Cells
HEK293T/17 is a human embryonic kidney cell line (ATCC, CRL-11268). The HEK-ACE-2 adherent cell line was obtained through BEI Resources (NR-52511). All adherent cells were cultured at 37 °C with 8% CO2 in flasks with Dulbecco’s modified Eagle medium (DMEM) supplemented with 10% fetal bovine serum (FBS) (Hyclone) and 1% penicillin-streptomycin (PenStrep).
HEK293F is a female human embryonic kidney cell line transformed and adapted to grow in suspension (Life Technologies). HEK293F cells were grown in 293FreeStyle expression medium (Life Technologies), cultured at 37 °C with 8% CO2 and shaking at 130 rpm. Expi293F cells are derived from the HEK293F cell line (Life Technologies). Expi293F cells were grown in Expi293 Expression Medium (Life Technologies), cultured at 36.5 °C with 8% CO2 and shaking at 150 rpm.
Vero E6 (CRL-1586, American Type Culture Collection), Vero-TMPRSS2 (a gift of S. Ding, Washington University) and Vero-hACE2-TMPRSS2 (a gift of A. Creanga and B. Graham, National Institutes of Health (NIH)) cells were cultured at 37 °C in DMEM supplemented with 10% FBS, 10 mM HEPES (pH 7.3), 1 mM sodium pyruvate, 1× nonessential amino acids and 100 U ml−1 PenStrep. Vero-TMPRSS2 cell cultures were supplemented with 5 μg ml−1 blasticidin. TMPRSS2 expression was confirmed using an anti-V5 antibody (Thermo Fisher Scientific, 2F11F7) or anti-TMPRSS2 mAb (Abnova, Clone 2F4) and APC-conjugated goat anti-mouse IgG (BioLegend, 405308). Vero-hACE2-TMPRSS2 cell cultures were supplemented with 10 μg ml−1 puromycin.
mAbs
The murine mAbs SARS2-02 and SARS2-38 studied were isolated from BALB/c mice immunized with SARS-CoV-2 spike and RBD proteins and have been described previously17. Genes encoding CR3022, B38 and CV30 heavy and light chains were ordered from GenScript and cloned into pCMV/R. Antibodies were expressed by transient cotransfection of both heavy- and light-chain plasmids in Expi293F cells using PEI-MAX (Polyscience) transfection reagent. Cell supernatants were harvested and clarified after 3 or 6 days, and protein was purified using protein A chromatography (Cytiva). SPD-M162 was obtained from AcroBiosystems (AM122).
Live virus production
The 2019n-CoV/USA_WA1/2020 isolate of SARS-CoV-2 was obtained from the US Centers for Disease Control. The Alpha isolate was obtained from a nasopharyngeal sample after propagation on Vero-hACE2-TMPRSS2 cells3. The chimeric WA1/2020 displaying Beta virus has been described previously3. All viruses were deep-sequenced and tittered on Vero-TMPRSS2 cells, and experiments were performed in an approved biosafety level 3 facility.
Pseudovirus production
Murine leukemia virus (MLV)-based and human immunodeficiency virus (HIV) SARS-CoV-2 S pseudotypes were prepared as previously described20,21. Briefly for MLV, HEK293T cells were cotransfected using Lipofectamine 2000 (Life Technologies) with an S-encoding plasmid, an MLV Gag–Pol packaging construct and the MLV transfer vector encoding a luciferase reporter according to the manufacturer’s instructions. For HIV, HEK293T cells were cotransfected using Lipofectamine 2000 (Life Technologies) with an S-encoding plasmid, an HIV Gag-Pol, Tat, Rev1B packaging construct and the HIV transfer vector encoding a luciferase reporter according to the manufacturer’s instructions. Cells were washed three times with Opti-MEM before transfection and incubated for ~5 h at 37 °C with transfection medium. DMEM containing 10% FBS was added for ~60 h. The supernatants were harvested by spinning at 2,500 g, filtered through a 0.45-mm filter, concentrated with a 100-kDa membrane for 10 min at 2,500 g and then aliquoted and stored at −80 °C before use.
