models the qPaint docking
strand system from Ref. [33] and the $20$nt structure represents the molecular
positioning system created by Gopinath and collaborators in Ref. [34].

Initial unbiased oxDNA simulations indicated the presence of structural
curvature upon extension of overhangs, as can be seen in the calculated mean
structure (Fig. 2$a$). We next employed umbrella sampling to quantify the
magnitude of curvature in rectangular origami structures with overhangs.
Umbrella sampling (US) is an enhanced sampling technique that allows us to
efficiently sample all values along our chosen order parameter (OP) by
introducing an external harmonic potential that biases the simulation to
sample all desired states of the OP that represents different conformations of
the structure (see Methods) [35, 23, 36, 37]. To model structural curvature,
we chose our OP to be the distance between the centers of mass (COM) of the
origami’s long edges (see Fig. 2), titled as the end-to-end distance ($R_{\rm
ee}$), following the approach from Ref. [36].

The simulations allow us to assign probabilities to observe particular values
of our OP in the conformational ensemble, which we use to quantify the
rectangular origami’s preference to exhibit different magnitudes of curvature
as a function of the end-to-end distance between edges of the origami ($R_{\rm
ee}$), as it represents a one-dimensional description of the curvature. The
$R_{\rm ee}$ was sampled from $0.62$ nm to $62$ nm.

In addition to the $2$D origami from Ref. [33], we used oxDNA simulations
(with similar OP choice, see Methods) to study the bending of the anti-
parallel double layer rectangular origami from the work of Thubagere el al.
[30] and the six helix bundle rectangular origami from Dong el al. [38]. We
studied their conformations both with and without 20nt long overhangs (see
Fig. 8).

To compare the curvature exhibited by different structures, for all the
studied designs we plot the free energy as a function of the end-to-end
distance ($R_{\rm ee}$), obtained from the probability $p(R_{\rm ee})$ as
$F(R_{\rm ee})/k_{\rm B}T=-\ln{{p(R_{\rm ee})}}+C$, where we set constant $C$
such that $F(R_{\rm ee})$ is equal to 0 for the most probable value of $R_{\rm
ee}$ (i.e. in its minima)[39]. For each studied system, we also highlight in
the plot (as a colored dot) the weighted average end-to-end distance $\langle
R_{\rm ee}\rangle_{p}=\sum_{R_{\rm ee}^{i}}p(R_{\rm ee}^{i})R_{\rm ee}^{i}$,
where $R_{\rm ee}^{i}$ are all the binned values of the end-to-end distance of
$R_{\rm ee}$ that were sampled during the simulation.

###  II.2 Effects of Overhang Length

To investigate the impact that different lengths of overhang extensions had on
inducing the rectangular origami to curve, we simulated structures with
varying number of nucleotides in their single-stranded poly-T overhangs. Free-
energy profiles were computed for a rectangular structure with no overhangs,
and then for three nucleotides, nine nucleotides, and twenty nucleotide-long
overhangs respectively. All considered systems had the same density of
overhangs, $169$ overhangs in total attached to the $2$D origami tile. We
observe that the umbrella sampling simulation results show significant
curvature in all origami structures with added overhang extensions. With the
increasing length of the overhang, the probability of exhibiting a greater
magnitude of curvature also increased (Fig. 3).

The rectangular structure with zero overhangs showed a weighted average
$R_{\rm ee}$ value of $55.07\pm 0.11$ nm, while the $3$nt, $9$nt, and $20$nt
overhang structures had weighted average values of $50.59\pm 0.12$ nm,
$44.74\pm 0.10$ nm, and $23.48\pm 0.12$ nm respectively (shown as colored dots
in Fig. 3). These values quantitatively show a significant difference in the
average curvature of the four different structures, where longer overhangs
lead to increased curvature.

Further, while the weighted average values are valuable for comparisons of
curvature between different structures, the individual flexibility of a
structure can be seen from the differences between end-to-end distance free-
energy profiles for the respective overhang lengths studied (Fig 3). From the
relative flatness of the free-energy profiles, it can be seen that the
structures have immense flexibility in exploring conformations outside of the
minimum. For example, the $2$D origami with $9$nt overhangs has a free energy
minimum at $R_{\rm ee}=48$ nm, but is only about $7$ times less likely to
visit $R_{\rm ee}$ values of $30$ nm and $150$ times less likely to visit
$R_{\rm ee}$ values of $7$ nm, and hence it is expected to sample these
conformations frequently in the bulk. Thus, to understand both the structure
and how flexible DNA origami will behave in solution and how likely certain
conformations are, it is vital to obtain more accurate and complete
information than static structural properties (e.g. AFM image) can provide us.

