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Coupling electromagnetic fields with biological processes through fluorescence has revolutionized quantitative biology9. Meanwhile, quantum-sensing tools (that is, those for which function arises from electron-spin- or nuclear-spin-dependent processes) have been developed for their unique advantages in biological applications, but have until recently been limited to realizations using non-biological probes[1](#ref-CR1 “Simpson, D. A. Quantum probes for biology: unlocking single molecule dynamics. Nano Today …
Main
Coupling electromagnetic fields with biological processes through fluorescence has revolutionized quantitative biology9. Meanwhile, quantum-sensing tools (that is, those for which function arises from electron-spin- or nuclear-spin-dependent processes) have been developed for their unique advantages in biological applications, but have until recently been limited to realizations using non-biological probes1,2,3 or measurements under ex vivo conditions4,5,6,10. We previously reported the development of a library of magneto-responsive fluorescent protein (MFP) variants derived from the LOV2 domain (broadly termed MagLOV), which exhibit fluorescence signals with large magnetic-field effects (MFEs)8 (Fig. 1a). With this work, we demonstrate that at room temperature, we can detect optically detected magnetic resonance (ODMR)11,12 in living cells expressing these fluorescent proteins, including at the single-cell level. The ODMR signature implies a quantum system with properties and dynamics influenced by the local environment, opening up a broad range of possibilities for cellular biosensing1. The ODMR arises from electron spin resonance (ESR) that we propose originates from a spin-correlated radical pair (SCRP)11,13 (Fig. 1b) involving the LOV2 domain non-covalently bound flavin cofactor chromophore. This theory is based on previous evidence14 and supported by the MFE, ODMR and spectroscopic studies we present.
Fig. 1: MFE and ODMR in MFPs.
a, Structure of AsLOV2 PDB 2V1A58 with MagLOV 2 mutations highlighted. Spin transitions driven by radio-frequency (RF) fields in the presence of a static magnetic field are optically detected via fluorescence measurements. LED, light-emitting diode. b, Simplified photocycle diagram in the case of a large external magnetic field. The radical pair is born in a triplet state (| {\rm{T}}\rangle ) with spin projections (| {{\rm{T}}}_{0}\rangle ), (| {{\rm{T}}}_{+}\rangle ) and (| {{\rm{T}}}_{-}\rangle ) (refs. 20,21) and undergoes field-dependent singlet–triplet interconversion to the singlet state, (| {\rm{S}}\rangle ), driven by nuclear-electron spin–spin interactions. c, Microscope measurement of a single cell expressing MagLOV 2 showing an MFE of about 50%. For MFE measurements, the magnetic field was switched between 0 mT and 10 mT, here with a period of 20 seconds. The intensity over time is integrated over pixels covering the single cell, with a background photobleaching trendline removed. MFE is calculated as (({\mathcal{I}}-{{\mathcal{I}}}_{\mathrm{off}})/{{\mathcal{I}}}_{\mathrm{off}}=\Delta {\mathcal{I}}/{{\mathcal{I}}}_{\mathrm{off}}). d, Data from a single cell expressing MagLOV 2 shows an ODMR signal with about 10% contrast. The static field B0 is about 21.6 mT. The blue line (shading) is the mean (standard deviation) of all single-cell data in a field of view (about 1,000 cells). Inset: microscope image cropped to a single cell expressing MagLOV 2. Scale bar, 2 μm. e, The static magnetic field B0 was varied by adjusting the magnet’s position, and the ODMR spectra recorded. The blue line shows the theoretical prediction for the resonance frequency of an electron spin with gyromagnetic ratio ({\overline{\gamma }}_{e}=28,{\rm{MHz}},{{\rm{mT}}}^{-1}) or g**e = 2.00, with the shaded region representing uncertainty (±0.25 mT) in the magnetic-field strength (as determined by a Hall probe) at the sample position.
Both MFE and ODMR signals are straightforward to detect in cells on a standard wide-field fluorescence microscope, supporting further development and application of this discovery. Beyond the ease of detecting MFPs’ magnetic resonance via emission, MFPs are advantageous over other candidate spin sensors for biological uses because they can be expressed directly in the host organism, allowing direct coupling and regulation by biological processes, and because their performance can be engineered genetically, such as through rational design or directed evolution. This engineerability is demonstrated through a selection approach previously reported8 and here used to generate protein variants specialized for sensing applications.
