iMAX FRET (Information Maximized FRET) for Multipoint Single-Molecule Structural Analysis

Understanding the structure of biomolecules is vital for deciphering their roles in biological systems. Single-molecule techniques have emerged as alternatives to conventional ensemble structure analysis methods for uncovering new biology in molecular dynamics and interaction studies, yet only limited structural information could be obtained experimentally. Here, we address this challenge by introducing iMAX FRET, a one-pot method that allows ab initio 3D profiling of individual molecules using two-color FRET measurements. Through the stochastic exchange of fluorescent weak binders, iMAX FRET simultaneously assesses multiple distances on a biomolecule within a few minutes, which can then be used to reconstruct the coordinates of up to four points in each molecule, allowing structure-based inference. We demonstrate the 3D reconstruction of DNA nanostructures, protein quaternary structures, and conformational changes in proteins. With iMAX FRET, we provide a powerful approach to advance the understanding of biomolecular structure by expanding conventional FRET analysis to three dimensions.


Materials and Methods Protein expression and purification
Divalent streptavidins were expressed in Escherichia coli, refolded from inclusion bodies, and purified by ammonium sulfate precipitation and ion-exchange chromatography, as reported in the original paper 1 .Tetravalent recombinant (wild-type) streptavidin was procured from Thermo Scientific.Plasmids encoding SBD2 (T369C/S451C) and SBD2 (T369C/S451C/D417C) 2 were a generous gift from Prof. Bert Poolman (Department of Biochemistry, University of Groningen, The Netherlands), and the proteins were expressed and purified using the reported protocol 2 .

Protein labeling
Cysteine labeling was carried out as reported previously 2 with slight modifications as follows.Cysteine residues of purified proteins (25µM in the total volume of 50µl In PBS) were reduced with 50mM Tris(-2carboethyl)phosphine (TCEP) at 40-fold molar excess for 30 minutes.Excess TCEP was removed with ZebaTM Spin desalting columns 7kDa MWCO (ThermoFisher) as it may interfere with the Maleimide reaction 3 .The proteins were then labeled with 25-fold molar excess monoreactive maleimide-Dibenzocyclooctyne (DBCO) (Sigma Aldrich) in Phosphate Buffered Saline (PBS) pH 7.4 overnight at room temperature.Excess maleimide-DBCO was removed with Zeba columns and reacted with 10-fold molar excess (ratio 1:10, cysteine to linker) of monoreactive Azidobenzoate-(5') functionalized DNA in PBS pH 7.4 and incubated overnight at room temperature.

