A nitrogen-vacancy spin based molecular structure microscope using multiplexed projection reconstruction

Abstract

Methods and techniques to measure and image beyond the state-of-the-art have
always been influential in propelling basic science and technology. Because
current technologies are venturing into nanoscopic and molecular-scale
fabrication, atomic-scale measurement techniques are inevitable. One such
emerging sensing method uses the spins associated with nitrogen-vacancy (NV)
defects in diamond. The uniqueness of this NV sensor is its atomic size and
ability to perform precision sensing under ambient conditions conveniently
using light and microwaves (MW). These advantages have unique applications in
nanoscale sensing and imaging of magnetic fields from nuclear spins in single
biomolecules. During the last few years, several encouraging results have
emerged towards the realization of an NV spin-based molecular structure
microscope. Here, we present a projection-reconstruction method that retrieves
the three-dimensional structure of a single molecule from the nuclear spin
noise signatures. We validate this method using numerical simulations and
reconstruct the structure of a molecular phantom \b{eta}-cyclodextrin,
revealing the characteristic toroidal shape.

Full text

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
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A nitrogen-vacancy spin based
molecular structure microscope
using multiplexed projection
reconstruction
Andrii Lazariev
1
& Gopalakrishnan Balasubramanian
1,2
Methods and techniques to measure and image beyond the state-of-the-art have always been
inuential in propelling basic science and technology. Because current technologies are venturing into
nanoscopic and molecular-scale fabrication, atomic-scale measurement techniques are inevitable.
One such emerging sensing method uses the spins associated with nitrogen-vacancy (NV) defects
in diamond. The uniqueness of this NV sensor is its atomic size and ability to perform precision
sensing under ambient conditions conveniently using light and microwaves (MW). These advantages
have unique applications in nanoscale sensing and imaging of magnetic elds from nuclear spins in
single biomolecules. During the last few years, several encouraging results have emerged towards
the realization of an NV spin-based molecular structure microscope. Here, we present a projection-
reconstruction method that retrieves the three-dimensional structure of a single molecule from the
nuclear spin noise signatures. We validate this method using numerical simulations and reconstruct
the structure of a molecular phantom β-cyclodextrin, revealing the characteristic toroidal shape.
Nuclear magnetic resonance (NMR) is a widely applied technique that infers chemical signatures through
magnetic dipolar interactions. Magnetic elds arising from nuclear spins are weak, so conventional NMR
measurement requires a sizable number of spins, approximately 10
15
, to achieve reasonable signal-to-noise
ratio (SNR)
1
. is sensitivity limitation permits only ensemble-averaged measurements and forbid any
possibilities of studying individual molecules or their interactions. ere is a continuous eort to use
hybrid detection strategies to improve the sensitivity and, thus, achieve single molecular sensing with
spin information. Spin-polarized scanning tunneling microscopy (STM)
2
and magnetic resonance force
microscopy (MRFM)
3
have displayed remarkable abilities in imaging structures with chemical contrast
to single electron spins
3
and few thousand nuclear spins
4
. eir extreme sensitivity imposes restrictions
on the permissible noise oor, so the microscope is operable under cryogenic conditions.
It was the rst room-temperature manipulation of a single spin associated with the nitrogen-vacancy
(NV) defects in diamond
5
that brought the NV center into quantum limelight. In this seminal paper,
Gruber et al. envisaged that material properties can be probed at a local level using optically detected mag-
netic resonance (ODMR) of NV spin combined with high magnetic eld gradients ensemble averaging
5
.
Later, Chernobrod and Berman proposed scanning-probe schemes to image isolated electron spins based
on ODMR of photoluminescent nanoprobes
6
. Perceiving the uniqueness of single NV spin and combin-
ing coherent manipulation schemes
7,8
, independently proposals
9,10
and experimental results
11,12
emerged,
ascertaining NV spin as an attractive sensor for precision magnetometry in nanoscale
13–15
.
Spin sensor based on NV defects is unique because it is operable under ambient conditions and
achieves sucient sensitivity to detect few nuclear spins
16–20
. e hydrogen atoms that are substantially
1
MPRG Nanoscale Spin Imaging, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
2
Center
Nanoscale Microscopy and Molecular Physiology of the Brain (CNMPB), Göttingen, Germany. Correspondence and
requests for materials should be addressed to G.B. (email: gbalasu@mpibpc.mpg.de)
Received: 02 April 2015
Accepted: 19 August 2015
Published: 15 September 2015
OPEN