We demonstrate applications of MFPs as reporters that can be used for lock-in signal amplification in noisy measurement environments (as often encountered in biological applications15), and to enable signal multiplexing by engineering variants with differing dynamic responses. We also show that the MagLOV MFE is attenuated by interaction with magnetic resonance imaging (MRI) contrast agents, with a dose-dependent effect consistent with spin relaxation, implying MagLOV’s ability to sense the surrounding environment. Finally, we realize applications to spatial imaging; because the ODMR resonance condition depends on the static magnetic field at the location of the protein, it is possible to use gradient fields (as in MRI) to determine the spatial distribution of MFPs with scattering-independent measurements of a sample’s fluorescence. We demonstrate this by building a fluorescence MRI instrument based on a small-animal MRI coil with a one-dimensional magnetic gradient, which we apply to simultaneously localize the depth position of multiple bands of bacterial cells embedded in a three-dimensional volume. Ultimately, this work represents a proof of principle for MFPs and their applications, which may develop into a paradigm of quantum-based tools for biological sensing, measurement and actuation.
ODMR in living cells
Reaction yield detected magnetic resonance (RYDMR; a form of ODMR) is both a diagnostic test for the existence of a proposed SCRP16 and, owing to its relative simplicity, an effective measurement modality for performing readout from quantum-sensing devices in biological and materials applications1,2,17,18,19. ODMR studies the spin dynamics of such systems through the application of oscillating radio-frequency magnetic fields, B1, resonant with spin transition energies, and facilitates optical readouts through light emission or absorption. SCRPs are transient reaction intermediates, often generated by (photoinitiated) rapid electron transfer from a donor (in biological systems, often an aromatic amino acid) to an acceptor—here flavin mononucleotide (FMN), which serves as the field-sensitive fluorophore in our system. As electron transfer occurs under conservation of total spin angular momentum, the total spin of the radical pair is defined by that of its molecular precursor (either a singlet (| {\rm{S}}\rangle ) (S = 0) or a triplet state (| {\rm{T}}\rangle ) (S = 1), where S is the total spin quantum number). If the radicals in the pair are weakly coupled, the spin system is created in a superposition of the uncoupled states. Consequently coherent interconversion occurs between the (| {\rm{S}}\rangle ) and (| {\rm{T}}\rangle ) states, driven by the interactions between electron and nuclear spins (such as 1H and 14N; Fig. 1b). At zero and low static magnetic fields, this interconversion occurs rapidly involving all four states, but at higher fields, singlet–triplet mixing is restricted to (| {\rm{S}}\rangle ) and (| {{\rm{T}}}_{0}\rangle ) with (| {{\rm{T}}}_{\pm }\rangle ) energetically isolated from (| {\rm{S}}\rangle ) and (| {{\rm{T}}}_{0}\rangle ) by Zeeman splitting20,21. Importantly, singlet and triplet radical pairs have different fates: whereas the singlet pair is able to recombine to yield the ground-state donor and acceptor, the triplet cannot do so and instead forms other forward photoproducts (for example, by protonation or deprotonation), a route also open to the singlet pair. Under continuous illumination, the impact of the field on the singlet–triplet interconversion can be detected conveniently if either donor or acceptor or both form fluorescent excited states. In this case, a drop in fluorescence with an applied strong (about 10 mT) magnetic field (B0) is expected for a triplet-born pair as mixing into the recombining singlet state is impeded; hence, the system exhibits an MFE. Meanwhile, application of an additional resonant radio-frequency field (B1) would reconnect (| {{\rm{T}}}_{0}\rangle ) with (| {{\rm{T}}}_{\pm }\rangle ), leading to an increase in fluorescence intensity, measured as ODMR.
This hypothesis motivated consideration of MFE and ODMR measurements as approaches to confirm that the radical pair mechanism of MagLOV is triplet-born20. Previous studies have similarly explained MFEs arising from interactions between a flavin cofactor and protein in terms of the SCRP mechanism22,23,24,25,26,27,28, with the most prominent example being cryptochromes implicated in avian magnetoreception29,30,31,32. Furthermore, radical-pair intermediates are known to form in the LOV2 domain Avena sativa phototropin 1 (AsLOV2) variant C450A (the precursor protein to MagLOV)33, as well as in related LOV domains34,35,36. Parallel with our results, ODMR has recently been reported in purified enhanced yellow fluorescent protein (EYFP) at room temperature, and in mammalian cells at cryogenic temperature10, and subsequent preprints have reported ODMR in purified protein solutions of Drosophila melanogaster cryptochrome (DmCry), mScarlet-flavin and MagLOV at room temperature, as well as mScarlet-flavin in Caenorhabditis elegans at room temperature32,37.
