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Small-angle x-ray drop (SAXS) is a able address to delving the structure, dynamics, and conformational transitions of biological macromolecules and their complexes in chargeless band-aid (1–3). In a archetypal SAXS experiment, macromolecules in band-aid are apparent to an x-ray beam, and the broadcast photons are detected and analyzed (Fig. 1A). An important advantage of SAXS is that it does not crave condensate of the sample. It can delving macromolecules beneath a ambit of band-aid conditions, from (near) physiological to awful denaturing. This enables, for example, the apprehension of conformational changes as a action of pH, temperature, salt, or ligand concentration. The actuality that SAXS is a band-aid address is a disadvantage; however, that advice is absent due to rotational averaging, and it does not accommodate the diminutive resolution accomplished by crystallography, nuclear alluring resonance spectroscopy, and cryo–electron microscopy (cryo-EM).

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(A) Schematic of SAXS measurements. The adventure synchrotron-generated x-ray axle (red line) is apparent with x-ray optics. Audible gold-labeled macromolecules are placed into the x-ray axle in a sample cell. The absolute axle is blocked by a axle stop, and broadcast photons are detected appliance a charge-coupled accessory (CCD) detector. (B) Drop acuteness blueprint for a audible labeled molecule. The drop arresting can be addle into a sum of the alone drop contributions: the gold characterization scattering, the gold-macromolecule cross-term, and the drop from the macromolecule only. (C) Schematic of the workflow to actuate the positions of gold labels about to low-resolution three-dimensional (3D) reconstructions of unlabeled macromolecules. The SAXS contour of the unlabeled sample is acclimated in ab initio about-face of a low-resolution archetypal consisting of copy residues or beads. Sterically accustomed gold characterization balloon positions are computed in the bean model. Beginning abstracts from the gold-labeled sample are compared to the computed drop contour for anniversary of the balloon positions, and the best-fitting positions are identified.

Despite the analogously bound advice content, it is accessible to reconstruct low-resolution 3D electron body maps from SAXS data. Algorithms for ab initio about-face of low-resolution 3D structures from 1D SAXS abstracts (4–6) accept sparked an diminutive advance of the use of SAXS to delving and archetypal the anatomy of biological macromolecules and their complexes. The basal acceptance of the about-face algorithms is to represent the atom of assimilation as a accumulating of chaplet or “dummy residues” and to optimize the bean positions to best fit the beginning drop profiles. The after-effects are low-resolution (~1 nm) 3D electron body maps of the samples (5–8). Unfortunately, appointment of authentic domains in high-resolution protein and RNA structures to positions in a low-resolution SAXS map is generally difficult and about requires added advice (9–15). Fundamentally, a SAXS altitude provides advice about the administration of pairwise distances aural a anatomy but, taken in isolation, does not acknowledge the specific identities of the atoms or residues that contributed to the distribution.

Recently, SAXS and aberrant SAXS (ASAXS) abstracts on molecules adapted by two gold nanocrystal probes accept been acclimated to admeasurement awful authentic ambit distributions amid the probes (16–23). While these approaches were able to actuate the acceding of the two gold labels actual precisely, a accepted adjustment to chronicle the characterization position or distances to ab initio–generated low-resolution maps is currently lacking. Here, we authenticate that audible gold nanocrystal labels absorbed to specific residues of biological macromolecules can serve as fiducial markers to accommodate a map from the primary adjustment (and therefore, area structure) to the low-resolution 3D electron body map computed from SAXS data. We appearance that our access is broadly applicative by evaluating its achievement on gold-labeled DNA and RNA constructs with accepted structures, appliance a ambit of ahead declared labeling strategies (16, 21, 22). In addition, we extend its appliance to gold-labeled proteins appliance a atypical labeling approach. Our after-effects advance that the positions of the gold labels can be assigned in the low-resolution map with near–base brace (bp) resolution (down to ~2 Å) and accredit the appointment of protein or nucleic acerbic subdomains.

According to the Debye blueprint (1), the drop acuteness from a accumulating of N scatterers is accustomed by(1)where fi and fj denote the alone drop factors of scatterers i and j, s is the consequence of the drive alteration [with s = 2⋅sin(θ)/λ, area 2⋅θ is the absolute drop bend and λ is the x-ray wavelength], and rij is the ambit amid the ith and jth scatterer. For a gold-labeled macromolecule, the drop contour I(s) contains contributions from the gold nanocrystal label, from pairs of scatterers in the macromolecule, and from pairs consisting of one macromolecular scatterer and the gold characterization (Fig. 1B). Therefore, the all-embracing drop contour depends on the position of the gold probes about to the macromolecule (Fig. 1B).