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
present in biomolecules possess nuclear spins. Mapping spin densities with molecular-scale resolu-
tion would aid in unraveling the structure of an isolated biomolecule
21,22
. is application motivates to
develop an NV spin-based molecular structure microscope
23–26
. e microscope would have immense
use in studying structural details of heterogeneous single molecules and complexes when other structural
biology tools are prohibitively dicult to use. For example, NV spin-based molecular structure micro-
scope would nd profound implications in the structure elucidation of intrinsically disordered structures,
such as the prion class of proteins (PrP). is family of proteins is known to play a central role in many
neurodegenerative diseases
27
. Understanding the structure-function relationship of this protein family
will be crucial in developing drugs to prevent and cure these maladies.
e NV spin is a high dynamic range precision sensor
28,29
; its bandwidth is limited only by the coherence
time and MW driving-elds
30,31
. e broadband sensitivity has an additional advantage because multi-
plexed signals can be sensed
32–34
. Fully exploiting this advantage, we present a projection-reconstruction
method pertaining to an NV spin microscope that encodes the spin information of a single molecule
and retrieves its three-dimensional structure. We analyze this method using numerical simulations on a
phantom molecule β -cyclodextrin. e results show distinct structural features that clearly indicate the
applicability of this technique to image isolated biomolecules with chemical specicity. e parameters
chosen for the analysis are experimentally viable
4,35–37
, and the method is realizable using state-of-the-art
NV sensing systems
23,24,35
. We also outline some possible improvements in the microscope scheme to
make the spin imaging more ecient and versatile.
At equilibrium, an ensemble of nuclear spins following the Boltzmann distribution tends to have a
tiny fraction of spins down in excess of spins up. e expression for this population dierence is given
by the Boltzmann equation:
γ
π
Δ= (−)≈ ,
()
Δ/
NNeN
hB
kT
1
2
1
EkT
where N is the number of spins, Δ E is the energy level dierence, k is the Boltzmann constant, T is the
temperature, h is the Planck constant, γ is the gyromagnetic ratio, and B is the magnetic eld. For room
temperature and low-eld conditions (Δ E ≪ k), an approximation is made in equation (1). e spins
reorient their states (↑ -↓ , ↓ -↑ ) with a characteristic time constant while conserving this excess popula-
tion. e average value of this excess spins remains constant while the root mean square (r.m.s.) value
of this uctuation over any period is given by
σ ∝√N
. is statistical uctuation in the net magnetiza-
tion signal arising from uncompensated spins is called spin noise, and it is relevant when dealing with
small numbers of spins. Combining spatial encoding using the magnetic eld gradients and passively
acquiring spin noise signals, Müller and Jerschow demonstrated nuclear specic imaging without using
RF radiation
38
. e spin noise signals become prominent when we consider fewer than 10
6
spins.
Considering solid-state organic samples with spin densities of 5 × 10
22
spins/cm
3
, this quantity of spins
creates a nanoscale voxel
36
. Spin noise signals arising from a few thousand nuclear spins were sensed
using MRFM and used to reveal a 3D assembly of a virus
4
. More recently, using NV defects close to the
surface of a diamond, several groups were able to detect the nuclear spin noise from molecules placed
on the surface under ambient conditions
19,20,25
.
If a magnetic eld sensor is ultra-sensitive and especially sample of interest is in nanoscale
13
, it is
convenient to use spin noise based imaging. e advantage being, this sensing method does not require
polarization or driving nuclear spins. Dynamic decoupling sequences, such as (XY8)
n=16
, are used for
sensing spin noise using NV. e method uses pulse timings to remove all asynchronous interactions
and selectively tune only to the desired nuclear spin Larmor frequency
17,19,25
. e NV coherence signal is
recorded by varying the interpulse timings over a desired range. e acquired signal is deconvoluted with
the corresponding lter function of the pulse sequence to retrieve the power spectral density of noise or
the spin noise spectrum
39
. is approach has been proved to be sensitive down to a single nuclear spin
in the vicinity
20
as well as to a few thousand of nuclear spins at distances exceeding 5 nm
19
. Correlation
spectroscopy approaches are able to achieve sub kHz line widths
32
even for shallow NV spins
40
. e spin
sensing results clearly demonstrate the potential of NV spin sensor as a prominent choice for realizing a
molecular structure microscope that is operable under ambient conditions.
Spin imaging method
Several dierent schemes are currently being considered for nanoscale magnetic resonance imaging
(MRI) using NV-sensors: scanning the probe
12,15,41
, scanning the sample
23,24
and scanning the gradi-
ent
12,35
. e rst two rely on varying the relative distance and orientation of the sensor to the sample,
thereby sensing/imaging the near-eld magnetic interaction between the NV spin and the spins from
the sample. is sensing could be performed either by passively monitoring the spin uctuation
19
or
by driving sub-selected nuclear spins by RF irradiation
18
. is approach is particularly suitable when
dilute spins need to be imaged in a sample or for samples that are sizable. ese methods read spin
signal voxel-by-voxel in a raster scanning method, so they are relatively slow but have the advantage of
not needing elaborate reconstruction
23,24
. For the method presented here to image a single molecule, we
employ scanning the gradient scheme
12,35
.