First, we measured the MagLOV MFE (see example trace in Fig. 1c) using a custom-built fluorescence microscopy platform, confirming that the variant MagLOV 2 exhibits a large MFE of (\Delta {\mathcal{I}}/{{\mathcal{I}}}_{\mathrm{off}}=-50 % ), where ({{\mathcal{I}}}_{{\rm{on}},{\rm{off}}}) is the fluorescence intensity when the electromagnet is on or off, and (\Delta {\mathcal{I}}={{\mathcal{I}}}_{{\rm{off}}}-{{\mathcal{I}}}_{{\rm{on}}}). In Fig. 1d, we show the ODMR resonance of a single cell and the ODMR resonance averaged over many (about 1,000) cells in a field of view. As expected, the signal-to-noise is significantly improved by averaging over many cells; however, it is also possible to extract an ODMR signal from a single cell, with an ODMR contrast of 10% (Fig. 1d). The remarkable per-cell magnetic sensitivity of η0 = 26 μT Hz−1/2 (Supplementary Note 1) is afforded by a combination of optical detection and the high spin polarization of the radical-pair system1. Next, we recorded ODMR spectra at various static (B0) fields by adjusting the z position of the static magnet (Fig. 1e). The central ODMR resonance follows the expected ESR relationship ({f}_{\mathrm{RF}}={\bar{\gamma }}_{e}{B}_{0}) (with ({\bar{\gamma }}_{e}) the electron gyromagnetic ratio), confirming that the radio-frequency field is driving spin transitions of a spin-1/2 electron. Finally, we performed additional control experiments confirming the ODMR signal’s source, verifying against negative controls that an ODMR signal is present only when the MagLOV protein is present (Supplementary Note 2).
Engineering of MFEs
The AsLOV2 domain has been widely used as a starting point for engineering optogenetic and other light-dependent protein functionalities38. For MFPs, depending on a target application (such as lock-in signal detection, multiplexing or sensing), one could choose to optimize for metrics including MFE size, rate of MFE saturation, ODMR contrast, ODMR saturation rate and others. Here we demonstrate this potential by performing selection to improve MFE contrast and saturation rate, generating variants specialized for applications demonstrated later in our work.
Starting from ancestor variant AsLOV2 C450A (refs. 8,39), we used directed evolution to create variants of MFPs (summarized in Supplementary Note 3). This engineering process involved successive rounds of mutagenesis (introducing all single amino acid changes to a given variant), followed by screening of samples from this variant library to select for increased MFE magnitude, eventually yielding MagLOV 2. To demonstrate the possibility of selecting on another metric using the same methodology, we further engineered MagLOV 2 by selecting for maximization of saturation rate (rather than magnitude) of MFE, producing ‘MagLOV 2 fast’. We chose four variants to characterize in detail, which was done both using single-cell microscopy (Fig. 2a) and measurement of bulk cell suspensions (Supplementary Note 4).
Fig. 2: Engineering of MFE and ODMR dynamics.
a, MFP variants were engineered by mutagenesis and directed evolution; from AsLOV2 R2 to MagLOV 2 selection was performed to increase the MFE magnitude at saturation, whereas MagLOV 2 fast was selected for increased rate (that is, reduced time constant τ when the MFE with time t is modelled as e−t/τ (ref. 25), shown in red fit). In these measurements, a magnetic field of B0 = 10 mT was switched on and off with a period of 20 seconds. The traces shown are the average (and standard deviation, shaded) over multiple periods. As a result, part of the variability results from the background photobleaching curve fit which attempts to match the true background curve (see Supplementary Note 9 for details). b, A similar experiment was performed using ODMR on-resonance, with a constantly applied static field of B0 = 21.6 mT and corresponding resonant field B1 frequency of ωRF = 604 MHz switched on and off with a 20-second period, averaged as above. Both sets of experiments were performed in identical imaging set-ups with an illumination intensity of about 800 mW cm−2 at 450 nm. Note that B0 in a is half that of B0 in b, explaining why the ODMR contrast is in some instances larger than the MFE.