###  II.3 Entropy as the Driving Force

To study the cause behind the induction of curvature through the addition of
overhang extensions, we performed simulations with a modified oxDNA model
where non-bonded interactions were turned off between specific groups of
nucleotides for the origamis with $9$nt and $20$nt long single-stranded
overhangs. We expect that the excluded volume interactions (two strands cannot
occupy the same space at the same time) are the primary driving force behind
the observed curvature. The single-stranded overhangs need to avoid
overlapping with each other. The likelihood that two of the neighboring
overhangs will clash with each other is lower if the $2$D origami is curved.
Furthermore, the amount of volume accessible to an overhang strand (Fig. 1$c$)
will increase (Fig. 1$d$) if the $2$D origami bends more, thus making the bent
configuration more favorable for entropic reasons, as the overhangs will have
larger conformational volume accessible. The amount of volume accessible to
single-stranded DNA overhangs was also previously shown to be able to modulate
the free-energy landscape of a DNA hinge nanostructure [40].

Figure 4: A schematic illustration of modified interaction potentials in the
oxDNA models to test the effects of overhangs on DNA tile conformations: $(a)$
Non-modified interactions: the overhangs cannot occupy the same space at the
same time due to excluded volume interaction (regions where the overhangs can
”clash” with each other or the DNA tile highlighted in orange). $(b)$ A
modified interaction where we switch off interaction between all pairs of DNA
overhangs. $(c)$ A modification of the interactions where we switch off
interactions between the overhangs and the nucleotides that are part of the 2D
DNA origami tile. $(d)$ A modification where we switch off both interactions
between pairs of overhangs, as well as between overhangs and nucleotides
belonging to the the tile.

To study these phenomena, we simulated three different system modifications to
decompose the underlying effects of the curvature (schematically illustrated
in Fig. 4). In the first modification, we explicitly switched off in the
simulations all interactions between all pairs of overhangs, allowing the
overhangs to pass through each other (Fig. 4$b$). For the second modification,
we switched off interactions between the nucleotides in the single-stranded
overhang extensions and the nucleotides in the rectangular origami’s base,
thus allowing the overhangs to freely pass through the origami surface (Fig.
4$c$). Finally, in the third modification, we combined both prior approaches
and switched off the interactions between the overhangs with the rectangular
tile as well as interactions with other overhangs (Fig. 4$d$).

For each of the modified simulations, we ran umbrella sampling simulations to
reconstruct the free-energy profile of the end-to-end distance $R_{\rm ee}$
for the systems with $9$nt and $20$nt long single-stranded overhangs (Fig. 5).

Figure 5: Entropy as the Driving Force. Non-bonded interaction potentials of
the overhang extensions for the $(a)$ $9$nt and $(b)$ $20$nt systems were
modified to decompose the source of curvature. When the interactions of the
overhangs with the rectangular tile are switched off the curvature of both
systems closely mirrors the zero overhang curvature, indicating this
interaction to be the main source of curvature. When the overhangs
interactions with other overhangs are turned off the $20$nt system has a
moderate change in curvature while the $9$nt system does not change, leading
to the conclusion this condition is impactful only for long overhangs.

Analyzing the modified simulations for the $20$nt overhangs structure, the
free-energy profile for the first modification (interaction of overhangs with
other overhangs switched off) moderately shifts the weighted average of the
$R_{\rm ee}$ from $23.48\pm 0.12$ nm to $37.66\pm 0.17$ nm. The second
modification (overhangs interaction with DNA origami surface switched off)
heavily shifted the average $R_{\rm ee}$ values to $54.04\pm 0.13$ nm,
corresponding to structure with greatly reduced curvature. The third condition
(interaction with other overhangs and DNA origami surface switched off) has a
weighted average $R_{\rm ee}$ of $54.78\pm 0.14$, nearly identical to the flat
DNA origami with no overhangs.