An overview of our access is as follows: We anon admeasurement the drop profiles of the bald gold probes IAu(s), the unlabeled macromolecule Imol(s), and the macromolecule with a audible absorbed gold delving IL(s). We compute the contour for cross-scattering amid the gold delving and the macromolecule, IAu-mol(s), by abacus the gold delving contour and the unlabeled macromolecule contour from the contour of the apart labeled macromolecule, afterwards normalization. The drop contour of the unlabeled macromolecule was acclimated to accomplish an ab initio low-resolution 3D electron body map. The low-resolution bean archetypal was afresh acclimated to accomplish a set of sterically accustomed balloon gold positions. The experimentally abstinent cross-scattering appellation IAu-mol(s) was afresh compared to the predicted cross-scattering acceding for anniversary of the balloon gold characterization positions. The balloon position that gives the best fit was articular as the best acceptable gold characterization placement. A schematic of our workflow is presented in Fig. 1C.

We acclimated 7 Å–radius thioglucose-passivated gold nanocrystals actinic by the Brust adjustment (see Abstracts and Methods) as fiducial markers absorbed to a ambit of altered biological macromolecules. As assay samples, we acclimated (i) double-stranded DNA (dsDNA) molecules alignment from 10- to 35-bp breadth labeled at their ends; (ii) dsDNA molecules of a anchored breadth of 26 bp internally labeled at assorted positions; (iii) kinked-turn RNA constructs labeled at two agnate ends of the RNA motif; and (iv) the signaling protein calmodulin labeled at two altered positions, agnate to the two lobes of its accepted anatomy (see Abstracts and Methods for capacity of the sample alertness and labeling procedures). SAXS abstracts were recorded at beamline 12-ID of the Advanced Photon Source (APS) and at beamline 4-2 of the Stanford Synchrotron Radiation Lightsource (SSRL) (Fig. 1A and Abstracts and Methods). Because akin sample concentrations are bald in the assay but arduous to accomplish experimentally (16), we adapted acuteness profiles computationally (see Abstracts and Methods). In the aboriginal step, IL(s) was normalized by analogous its appendage to the appendage of IAu(s) at s ≥ 0.04 Å−1 (see Abstracts and Methods for details), area the drop is bedeviled by the gold delving (compare Fig. 2, A and B, chicken ambit and red lines). In the added step, Guinier assay was activated to appraisal the advanced drop acuteness for all drop profiles (Fig. 2, A and B) and acclimated to adapt the molecule-only drop contour Imol(s).

(A and B) SAXS profiles and Guinier fits for adumbrative samples [20-bp end-labeled DNA in (A) and calmodulin labeled at position N111C in (B)]. Beginning SAXS profiles are apparent as circles and the cardinal of s-bins is bargain for clarity. Guinier fits to actuate I(0) are apparent as solid lines. (C and D) 3D reconstructions of 20-bp DNA in (C) and calmodulin in (D). The accepted high-resolution structures are superimposed (27). (E and F) Balloon gold characterization positions (blue spheres) afflicted about the envelope of the 3D about-face for the 20-bp DNA (E) and calmodulin (F). (G and H) Afflicted absolute acuteness profiles for a bargain set of balloon gold characterization positions for 20-bp DNA (G) and calmodulin (H). All balloon profiles were ordered from the best to the affliction fitting, and every 20th ambit is apparent for clarity, constant in 91 traces for 20-bp DNA (G) and 1200 traces for calmodulin (H).

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Next, we analyzed the gold-only drop IAu by decomposing the beginning drop arresting into a beeline aggregate of abject profiles for all-around scatterers (fig. S1) (16). Non-negative diminutive aboveboard fits showed acceding with the beginning abstracts (fig. S2) and adapted a attenuated admeasurement administration of the gold nanocrystals used. The adapted representation of the gold drop was acclimated afterwards as the anatomy agency fAu(s) for the gold particles in appraisal of the Debye blueprint (Eq. 1).

We congenital ab initio low-resolution models of the macromolecules beneath abstraction appliance the drop abstracts from the unlabeled macromolecules appliance accustomed procedures (see Abstracts and Methods). The low-resolution reconstructed electron body maps appearance acceding with the high-resolution structures for all abstinent DNA constructs d accepted B-form DNA braid geometries (Figs. 2C, 3, and 4B) (24), the RNA kink-turn burden (Fig. 5B) (22, 25, 26), and the calcium-bound holo anatomy of calmodulin (Fig. 2D) (27, 28).

(A) Accessory anatomy of the 35-bp DNA bifold and the gold characterization position adumbrated on the 3′ end of the aerial strand. (B) Mapping gold characterization positions to 3D reconstructions appliance SAXS abstracts for end-labeled DNA. Larboard column: Schematic representations of the 10-, 15-, 20-, 25-, 30-, and 35-bp DNA constructs end-labeled with gold nanocrystals acclimated in the study. Boilerplate and adapted columns: Ancillary (middle) and advanced (right) bend of the 3D reconstructions of the unlabeled samples (shown as gray spheres) and mapped positions of the gold labels (blue to red spheres; dejected spheres accord to the best fit). The adjustment of the gold labels at the end and askance is reproduced well.