D614G SARS-CoV-2 S (YP 009724390.1), Alpha S, Beta S and Delta S pseudotypes VSVs were prepared as described previously22. Briefly, 293T cells in DMEM supplemented with 10% FBS, 1% PenStrep seeded in 10-cm dishes were transfected with the plasmid encoding for the corresponding S glycoprotein using Lipofectamine 2000 (Life Technologies) following the manufacturer’s indications. One day after transfection, cells were infected with VSV(G*ΔG-luciferase) and after 2 h were washed five times with DMEM before adding medium supplemented with anti-VSV-G antibody (ATCC, I1- mouse hybridoma supernatant, CRL- 2700). Virus pseudotypes were harvested 18–24 h after inoculation, clarified by centrifugation at 2,500 g for 5 min, filtered through a 0.45-μm cutoff membrane, concentrated 10 times with a 30-kDa cutoff membrane, aliquoted and stored at −80 °C.
Mouse serum
Female BALB/c (stock 000651) mice were purchased at the age of 4 weeks from The Jackson Laboratory and maintained at the Comparative Medicine Facility at the University of Washington (Seattle, WA), accredited by the American Association for the Accreditation of Laboratory Animal Care International. At 6 weeks of age, mice were immunized, and 3 weeks later, animals were boosted. Before inoculation, immunogen suspensions were gently mixed 1:1 vol/vol with AddaVax adjuvant (Invivogen) to reach a final concentration of 0.009 or 0.05 mg ml−1 antigen. Mice were injected intramuscularly into the gastrocnemius muscle of each hind leg using a 27-G needle (BD) with 50 ml per injection site (100 ml total) of immunogen under isoflurane anesthesia. To obtain sera, all mice were bled 2 weeks after prime and boost immunizations. Blood was collected via submental venous puncture and rested in 1.5-ml plastic Eppendorf tubes at room temperature for 30 min to allow for coagulation. Serum was separated from hematocrit via centrifugation at 2,000 g for 10 min. Complement factors and pathogens in isolated serum were heat-inactivated via incubation at 56 °C for 60 min. Serum was stored at 4 °C or −80 °C until use. Mouse sera in this study were used in a previous study17.
Human serum and ELISA
Immune human sera/plasma specimens were from persons with documented SARS-CoV-2 infection in the United States between February and August 2020. Samples were obtained before vaccination or after vaccination with BNT162b2 or M1273 mRNA, after obtaining informed written consent in an institutional review board-approved protocol23. Antibodies to the SARS-CoV-2 spike protein were measured using an ELISA specific for anti-S1 IgG (Euroimmun). Antibody levels were quantified by conversion of the optical density to a z-score relative to prepandemic serum anti-S1 IgG concentrations, as previously described23. Sera tests were serial specimens obtained following immunization of laboratory volunteers in an institutional review board-compliant protocol. The negative samples (no SARS-CoV-2 nAbs) were serum samples collected for VZV research in 2016 and 2017, before SARS-CoV-2 was spreading in the United States.
General procedures for bacterial protein production and purification
The E. coli Lemo21(DE3) strain (New England Biolabs) was transformed with a pET29b+ plasmid encoding the synthesized gene of interest. Cells were grown for 24 h in LB medium supplemented with kanamycin. Cells were inoculated at a 1:50 ml ratio in the Studier TBM-5052 autoinduction medium supplemented with kanamycin, grown at 37 °C for 2–4 h and then grown at 18 °C for an additional 18 h. Cells were collected by centrifugation at 4,000 g at 4 °C for 15 min and resuspended in 30 ml lysis buffer (20 mM Tris-HCl, pH 8.0, 300 mM NaCl, 30 mM imidazole, 1 mM PMSF and 0.02 mg ml−1 DNase). Cell resuspensions were lysed by sonication for 2.5 min (5 s cycles). Lysates were clarified by centrifugation at 24,000 g at 4 °C for 20 min and passed through 2-ml Ni-NTA nickel resin (Qiagen, 30250) pre-equilibrated with wash buffer (20 mM Tris-HCl, pH 8.0, 300 mM NaCl and 30 mM imidazole). The resin was washed twice with 10 column volumes (CVs) of wash buffer, and then eluted with 3 CVs elution buffer (20 mM Tris-HCl, pH 8.0, 300 mM NaCl and 300 mM imidazole). The eluted proteins were concentrated using Ultra-15 Centrifugal Filter Units (Amicon) and further purified by using a Superdex 75 Increase 10/300 GL (GE Healthcare) size exclusion column in TBS (25 mM Tris-HCl, pH 8.0, and 150 mM NaCl). Fractions containing monomeric protein were pooled, concentrated and snap-frozen in liquid nitrogen and stored at −80 °C.
