Quantum-enhanced diamond molecular tension microscopy for quantifying cellular forces

The constant interplay and information exchange between cells and the microenvironment are essential to their survival and ability to execute biological functions. To date, a few leading technologies such as traction force microscopy, optical/magnetic tweezers, and molecular tension–based fluorescence microscopy are broadly used in measuring cellular forces. However, the considerable limitations, regarding the sensitivity and ambiguities in data interpretation, are hindering our thorough understanding of mechanobiology. Here, we propose an innovative approach, namely, quantum-enhanced diamond molecular tension microscopy (QDMTM), to precisely quantify the integrin-based cell adhesive forces. Specifically, we construct a force-sensing platform by conjugating the magnetic nanotags labeled, force-responsive polymer to the surface of a diamond membrane containing nitrogen-vacancy centers. Notably, the cellular forces will be converted into detectable magnetic variations in QDMTM. After careful validation, we achieved the quantitative cellular force mapping by correlating measurement with the established theoretical model. We anticipate our method can be routinely used in studies like cell-cell or cell-material interactions and mechanotransduction.


Introduction
Biochemical factors in the environment are known to affect living organisms and have been investigated for quite a long time (1, 2). Interestingly, recent evidence has also shown that physical cues such as mechanical forces can constantly be generated inside biological systems and get transmitted to their surroundings (3)(4)(5). The involved mechanical information not only result in deformation and motion but also stimulate physiological functions of lives (6)(7)(8). Normally, the forces associated with a single cell can range from piconewtons to several nanonewtons, corresponding to molecular and cellular level, respectively (9,10). In this regard, inventing a reliable tool to quantify the mechanical interactions between the cell and substrate, especially at the single cellular level, is crucial for our basic understanding of many important biological processes such as morphogenesis, tissue repair and tumor metastasis (5,11).
Various methods have been successfully developed for measuring cellular adhesive forces in the past few decades. In general, these approaches can be divided into three categories: 1) the first type relies on monitoring the deformation of the substrate to estimate the force, with prime examples being the so-called cellular traction force microscopy (TFM) and micropillar-based force measuring apparatus (12); 2) the second category is the single cell force spectroscopy by using an instrument like atomic force microscopy (AFM) or magnetic/optical tweezer systems (13); and 3) the third kind is the molecular tension-based fluorescence microscopy (MTFM) or similar tension gauge tether (TGT) systems with the help of force-sensitive fluorophores (14,15).
Although these techniques have been well established as standard tools in mechanobiology study, several issues have also been raised during their implementation in actual cellular measurements. For example, the intrinsic experimental caveats of conventional TFM are known to be computationally intensive and, furthermore, such method can mainly sense the shear tractions at nanonewton (nN) level (16,17). In addition, the MTFM and TGT suffers from photo-bleaching of fluorophores with a stochastic nature (18,19). Therefore, the development of a new technique to accurately measure the cell adhesive forces, preferred in a fluorescent label-free manner, is vital to the development of mechanobiology.
Despite all these exciting progresses, to the best of our knowledge, the direct sensing of weak mechanical signals in living systems has never been achieved yet.
Here, by combining next-generation quantum measurement platforms, with innovative biointerface engineering technologies, we have developed a novel method,