(A) Accessory anatomy of the 26-bp DNA duplex. Black belletrist announce bases acclimated for centralized labeling. The aforementioned blush cipher is acclimated in (B) and (C). (B) Low-resolution appearance reconstructions of the unlabeled DNA (gray) superimposed on a high-resolution structure. The best-fitting characterization positions for the six altered centralized gold characterization positions are apparent as black spheres. (C) Ambit to the centermost of the DNA computed as the beggarly and SD of the best 50 reconstructed and filtered characterization positions for anniversary adapter point as a action of the ambit of the labeled abject from the centermost of the braid [converted appliance a circling acceleration per abject of 3.3 Å (16, 17)]. The abject band indicates 45°. The RMSD amid computed and accepted positions is 2.1 Å.

(A) Accessory anatomy of the RNA kink-turn and the two labeling positions at the 3′ ends for the alone constructs. The 3-nt kink-turn appendage is displayed with a baby vertical offset, and the three-base conflict arena is apparent in orange. (B) Appearance about-face of the unlabeled RNA kink-turn (light gray shape) superimposed with the high-resolution anatomy (22). (C) Low-resolution archetypal (gray spheres) and best-fitting gold nanocrystal positions (blue and red spheres) afterwards filtering. (D) Besprinkle artifice of filtered gold characterization positions. The x arbor amount of the adapted characterization positions is advised against the all-embracing ambit to the geometrical centermost of the low-resolution appearance reconstruction.

To actuate the gold characterization position, we created gold brand balloon positions by about breeding ~100 positions on an 11 Å–radius apple (corresponding to the addendum of the 7 Å–radius gold atom and the ~4 Å linker) about anniversary bean in the low-resolution about-face (see Abstracts and Methods). Subsequently, positions that aftereffect in steric clashes were eliminated. The sterically accustomed balloon positions (typically ~1000 to 25,000 for the structures advised here) belted the absolute reconstructed low-resolution maps (Fig. 2, E and F). We afresh computed the absolute drop acuteness for every gold characterization balloon position by abacus the gold-labeled and unlabeled macromolecule drop acceding to the afflicted drop cross-term amid the gold brand and the macromolecule. We begin that altered balloon positions resulted in decidedly altered afflicted drop intensities Itotal(s), with the constant profiles depending on the about label-molecule adjustment (Fig. 2, G and H), suggesting that the drop profiles of the gold-labeled macromolecules accommodate the adapted advice about the about gold probe–macromolecule arrangement. To actuate the best balloon position, we evaluated the normalized aboveboard aberration amid the computed profiles and the beginning drop contour of the labeled macromolecules (Eq. 13). The balloon positions were ordered from the best to affliction fitting. We associated the best-fitting balloon position with the best acceptable gold brand placement.

We aboriginal activated our action to actuate the gold characterization positions to end-labeled dsDNA molecules alignment from 10 to 35 bp (table S1). The low-resolution reconstructed structures apparent annular shapes with a amplitude and breadth as accepted for our altered DNA constructs (Fig. 3B). The afflicted profiles for the gold anatomy agency model, the 3D bean reconstruction, and the best-fitting balloon position showed accomplished acceding with the beginning abstracts for the gold nanocrystals, the unlabeled DNA molecules, and the labeled molecules, appropriately (fig. S2).

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All balloon gold characterization positions were ordered from best to affliction applicative for anniversary DNA length. For visualization, the best 100 positions (out of a absolute of 1055 to 2521) are shown, with the top 10 positions black from dejected to white and the aing 90 positions black from white to red. The best-fitting positions were amid at the ends of the reconstructed annular body maps for all advised DNA lengths and off the annular arbor (Fig. 3B), as accepted for the end-labeled constructs with a linker that positions the gold nanocrystal characterization off-axis (17, 23). The DNA constructs are about symmetric beneath both circling forth the braid arbor and barter of the ends. These symmetries are arresting in the reconstructed characterization positions: At anniversary end, the best-fitting positions resulted in a doughnut-like appearance (Fig. 3B, right). In addition, we empiric well-fitting gold characterization positions at both ends of the reconstructed annular shapes.

Because the drop accession (in particular, the advanced scattering) increases about quadratically with diminutive accumulation (1, 2), the accession of the DNA about to the (fixed-size) gold characterization increases with accretion DNA breadth for the gold-labeled DNA constructs (fig. S2, analyze the aboveboard and amphitheater abstracts points). The beyond about arresting from the DNA appears to enhance the accession accurateness in our gold characterization appointment procedure, as apparent by a bargain besprinkle and stronger assimilation of the best-fitting balloon positions for the best DNA constructs (Fig. 3B). In summary, the abstracts for end-labeled DNA constructs authenticate that it is accessible to anxiously accredit the characterization positions to the end of the braid and off-axis for all advised DNA lengths.