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
Here, we present a three-dimensional imaging method that is especially suiting for nanoscale-MRI
using NV spins. e multiplexed spin-microscopy method uses a projection-reconstruction technique to
retrieve the structure of a biomolecule. Figure1a shows a schematic of the setup that is similar to those
utilized in nanoscale magnetometry schemes
12,35,42
. We place the sample of interest (a biomolecule) on
the diamond surface very close to a shallowly created NV defect
43
. Achieving this could be perceived as
a dicult task, but recent advancements in dip pen nanolithography (DPN)
44
and micro-contact print-
ing (μ CP)
45
for biomolecules have been able to deposit molecules with nanometer precision. Another
approach is to cover the surface with monolayer of molecules, or to use sub-monolayer concentrations
but ensuring that a single biomolecule is able to be located within few nm from the NV sensor.
e encoding stage proceeds in the following manner: a shaped magnetic tip is positioned such that
we subject the sample to a magnetic eld gradient on molecular scales (2–5 G/nm)
4,35
. In this condi-
tion, nuclear spins present in the biomolecule precess at their Larmor frequencies depending on their
apparent positions along the gradient (Fig.1b). e spin noise signal of the precessing protons from the
sample is recorded using an NV center in close proximity
19
. Because of the presence of a eld gradient
on the sample, ne-features appear in the noise spectrum. ese unique spectral signatures correspond
to nuclear spin signal contributions from various isomagnetic eld slices
38
(Fig. 1c,d). Directions of
eld gradient applied to the molecule are changed by moving the magnetic tip to several locations.
Figure 1. Schematics of the molecular scale spatial encoding using magnetic eld gradients. (a)
Schematic representation of a biomolecule in the vicinity of an NV-center; ω
L
in the inset signies the
Larmor peak position in the spectrum. (b) Gradient encoding of the molecule’s proton density; a spectrum
is presented in direction of the gradient vector. (c,d) Schematic representation of dierent magnetic eld
gradients induced by an approached magnetic tip; insets: their inuence on the spectrum.