Construction of a robust quantum diamond biosensing platform
The key of our novel sensing platform, namely the QDMTM, was to correlate (as shown in Scheme 1) NV spin relaxometry with force-induced polymer stretching, which was documented using the well-known Worm-Like Chain model (55). In the case where the magnetic labels (Gd 3+ ions) were attached to the diamond surface through spring-like polymer, the relationship between the relaxation rate Γ1 and NV-Gd 3+ distance h has been known to obey the following relationship (56): We adopted our previously developed single-crystalline ultrathin diamond membrane (~ 30 µm) with shallow implanted NV centers to work as a widefield quantum sensing substrate. To enable the NV-based measurement of the integrin-based cell adhesive force, such mechanical signals can be converted to magnetic ones using a transducer, i.e., the tailor-made force-responsive polymer (Fig. 1A, Scheme S1 and fig.   S1). Specifically, it contained an integrin ligand Cyclo(RGDfK) and a molecular magnet Gd 3+ on one side, the main molecular chain polyethylene glycol (PEG) serving as the spring element in the middle and a silane anchor on the other end for immobilization ( fig. S2). The PEG chain serving an entropic spring was capable of sensing forces on the order of a few tens of pN (19) and provided a bioinert background to avoid non-specific interactions with cells (57). The deformation of the PEG chain altered the distance between the Gd 3+ ions and the NV centers, leading to the change of NV spin relaxation time T1 (1/Γ1) which can be quantitatively measured (43).
Anchoring these force-responsive polymers within the effective sensing range of NV centers (~25 nm above the diamond surface (58)), meanwhile, minimizing the thickness of any functionalization layer while retaining excellent surface morphology and coverage is crucial for the T1 test. To enable the conjugation of the designed polymers to the chemically inert surface of diamond, we firstly managed to deposit a stable layer of hybrid silica, and such an interface with high reactivity without further activation was sufficient to enhance intra-layer interactions (59) and stabilize the PEG coating. Benefited from this silica layer, the polymer could be easily immobilized onto the diamond surface to construct the desired force sensing platform in mild conditions to avoid detrimental influence on the spin property of NV centers ( fig. S3). The X-ray photoelectron spectroscopy (XPS) results confirmed the successful conjugation of the force-responsive polymers onto the diamond surface ( fig. S4 and Table S1). The length of the immobilized PEG polymer was ca. Meanwhile, no cells could adhere on the polymer coatings without RGD ligands for at least 7 days ( Fig. 1E and fig. S8). These results demonstrated that the polymer coating only interacted with cells through integrin-RGD adhesion and could keep stable for at least several days in cell incubation conditions. This was actually consistent with our reference test with the same polymer brushes on silicon wafer, i.e., the thickness of the PEG-coated layers (containing hybrid silica layer) kept constant after 5 days of immersing in phosphate-buffered-saline (PBS) buffer ( fig. S5).

Validation of quantum-enhanced force sensing
To demonstrate the sensing capability of our customized widefield quantum diamond microscope (detailed in the methods section), we firstly investigated the influence of ferritin (a kind of paramagnetic species (62) as shown in Fig. 2A) solution on the NV spin relaxation in constructed PEGylated sample (without RGD ligands and magnetic labels). As shown in Fig. 2, B and C, the AFM image clearly indicated that there has been a dense packaged layer of ferritin formed on top of the diamond surface (after immersing in 1 mg/ml aqueous ferritin solution for 2 hours without rinsing). In the corresponding T1 mapping images and histogram (Fig. 2D, left and middle panel, Fig.   2E), we found that the ferritin-deposited diamond surface showed a significantly shorter T1 value (~ tens of µs), i.e., almost one order of magnitude lower than that in PBS cases (~ hundreds of µs). These findings indicated that the presence of ferritin molecules (or gadolinium ions as shown in fig. S9) significantly affects the NV spin relaxation as revealed by T1 values (62). Interestingly, we have actually found the T1 value could be recovered after gently washing with PBS ( Fig. 2D, right panel, Fig. 2E), indicating the coated PEG chains successfully prevented the non-specific adsorption of proteins. To validate the designed QDMTM, we firstly managed to alter the conformation (collapse-extended) of force-responsive polymers in model conditions, which mimics the polymer chain stretched by cellular forces. Specifically, it is well-known that the hydration (e.g., sample immersed in water) could extend the PEG chains while dehydration (e.g., sample exposed to air) would collapse the PEG chains (63).
Therefore, the distance between the Gd 3+ magnetic labels and the NV centers can be

Semi-quantitative mapping of cell adhesive forces
By seeding the maturely adhered NIH 3T3 cells on diamond surface modified with force-responsive polymers, we started to demonstrate the detection of cellular adhesion forces using QDMTM. Cell adhesive force is transmitted to the environment through integrin-ligand interactions (64), and the force-responsive polymers were used to convert the mechanical input to the magnetic output. As illustrated in Scheme 1, the RGD end of the polymer was assumed to be recognized by integrins and dragged by the cellular traction force. The PEG entropic spring was stretched, and the Gd 3+ magnetic labels, located just next to the RGD ligands, were moved away from the diamond surface. This distance change could be quantitatively detected via the NV spin relaxometry, i.e., the larger force-induced conformation changes (of polymer) the longer the T1 value is (of NV centers).