The observed differences in MFE can be interpreted based on past work investigating flavin magnetic-field-sensitive photochemistry: MFE enhancement kinetics (that is, time to MFE saturation) are determined by the ratio between the rates that donor and acceptor free radicals return to the ground state25. With the mutations introduced in MagLOV 2 fast, the time constant of the response is decreased, which may indicate that the acceptor return rate increases relatively to the donor. Interestingly, we observe the ODMR contrast and rates of each variant differ significantly (Fig. 2b), but not necessarily in simple correlation with MFE magnitude. This raises the possibility of engineering orthogonal fluorescence signatures, expanding again the number of tags available for multiplexing. For instance, with further engineering the total might be (number of emission colours) × (number of resolvable MFE signatures) × (number of resolvable ODMR signatures).
Bound flavin and radical-pair mechanism
Adopting the SCRP model prompts consideration of the electron donor and acceptor identities. Both previous studies33,35 and our spectral data (Fig. 3) support the identification of the acceptor molecule as the FMN cofactor. For all variants of MFPs expressed in cells, we find that the wavelength-resolved fluorescence intensity modulated by the applied magnetic field ((\Delta {\mathcal{I}})) (Fig. 3a,b) matches the FMN emission spectrum39,40, supporting that both MFE and ODMR are detected on the flavin emission. The excitation spectrum shows vibrational fine structure (Fig. 3c) and is in excellent agreement with the dark-state absorption spectrum of AsLOV2 C450A (ref. 41), confirming that the emission originates from bound FMN. Furthermore, this corroborates control experiments (Supplementary Note 2) that show that observed ODMR signatures are not a result of cellular autofluorescence. The absorption spectrum of purified MagLOV 2 fast, before and after continuous irradiation with blue light, is shown in Fig. 3d (the full temporal evolution is provided in Supplementary Note 4). The slow formation of the stable radical FMNH• after several minutes of illumination is characterized by the appearance of a broad band featuring 2 peaks centred around 575 nm and 615 nm, as observed for AsLOV C450A, and accompanied by the expected decrease in ground-state absorption, centred around 450 nm (ref. 41). At later times, most of the flavin is converted to the fully reduced form, FMNH−, resulting in a rise in absorption around 325 nm, although some remains present as FMN and FMNH•. The blueshift in MagLOV-bound FMN absorption relative to AsLOV C450A, evident both in the excitation and absorption spectra, may indicate a change in polarity of the flavin binding pocket. The observed photostability of MagLOV correlates with the slow formation of FMNH• on a timescale of minutes in these conditions. In comparison, related flavoproteins, such as cryptochrome, are reduced to the semiquinone state within seconds, even under much weaker irradiation intensities42. Unlike the recently reported MFE in mScarlet3 and FMN mixtures, which rely on a bimolecular reaction between the excited-state mScarlet3 and a fully reduced flavin in solution28, MagLOV requires no pre-illumination or additives for an MFE to develop as the FMN is non-covalently bound.
Fig. 3: Spectroscopic characterization evidences bound flavin-based radical pair.
a, Normalized emission spectra with 450-nm excitation acquired for cell suspensions in PBS buffer. The spectra have been smoothed with a moving average filter of 1-nm bandwidth. b, Wavelength dependence of magnetic-field-induced change of emission intensity where (\Delta {\mathcal{I}}={\mathcal{I}}({B}_{0}=10,{\rm{mT}})-{\mathcal{I}}({B}_{0}=0,{\rm{mT}})). It is noted that here we display the absolute intensity change as division by ({\mathcal{I}}({B}_{0}=0,{\rm{mT}})) would obscure the wavelength dependence. A moving average filter of 1-nm bandwidth was applied to the spectra. c, Normalized excitation spectra for 510-nm emission for bulk MagLOV cell suspensions in phosphate-buffered saline (PBS) buffer. Vibrational fine structure (multiple peaks) in the S0 → S1 and S0 → S2 bands (where Sn is the nth excited singlet state) centred at about 450 nm and about 350 nm, respectively, indicates that the emitting flavin is bound. d, Ultraviolet–visible absorption spectrum of purified MagLOV 2 fast at different times after the onset of blue LED illumination. Inset: a reduced wavelength range with the characteristic absorption of FMNH•. Literature reference spectra are shown as dashed lines41,59,60. e, Proposed photoscheme. Following photoexcitation (kExc), the excited singlet flavin (1FMN*) can either emit a photon (kF) or undergo intersystem crossing (ISC) to the excited triplet state (3FMN*). The primary radical pair (RP1) is formed by electron transfer (ET) from a nearby donor, and can undergo singlet–triplet interconversion, which is altered in the presence of an applied magnetic field (B). Only the overall singlet RP can undergo back-electron transfer (BET) to reform the ground state, whereas either RP can form secondary (perhaps spin uncorrelated) radicals (RP2) through protonation and/or deprotonation reactions (kH/Dep). These long-lived secondary radicals return to the ground through slow redox reactions (kFMNH, kD).