To assay our adjustment for labels absorbed in the autogenous of a nucleic acerbic sequence, we acclimated dsDNA gold constructs with a anchored breadth of 26 bp and capricious centralized characterization positions (Fig. 4A and table S2). Again, the altered afflicted profiles gave accomplished fits to the beginning drop profiles of the single-labeled DNA, the unlabeled DNA, and the gold nanocrystals (fig. S3). The abstracts announce that audible characterization positions crop altered cross-scattering acceding (fig. S3, red lines) and, thus, can be distinguished. All balloon characterization positions were afresh ordered from best to affliction fitting, and the best-fitting positions for anniversary of the centralized characterization placements are apparent in Fig. 4B. The classification for the centralized characterization positions is based on the ambit of the labeled abject position (in bases) and the DNA fiber (strand A or B; table S2), counting from the 5′ ends. For example, A4 (Fig. 4B, amethyst sphere) carries a characterization on the fourth abject from the 5′ end of DNA fiber A, and B11 (Fig. 4B, dejected sphere) carries a characterization on the 11th abject of DNA fiber B. For example, as expected, the A4 (Fig. 4B, amethyst sphere) characterization position is amid a the end of the reconstructed DNA atom (Fig. 4B, gray envelope), admitting the B11 (Fig. 4B, dejected sphere) position was bent to be about at the beggarly of the duplex. We computed the beggarly and SD of the ambit from the centermost of the reconstructed appearance forth the circling arbor (indicated by the arrows in Fig. 4B) for the 50 best-fitting positions for all six internally labeled constructs. We agenda that, agnate to the end-labeled DNA constructs discussed in the antecedent section, the actual aerial amount of acceding of the bald DNA bifold does not acquiesce us to abnormally accredit the ends. However, we can actuate the ambit from the centermost of the bifold with aerial accurateness for anniversary of the characterization positions: The reconstructed characterization positions are compared to the ambit from the centermost that is accepted from the DNA structure, demography into annual that the characterization position is confused by hardly beneath than one abject in the 3′ administration because of the acclimatization of the adapter to the DNA (Fig. 4B) (21). Overall, we acquisition acceding amid the computed and accepted characterization positions [the basis beggarly aboveboard aberration (RMSD) is 2.1 Å and the bargain χ2 = 1.7; Fig. 4C]. We accepted characterization positions A8 and B17 to accept about identical distances to the center, which is reproduced able-bodied by the best-fitting balloon positions (Fig. 4). We can anxiously analyze the position of labels afar by alone 1 to 2 bp (Fig. 4C), agnate to a ambit of ~3 to 5 Å. The boilerplate aberration amid abstinent and accepted positions is 0.6 bp or 1.9 Å. Together, our after-effects advance that our action to accredit the position of gold labels can accomplish a few Ångström resolution, aing to the resolution accomplished in x-ray drop interferometry abstracts with two gold labels (16, 20–23, 29, 30) and bigger than the ~10 Å resolution for accepted SAXS measurements.

Having approved the annual of our adjustment to DNA, we aing activated it on gold-labeled RNA constructs. We acclimated an RNA kink-turn burden (table S3) that was adapted with gold nanoparticles at the 3′ end positions (Fig. 5A) (22, 29). RNA kink-turn motifs are frequently begin in anatomic RNAs, including the ribosome. They abide of a 3–nucleotide (nt) appendage belted by a GA/AG bike abject pair, which stabilizes a coil of added than 90° in the crabbed helices (22, 25, 26). Again, ab initio appearance about-face was acclimated aboriginal to compute a low-resolution electron body map, which showed acceding with a high-resolution archetypal (Fig. 5B) (22). The experimentally recorded and reconstructed profiles were afresh in acceding for the best-fitting balloon positions at both delving locations (fig. S4). The balloon positions were filtered (see Abstracts and Methods), and the final afflicted delving positions for the two gold labels were amid on adverse abandon of the RNA kink-turn burden (Fig. 5, B and C). The computed gold characterization positions (Fig. 5B, dejected and red spheres) appearance acceding with the positions of the probe-modified bases in the high-resolution model. For added assay and quantification, the low-resolution body map and the afflicted balloon credibility were accumbent (Fig. 5B). The positions of the balloon credibility forth the x arbor were authentic as in Fig. 5C, and their distances from the geometrical centermost of the reconstructed appearance were afflicted (Fig. 5, B and C, gray shape). We agenda that the RNA kink-turn burden in our abstraction is about symmetric, accepting 12-nt pairs in the “arms” on either ancillary of the 3-nt axial kink-turn bulge. The alone aberration amid the two accoutrements is that one ancillary is absolutely base-paired, admitting the added ancillary has a three-base conflict aing to the axial appendage (Fig. 5D and table S3). The bright break of the adapted characterization position for the labels at the two audible termini demonstrates that specific nucleotide sequences can be actually amid in low-resolution reconstructed body maps, alike for almost accessory differences in the structures.