Plasmid construction for RBD
The SARS-CoV-2 RBD (UniProt: P0DTC2) (BEI NR-52422), Alpha (N501Y), Beta (K417N, E484K and N501Y) and Delta (L452R and T478K) constructs were synthesized by GenScript into pcDNA3.1- or CMVR with an N-terminal mu-phosphatase signal peptide and a C-terminal octa-histidine tag (GHHHHHHHH). The boundaries of the construct are N-328RFPN331 and 528KKST531-C (ref. 17).
Transient transfection
RBD proteins were produced in Expi293F cells grown in suspension using Expi293F expression medium (Life Technologies) at 33 °C, 70% humidity, 8% CO2 rotating at 150 rpm. The cultures were transfected using PEI-MAX (Polyscience) with cells grown to a density of 3.0 million cells per milliliter and cultivated for 3 days. Supernatants were clarified by centrifugation (5 min at 4,000 rcf), addition of polydiallyldimethylammonium chloride solution to a final concentration of 0.0375% (Sigma Aldrich, 409014) and a second spin (5 min at 4,000 rcf).
Purification of RBD
His-tagged RBD was purified from clarified supernatants via a batch bind method, where each clarified supernatant was supplemented with 1 M Tris-HCl, pH 8.0, to a final concentration of 45 mM and 5 M NaCl to a final concentration of 310 mM. Talon cobalt affinity resin (Takara Bio) was added to the treated supernatants and allowed to incubate for 15 min with gentle shaking. Resin was collected using vacuum filtration with a 0.2-mm filter and transferred to a gravity column. The resin was washed with 20 mM Tris, pH 8.0, 300 mM NaCl, and the protein was eluted with 3 CVs of 20 mM Tris, pH 8.0, 300 mM NaCl and 300 mM imidazole. The batch bind process was then repeated and the first and second elutions combined. SDS-PAGE was used to assess purity. Following immobilized metal affinity chromatography purification, the elution was concentrated and applied to a Cytiva S200 Increase column equilibrated with 20 mM Tris 150 mM NaCl, pH 8.0, and the peak of interest was collected and quantified using A280. The purified RBD was qualified using BLI to confirm binding using CR3022 and hACE2-Fc.
In vitro bioluminescence characterization with mAbs
A Synergy Neo2 Microplate Reader (BioTek) was used for all in vitro bioluminescence measurements. Assays were performed in 50% HBS-EP (GE Healthcare Life Sciences) plus 50% Nano-Glo assay buffer. For each well of a white opaque 96-well plate, 5 μl of 10× lucCage, 5 μl of 10× lucKey, 5 μl of 10× RBD and 5 μl of 10× antibody and remaining volume of buffer for in total 50 μl were mixed to reach the indicated concentration and ratio. The lucCage and lucKey components were incubated for 30 min at room temperature to enable pre-equilibration. The plate was centrifuged at 1,000 g for 10 s and incubated at room temperature for a further 30 min. Then, 15 μl of 100× diluted furimazine (Promega, Nano-Glo luciferase assay reagent) was added to each well. Bioluminescence measurements in the absence of target were taken every 1 min (0.1 s integration and 10 s shaking during intervals) for a total of 30 min. To calculate the percent decrease in dynamic range for the graphs, the following formula was used:
$${mathrm{Fraction}},{mathrm{of}},{mathrm{lucCageRBD}},{mathrm{dynamic}},{mathrm{range}},{mathrm{lost}} = 1 – frac{{L_x – L_{mathrm{min}}}}{{L_{mathrm{max}} – L_{mathrm{min}}}},$$
where Lx is the luminosity with 5 nM RBD and the tested antibody concentration, Lmin is the luminosity when no RBD is added, and Lmax is the luminosity when only 5 nM RBD is added. To derive EC50 values from the bioluminescence-to-analyte plot, the top three peak bioluminescence intensities at individual analyte concentrations were averaged, subtracted from blank and used to fit the sigmoidal 4PL curve.