The formation of FMNH• from the excited triplet state, 3FMN*, probably proceeds via initial formation of FMN•− in an SCRP on a nanosecond timescale as in AsLOV C450A (ref. 33), followed by slow protonation. Alternatively, FMNH• could be formed by proton-coupled electron transfer. A proposed photoscheme is given in Fig. 3e, and a model based on this photoscheme is simulated in Supplementary Note 5, which successfully fits both the experimental MFE and ODMR data. In cryptochrome, the SCRP is formed by a cascade of electron transfers along a tryptophan tetrad30; however, a single donor aromatic amino acid can be sufficient, as demonstrated by the magnetosensitivity of cryptochrome-mimicking flavomaquettes43,44 and FMN bound inside the bovine serum albumin protein45. Regarding the donor species, single-point mutations in AsLOV2 C450A leading to quenching of the emissive NMR signal suggest W491 as the electron donor46, which was corroborated by isotopic labelling of Trp residues47. However, given the extent of mutations in the variants studied here, we cannot confirm that W491 is still the counter-radical. For example, in the structurally related iLOV-Q489, derived from the Arabidopsis thaliana phototropin-2 (AtPhot2) LOV2 domain, transient absorption spectra revealed that a neutral tryptophan radical, Trp•, is formed in conjunction with FMNH•, and photoinduced flavin reduction in single-point mutations of selected tyrosine and tryptophan residues suggested that several amino acids might be involved in SCRP formation48.
Multiplexing and lock-in measurements
Our library of MFP variants shows differences in the rate and magnitude of response across both MFE and ODMR characterization (Fig. 2). Where such differences can be engineered orthogonally between variants, they open the possibility of using libraries of MFP reporters as a multiplexing tool to extract several signals from a single measurement modality (Fig. 4). As a demonstration, we characterized two cell populations expressing different MFP variants, for which distributions of MFE saturation timescales fit to single cells show strong separation (Fig. 4b). This enabled population decomposition when we applied a classification algorithm to a mixed population of about 2,000 cells (Fig. 4c). The classifier was trained on MFE traces normalized by amplitude (on a per-cell basis), meaning that it utilizes only the relative shape of the curves and not the magnitude of the MFE. Therefore classification is robust to scaling or offsets in the absolute brightness of the signal, as might be caused by scattering or autofluorescence (which pose practical limits on many sensing applications as described in Supplementary Note 6). Future application of this subpopulation labelling technique would benefit from engineering of variants with greater variation in dynamics such that the separation of histograms (as in Fig. 4b,c) is significantly greater than each population’s intracellular variability.
Fig. 4: Multiplexing and lock-in applications using MFE.
a, MagLOV variants can be used to label cell populations, which can be identified when mixed based on differing MFE responses. b, Exponential curves with timescale parameter τ were fit to the MFE of each cell in each field of view. Here populations are measured separately, illustrating that MagLOV 2 has a greater MFE saturation timescale than AsLOV R5. c, Populations were mixed in an equal ratio and a classifier (Methods) trained on the time-series data in b was used to classify the mixture into two subpopulations. d, Schematic of the microfluidic chip, composed of single-cell-wide trenches (vertical channels). Cells were engineered to weakly express MagLOV and co-express mCherry for ground-truth identification, and mixed with another cell population expressing only EGFP. Cells are classified based on MFE response, demonstrating the possibility of identifying MagLOV reporters mixed with other, non-magnetic responsive fluorescent reporters in the same spectral range, and under conditions where MagLOV produces only a small signal. e, Cropped view of single trenches, with cells circled in red as identified by a cell-segmentation algorithm. Scale bar, 2 μm. f, Time series of the 450-nm illumination fluorescence for the individual cells depicted in e over time, as a magnetic field B0 = 10 mT is switched on and off (red line). Traces for each cell in the trench (grey) and the average over all the cells in the trench (black) are shown. g, Confusion scatter plots for classifying whether cells express MagLOV or EGFP based on magnetic response, taking presence of mCherry fluorescence (red highlights) as ground-truth control and using the MFE lock-in value as the predictor. The balanced accuracy by cells and by trenches is 0.99. h, The standard deviation σ of the lock-in values in g is calculated between cells in each of the trenches (blue histogram), and between all cells in all trenches.