Quantitative mapping of cell adhesive forces
The force exerted on the QDMTM can be further quantified, as the cell adhesive forces could be revealed by relative T1 changes (Fig. 5). Based on the model built above for measuring the cellular force (Fig. 6A), the distance between Gd 3+ molecules and NV Information simulation). Based on the simulation result, extensions of PEG are ranging from 3.5 nm to 5.5 nm, and the tension loaded on single PEG is around 10 pN, which agrees with the previous study (19,70). This semi-quantitative model can guide choosing suitable PEG length to tune the 'most sensitive range' of our sensor, making it competent for sensing different force ranges, enlarging the application scenarios of this new development kit. Overall, this novel force-sensing tool, namely the QDMTM, will allow to enhance sensitivity as well as resolution in time and space in comparison to available traction force microscopy. Also quantum tension sensors may be reused after cleaning which will also enhance absolute precision of sensors for comparing different samples. It can fundamentally change the way how we study important issues like cell-cell or cellmaterial interactions, and hence bring impact to the field of biophysics and biomedical engineering. In addition, the data on the cellular forces transmitted through cell adhesions to be generated by this study are also expected to be useful in guiding and assisting the development of future theories on mechanosensing and mechanotransduction. Meanwhile, the silica QCM chips were used for the QCM test. Detailed information on the test parameters has been provided in the Supporting Information.

Widefield quantum diamond microscopy
This wide-field quantum diamond microscope mainly includes three subsystemsthe optical system, the MW system and the control system.

NV spin relaxometry measurements
After being polarized by a green laser pulse, the electron spin of the NV centers will relax to thermal equilibrium state from polarized state which is named longitudinal relaxation. The longitudinal relaxation rate Γ1 is principally dominated by spin-lattice interaction and fluctuating magnetic field generated by the nearby spin impurities, such as ferritin and Gd 3+ used in the experiments to modulate the relaxation rate.
In our sensing protocols, the NV center is polarized to |0⟩ state by a 1 μs laser pulse with the power of 18 kW/cm 2 firstly. After 500 ns, a -pulse of microwave is exerted to flip the NV center from |0⟩ state to |1⟩ state. Then after a waiting time , another 1 μs laser pulse is applied to read out the spin state of the NV center and polarize the NV center. The above pulse sequences as a unit sequence will be repeated tens of thousands of times to obtain a bright enough fluorescent signal. Due to the camera's inability to switch on and off quickly, the camera remains in an exposure state throughout the tens of thousands of repetitions of the unit sequence with a specific waiting time . To reduce the influence of background signal, we repeated the above unit sequence but turned off the microwave to perform a control measurement.
Therefore, the NV center relaxed from the |0⟩ state to the |1⟩ state in this measurement. By performing element-wise division between the image matrices without and with microwave, the impact of the background signal will be minimized and the T1 trace of the fluorescence intensity could be obtained. Finally, through fitting the T1 fluorescence trace with the formula of ( ) = • −( ) + , we can get the T1 value.

Seeding cells on the diamond-based sensing platform
According to the cell force measurement, we immobilized force sensor diamond (2 mm × 2 mm× 0.03 mm, Applied Diamond Inc., Electronic Grade) onto microwave antennas with an omega structure (280 microns in diameter) by using PDMS cured at 60°C (Dow Corning Sylgard 184; monomer: crosslinker = 10: 1). Samples were sterilized for 1 hour with 70% ethanol. The density of 10 4 /ml NIH 3T3 cells were cultured on the above-encapsulated diamond slides for 6 h and stability of cell adhesion was observed.

Measurements of cell adhesion forces via NV spin relaxometry
Cells were washed once with cell culture medium and twice with PBS before fixation with 4% paraformaldehyde at room temperature for 15 min. Force sensor samples with adherent mature cells were then washed three times with PBS. Thoroughly cleaned diamonds were immersed in PBS for T1 testing at room temperature. For ΔT1 of Fig.   5D obtained by selecting the region T1 (Fig. 5, A to C, marked i, ii, iii and iv) minus the reference value (obtained by Fig. 3E). given. (55,(73)(74)(75)(76)(77)(78)(79)(80)(81)(82) Supplementary Materials for

Synthesis of BRD (BCN-RGD-DOTA)
Synthesis of BRD was carried out in two-step reaction with high conversion rate, as shown in scheme S1. Scheme S1.
General procedure for the synthesis of the BCN-RGD-DOTA (BRD).