Having approved our adjustment for a ambit of DNA and RNA constructs that relied on authentic labeling chemistries, we aing developed a acceding to attach the aforementioned gold nanocrystal labels to proteins. The adeptness to characterization proteins extends our access to the third above chic of biological macromolecules. We acclimated two altered mutants of the calcium-binding agent protein calmodulin that backpack single-cysteine mutations at called positions (R37C and N111C; see Abstracts and Methods) as a archetypal system. We took advantage of the thiol ancillary alternation of cysteine to brace gold nanocrystals anon to the called positions of the protein (31–33). We focused on the calcium-bound state, that is, the holo anatomy of calmodulin, which appearance two almost annular and audible lobes (27).

While calmodulin is able-bodied accepted to abide ample conformational changes aloft Ca2 bounden or interactions with added bounden partners, beneath the altitude of our acceding (≥5 mM Ca2 ; altitude with 5 and 10 mM Ca2 gave identical results, aural error; fig. S5A), calmodulin has two adamant annular Ca2 -binding domains affiliated by an α-helical linker arena that provides interdomain adaptability (34–40). The acceptance of an all-embracing bankrupt protein with two lobes that are affiliated by a linker arena with some adaptability is authentic by several ambit of evidence: (i) the Kratky representation [s2⋅I(s) against s] of the drop abstracts is apocalyptic of a bankrupt protein (fig. S5B); (ii) the histogram of pairwise ambit P(r) is constant with the archetypal bend dodo appearance of calmodulin in the attendance of Ca2 (fig. S6F) (36, 41, 42); (iii) our beginning SAXS profiles are analytic aing to the predicted contour (43) from an accessible bright anatomy (Fig. 2D) of Ca2 -bound calmodulin (fig. S5C), in band with antecedent SAXS appointment (42), but the accept at s ≈ 0.025 Å−1 is beneath arresting in the beginning data, advertence a abate break amid the two domains than in the bright structure; and (iv) assorted ab initio about-face runs converged on a audible structure, as adumbrated by pairwise normalized spatial alterity (44) ethics of ≈0.5, in acceding with antecedent SAXS appointment that has modeled calmodulin with a audible anatomy beneath agnate beginning altitude (42).

The two mutants were called such that the cysteines are positioned at the apparent of the two altered lobes and placed to abstain steric clashes of the gold labels with the protein. Labeling of agnate calmodulin constructs with cyanine dyes (45) or ample gold nanoparticles (~40 to 60 nm in bore via a biotin-streptavidin linkage) (46) larboard them absolutely functional. In addition, adapter of ~1.5-nm gold nanoparticles coated with uncharged ligands, agnate to the particles acclimated in this work, anon to cysteine residues of cytochrome c did not adjy the anatomy of the bankrupt protein (32).

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For abstracts assay and gold brand position about-face of the labeled calmodulin data, we acclimated the aforementioned action as for the labeled nucleic acerbic constructs. For anniversary construct, the best-fitting balloon positions were afflicted and sorted according to the affection of fit. The best balloon positions were filtered as declared in Abstracts and Methods. The reconstructed acuteness profiles appearance actual aing affinity to the experimentally abstinent profiles (fig. S7). The best-fitting balloon positions afterwards clarification for the R37C (Fig. 6A, blooming spheres) and N111C constructs (Fig. 6A, red spheres) bout the positions of these amino acids in the high-resolution structures (Fig. 6, A and B). The Ca2 -bound calmodulin has two about symmetric helix-loop-helix domains afar by a linker (27); the bright break of the reconstructed gold characterization positions suggests that our adjustment can accredit the authentic positions of both labels admitting the adaptability of the axial linker and accordingly analyze domains with alike almost baby differences in structure.

(A) Bright anatomy of Ca2 -bound calmodulin (27) with mutated amino acerbic positions adumbrated by black spheres (R37, blue; N111, red). (B) View of the 3D reconstructions of the unlabeled protein (shown as amber spheres) and mapped positions of the gold labels at R37C (blue) and N111C (red) as black spheres for the filtered final characterization positions. The adjustment of the gold labels at the appointed positions is able-bodied reproduced.

We acclimated SAXS abstracts to actuate gold nanocrystal characterization positions about to low-resolution electron body maps computed from SAXS abstracts for a ambit of biological macromolecules, including 10- to 35-bp-long end-labeled dsDNA, internally labeled dsDNA, an RNA kink-turn motif, and calmodulin as a protein archetypal system. Combined, our after-effects appearance that our adjustment is broadly applicative to all above classes of biological macromolecules and that, by appliance baby (~7 Å in radius; ~80 gold atoms) gold nanocrystals as fiducial markers, the position of gold probes and the agnate labeled residues can be accurately amid in low-resolution reconstructions. Free the 3D position of specific labeled residues allows the adjustment of the macromolecule to be placed aural the macromolecular shape. The gold-labeling access distinguishes altered domains and accessory anatomy elements.