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
isgradient gives distinct projection perspectives while the spin noise spectrum contains the corre-
sponding nuclear spin distribution information. ese signals are indexed using the coordinates of the
magnetic tip with respect to the NV defect as Θ and Φ (measured using high-resolution ODMR) and
are stored in a 3D array of S(Θ, Φ, ω) values. We require encoding only in one hemisphere because of
the linear dependence (thus redundancy) of the opposite gradient directions. For a simple treatment,
we assume the gradients to have small curvatures when the magnetic tip to NV sensor distances are
approximately 100 nm (i.e. a far eld). is assumption is along the lines of published works and is valid
for imaging biomolecules of approximately 5 nm in size at one time
4,35
. e eects of non-axial eld from
the gradient source inuencing the spin properties of NV could be minimized by applying a static eld
(B
0
) of appropriate strength that is well aligned with the NV axis.
e reconstruction procedure is as follows: by knowing the complete magnetic eld distribution from
the tip
42
, we can calculate the gradient orientation (θ, ϕ) at the sample location for any tip position
(Θ, Φ) and rescale the spectral information to spatial information in 1D: ω = γr∇ B. In this way, the
encoded data set matrix dimensions are transformed into θ, ϕ and r.
θϕ δθϕθϕθ(, ,)∝(,,)(+ +−)
()
∭
sr Bxyz xyzrdxdydzsincos sinsin cos
2
rms
Here, B
rms
(x, y, z) is the magnetic eld uctuation caused by the number of nuclear spins N(x, y, z)
contained in the respective isomagnetic eld slices. As nuclear spin Larmor frequencies within every slice
are identical, they all contribute to same frequency component in noise spectrum
38,46
.
erefore, the 1D signal we recorded is an integrated eect from the spins in the respective planes
(refer to equation (2)). e next procedure follows along the lines of a ltered back-projection principle
to remove high-frequency noise and projection artifacts. Here, we should ensure appropriate quadratic
lters because the signal is a plane integral but not a line integral as in X-ray computed tomography
(CT)
46
. e rescaled signal s(r, θ, ϕ) is ltered using a quadratic cuto in the frequency domain. We per-
form the reconstruction in the following way; an image array is created with n
3
dummy elements in three
dimensions I(x, y, z). Any desired index r
i
, θ
j
, ϕ
k
from the signal array is chosen, and the corresponding
value s(r
i
, θ
j
, ϕ
k
) is copied to the image array at location index z = r
i
. e values are normalized to n and
replicated to every cell in the xy-plane at the location z = r
i
. e elements of the xy-plane are rotated to
the values − θ
j
, − ϕ
k
following the transformation given by ane matrices shown in equation (3).
() ()
() ()
θθ
θθ
ϕϕ
ϕϕ







′
′
′







=









−−−
−

















(− )(−)
−(−) ()




















()
x
y
z
x
y
z
1
cossin 00
sincos 00
0010
0001
cos0sin0
0 100
sin0cos0
0 001
1
3
jj
jj
kk
kk
e values are then cumulatively added to the dummy elements and stored in the transformed index.
is procedure is repeated for every element in the signal array so that the corresponding transformed
array accumulates values from all of the encoded projections. e transformed array with units in nm
contains raw projection-reconstructed images. is array is then rescaled to account for the point spread
function of NV spin and single proton interaction
23
. e resulting 3D matrix carries nuclear spin density
in every element and contains three-dimensional image of the molecule.
Results
To evaluate this technique, we considered a simple molecule of β -cyclodextrin as a molecular phantom.
is molecule has a toroidal structure with an outer diameter of 1.5 nm and an inner void of 0.6 nm
(Fig.2a). We specically selected this molecule so that we could easily visualize the extent of the struc-
tural details that can be revealed by reconstruction. We used the crystallographic data of β -cyclodextr in
from the Protein Data Bank and considered the coordinate location of all the hydrogen atoms for the
numerical simulations performed using MATLAB. Some relevant information about the molecular spin
system and parameters used for the simulations is listed in Table1.
We virtually position the molecule in the proximity of an NV defect that is placed 5 nm beneath the
surface of the diamond. At these close distances, the spin noise from hydrogen atoms is sensed by the
NV spin
19
. We compute the uctuating magnetic eld amplitude (r.m.s.) produced by proton spins at the
location of the NV spin by using the expression given by Rugar et al.
23
. e β -cyclodextrin molecule,
when placed in the vicinity, produces a eld of about 94 nT (r.m.s.), matching reported values
19
. We
subject the molecule to the magnetic eld gradients of 3 G/nm, and this produces spread in Larmor
frequencies of 30.6 kHz for the hydrogen spins in the examined volume (
3
times molecule size). As
explained before, we compute the B
rms
eld produced by hydrogen spins in each isoeld slice set by the
spectral resolution ~1.3 kHz. e
1
H spins in respective slices precess at their characteristic Larmor fre-
quencies, so the noise spectrum reveals spectral features containing information about spin density dis-
tribution along the gradient direction. We show the computed spin noise spectra (B
rms
vs. frequency
shis) from the β -cyclodextrin molecule representing two dierent gradient orientations in Fig.2b.