Using a microfluidic set-up (in which populations of five to eight clonal cells are confined in individual trenches; Supplementary Note 7), we further investigated the sources of intracellular variability of MFP variants, and demonstrate the possibility of lock-in detection in weak signal environments. With MFE-based lock-in detection45, cells with minimal MagLOV expression could be identified distinctly from cells expressing enhanced green fluorescent protein (EGFP)49 with a balanced accuracy of about 0.99 (using a second fluorescence reporter, mCherry, as ground truth), with accuracy improving when averaging over a trench compared with distinguishing single cells (Fig. 4e–g). This approach allows variability to be attributed to inter-clonal or intra-clonal sources; we observe that mean intra-trench variability (quantified by standard deviation over cells in one trench) is approximately half that of the variability over all MagLOV-positive cells (Fig. 4h). This suggests that approximately one-quarter of the total variance arises from intra-clonal noise sources (for example, phenotypic variability over two or three generations, camera and accompanying measurement noise), with inter-clonal sources (longer-term phenotypic variability, variation in local environment) contributing the remaining three-quarters.
Application to spatial localization
Methods for the spatial localization of fluorescence signals in biological samples such as cell cultures and tissue samples are of significant interest for both diagnostics and treatment development50,51. However, techniques based on localization using fluorescence, for example, fluorescence-modulated tomography, are challenging owing to the inherent scattering and absorbing nature of tissue, and the requirement to localize the fluorescence via detailed modelling and inversion of the optical signal52. As such, we sought to explore whether MagLOV could be used as a fluorescent marker localized by optically detected MRI.
First, we tested localizing MagLOV in the wide-field microscope set-up, using a permanent magnet to vary the resonance condition across the field of view (Fig. 5a). The sequence of images acquired during a radio-frequency B1 frequency sweep was integrated over cross-sections in which the B0 field is approximately constant, yielding an image (Fig. 5b) where the frequency of peak response (y axis) denotes the position in space along the z axis, which varies across a 0.5-mm field of view as anticipated for a field gradient of 1 mT mm−1.
Fig. 5: Spatial localization using ODMR.
a, Schematic of the wide-field microscopy set-up for demonstrating localization of cells in a two-dimensional plane. The permanent magnet creates an approximately linear gradient field B0 along the z axis, perpendicular to the radio-frequency B1 field (which rotates at the Larmor frequency around z) generated by the radio-frequency coil. The frequency of B1 is scanned while the entire field of view is imaged. b, Subsequently, the images are divided into regions (red highlight in a) and integrated over that region. The integrated brightness versus frequency forms a one-dimensional spatial map—in this case, the sample is present in the entire field of view, thus we see a diagonal line, shifting by about 14 MHz over the 0.5-mm field of view as anticipated for the 1 mT mm−1 field gradient.** c**,d, Schematic of the custom-built MRI set-up illustrating the optical illumination and collection paths (c) and the magnetic-field gradient inside the resonant MRI coil (d). e,f, We embedded cells expressing MagLOV 2 fast (chosen for its ODMR contrast, fast saturation and low overall brightness to make detection challenging) into a polydimethylsiloxane (PDMS) sample at two different positions along the coil axis separately (e) and simultaneously (f). Lock-in ODMR detection was used to locate the samples along the coil axis. The red and blue curves are raw measurements, and the grey shaded regions are after processing with a deconvolution algorithm (which uses the known ESR linewidth from Fig. 1 but makes no assumption about the number or location of peaks). The location of the samples is identifiable on their own, and resolvable via deconvolution together. Against a ground-truth separation of 7.5 mm, deconvolved individual samples had a calculated peak separation of 6.6 mm and the combined sample 6.1 mm. Using the individual sample data to calibrate the measurement yields a combined-sample distance estimate of approximately 6.9 mm.
Next, we converted a preclinical MRI 28-mm-diameter ‘birdcage’ radio-frequency coil, used for creating a spatially highly homogeneous B1 radio-frequency field at 500 MHz, into an optically detected fluorescence MRI instrument via integration of a fibre-coupled illumination system and imaging using a photodiode (Fig. 5c,d and Supplementary Note 8). It is noted that the photodiode is in effect a ‘single-pixel’ detector, meaning that it collects no spatial information and directional scattering of light would cause no reduction in information of final signal (apart from a possible decrease in absolute brightness). As the static B0 field is swept, the radio-frequency field B1 is switched on and off such that the ODMR contrast can be measured via lock-in detection. We found that good localization could be achieved when isolating single samples at different positions (Fig. 5e), and despite an increase in noise, deconvolution of the signal enabled two samples at diff