Single-molecule Setup
All iMAX FRET measurements were performed on a custom-modified prism-type TIRF microscopy setup built around an inverted fluorescence microscope (Nikon, Ti2e) 4 .For illumination of samples immobilized on a quartz slide surface, a 532 nm diode-pumped solid-state laser and 640 nm diode laser (Oxxius, L6Cc) were directed to the surface with an incidence angle below the critical angle via a prism installed above the slide.Fluorescence signals of Cy3 and Cy5 dyes collected by an objective lens (Nikon, CFI Plan Apochromat VC 60X WI) placed below the quarts sample chamber were spectrally divided by a dichroic mirror (Chroma, T635lpxr) after removing scattered laser light by a laser blocking filter (Semrock, NF03-405/488/532/635E-25). The fluorescence signals were further cleared by bandpass filters (Chroma, ET585/65m for Cy3 and ET655LP for Cy5) and imaged on a sCMOS camera (Photometrics, PrimeBSI).The two lasers were operated with a trigger signal generated by the sCMOS camera for ALEX illumination scheme 5 .All the instruments were controlled by using commercial software (NIS elements, Nikon).
Generally, for single-molecule studies, immobilization is carried out by biotin-streptavidin interactions 4 .However, it is highly difficult to precisely control the number of biotin molecules on the traditionally passivated surfaces (with Biotin-PEG).This raises the possibility of 2 or more binding pockets of streptavidin being occupied by biotins on the slide, leaving only one or two for actual fingerprinting.Thus, we modified the immobilization strategy for tetravalent and divalent streptavidin experiments (Fig. 4): Quartz slides were sonicated for >15min in Acetone, Methanol, and finally 1M KOH with washes with MilliQ in between.Next, the slides were flamed using a burner to remove organic residue if any, and immediately placed back in MilliQ.Finally, the slides were dried using a nitrogen blowgun and used for making the flow cell as explained above.The unused slides were stored at RT. 50µl of 1mg/ml of BSA-Azide (Click chemistry tools, 1535) was incubated with 15µl of 100uM (5') DBCO-DNA-Biotin (3') overnight in the dark at room temperature.10nM of the resultant BSA-DNA-Biotin was added (50µl total volume) to the flow-cell and incubated for 10min.Excess BSA and free DNA were removed with 100µl T50.Next, 50µl of 1nM tetravalent or divalent Streptavidin was added to the channel and incubated for 5min.The excess was washed with 100µl of T50.Next, 100nM biotinylated docking strands were added to the flow cell and incubated for 30 min to ensure the labeling of all the streptavidin pockets.Unbound DNA was washed away with 100 µL T50.Following, 50 µL of 10 nM donor-labeled imager strands and 100 nM of acceptor-labeled imager strands prepared in the imaging buffer were injected into the flow cell.

Single-molecule fluorescence and FRET data analysis
The data collection and analysis were performed in multiple steps as reported previously 6 .A custom Python script was used to extract time traces of individual molecules from a sCMOS image collected at 0.1s exposure time per frame.Two-state K-means clustering algorithm were applied to the Cy3 and Cy5 fluorescence intensity traces to detect individual binding events of fluorescence imager strands.In order to ensure accurate results, binding events lasting for three or more consecutive frames were selected for further analysis.FRET efficiencies were calculated for each imager strand binding event and used to construct the FRET kymograph and histogram.From the events in which the acceptor probe dissociated or photobleached before the donor probe, we calculated the beta (leakage) and gamma correction factors for accurate FRET efficiency calculation following the method reported in a previous study 7 .Gaussian mixture modeling was applied to automatically classify populations in the FRET histogram.The Python-based automated analysis code can be freely accessed at the following link: https://github.com/kahutia/transient_FRET_analyzer2.

Supplementary Text Monte Carlo simulations
In iMAX FRET, which has multiple identical docking sites, the chance of having single-pair FRET events, i.e. simultaneous binding of one Cy3-and one Cy5 probes, largely depends on the probe binding kinetics.Experimentally, the binding frequency and binding dwell time of a probe can be controlled by the concentration and the length of the DNA probe, respectively.To find the optimal condition that maximizes the chance of having FRET events, we carried out series of Monte Carlo simulations at various kinetic rates.We defined a system with three docking sites each of which had three states of 1) probe unbound, 2) Cy3 probe bound and 3) Cy5 probe bound states.Given transition rates of the two probes, each docking site of the system was allowed to freely transit between states 1 and 2 or states 1 and 3, but not between 2 and 3.Each simulation ran for 1-million-time steps from which we typically observed >5000 transitions.We then selected events in which the system entered into the single-pair FRET emitting state, in which only one Cy3 and Cy5 probe were bound among the three docking sites.After removing events that lasted shorter than three consecutive time steps, the number of the selected single-pair FRET events and the total time spent of the system in them were studied to understand the effect of probe binding kinetics.The simulation code was written in Matlab and freely available upon request.