Synthesis of Silane-PEG-N3
The 1 ml toluene was added into the flask under argon flux to dissolve N3-PEG-NH2

Constructing force-responsive polymers on diamond surface
Single-crystalline diamond slides were sonicated in acetone and isopropanol for 5 min in each and dried with nitrogen. The diamond slides were cleaned and chemically activated by freshly prepared piranha solution (H2SO4/H2O2=7:3) at 90°C for 1 hour, followed by thoroughly rinsing with ultrapure water and ethanol as well as drying with nitrogen (the samples were named as Pristine Diamond).
The 20 µl tetraethyl orthosilicate (TEOS) was added to a mixture of ethanol (2850 µl), ultrapure water (150 µl) and hydrochloric acid (10 µl) by dropwise for 1 hour. Then The PEGylated surfaces were immersed in 1.0 ml of the BRD solution for 24 hours.
Afterwards, the slides were removed and washed with dimethylformamide and ethanol, followed by drying with nitrogen to obtain biofunctionalized diamond surfaces. Finally, the gadolinium ions were loaded by immersing the BRD-modified diamond slides into 0.5 mg/ml GdCl3*6H2O water solution for 2 hours and washed with ethylenediaminetetraacetic acid disodium salt (EDTA-2Na, 0.4 mg/ml) for 1 hour. after the chelation, the slides were cleaned with water and ethanol, and dried with nitrogen to achieve force-responsive polymers modified diamond surfaces (the samples were named as Force sensor).
Silicon wafers were used for similar modification processes, named Si, Si-Silica-coated, Si-PEGylated, and Si-Force sensor.

Reuse of the diamond slides
The Force-sensor can be simply removed by NaOH and piranha solution, providing an easily recyclable NV quantum sensor. Briefly, the functionalized diamond slides were firstly immersed in 1 M NaOH solution at 80°C for 12 hours, and then in piranha at 90°C for 1 hour. The corroded slides were extensively rinsed with ultrapure water and sonicated with acetone and 2-isopropanol for 5 min in each and dried with nitrogen.
Besides, the slides can be also soaked in a 1:1:1 mixture of nitric acid, perchloric acid and sulphuric acid at boiling temperature (73).   In addition, after the chelation, EDTA-2Na was used to clean the free Gd 3+ trapping in the PEG chains. The stability constants of EDTA-2Na with Gd 3+ ions were lower than that of DOTA, thus, the chelated Gd 3+ was stable during purification (75).

Stability test
For the coating stability test, we soaked the Si-PEGylated in PBS solution for 5 days and then rinsed them three times with ultrapure water before drying with nitrogen gas.

Atomic force microscopy (AFM)
The surface morphology of the modified diamonds was recorded by NanoWizard 4 XP scanning probe microscopy (   After 3 days of cell culture with NIH 3T3 fibroblasts, the tissue culture polystyrene (TCPS) and Silica-coated diamond surfaces were covered with well-spread cells.
Siloxane materials are reported to be not hydrothermally stable, herein, BTSE not only produces more Si-OH but also increases the stability of the silica layer (76,77).
Besides, the hybrid silica can be further modified without decreasing the sensitivity of the measurement. These data demonstrated that the introduction of an "active" hybrid silica layer on the diamond surface is imperative to stabilize the force-responsive polymers.