Our appointment opens up several possibilities and approaching directions. The approved adeptness to site-specifically characterization proteins with baby gold nanocrystals creates the achievability of extending x-ray drop interferometry gold-gold ambit abstracts by SAXS (16, 17, 29) or ASAXS (23) to proteins and assay of the structural adjustment of protein–nucleic acerbic complexes. Appliance of our about-face adjustment to doubly gold-labeled macromolecules could accommodate added information, in particular, to dness ambiguities in the about placements of residues, for example, in reconstructions that accept centralized symmetry. Our accepted acceding assumes that the macromolecule of assimilation adopts a categorical anatomy or at diminutive one ascendant anatomy in solution. It ability be accessible to relax this acceptance in the future, back SAXS is capable, in principle, of acid conformational apparel (47–49). While labeling baby gold nanoparticles with uncharged ligands tends to advance the anatomy of proteins and nucleic acids, for macromolecules or complexes of alien structure, in general, testing the functionality and structural candor of the labeled constructs will be important.

While this proof-of-concept abstraction uses gold nanoparticles as labels, we apprehend our adjustment to be appropriately applicative to added labels, such as argent and platinum nanoparticles, which could accommodate appropriately adorable and erect labeling options and ability admittance accompanying abstracts of several brand positions appliance ASAXS. Finally, we ahead that our accepted access will not be bound to SAXS. Zhang and coworkers (50) afresh approved that gold labels can be acclimated to access structural and dynamical advice for labeled DNA duplexes in cryo-EM measurements. In conclusion, nanometer-sized metal probes accommodate a able new access to free absolute balance positions in a biological macromolecule. We ahead that this access will accommodate new and quantitative insights into macromolecular structure, dynamics, and interactions.

Water-soluble gold nanocrystals were actinic and antiseptic as declared ahead (16, 17, 29). The constant gold nanocrystals were passivated with a 1-thio-β-d-glucose ligand carapace to balance the gold nanoparticles and to accomplish a awful monodisperse admeasurement administration (fig. S1) (51).

All DNA/RNA sequences acclimated in this abstraction are accustomed in tables S1 to S3. The DNA and RNA oligonucleotides for gold labeling at the ends were able on an automatic ABI 394 DNA synthesizer (Applied Biosystems), and thiols were congenital appliance a C3-thiol-modifier (part #20-2933-41, Glen Research) on the 3′ end of the single-stranded DNA or RNA. Oligonucleotides were antiseptic appliance ion-exchange high-performance aqueous chromatography (HPLC), followed by reversed-phase HPLC. The coupling of the gold nanoparticles to the 3′ ends of DNA was as declared by Mathew-Fenn et al. (16, 17), and the acceding for gold-labeling RNA constructs was agitated out as declared by Shi et al. (22). Briefly, a fivefold balance of gold nanocrystals was alloyed with the thiol-modified single-stranded DNA or RNA molecules in a absorber band-aid at a pH of 9.0. Afterwards 2 hours, bachelor gold nanoparticles or gold nanocrystals conjugated with assorted single-stranded DNA strands were removed by ion-exchange HPLC, and the artefact was stored at −20°C. A NanoDrop ND-1000 (NanoDrop Technologies) was acclimated to actuate final sample concentrations by quantifying the absorbance at 260 and 360 nm. The single-stranded DNA oligonucleotides were annealed with their commutual strands at allowance temperature for 30 min, admitting RNA oligonucleotides were annealed at 40°C for 30 min.

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The action for advancing the internally labeled DNA constructs was as declared (21). The oligonucleotides (table S2) with centralized amino-modified thymine (Amino-Modifier, C2 dT) were able on an ABI 394 DNA synthesizer (part #20-2933-41, Glen Research) and reacted with a band-aid absolute 1 mg of succinimidyl 3-(2-pyridyldithio)propionate per 10 μl of dimethyl sulfoxide, and the disulfide arch was broken afterwards appliance a band-aid composed of 200 mM dithiothreitol (DTT) and 50 mM tris-HCl (pH 9.0). Finally, commutual DNA strands were alloyed and antiseptic by anion barter HPLC to access authentic single-labeled samples.

We acclimated calmodulin as a protein archetypal system. Calmodulin is a able-bodied characterized and abiding protein with a accepted bright structure; in addition, it has the advantage that the agrarian blazon is artlessly cysteine-free. Calmodulin was bidding and labeled with gold nanocrystals as follows: A audible cysteine was alien in sea brat calmodulin by agency of the alteration R37C or N111C. This calmodulin was bidding in Escherichia coli and antiseptic as declared by Gopalakrishna and Anderson (52). The calmodulin [800 μM in 50 mM tris-HCl (pH 7.4) and 1 mM DTT] was incubated in 150 μl of 10 mM DTT and 50 mM tris-HCl (pH 9.0). Balance DTT was removed by a fast-flow G25-sepharose circuit filtration cavalcade (GE Healthcare), and anon afterwards purification, a 5:1 arrangement of antiseptic and desalted gold nanocrystals to protein and 20 μl of 1 M tris-HCl (pH 9.0) were added to the band-aid and incubated for 2 hours at allowance temperature. The acknowledgment was chock-full by abacus 15 μl of 2 M ammonium acetate band-aid (pH 5.6). Finally, unreacted gold nanocrystals and unlabeled proteins were removed appliance the Superdex 75 gel filtration column.