The change in the $R_{\rm ee}$ value for the $9$nt long overhangs shows a
different trend for the first modification (no interactions between
overhangs), as the free-energy profile remains nearly identical as to the case
where no modification is introduced, implying that for these short overhangs,
the effects of overhangs interacting through excluded volume are negligible.
The second modification (switching off interactions between overhangs and DNA
origami surface) shows an increases in the average $R_{\rm ee}$ value from
$44.74\pm 0.10$ nm to $53.62\pm 0.10$ nm, corresponding to decrease in
curvature. Thus, for shorter overhangs, the entropic origin of curvature
appears to be only due to the increased conformational space of individual
overhangs, rather than due to the clashes with other overhangs.

Overall, these results show that the interactions between the overhang
extension with the rectangular tile structure are the main contributing factor
in causing the rectangular origami to curve. By adopting a curved surface, the
number of conformational states that the overhangs extensions are able to
explore increases, and consequently the curved structure is entropically
favored (Fig. 1$c$,$d$).

In addition to the curvature caused by the interaction between the overhangs
and the rectangular tile, the interactions between the overhangs themselves
also influence the curvature, but the result is only observed for longer
extensions. Even though the typical distance between $9$nt long overhangs are
such that they are able (in a rare case) to potentially overlap, it does not
meaningfully reduce the state-space accessible to the overhangs and hence does
not affect the curvature of the DNA origami tile. All of the studies where we
used modified interactions to study the effect of overhang were performed at
1M salt concentration, so there were no long-range electrostatic interactions
present as the Debye-Hückel length of the electrostatic potential in the model
at 1M salt is about equal to the radius excluded volume of each backbone site,
the dominant interaction between the overhangs and the tiles is hence just the
excluded volume potential.

As can be seen from the free-energy profiles of the studied systems, such as
in Fig. 2, the addition of overhangs also lowers the free-energy barrier to
sample different conformations of the DNA tile. For instance, the free-energy
difference between the approximately flat tile (end-to-end distance 55.07 nm)
and the bent tile (22.48 nm end-to-end distance) is 9.02 $k_{\rm B}T$, while
for the system with 9 nucleotide long overhangs, it is only 3.85 $k_{\rm B}T$,
effectively making the tile more flexible due to the bent state becoming more
likely and hence more easily accessible.

Figure 6: Effect of different overhang conditions. Free energy profile of
$(a)$ $9$nt and $(b)$ $20$nt modified overhang systems. When the complementary
strand of the overhang extension is added to create double-stranded overhangs,
the curvature of both the $9$nt and $20$nt structures increases. Inversely, if
the number of single-stranded extensions is reduced to $85$ overhangs, the
curvature of the structures decrease. Mean structures of $(c)$ $9$nt and $(d)$
$20$nt overhang conditions illustrate these differences.

###  II.4 Effects of Overhang Duplexes and Density

To analyze the effect of overhang extensions in complex with their
complementary strands as well as different densities of overhangs, we designed
and simulated origami structures with $169$ duplex overhangs (”dense” system),
and ”half-dense” structures with $85$ single-stranded overhangs and finally
structures with $85$ duplex DNA overhangs (”half-dense” double-stranded). The
double-stranded DNA overhang structures were designed to model a rectangular
tile system in complex with complementary functionalized DNA strands. The half
density structures are a model for a system in which further precision in the
locations of the overhang extensions are necessary, leading to a reduced
number of rationally placed overhangs.

The free-energy profiles (see Fig. 6) show that the formation of DNA duplex
overhangs increases the curvature of both the $20$nt and $9$nt duplex overhang
structures relative to their single stranded counterparts. While the free-
energy minima of the $20$nt duplex overhang structure does not change compared
to the $20$nt single-stranded overhang structure, an effective overall
decrease in curvature can be seen from the shift in the weighted average
value. The weighted average $R_{\rm ee}$ for the $20$nt duplex overhang
structure was $18.03\pm 0.17$ nm, as compared to $23.48\pm 0.12$ nm for the
$20$nt single-stranded overhang structure. Similarly for the $9$nt long
overhangs, the weighted average decreased to $33.20\pm 0.14$ nm for the duplex
overhangs from $44.74\pm 0.10$ nm for the single-stranded overhangs, in
addition to a shift in the free-energy minima from $35$ nm to $48$ nm. Our
simulations show that once our rectangular DNA origami structure with dense
overhangs is functionalized by binding the overhangs by a complementary strand
(and thus creating duplex overhang), the flexible structure will experience
further curvature.