Detection of spiked RBD in human serum specimens
Serum specimens were derived from excess plasma or sera from adults (>18 years) of both genders provided by the Director of the Clinical Chemistry Division, the hospital of University Washington. Serum specimens were obtained in compliance with approval by the University of Washington Human Subjects Division. All anonymized donor specimens were provided deidentified. Because the donors consented to have their excess specimens be used for other experimental studies, they could be transferred to our study without additional consent. All samples were passed through 0.22-μm filters before use, and 5 μl of 10× monomeric RBD (10 or 1,000 nM), 5 μl of 10× lucCage (10 nM), 5 μl of 10× lucKey (10 nM), 5 μl of 10× Antares2 (0.5 nM) and the indicated amount of human donor serum or simulated nasal matrix were mixed with 1:1 HBS/Nano-Glo assay buffer to reach a total volume of 50 μl. The plate was centrifuged at 1,000 g for 10 s. After 30-min incubation, 15 μl of 100× diluted furimazine in buffer was added to each well. Bioluminescence signals were recorded from both 470/40-nm and 590/35-nm channels every 1 min for a total of 30 min. The ratio (R) at each time point was calculated by the following equation as previously described11:
$$R = frac{{T_{470 mathrm{nm}} – T_{590 mathrm{nm}} times 0.43}}{{T_{590 mathrm{nm}}}},$$
where T470 nm and T590 nm are the total luminescent signals at 470 nm and 590 nm, respectively. For calculating the fraction of lucCageRBD dynamic range lost for serum samples in Extended Data Fig. 6, the following equation was used:
$${mathrm{Fraction}},{mathrm{of}},{mathrm{lucCageRBD}},{mathrm{dynamic}},{mathrm{range}},{mathrm{lost}} = 1 – frac{{R_x – R_{mathrm{min}}}}{{R_{mathrm{max}} – R_{mathrm{min}}}},$$
where Rx is the R with 1 nM RBD in serum sample, Rmin is the R of serum sample but no RBD, and Rmax is the R of 100 nM RBD in the same serum sample.
To assay 64 serum samples in Fig. 2 and Extended Data Fig. 8 (including 40 from either convalescent or vaccinated patients and 24 pre-2019 donors), 5 μl proper diluted serum sample and 5 μl of 10 nM RBD (WT or Delta) were premixed in DPBS for 20 min at room temperature. A 15-μl mixture containing 5 μl lucCageRBD (10 nM), 5 μl lucKey (10 nM) and 5 μl Antares2 (0.2 nM) was subsequently added to each well and incubated for another 10 min; 25 μl furimazine substrate (200× dilution) was added to each well, and luminescence signals were acquired immediately by Neo2 plate reader at 470/40-nm and 590/35-nm channels for a total of 20 min (1-min interval and 0.1-s exposure, and instrumental gain values were set to 120 at the 470-nm channel and 145 at the 590-nm channel). The final assay concentration contains 1 nM lucCageRBD, 1 nM lucKey, 20 pM Antares2 and 1 nM RBD. The person performing the lucCageRBD assays was blinded as to the serum samples being tested, and another person analyzed the assay data. For calculating the fraction of lucCageRBD dynamic range lost for serum samples in Fig. 2 and Extended Data Fig. 8, the following equation was used:
$${mathrm{Fractional}},{mathrm{decrease}},{mathrm{in}},{mathrm{lucCageRBD}},{mathrm{signal}} = 1 – frac{{R_x – R_{mathrm{min}}}}{{R_{mathrm{min}}}}.$$
To simplify the calculation, Rx here is reported as the ratio of the total luminescent signal at 470 nm over 590 nm (T470 nm/T590 nm) with 1 nM RBD in serum sample and Rmin is the ratio of serum sample without the addition of RBD. Ten steady-state ratio values were averaged and assigned as Rx of the corresponding sample. Rmax was omitted herein because Rmax was unreliable with some samples due to high nAb titer.