Structure prediction and classification
A computational pipeline for the reconstruction of 3D-shapes and shape classification was implemented in Python 3.9.Briefly, the number of dyes is determined from the number of FRET efficiency values, which are translated to distances.Distances are used to construct all distinct distance matrices (D) using pre-computed index matrices.Each distance matrix is then converted to a coordinate matrix as follows 8 .We construct the Gramm matrix (M), where i,j are row and column index respectively.After eigenvalue decomposition,  =  % the coordinate matrix X can be calculated by sorting U and S by descending order of eigenvalue size, taking the first 3 columns of U (U[:, :3]) and first 3 eigen values (S[:3]) and calculating: Poorly fitting distance matrices generate negative eigenvalues and are excluded.Finally, the remaining coordinate matrices are calculated back to distance matrices, and the coordinate matrix for which distances are closest to the original FRET efficiency-derived distances is returned.The algorithm was implemented in numpy (v1.21.5) 9 with distance matrix calculation as implemented in scipy (v1.8.0) 10 .
Numerical embedding of 3D shapes for classification was done using the Geometricus package (v0.3.0) 11.Embedded coordinates were concatenated to the FRET fingerprint, after which a boosted tree classifier implemented using the XGBoost package (v.1.6.1) 12 was trained and tested on the data using a 10-fold cross validation scheme.The analysis code is freely available at https://github.com/cvdelannoy/iMAX-FRET.

Preparation of the custom DNA nanostructure for Förster radius fitting and classifier applicability analysis
The position of docking site 2 was changed to three different locations (Figure S4a) using click chemistry.To achieve this, alkyne handles were introduced into the DNA backbone at three different locations one at a time in separate constructs.The docking strand for site 2 was designed to contain an azide handle at its one end.The alkyne and azide-containing DNAs were reacted using copper-click chemistry.The clicked DNA products (cyan box, Figure S4b) were gel purified and then the triangles were assembled to generate three structurally similar nanostructures (Figure S4a, bottom left).The positional changes between the (variable) docking site 2 and the fixed docking site 3 were reflected in the FRET values (Figure S4c and d), while it remained constant for all the triangles for the undeviating distance between docking sites three and four (Figure S4e).We could similarly recapitulate the change in FRET values in three coordinates i.e. docking sites two, three and four (Figure S4f).

Conversion of FRET efficiency into the distance R
The following sixth-power relation between R and E was used to calculate the distance based on the experimentally acquired FRET efficiency.
The Förster radius (R0), a parameter that combines the influence of dye and medium properties, and relative dye orientations, was fitted using the above custom DNA construct with dyes positioned at known locations along one DNA arm (Figure S4g).

DNA structure modeling for Förster radius fitting
The Förster radius (R0) denotes the dye distance at which the FRET efficiency is 0.5 and constitutes an essential parameter for the accurate calculation of distances from FRET efficiencies 13 .It factors in dye quantum yields and relative orientations, and the refractive index of the medium.In many applications, it suffices to approximate this value as a constant, however in structural biology, this may lead to unacceptable discrepancies with actual distances, as the effect of local environment and setup is ignored.Here we have used an elegant experiment to determine R0, using our DNA nanostructure.Briefly, we measure FRET efficiencies for four triangles, created by click-chemistry (detailed in Figure S4).
To determine the Förster radius for our experiments, a single side of the DNA nanostructure was outfitted with clicked docking strands at positions 4, 7, and 15 th base from a reference position.FRET efficiencies between clicked docking strands, the reference position, and a third position at one of the other angles of the nanostructure were then measured.We then used a parameter optimization approach with a tree-based Parzen estimator (TPE) implemented in the hyperopt package (v.0.2.7) 14 to estimate the Förster radius.Briefly, this algorithm generates randomized proposals for all one or more variable parameters within given ranges and chooses the combination that minimizes the objective function.The TPE constrains the parameter space based on objective values of previous rounds so that the next guess is more likely to return a lower objective value.Using this approach, we simultaneously fitted Förster radius, linker length, and two DNA geometry parameters (twist and axial rise) after 100 iterations.Here, DNA geometry parameters were allowed to vary slightly to account for unnatural stresses in the nanostructure.As an objective function, the squared sum of the difference between the modeled dye position after triangle construction using given FRET efficiencies (see above) and the expected position given the DNA geometry was used.Table S2 denotes ranges, step sizes, and fitted values for all parameters.Overall FRET values also shifted for triangles as well for all positions with respect to the original triangle (iv).g, 3D reconstruction of dsDNA strand (blue/white) with dye positions (red spheres) of three triangles with the same base reconstructed from FRET efficiencies.Triangles differed in the position of their third dye, which was located at nucleotides with indices 4, 7, or 15, counted from the base.Förster radius, DNA twist, DNA axial rise, and dye-DNA linker length were optimized using a tree-based Parzen estimator-based approach.Black numbers and dots denote expected dye positions and indices for linkers attached to different nucleotides, based on DNA geometry and linker length.Images rendered at two different view angles were generated in Blender (v3.6).h, our integrated computational approach can differentiate the 3D structures from each other on a single molecule level with up to 60% accuracy.