We further observed that when the density of the overhangs was approximately
cut in half from $169$ to $85$, the curvature of the structure decreases (Fig.
6), consistent with the fact that the entropic advantage of bending the
origami will be lower for smaller number of the overhangs. We next compared
the double-stranded overhangs and single-stranded overhangs for the half-
density systems with $85$ overhangs. Just as we observed for the dense system
with $20$nt nucleotide long overhangs, the $20$nt duplex overhangs structure
had increased curvature (average $R_{\rm ee}=45.23\pm 0.24$) compared to the
single-stranded ones (average $R_{\rm ee}=48.87\pm 0.18$). However, we observe
that $9$nt duplex overhangs weighted mean end-to-end distance is slightly
higher (less curved structure) than for the $9$nt single-stranded duplex,
which is the opposite effect from what we observed for the dense system with
$169$ overhangs.

The duplex overhangs behave more like wider stiff rods, whereas single-
stranded DNA overhangs behave as freely-jointed chains with excluded volume.
Thus, we expect the entropic penalty due to the overhangs clashing with other
overhangs to increase with double-stranded overhangs compared to single-
stranded, an effect which is more pronounced for the longer ($20$nt)
overhangs. However, the fact that the structure with $9$nt single-stranded
overhangs is slightly more curved than DNA origami with $9$nt duplex
overhangs, is indicative that the duplex overhangs are clashing less with the
DNA origami surface than the single-stranded ones.

Finally, the sequence effects of the single-stranded regions was investigated
by using the sequence-dependent version of the oxDNA model [18], which has
parameterized stronger Adenine-Adenine stacking compared to Thymine-Thymine
stacking. The simulations (Supp. Materials Fig. S3) showed that there was no
effective difference in the curvature of the structures when the nucleotide
sequence was Thymine or Adenine and hence that the greater tendency for
adenine’s to stack compared to thymine does not affect the origami’s
structural curvature.

###  II.5 Effects of Temperature and Salt Concentration

In all cases considered above, we fixed temperature to $20^{\circ}$C and salt
concentration in the oxDNA model to $1$M. To characterize how the curvature of
the rectangular tile origami might respond to different temperatures and salt
concentrations, we computed free-energy profiles of end-to-end distance at
four different temperatures and salt concentrations for the $20$nt long
single-stranded overhang and no-overhang DNA origami structures. Simulations
were run at $10^{\circ}$C, $20^{\circ}$C, $30^{\circ}$C, and $40^{\circ}$C as
well as at salt concentrations of $0.2$ M, $0.6$ M, $0.8$ M, and $1$ M (shown
in Fig. 7).

Figure 7: Effect of different temperatures and salt concentrations. Free
energy profiles of $(a,c)$ no overhangs and $(b,d)$ $20$nt overhangs at
various temperatures and salt concentrations. For both no overhang and $20$nt
structures, when the temperature is increased the curvature is negligibly
effected. When the salt concentration is decreased, the curvature of the
structure decreases due to the increase in electrostatic repulsion between
charged backbone sites in the rectangular tile.

The free-energy profiles of end-to-end distance (and hence the curvature of
the DNA origami) change only slightly between different temperatures,
corroborating the entropic origin of the curvature.

When the salt concentration is varied, we see that as the salt concentration
decreases, the curvature of the structure also decreases. Our oxDNA model
implements salt effects using Debye-Hückel potential [18], where the backbone
sites of the nucleotides in the model interact with repulsive interaction with
an effective charge. With decreasing salt concentration, the effective
excluded volume occupied by the overhangs increases, and while the curvature
does not change drastically from $1$ to $0.6$ M salt, we observe moderately
less curvature for $0.2$ M salt. The large magnitude change in curvature for
$0.2$ M salt as compared to other salt concentrations can be attributed to the
exponential increase in the Debye length as the salt concentration approaches
$0$. The increased electrostatic repulsion between the nucleotide backbones in
the origami helices effectively flattens the structure, as can be seen for
system with no overhangs (Fig. 7). For the 20nt overhang lengths, while they
have larger excluded volume at lower salts, the flattening of the origami at
low salt concentrations still leads to larger average $R_{\rm ee}$ (smaller
curvature) at lower salt concentrations.