In vitro bioluminescence characterization of lyophilized biosensors
Five microliters of 10× lucCage and 5 μl of 10× lucKey were added to each well of a white opaque 96-well plate and lyophilized overnight. The biosensor was reconstituted in 10 μl dH20 before testing, and then 84 μl of 50% HBS-EP (GE Healthcare Life Sciences) plus 50% Nano-Glo assay buffer was added to each well. The lucCage and lucKey components were incubated for 30 min at room temperature to enable pre-equilibration. One microliter of 100× diluted furimazine was added to each well. The plate was centrifuged at 1,000 g for 10 s. Then, 5 μl serially diluted target RBD was added to each well and measured in a A Synergy Neo2 Microplate Reader. Measurements were taken every 1 min (0.1-s integration and 10-s shaking during intervals) for a total of 90 min.
BLI
Protein–protein interactions were measured by using an Octet RED96 System (ForteBio) using streptavidin-coated biosensors (ForteBio). Each well contained 200 μl solution, and the assay buffer was HBS-EP + buffer (GE Healthcare Life Sciences, 10 mM HEPES, pH 7.4, 150 mM NaCl, 3 mM EDTA, 0.05% (v/v) surfactant P20) plus 0.5% non-fat dry milk blotting grade blocker (Bio-Rad). The biosensor tips were loaded with analyte peptide or protein at 20 μg ml−1 for 300 s (threshold of 0.8-nm response), incubated in HBS-EP + buffer for 60 s to acquire the baseline measurement, dipped into the solution containing cage and/or key for 1,800 s (association step) and dipped into the HBS-EP + buffer for 1,800 s (dissociation steps). The binding data were analyzed with the ForteBio Data Analysis Software version 9.0.0.10.
Live and pseudovirus entry and serum neutralization assays
SARS2-02 and SARS2-38 were assayed for neutralization potency by focus-reduction neutralization test as described previously24 and using Vero-TMPRSS2 cells. Briefly, serial dilutions of antibody were incubated with 2 × 102 focus-forming units of SARS-CoV-2 of the indicated strain for 1 h at 37 °C in duplicate. Immune complexes were then added to Vero-TMRPSS2 cell monolayers in a 96-well plate and incubated for 1 h at 37 °C before the addition of 1% (w/v) methylcellulose in MEM. Following incubation for 30 h at 37 °C, cells were fixed with 4% paraformaldehyde, permeabilized and stained for infection foci with a mixture of mAbs that bind various epitopes on the RBD and NTD of spike (SARS2-02 and SARS2-38; diluted to 1 µg ml−1 total mAb concentration). Antibody–dose response curves were analyzed using nonlinear regression analysis (with a variable slope) (GraphPad Software).
For the mAbs CV30, B38 and CR3022 and for the vaccinated human serum samples with pseudovirus, HEK-hACE2 cells were cultured in DMEM with 10% FBS (Hyclone) and 1% PenStrep with 8% CO2 in a 37 °C incubator (Thermo Fisher Scientific). Before plating, 40 µl poly-lysine (Sigma) was placed into 96-well plates and incubated with rotation for 5 min. Poly-lysine was removed, plates were dried for 5 min then washed 1× with water before plating 2 × 104 cells. The following day, cells were checked to be at 80% confluence. In a half-area 96-well plate a 1:3 serial dilution of mAb or sera was made in DMEM in 22 µl final volume. 22 µl pseudovirus was then added to the serial dilution and incubated at room temperature for 30–60 min. HEK-hACE2 plate media was removed and 40 µl of the sera/virus mixture was added to the cells and incubated for 2 h at 37 °C with 8% CO2. Following incubation, 40 µl 20% FBS and 2% PenStrep containing DMEM was added to the cells for 24–48 h. Following the infection, One-Glo-EX (Promega) was added to the cells in half culturing volume (40 µl added) and incubated in the dark for 5 min before reading on a BioTek plate reader. Measurements were done on all mAbs and human serum samples from each group in at least duplicate. Relative luciferase units were plotted and normalized in Prism (GraphPad) using a zero value of cells alone and a 100% value of 1:2 virus alone. Nonlinear regression of log(inhibitor) versus normalized response was used to determine IC50 values from curve fits.