SAXS abstracts were performed at the BESSRC-CAT beamline (53) 12-ID of the APS (for end-labeled DNA and calmodulin) and at beamline 4-2 of the SSRL (for end-labeled and internally labeled DNA and the RNA kink-turn). At beamline 12-ID, we acclimated an x-ray activity of 12 keV, a sample detector ambit of 1 m, and a custom-built sample corpuscle (54). For calibration, a argent behenate accepted was acclimated to locate the axle centermost and calibrate the drop angle. An acknowledgment time of 10 × 1 s and a CCD detector were acclimated for abstracts collection. Abstracts were bargain appliance the Goldcontrol software package. At SSRL, an x-ray activity of 9 keV and a sample-detector ambit of 1.5 m or an x-ray activity of 11 keV and a sample-detector ambit of 1.1 m were chosen. Abstracts were calm appliance a beeline position–sensitive proportional adverse (LPSPC) in 10 1-min exposures and a Mar CCD165 (MAR) in 20 15-s exposures. Abstracts calm appliance the LPSPC detector were bargain with the OTOKO and SAPOKO software packages, and abstracts calm appliance the MAR detector were bargain with the BlueIce software amalgamation and added scripts provided at the beamline.

All SAXS abstracts for DNA samples were performed in 70 mM tris-HCl absorber (pH 8.0) with 100 mM NaCl and 10 mM sodium ascorbate added. SAXS abstracts for RNA kink-turn samples were acquired in 70 mM tris-HCl absorber (pH 7.4) with 60 mM NaCl, 10 mM MgCl2, and 10 mM sodium ascorbate added, and altitude for calmodulin samples acclimated 60 mM tris-HCl absorber (pH 8.0) with 100 mM NaCl, 10 mM sodium ascorbate, and 5 mM CaCl2, unless contrarily indicated. Samples were abstinent at allowance temperature in sample beef with a 2-mm aisle breadth and 25-μm mica windows (54). Absorber profiles were abstinent afore and afterwards anniversary sample appliance identical procedures and subtracted for accomplishments correction. Drop curves absolute dsDNA were recorded at 50 μM and dsRNA at 30 μM sample concentration, admitting calmodulin abstracts were acquired at 250 μM.

We acclimated SAXS3D (6) and DAMMIN (5, 55) to reconstruct the low-resolution bean models from the drop profiles of the unlabeled samples. In all cases, again DAMMIN runs converged and yielded structures with pairwise normalized spatial alterity (44) ethics of <1.0. Custom-written MATLAB scripts were acclimated to fit the acuteness contour of the unlabeled sample appliance the reconstructed bean archetypal and the gold-only drop profile, and to reconstruct the macromolecule–gold characterization arrest term. These acuteness patterns were acclimated to reconstruct position-dependent drop profiles of gold label–molecule constructs, as declared below. In addition, radii of ambit and P(r) functions were computed for all samples appliance PRIMUS (56) and are presented in table S4 and fig. S6.

Our assay of the labeled samples requires adapted normalization of the drop intensities for the labeled, unlabeled, and gold-only samples. In principle, this normalization is not all-important if all three samples are abstinent at identical (molar) concentrations. However, in practice, it is difficult to adapt altered samples at absolutely akin concentrations, and therefore, the afterward normalization action was implemented. First, the acuteness contour of the gold nanocrystal–labeled sample IL(s) was akin to the acuteness contour of the gold nanoclusters IAu(s) in such a way that the best overlap of both drop profiles was accomplished for intensities at s > 0.04 Å−1 area the drop of the labeled sample is bedeviled by the gold nanocrystal (Fig. 2, A and B) (16, 17). Second, Guinier assay was agitated out for all three profiles to actuate the advanced drop intensities IAu(0), IL,N(0), and Imol(0) appliance PRIMUS (56), area IL,N(s) denotes the gold-labeled contour afterwards the antecedent normalization to the gold-only profile. For the advanced drop intensity, that is, for the absolute s → 0, the Debye blueprint simplifies to(4)where we accept afflicted identical fi and authentic the drop amplitude A in the aftermost step. The drop acuteness of the labeled sample is the sum of the normalized drop acuteness of the gold crystal, normalized unlabeled molecule, and the drop cross-term of gold bright and unlabeled molecule.(5)(6)

Using the Guinier extrapolated IAu(0) as A2Au(0) and IL,N(0) as A2L,N(0), this boxlike blueprint can be apparent for Amol(0); the band-aid with the abrogating basis for Amol(0) amount was alone as abrogating ethics for Amol(0) were aerial in this context. Appliance the computed amount Amol from Eq. 6, the ascent amount cunlabeled was afflicted as the arrangement amid the computed A2mol and the Guinier extrapolated Imol(0) of the beginning abstracts for the unlabeled sample to calibration the beginning contour of the unlabeled sample for the added assay declared below.(7)(8)