###  II.6 Anti-Parallel Double Layer and Six Helix Bundle Rectangles

To compare the effects overhang extensions have on $3$D rectangular structures
as opposed to the $2$D structure, we simulated two rectangular origami planes
with 3D architectures. One of the structure is made of two anti-parallel $2$D
rectangles (Fig. 8$b$), while the other is a rectangle made of six helix
bundles (Fig. 8$c$) [30, 38]. We extended twenty nucleotide overhangs from the
staple strands of both systems.

Figure 8: $(a)$ Free-energy profiles of $3$D rectangular origami structures.
$(b)$ The double layer anti-parallel $20$nt overhangs and $(c)$ six helix
bundle $20$nt overhangs structures show a remarkable increase in rigidity
compared to the $2$D rectangular structure. The anti-parallel and six helix
bundle free energy profiles show a much steeper rise in free energy upon
perturbations from the free energy minimum indicating low flexibility, with
weighted averages at $50.49\pm 0.02$ nm and $50.04\pm 0.03$ nm respectively.

The free-energy profiles of both of the $3$D rectangular structures show a
immense increase in structural rigidity. The steepness of the free-energy
profiles around the free-energy minimum as compared to the single layer $2$D
rectangular origami indicates that the end-to-end distance between edges of
the structures are nearly constant, with huge penalty for bending. The anti-
parallel structure (Fig. 8$b$) has a free-energy minimum of end-to-end
distance at $50.45$ nm and weighted average of $50.49\pm 0.02$ nm, and
similarly the six helix bundle (Fig. 8$c$) has a minimum of $49.95$ nm and a
weighted average of $50.04\pm 0.03$ nm. In comparison, the single layer DNA
origami with $20$nt overhangs that we studied in previous sections has an end-
to-end distance minimum at $16.42$ nm and a weighted average of $23.48\pm
0.12$ nm, which is due to an underlying skewed distribution with a higher
probability for states beside the minimum. In contrast, the measured values
for $3$D double-layered structures indicate a rigid body with a large free-
energy penalty for perturbations away from the minimum. We note that these
$3$D designs are preferred choice for application where flexibility of the
structure should be minimal and prevent any cross-talk between the molecules
attached to the structure surface [30].

###  II.7 Experimental study of the overhang-induced bending

Figure 9: $(a)$ Schematic representation of experimental hypothesis. The top
row illustrates the mechanism of multimers and aggregates formation, which are
the most probable outcomes of locking strand hybridization for a twist
corrected rectangular DNA origami with no overhangs, except those on the edges
designed for locking strand hybridization. The bottom row depicts the
formation of nanotubes, which are the most likely outcome of locking strand
hybridization of a twist corrected rectangular DNA origami with densely placed
20nt overhang extensions. $(b)$ Four conditions are shown using oxDNA mean
structures of rectangles with lockable edges: no overhangs , no overhangs with
lock strand resulting in a representative multimer (i.e. trimer), 20nt
overhang extensions, and 20nt overhang extensions with a lock strand. $(c)$
TEM images of aforementioned four conditions (Scale bar: 50 nm) Figure 10:
Image of gel electrophoresis experiment featuring four conditions of DNA
origami rectangles with lockable edges: no overhangs , no overhangs with a
locking strand, 20nt overhang extensions, and 20nt overhang extensions with a
locking strand. Corresponding oxDNA mean structures are overlaid below the
well. For the second condition, one possible multimer (trimer) is shown, with
an arrow pointing to the trimer band on the gel. The gel revels the formation
of multimers and aggregate in the condition with no overhangs and a locking
strand, while monomers are observed in all other conditions.

To validate the phenomenon of overhang-induced curvature in flexible DNA
origami structures, as revealed by our umbrella sampling simulations, we
performed experiments for qualitative confirmation. We hypothesized that
adding overhang extensions to the long ends of the rectangle–extensions that
could hybridize to form a nanotube in the presence of a locking strand–the
20nt overhang rectangle would preferentially form nanotubes. In contrast, a
rectangle without overhangs (except the lockable ones) would more likely form
multimers and aggregates(Fig. 9$a$). A high density of overhangs would induce
curvature, bringing the two ends of the rectangle into close proximity and
favoring nanotube formation, whereas a flat sheet without overhangs would tend
to interact and bind with other nearby rectangular DNA origamis structures.