Fig. S8.
Optical microscopy images of NIH 3T3 cells adhered on the Silica-coated, PEGylated functional diamond surfaces after 1 day, 2 days, 3 days, and 7 days of cell culture (Scale bar indicates 100 m).
When the diamond slides were immersed in the 1 mM GdCl3 solution, the T1 decreased 13 times compared with it in the pure water. We blocked part of the diamond with polydimethylsiloxane (PDMS). The PDMS decreased the T1 value of the slide to 68% in pure water, which may attribute to the impurity of the metal catalyst for PDMS synthesis (78). After immersing in the GdCl3 solution, the T1 value of the PDMS blocked region was 4 times higher than the unblocked region because the PDMS reduced the diffusion of Gd 3+ to the diamond surface.   Representative fluorescence images of F-actin and vinculin of NIH 3T3 staining after T1 measurements. Yellow boxes indicate pseudopodia and green boxes indicate focal adhesions, respectively. According to the images, the length of ~3 μm can be defined as the cell edge region (Fig. 5, A to C marked i, ⅱ, ⅲ, ⅳ).
According to the stability test of the functional coatings, NIH 3T3 cells were seeded on the functionalized diamond slides (3 mm × 3 mm × 0.25 mm, Element Six, Optical Grade) for 16 hours to 7 days, followed by optical or fluorescent images acquisition.

Immunofluorescence staining and microscopy
Cells were washed once with cell culture medium and twice with PBS before fixation with 4% paraformaldehyde at room temperature for 15 min. Samples were then washed three times with PBS. Cells were permeabilized with 0.25% v/v Triton-X 100 in PBS for 10 min at room temperature, then washed three times with PBS. Nonspecific antibody adsorption was blocked by incubating samples with 1% w/v bovine serum albumin in PBST (0.1% v/v Triton-X 100 in PBS (PBST)) at room temperature for 45 min. Following primary antibody incubation (1:100, vinculin, Thermo), samples were washed twice with PBST and three times with PBS. Samples were then incubated with secondary antibodies, phalloidin 488 (Abcam, 1:1000) and DAPI at room temperature for 1 h, followed by washing three times with PBS. Immunofluorescence images were acquired and analyzed via confocal microscope (Zeiss710).

The physical model of calculating Gd's influence on the T1 of NV Center
From Fermi's Golden rule, we can estimate the relation rate of NV center (79): where 1 is the T1 of NV in the bulk diamond. (We set it as 900 ns in this simulation based on experiment data.), 0 is the NV zero-field splitting, where 0 2 = 2.87 (80).
is the gyromagnetic ratio obtained from the experiment. and are shown in Fig. S12.

Fig. S12.
The schematic diagram of the model. The determination of simulation parameters a. The density and depth of NV centers: The same bulk diamond as used in other work has been adopted in our experiments (56). The density and depth of NV centers within the bulk diamond are 1000/um 2 and 5 nm, respectively.
b. The density and depth of Gd 3+ molecules: The initial z-location of the Gd 3+ is determined by the Flory model of the PEG. For the PEG we use (Mw: ~1000 g/mol), the Flory radius of the PEG is R F = N 3 5 • l ≈ 2.25nm, if we also take the radius of Gd 3+ molecule (about 0.51 nm) into consideration, the Gd 3+ molecule is 2.76 nm away from the diamond surface at their free state. Based on the T1 value we measured after complete force-responsive polymer modified diamond, the Gd 3+ molecule density is set to 9000/μm 2 in order to match the experimental data.

The effective interaction range between Gd 3+ molecules and NV centers
For a single NV center, we need to consider the influence of adjacent Gd 3+ molecules.
In the calculation, we take the Gd 3+ molecules inside a circle region around NV centers into consideration. We call the region effective interaction range. Based on the calculation (Fig. S13), for a single NV center, if the interaction range is larger than the effective interaction range, the additional Gd 3+ will not influence the longitudinal relaxation process of the NV centers. Based on this, for each NV centers, we only consider influence of the Gd 3+ molecules in the effective interaction range of the NV centers.

The PEG model: a. Theory model and experiment data for PEG
For the extension process of the PEG, the Worm-Like Chain model (55) is suitable to describe it. The previous study shows that the result of the experiment performed in PBS buffer, which is the same buffer we use in our experiment, can be well described by the model (81).

b. The PEG in our experiment
In our experiment, the molecular weight of the PEG we use is 1000, and the Persistence  S14).

c. Flory model of the PEG
When PEG is in a good solution, it can be described by the Flory model (82). The free length of it is Flory radius, which is: For the PEG we use in this experiment, the Flory radius is 2.25 nm, which means that when there is no external force applied on PEG, the extension of it is 2.25 nm.