Sensor simulations
Mathematical models describing the ternary and quaternary sensor systems were simulated to test their responses to changes in their input parameters (concentrations and affinities of intervening species). Systems of ordinary differential equations describing the kinetics of the interactions between the species involved in each sensor were numerically integrated using integrate.odeint() as implemented in Scipy (version 1.6.3) (ref. 25). Steady-state values were used to determine the distribution of species at thermodynamic equilibrium.
The ternary system is composed of the following species: ACE-2, RBD, nAb, ACE-2:RBD and RBD:nAb. The following set of equations was used to describe the system:
$$frac{{dleft[ {mathrm{ACE2}} right]}}{{dt}} = – k_1left[ {mathrm{ACE2}} right]left[ {mathrm{RBD}} right] + k_{ – 1}left[ {mathrm{ACE2:RBD}} right]$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{RBD}} right]}}{{dt}} = – k_1left[ {mathrm{ACE2}} right]left[ {mathrm{RBD}} right] + k_{ – 1}left[ {mathrm{ACE2:RBD}} right]\qquadqquad – k_2left[ {mathrm{RBD}} right]left[ {mathrm{nAb}} right] + k_{ – 2}left[ {mathrm{RBD:nAb}} right]end{array}$$
$$frac{{dleft[ {mathrm{nAb}} right]}}{{dt}} = – k_2left[ {mathrm{RBD}} right]left[ {mathrm{nAb}} right] + k_{ – 2}left[ {mathrm{RBD:nAb}} right]$$
$$frac{{dleft[ {mathrm{ACE2:RBD}} right]}}{{dt}} = k_1left[ {mathrm{ACE2}} right]left[ {mathrm{RBD}} right] – k_{ – 1}left[ {mathrm{ACE2:RBD}} right]$$
$$frac{{dleft[ {mathrm{RBD:nAb}} right]}}{{dt}} = k_2left[ {mathrm{RBD}} right]left[ {mathrm{nAb}} right] – k_{ – 2}left[ {mathrm{RBD:nAb}} right],$$
where ki describe bimolecular association rate constants and k–i represent unimolecular dissociation rate constants. K1 = k−1/k1 and K2 = k−2/k2 describe the equilibrium dissociation constants for the ACE-2:RBD and RBD:nAb complexes, respectively. For all ternary system simulations, K1 was set to 15 nM (ref. 26). For consistency with the metric used to report on the quaternary system response (fraction of lucCageRBD dynamic range lost; described in section ‘In vitro bioluminescence characterization with monoclonal antibodies’), simulations for the ternary system were reported as:
$${mathrm{Fraction}},{mathrm{sensor}},{mathrm{dynamic}},{mathrm{range}},{mathrm{lost}} = 1 – L_{x}/L_{mathrm{max}},$$
where Lx is the signal observed when all three species are present, and Lmax is the response when nAb is absent.