Using oxView, we designed overhang to extend from the edge of the twist
corrected rectangular origami, and a $16$ nucleotide long locking strand to
hybridize them together. Each lockable overhang contained a $6$ nucleotide
poly-T spacer followed by $8$ nucleotides complementary to half of the locking
strand. Using this design, we explored four conditions, both in simulation and
experiments. The first condition involved a rectangle with only the necessary
overhang extensions for locking, but without the addition of the locking
strand. The second condition using the same structure but included the locking
strand. The final two conditions utilized a rectangle with 20nt overhang
extensions, where in one case the locking strand was not added and another
where it was added.

Gel electrophoresis was preformed on these four conditions, and representative
mean structures from the simulations were overlaid on the gel (Fig. 10). The
gel reveled that the system with no additional overhangs, and without the
locking strand, yielded the designed rectangular sheets, as evidenced by a
single band. Upon adding the locking strand to this structure, we observed the
formation of aggregates and multimers, seen as the aggregate band at the top
the well and a smear with multiple bands indicating a gradient of migration
speeds. One of the possible multimers, a trimer, was simulated and is
represented below the corresponding lane. The rectangle with added 20nt
overhang extensions also showed a monomer band. Importantly, when the locking
strand was added to this 20nt overhang structure we only observed a monomer
band. This final lane indicates that the overhang extensions indeed induced
the rectangle to curve, such that when the locking strand was added the
formation of a nanotube was the most probable state. This is in stark
comparison to the structure without the overhang extensions which instead
formed a distribution of aggregates and multimers.

Following the gel electrophoresis experiment, we preformed TEM imaging for all
four conditions to corroborate the gels results (Fig. 9$b$). The TEM images
showed indeed aligned with our hypothesis: the addition of the locking strand
led to the formation of closed tubes in the condition with 20nt overhang
extension, whereas the rectangle without additional overhangs displayed
aggregates. Interesting, the condition with 20nt overhangs but without but the
locking strand exhibited a distribution of curved and flat structures. This is
in agreement with the free energy profile of the 20nt overhang structure,
which indicated that the rectangular origami would exist in a distribution of
states in solution. However, the TEM images showed a higher proportion of flat
structures than would be anticipated based on the free energy profile. This
discrepancy when considering that TEM imaging requires adhering the structure
to a charged surface, which would naturally skew the distribution toward a
higher likelihood of flat structures.

Two primary mechanisms can contribute to this phenomenon. The first is the
electrostatic attraction between the positively charged TEM imaging surface
and the negatively charged DNA backbone. This interaction would be at it
strongest when the maximum surface area of the DNA origami is in contact with
the surface. The most straightforward way to achieve this is by forcing the
rectangular origami to adopt a flat conformation. An alternative way to
increase surface area would be to have the overhang extensions lie flat on the
surface. However, this interaction encounters a limitation: adhering the
overhangs to the surface significantly restricts their accessible state space,
thereby substantially reducing their entropy, and consequently, the
probability of such an arrangement occurring.

The second mechanism contributing to the prevalence of flat structures is the
entropic penalty associated with confining overhang extensions to a surface.
If a curved structure with external overhang extensions adheres to a surface,
the overhangs must be pressed into the surface, reducing the system’s entropy.
Alternatively, the curved structure could flatten out, allowing the side
without overhangs to lie flat on the surface, allowing the overhang extensions
to explore the volume accessible to them above the TEM surface. These two
factors, the optimization of surface area contact between the origami and the
TEM surface, and the entropic penalty of confining overhangs- work in concert
to shift the distribution of state in favor of flat structures.

This hypothesis–that the TEM surface biases the distribution of curved to flat
states–is corroborated by both the gel and TEM image of the system with
overhangs and with the locking strand. The TEM image only shows monomer
nanotubes, while the gel displays a single band, confirmed to the the formed
nanotube by the TEM image. If the distribution of curved to flat states in the
TEM image of the 20nt overhang structure without the locking strand were
considered representative of the solution, one would expect the gel to show a
distribution of multimers and closed tubes. However, as only a monomer band is
observed, this supports the claim that the TEM surface has skewed the
distribution of states to show more flat structures than actually exists in
solution.