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Our adjustment requires a set of balloon gold characterization positions enveloping the low-resolution electron body map and compares the drop contour for agreement the gold characterization at anniversary alone balloon point to the beginning abstracts for the gold-labeled macromolecule. To access a set of accessible gold characterization positions, 100 accidental coordinates on a apple of 11 Å ambit [corresponding to the 7 Å gold nanocrystal ambit and the about 4 Å linker breadth (16, 17, 21, 58)] were generated about anniversary copy atom or bean in the reconstruction. Next, sterically banned positions were alone from this set of balloon gold positions by auctioning all balloon positions that were amid aural 7 Å (the nanocrystal size) of any bean of the reconstructed model. Control calculations with beneath or added balloon positions per bean (fig. S8) advance that 100 balloon positions accommodate acceptable accurateness for the appointment of best characterization positions while actuality computationally efficient.

Next, abstract drop profiles for the labeled atom with the gold characterization in anniversary of the balloon gold positions were calculated. This ciphering can be agitated out efficiently, back the drop cross-term acquired by arrest amid the gold nanocrystal and the macromolecule is the alone appellation afflicted by the characterization position about to the molecule. The acuteness of the cross-term was afflicted appliance the Debye blueprint (Eq. 1), including alone gold-molecule terms, that is, the basis i runs over all chaplet or point scatterers in the representation of the macromolecule (see Eq. 2), and ri is the ambit from bean i to the centermost of the gold label(9)The drop amplitude AAu(s) was bent by demography the aboveboard basis of the non-negative diminutive aboveboard fit to the beginning admeasurement abstracts of the gold nanocrystals.(10)

This action takes into annual the bend annex of the gold atom scattering. We agenda that Eq. 10 neglects the abstract allotment of the diminutive anatomy factors, that is, of the aberrant dispersion. However, contributions from the abstract allotment of the burning are negligible for our measurements, back we are abundantly far (≥80 eV) from the assimilation edges of all diminutive breed involved. Moreover, the diminutive drop amplitude Amol, approximated as s-independent, was afflicted via the afterward expression(11)

The ascent ethics c1 and c2 were acquired from applicative the Debye blueprint (Eq. 2). N is accustomed by the cardinal of copy atoms in the appearance about-face and s1 by the aboriginal drop bend s actualization in the amid beginning data. Afterwards accretion the cross-scattering appellation IAu-mol for every balloon gold characterization position appliance Eqs. 9 to 11, the cross-scattering acuteness profiles were summed with the reconstructed gold characterization IAu and unlabeled atom Imol drop appellation to get a reconstructed drop contour of the labeled sample Itotal (Fig. 1B)(12)

To actuate the best acceptable characterization position, we compared the computed drop profiles for the labeled atom Itotal to the experimentally abstinent drop profiles of the labeled samples appliance the afterward criterion(13)where IL,N is the beginning abstinent (normalized) drop contour of the gold-labeled sample; and IAu, Imol, and IAu-mol are the reconstructed drop acuteness profiles of the gold nanocrystals, the unlabeled macromolecule, and the cross-scattering term, respectively. The ascent ambit cmin,1 and cmin,2 were bent for every balloon position appliance the fminsearch action in MATLAB to abbreviate T. Finally, all balloon characterization positions were sorted by their T array from best to affliction fitting.

For some of the samples, the best-fitting gold characterization positions were added candy appliance the afterward assimilation approach. First, we computed the beggarly (x,y,z) position for the 10 best-fitting balloon positions. Next, we evaluated the ambit from the beggarly (x,y,z) position and the SD in anniversary Cartesian alike for the 100 best-fitting balloon positions. Credibility were alone if their ambit from the beggarly (x,y,z) position was greater than 1 SD in any of the three coordinates. The actual credibility were acclimated for added analysis.

Acknowledgments: We acknowledge T. Matsui and T. Weiss for the advice with abstracts at beamline 4-2 at the SSRL; S. Seifert for the advice with abstracts at beamline 12ID at the APS; and R. Das, S. Sedlak, Z. Ökten, and A. Dunn for discussions. Funding: This appointment was authentic by the German Analysis Foundation (SFB 1032) and the NIH (PO1 GM066275 to D.H. and DP-OD000429-01 to P.A.B.H.). This analysis acclimated assets of the APS, a U.S. Department of Activity (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory beneath arrangement no. DE-AC02-06CH11357. Columnist contributions: P.A.B.H., S.D., and J.L. advised the study. T.Z., R.S.M., X.S., and J.L. performed the experiments. T.Z. and J.L. analyzed the abstracts and implemented the characterization appointment method. All authors contributed to the autograph of the manuscript. Aggressive interests: The authors acknowledge that they accept no aggressive interests. Abstracts and abstracts availability: All abstracts bald to appraise the abstracts in the cardboard are present in the cardboard and/or the Supplementary Materials. The MATLAB codes acclimated to accomplish the appear after-effects and the raw drop abstracts that abutment the allegation are accessible from the agnate columnist aloft request. Added abstracts accompanying to this cardboard may be requested from the authors.

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