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
Figure 2. Simulations of projection-reconstruction method using a molecular phantom β-cyclodextrin.
(a) 3D visualization of hydrogen atoms in β -cyclodextrin molecule in a space lling representation. (b)
Simulated spin noise spectra for two dierent gradient orientations. (c) Encoded signal matrix (some slices
are omitted for visual clarity). (d) Reconstructed three dimensional image of a β -cyclodextrin molecule.
Quantity Value
Phantom molecule
Molecule name β -Cyclodextrin (Cycloheptaamylose)
Chemical formula C
42
H
70
O
35
Molecular weight 1135 g/mol (1.14 kDa)
Molecular size OD-15 Ǻ and ID- 6 Ǻ
Molecular shape Toroidal
Proton density 5.8 × 10
28
m
−3
(58 protons/nm
3
)
B
0
Field
B
0
Field 500 Gauss
1
H Larmor 2128.5 kHz
Encoding
Gradient (magnetic tip) 3 G/nm @ 100 nm
Larmor frequency spread 30.6 kHz
Spectral resolution (Δ f) 1.28 kHz
Signal B (r.m.s.)
10
4
–
1
H @ 7 nm
19
~ 400 nT
70–
1
H @ 5 nm ~ 94 nT
Signal acquisition time/point
Δ f = 1.3 kHz Δ f = 30 kHz
23
1
H using (XY8)n (SNR = 6)
23
586 sec 22 sec
+ DQC(XY8)n
47
37 sec 1.3 sec
+ Enhanced colle ction
48,50
1 sec 0.036 sec
Projections
Distinct projections
θ (0°–180°) and ϕ (0°–180°)
Total
81 [9 × 9]
3D structure acquisition time
~ 33 minutes
Table 1. Relevant parameters for imaging a molecular phantom β-cyclodextrin using NV spin based
molecular structure microscope by projection-reconstruction method.