##  III Conclusions

In this study we characterized the effect of site addressable functionalizable
overhang extensions on the structure of twist-corrected rectangular DNA
origami. We showed that upon extension of overhangs from the end of staple
strands, there was a significant induced curvature in the structure.
Furthermore, we quantified how the average curvature is influenced by
different variables including the overhang length, single-stranded versus
double-stranded overhangs, density of overhangs, overhang sequence,
temperature, and salt concentration. The insights provided by the computed
free-energy profiles paint a robust picture of the dynamics of flexible DNA
origami in solution. These results conclude that in order to rationally design
flexible DNA nanostructures with nanometer scale precision, it is vital to
take into account the effect that extensions will have on modifying the
resultant structure.

While in the past experimental evidence indicate the existence of this
phenomenon [41, 42, 43], this study was the first to rigorously quantify the
degree of curvature induced by the functionalization of origami by single-
stranded and double-stranded overhangs, with implications for designs with
other guest molecules (such as proteins or gold nanoparticles), which we
expect to show effects. We showed that as the number of nucleotides in the
overhang extensions increases, the average curvature of the rectangular
origami increases as well. In addition, we displayed how the curvature of the
origami structure increased as a response to the formation of double stranded
DNA overhangs.

By sampling the dynamics of an implicitly solvated DNA origami, oxDNA
accurately predicts how entropic effects impact structural properties.
Utilizing modified interaction potentials, we decomposed the entropic penalty
caused by excluded body steric interactions. The increased state space
accessible to the overhang extensions upon origami curvature results in a free
energy landscape with a high probability of curved states.

Furthermore, when the simulations of DNA origami are utilized to calculate
free-energy profiles though umbrella sampling simulations, we are able to
obtain a much more robust characterization of not only the mean conformation
of our nanostructure, but also obtain information on all possible states,
along with the associated probability, of flexible DNA origami.

Finally, we ran oxDNA molecular dynamics simulations of 3D anti-parallel
double layer rectangular DNA Origami and a six helix bundle rectangular DNA
Origami with 20nt overhang extensions. The simulations showed that there was a
significant increase in structural rigidity with negligible deformation of the
planar shape of both 3D nanostructures as compared to the 2D rectangular
origami. Hence, 3D DNA origami rectangles would be recommended in an
application where a planar structure is required or precise spatial resolution
needs to be retained upon overhang functionalization.

Overall, our findings provide an important quantification of the effects of
functionalization of the DNA origami on their conformational ensemble, with
implications for functional designs for fields such as photonics, diagnostics
and drug delivery. We also note the effect of origami curvature induced by
overhangs can be potentially exploited to induce desired curved shape on a DNA
origami surfaces. The typical conformation for all the structures that have
been simulated are provided in the Supp. Mat. (Fig. S4) and summarized in
Supp. Mat. Table S1.

The oxDNA model has been previously shown to successfully reproduce a range of
DNA properties, including the radius of gyration of ssDNA at different salt
concentrations [18], the thermodynamic and kinetic effects of single-stranded
stacking in hairpin loops [44, 45], as well as the conformations of 2D and 3D
DNA origami structures that are consistent with experimental SAXS and cryo-EM
measurements [23]. The simulations were performed using 0.2 to 1M salt, with
electrostatic effects approximated in the model by Debye-Hückel potential and
excluded volume interactions. DNA origami experiments are typically done at
high salt concentration (12 mM Mg2+, but have also been done at magnesium-free
high sodium buffer [46]), so the highly screened short-range electrostatic
repulsion between DNA strands should be accurately captured by the model.
Given the good agreement of the oxDNA model with available experimental data,
as well as the fact that the described behavior of steric occlusion between
overhangs and tiles and subsequent bending of the DNA origami tile is
consistent with our knowledge of DNA mechanics, we are confident are
predictions are robust and the oxDNA model parametrization is accurate to
capture this effect correctly, and is supported by our experimental results.

We make the computational methods and all the software tools developed here to
setup umbrella sampling of conformations of nanostructures with oxDNA model at
https://github.com/mlsample/ipy_oxDNA.git, along with tutorials and examples.
We also provide an automated setup that allows to run multiple instances of
oxDNA molecular dynamics simulations on a single GPU card. With our setup, we
were able to run in parallel on $40$ oxDNA simulations of a single DNA origami
on one 40GB NVIDIA A100 card. Running simulations in parallel on a single card
is multiple times faster than running one simulation after other. We observed
an increased throughput of $2$ times for $5$ simulations or $2.6$ times for
$40$ simulations in parallel on a single GPU card. Hence, our setup opens a
way for massively parallelized nanostructure characterization even with
limited computational resources.