Figure S4 :
Figure S4: iMAX FRET-based analysis of closely related DNA nanostructures a, In the complex DNA nanostructure, the position of Dock 2 is changed to three different positions giving rise to three FRET-D2 variations.b, Click-chemistry is used to attach an azide-linked Dock 3 to the backbone DNA with an alkyne handle.The clicked DNA products (cyan box) were gel extracted and then the nanostructures were reconstituted by hybridization.c, The FRET changes between the (variable) Dock 2 and fixed Dock 3 are reflected in the change in the differential position change of Dock 2. d, The changes in Dock 2 also changed the distance between sites 2 and 4, as confirmed by the changing FRET values.e, FRET values for the distances, between sites 3 and 4, as expected, remained largely unaffected.f, The change in FRET values in three points can be similarly recapitulated, for the triangles with imagers and Docks 2,3, and 4.Overall FRET values also shifted for triangles as well for all positions with respect to the original triangle (iv).g, 3D reconstruction of dsDNA strand (blue/white) with dye positions (red spheres) of three triangles with the same base reconstructed from FRET efficiencies.Triangles differed in the position of their third dye, which was located at nucleotides with indices 4, 7, or 15, counted from the base.Förster radius, DNA twist, DNA axial rise, and dye-DNA linker length were optimized using a tree-based Parzen estimator-based approach.Black numbers and dots denote expected dye positions and indices for linkers attached to different nucleotides, based on DNA geometry and linker length.Images rendered at two different view angles were generated in Blender (v3.6).h, our integrated computational approach can differentiate the 3D structures from each other on a single molecule level with up to 60% accuracy.

Figure S5 :
Figure S5: Immobilization scheme of streptavidins and their structural analysis a, BSA-Azide was immobilized on a quartz slide, conjugated with DNA with a DBCO handle at one end and biotin at the other.The presence of only one Azide per BSA molecule allowed the attachment of one biotin, and thus one streptavidin molecule per BSA molecule.Using this newly developed immobilization scheme, we could ensure that only one pocket is filled with biotin for immobilization and that the remaining 3 pockets are available for binding biotinylated docking sequences for fingerprinting.b, D2 symmetry of the wild-type streptavidin tetramer (from PDB ID: 3RY2).1,2,3 and 4 designate the numbering of subunits in the tetramer.Biotins (yellow space fills) are highlighted with dashed blue circles.c and d, With the use of imagers for probing as opposed to covalently conjugated dyes generally used in FRET assays, we could modify the location of dye to artificially change the distance between the 2 points.When 3' instead of 5' dye-labeled imagers were applied, we could see the relative FRET shift to lower efficiencies corresponding to the new distance, on the divalent structures.1,2 cis divalent streptavidin shows a change of 0.30 FRET value, while it is 0.43 for the 1,3 trans divalent streptavidin mutants.

Table S2 :
Förster radius fitting parametersRanges, step sizes, and fitted values for all parameters fitted by the tree-based Parzen estimator optimization algorithm.Here, the structure diameter spans the DNA strand diameter and two times the linker length.