The quaternary system is composed of the following species: closed state of the Cage-Latch, open state of the Cage-Latch (oCL), lucKey, RBD, nAb, lucKey:oCL, oCL:RBD, lucKey:oCL:RBD and RBD:nAb. Only the oCL is considered binding-competent, whereas the closed state of the Cage-Latch is not. The following set of equations was used to describe the system:
$$frac{{dleft[ {mathrm{cCL}} right]}}{{dt}} = – kleft[ {mathrm{cCL}} right] + k_{-} left[ {mathrm{oCL}} right]$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{oCL}} right]}}{{dt}} = kleft[ {mathrm{cCL}} right] – k_{-} left[ {mathrm{oCL}} right] – k_{1}left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}} right] + k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}} right]\ – k_{2}left[ {mathrm{oCL}} right]left[ {mathrm{RBD}} right] + k_{ – 2}left[ {mathrm{oCL}}:{mathrm{RBD}} right]end{array}$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{lucKey}} right]}}{{dt}} = – k_{1}left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}} right] + k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}} right]\ – k_{1}left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}}:{mathrm{RBD}} right] + k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]end{array}$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{RBD}} right]}}{{dt}} = – k_{2}left[ {mathrm{oCL}} right]left[ {mathrm{RBD}} right] + k_{ – 2}left[ {mathrm{oCL}}:{mathrm{RBD}} right] – k_{2}left[ {mathrm{lucKey}}:{mathrm{oCL}} right]left[ {mathrm{RBD}} right]\ + k_{ – 2}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right] – k_{3}left[ {mathrm{RBD}} right]left[ {mathrm{nAB}} right] + k_{ – 3}left[ {mathrm{RBD}}:{mathrm{nAb}} right]end{array}$$
$$frac{{dleft[ {mathrm{nAb}} right]}}{{dt}} = – k_{3}left[ {mathrm{RBD}} right]left[ {mathrm{nAB}} right] + k_{ – 3}left[ {mathrm{RBD}}:{mathrm{nAb}} right]$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{lucKey}}:{mathrm{oCL}} right]}}{{dt}} = k_{1}left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}} right] – k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}} right] \- k_{2}left[ {mathrm{lucKey}}:{mathrm{oCL}} right]left[ {mathrm{RBD}} right] + k_{ – 2}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]end{array}$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{oCL}}:{mathrm{RBD}} right]}}{{dt}} = k_{2}left[ {mathrm{oCL}} right]left[ {mathrm{RBD}} right] – k_{ – 2}left[ {mathrm{oCL}}:{mathrm{RBD}} right] – k_1left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}}:{mathrm{RBD}} right]\ + k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]end{array}$$
$$begin{array}{l}displaystylefrac{{dleft[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]}}{{dt}} = k_{1}left[ {mathrm{lucKey}} right]left[ {mathrm{oCL}}:{mathrm{RBD}} right] – k_{ – 1}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]\ + k_{2}left[ {mathrm{lucKey}}:{mathrm{oCL}} right]left[ {mathrm{RBD}} right] – k_{ – 2}left[ {mathrm{lucKey}}:{mathrm{oCL}}:{mathrm{RBD}} right]end{array}$$
$$frac{{dleft[ {mathrm{RBD}}:{mathrm{nAb}} right]}}{{dt}} = k_{3}left[ {mathrm{RBD}} right]left[ {mathrm{nAB}} right] – k_{ – 3}left[ {mathrm{RBD}}:{mathrm{nAb}} right],$$
where ki describes the bimolecular association rate constant and k−i represents the unimolecular dissociation rate constant. K1 = k−1/k1, K2 = k−2/k2 and K3 = k−3/k3 describe the affinities (equilibrium dissociation constants) for the binding interfaces lucKey:oCL, oCL:RBD and RBD:nAb, respectively. The binding of lucKey and RBD to the open Cage-Latch species is considered symmetrical (i.e., noncooperative), meaning that the binding events are independent. (K = k_ {-} /k = {mathrm{exp}}left( {Delta G_{mathrm{open}}/RT} right)) describes the unimolecular binding equilibrium of the Latch to the Cage, with (Delta G_{mathrm{open}}) the free energy of Latch opening, R the universal gas constant and T the thermodynamic temperature (set to 298.15 K for all simulations).
These systems were simulated over a range of species concentrations, as well as RBD:nAb affinities, to explore the behavior of each sensor, and gain insights into the influence of different variables on the position of the detection thresholds. The python code for running these simulations is provided as a Jupyter notebook: https://github.com/bwicky/covid_nAb_sensor_simulation.
Statistical analysis
No statistical methods were used to predetermine the sample size. No sample was excluded from data analysis, and no blinding was used. Deidentified clinical serum samples were randomly used for spiking in target proteins. Results were successfully reproduced using different batches of pure proteins on different days. Unless otherwise indicated, data are shown as mean ± s.e.m., and error bars in figures represent s.e.m. of technical triplicates. BLI data were analyzed using ForteBio Data Analysis Software version 9.0.0.10. All data were analyzed and plotted using GraphPad Prism 8.
Reporting Summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.