##  IV Materials and Methods

###  IV.1 Simulations

To simulate the structural dynamics of the DNA nanostructures, we use the
oxDNA coarse-grained model. Specifically, we used oxDNA$2$ [18] implemented on
GPU [26, 27]. The time-step used for all simulations was 15 fs, as previously
used for origami characterization [36]. Simulations were performed at 293.15 K
and 1 M salt concentration with averaged stacking and hydrogen bonding
strength unless otherwise specified. An Anderson-like thermostat was used for
temperature coupling and the salt concentration is modeled using the Debye-
Hückel potential. A diffusion coefficient of 2.5 in simulation units was used,
enabling us to sample longer timescales. The starting configurations were
prepared by the oxView tool [47, 48], where we extended a specified number of
staple strands to the $5^{\prime}$ end of the $2$D rectangular origami tile.

Umbrella sampling [49, 50] was then used to compute all of the free energy
profiles in this study. Adopting the approach from Ref. [36], we introduced a
biasing harmonic potential $V_{\rm bias}=\frac{k}{2}(R_{\rm
ee}-R_{0}^{w_{i}})^{2}$, where $R_{\rm ee}$ is the distance between the
centers of mass of the edges of the DNA origami, and $R_{0}^{w_{i}}$ is a
variable that is selected for a particular simulation window. For each studied
system, we simulated multiple independent windows, where a window is a
standalone simulation that was run for $20$ million simulation steps. For each
window $w_{i}$, we set a different value of $R_{0}^{w_{i}}$, ranging from
$0.62$ to $62$ nm using $100$ simulation windows with the increment between
each window being $0.62$ nm. The maximum order parameter value was $62$ nm,
was chosen because the average $R_{\rm ee}$ of the rectangular structure when
forced to be flat using a repulsion plane external potential was calculated to
be about $60$ nm, and we aimed to profile the structure slightly beyond flat
leading to our choice of $62$ nm as the maximum value. The minimum value of
$0.62$ was picked as a result of our decision to use $100$ simulation windows,
where $100$ windows starting at $62$ nm decreased by $0.62$ nm over our
windows leads to a minimum value of $0.62$ nm. We chose $100$ simulation
windows and the biasing harmonic potential with a spring constant $k=11.418$
pN/nm to guarantee sufficient overlap between neighboring windows. The $R_{\rm
ee}$ was fit to the angle between the center of the rectangle and the ends
using polynomial fitting Supp. Mat. (Fig S2).

Once the $100$ production windows were run, we used the Weighted histogram
analysis method [49, 50, 51] (WHAM) to unbias our simulations results and
provide free energy values as a function of our order parameter. We chose to
use $200$ bins for our WHAM analysis. The plotted free energy over $k_{\rm
B}T$ is calculated by dividing the WHAM calculated free energy by the
temperature. We used Ref. [51] for Monte Carlo bootstrapping error analysis to
create the error bars on the free energy values, which are also divided by the
temperature of the system. Using the free-energy values calculated from WHAM,
the weighted average of the end-to-end distance is then computed, using the
probability of respective end-to-end values. The error of the weighted average
was computed using parametric bootstrapping, modeling the free energy profiles
as a multivariate Gaussian with means equal to the free energy values and
standard deviations equal to the error provided by the WHAM Monte Carlo
bootstrapping error analysis.

###  IV.2 Experimental setup

The gel electrophoresis and negative staining TEM experiments to characterize
the nanostructure assemblies are detailed in Supplementary Material Section
S1. The staples for the nanostructure designs are listed in Table S2.
Additionally, all the experimentally realized designs were uploaded to
nanobase.org public repository [52] in the oxDNA file format.

##  V Acknowledgments

We acknowledge support from the ONR Grant N000142012094 and DURIP ONR grant
no. N000142112876. This material is based upon work supported by the National
Science Foundation under Grant No. 2227650. We further acknowledge use of the
Extreme Science and Engineering Discovery Environment (XSEDE), which is
supported by National Science Foundation grant number TG-BIO210009, as well as
Research Computing at Arizona State University for providing HPC resources. We
thank Jonathan Doye, Thomas Ouldridge, Paul Rothemund, and Matteo Guareschi
for helpful discussions and to Joel Joseph for help with the design of the
simulated structures.

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