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SCIENTIFIC RepoRts | 5:14130 | DOI: 10.1038/srep14130
For three-dimensional encoding and reconstruction, we considered 9 × 9 unique gradient orienta-
tions equispaced along dierent θ, ϕ angles. e spectral data are computed for every projection, con-
verted to spatial units and stored in a 3D matrix. is signal matrix is shown in Fig.2c as slices in the
r, θ dimensions. We apply the reconstruction algorithm as explained above to get the spatial distribu-
tion of hydrogen atoms. e structure of the reconstructed molecule clearly reveals its characteristic
toroidal shape (Fig.2d). e quality of the image reconstruction depends on the number of distinct tip
locations (or gradient orientations) used for encoding
38
. e simulations presented in Fig.2 display the
reconstruction quality achieved for a toroidal molecule, β -cyclodextrin, for a set of 81 measurements
used for encoding and decoding. If we consider the signal acquisition time of 22 seconds reported for a
single point spectral measurement
23
and calculate the time needed for achieving desired spectral resolu-
tion (~1.3 kHz), it results in long averaging times. We note that the signal acquisition time dramatically
reduces to ~1 second/point by using double-quantum magnetometry
47
together with enhanced uores-
cence collection
48
. In this case the complete image acquisition time becomes approximately 33 minutes
for the data set used here to reconstruct the molecular structure of an isolated β -cyclodextrin.
Discussion
e β -cyclodextrin molecule we have considered for simulations is a simple molecule, but it has a
characteristic toroidal structure and is easy to visualize. e results clearly showed molecular-scale res-
olution and provided information about the structure. e structural details and achievable resolution
depends on the following factors: e primary factor is the SNR obtainable when recording the noise
spectra. Demonstrations using double quantum transitions (m
s
= − 1
⇔
m
s
= + 1) achieved high-delity
spin manipulation
49
and improved sensing
47
; applying those techniques could improve signal quality. e
coherence time of the NV spin would be a factor in achieving better SNR
23
, but not the most decisive
one for noise spectroscopy, as shown using correlation spectroscopy technique to achieve sub-kHz line-
widths even in a shallow NV spin
40
. Spectral reconstruction using compressed sensing approach is
expected to considerably speed-up sensing
21,22,33,34
. In addition to this, improved uorescence collection
eciency from single NV defects can be achieved using nanofabricated pillars
50
, solid immersion lenses
51
and patterned gratings
48
. e primary source of noise being the photon shot noise, boosting signal
quality naturally increases the achievable resolution. Other techniques, such as dynamic nuclear polariza-
tion
52
, selective polarization transfer
17,19,20,22
, the quantum spin amplication mediated by a single external
spin
53
, could give additional signal enhancements. Schemes employing ferromagnetic resonances to
increase the range/sensitivity could provide other factors for resolution improvement
54,55
. e presented
method is ecient for the reconstructing structural information and spins distribution at the nanoscale
whenever it is possible to perform three-dimensional encoding. e encoding can be done either by using
an external gradient source
12,35,56
or by the eld gradient created by NV in its vicinity
20,57
.
It is important to consider nuclear spins from water and other contaminants that form adherent
monolayers on the surface of diamond
4,19,23,24
. e gradient encoding will register their spatial location
appropriately. Upon reconstruction, this would result in a two-dimensional layer seemingly supporting
the molecule of interest. is plane could come as a guide for visualization but can be removed by image
processing if required. Homo-nuclear spin interactions cause line broadening and become a crucial fac-
tor when dealing with spins adsorbed on a surface. Unwanted spin interactions can be minimized by
applying broadband, and robust decoupling methods such as phase modulated Lee-Goldburg (PMLG)
sequences
58
.
e factors determining the achievable structural resolution are the magnetic eld gradient, the SNR
of spin signals, number of distinct perspectives and the spectral linewidth of the sample. It is practical
to retrieve structural details with atomic resolutions by applying larger gradients, using SNR enhanc-
ing schemes, improving uorescence collection, and using decoupling. We have considered reported
parameters and demonstrated that our method can achieve molecular-scale resolution. Although con-
tinued progress clearly indicates that attaining atomic resolutions is within reach
35,59
. However, for many
practical applications, it is sucient to obtain molecular-scale structures that contain information rel-
evant to biological processes. e key feature of the NV-based molecular structure microscope is the
ability to retrieve the three-dimensional structural details of single isolated biomolecules under ambient
conditions without restrictions on the sample quality or quantity. ese will be very much useful for
studying hard-to-crystallize proteins and intrinsically disordered proteins. A molecular structure micro-
scope that has the potential to image molecules like prion proteins would be pivotal in understanding the
structure, folding intermediates and ligand interactions. ese insights would undoubtedly pave ways to
understand the molecular mechanisms of diseases pathways and develop ecient therapeutic strategies
for their treatment and prevention
60
.
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Acknowledgements
We acknowledge funding from the Max-Planck Society, Niedersächsisches Ministerium für Wissenscha
und Kultur and DFG Research Center Nanoscale Microscopy and Molecular Physiology of the Brain.
Author Contributions
A.L. and G.B. conceived the method. A.L. performed the numerical simulations and both authors
analysed the results. G.B. wrote the paper with input from A.L. Both authors reviewed the manuscript.
Additional Information
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Lazariev, A. and Balasubramanian, G. A nitrogen-vacancy spin based
molecular structure microscope using multiplexed projection reconstruction. Sci. Rep. 5, 14130; doi:
10.1038/srep14130 (2015).
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