Quantitation of ten 30S ribosomal assembly intermediates using fluorescence triple correlation spectroscopy

Abstract

The self-assembly of bacterial 30S ribosomes involves a large number of RNA folding and RNA-protein binding steps. The sequence of steps determines the overall assembly mechanism and the structure of the mechanism has ramifications for the robustness of biogenesis and resilience against kinetic traps. Thermodynamic interdependencies of protein binding inferred from omission-reconstitution experiments are thought to preclude certain assembly pathways and thus enforce ordered assembly, but this concept is at odds with kinetic data suggesting a more parallel assembly landscape. A major challenge is deconvolution of the statistical distribution of intermediates that are populated during assembly at high concentrations approaching in vivo assembly conditions. To specifically resolve the intermediates formed by binding of three ribosomal proteins to the full length 16S rRNA, we introduce Fluorescence Triple-Correlation Spectroscopy (F3CS). F3CS identifies specific ternary complexes by detecting coincident fluctuations in three-color fluorescence data. Triple correlation integrals quantify concentrations and diffusion kinetics of triply labeled species, and F3CS data can be fit alongside auto-correlation and cross-correlation data to quantify the populations of 10 specific ribosome assembly intermediates. The distribution of intermediates generated by binding three ribosomal proteins to the entire native 16S rRNA included significant populations of species that were not previously thought to be thermodynamically accessible, questioning the current interpretation of the classic omission-reconstitution experiments. F3CS is a general approach for analyzing assembly and function of macromolecular complexes, especially those too large for traditional biophysical methods.

The complete assembly mechanism for the 30S ribosome has remained elusive. Approximate rate constants and orders of binding are known from kinetic experiments, but kinetic profiles for individual protein binding and RNA folding steps are complex and defy simple models (1–8). The fundamentally kinetic process of ribosome assembly is thus still best understood in terms of the thermodynamic (9) maps generated by the Nomura group in the 1970s (10). The Nomura maps documented how the omission of one protein precludes incorporation of others, but only monitored stable protein-RNA interactions that would survive the biochemical purification steps including nonequilibrium ultracentrifugation. Recent RNA protection data suggest that weak protein-RNA interactions form rapidly during assembly (5, 6), raising the question of how completely the map represents the types of intermediates that form during assembly.

Nomura dependencies exist between three specific proteins, S7, S9, and S19, that bind the 16S rRNA (Fig. 1A) late in assembly (2, 4–8). In principle, binding of these three proteins to RNA could occur by any and all possible parallel pathways that are illustrated schematically in Fig. 1B. In the observed binding dependencies (10) (Fig. 1C) prior binding of S7 is required for stable incorporation of either S9 or S19, limiting the possible pathways to those in Fig. 1B drawn with solid lines and precluding the intermediates marked with asterisks. In general, kinetics of protein binding monitored by either isotope pulse-chase (5, 7) or time-resolved hydroxyl radical footprinting (6, 8) both suffer from the limitation that binding of each protein is measured as the average behavior of all of the populated intermediates that contain that protein (Fig. 1D). There is no information about the correlations in binding of any set of two or more proteins, and knowledge of dependencies and pathways are thus lost in the average. In the present example for proteins S7, S9, and S19, the challenge to resolve and quantitate the ten possible substoichiometric intermediates and quantitate them at equilibrium demands a new biophysical approach.

Fig. 1.

Experimental scheme for resolving all possible 30S ribosome intermediates for S7, S9, S19 binding. (A) Partial structure of the 30S subunit (29). Proteins S7, S9, and S19 bind the 3′ domain of the 16S rRNA late in assembly. (B) Assembly funnel diagram depicting all possible ways the three proteins could bind. Presumed assembly paths (black lines) connect ribosomal intermediates and multiple parallel paths connect unassembled states at the top with the completed quaternary complex at the bottom (energy minimum). (C) The 3′ portion of the classic thermodynamic assembly map (10) predicts that only S7 can bind independently to the 16S rRNA, and while binding of both S9 and S19 require prior binding of S7, they do not depend strongly on each other. By extension, the dashed assembly pathways are not taken, and three of the intermediates (*) are not formed. (D) The scheme for identifying all 10 ribosomal assembly intermediates uses three different FCS methods to each detect a different group of intermediates. FCS (15, 16) detects the sum of concentrations of all species labeled with a particular color of fluorophore, with independent measurements performed for each of three colors. While kinetic analysis of autocorrelation data identifies the fraction of proteins which are bound (35), single-color autocorrelation can not resolve different bound intermediates from each other. (E) FCCS (19) combines fluorescence from two different colors to identify intermediates with both fluorophores. Even with both FCS and FCCS, the composition of the mixture is ambiguous because the triple-labeled intermediate can not be resolved from any of the double-labeled intermediates. (F) F3CS combines fluorescence from three channels to identify intermediates with all three fluorophores, which completes the identification scheme and allows the concentrations of all ten intermediates to be determined. However, combining three signals by triple-correlation requires fundamental expansions of FCS theory and data analysis.

The stoichiometry of each intermediate would be obvious if proteins were tagged with different colored fluorophores and single intermediates could be observed (11, 12). However, with notable exceptions (13), such single-molecule experiments require subnanomolar sample concentrations in order to resolve individual molecules, and are thus unable to probe the weaker interactions that are generally implicated in the early stages of macromolecular assembly (14). When samples are measured at higher concentrations and 10–100 molecules are observed at once, the fluorescence intensity data are not as intuitively analyzed but information about linked binding persists in the way the fluorescence fluctuates. Fluorescence Correlation Spectroscopy (FCS) (15, 16) is a framework for analyzing fluctuations in high-concentration samples and even live cells (17, 18). By performing FCS on pairs of fluorescence traces, where each trace reports on a separate fluorophore, Fluorescence Cross-Correlation Spectroscopy (FCCS) (17, 19–22) identifies the coincident fluctuations that signify bound populations of the two subunits. Performing FCS on three channels would identify populations of intermediates that contain S7, S9, and S19. However, attempts to date have been based upon coincidence methods (23, 24) that are not rigorously compatible with FCS and FCCS and cannot distinguish double and triple-labeled particles at high concentrations.

Here, we develop Fluorescence Triple-Correlation Spectroscopy (F3CS), verifying a new theory (25) of FCS that was rederived for three sequential observations using the framework of High-Order Correlations (26). F3CS data are readily compatible with FCS and FCCS data and informative at high concentrations, and this is the key to quantifying the populations of ten 30S ribosomal assembly intermediates that differ by subunit stoichiometry. Using F3CS, it is possible to resolve intermediates along different S7-S9-S19 parallel assembly pathways and to begin to understand thermodynamic dependencies of weak protein-RNA interactions in intact complexes.

Results

Three-Color F3CS Scheme to Identify Ten Species in 30S Ribosome Assembly.

Given three ribosomal proteins labeled with three different fluorophores, the ten resulting species include three free proteins, three binary complexes, three ternary complexes, and the quaternary complex (Fig. 1D). The proportions of free and bound proteins can be readily determined using single color FCS, which detects the increase in diffusion time that occurs when the small proteins bind the 0.5 MDa 16S rRNA. However, single color FCS data alone do not provide information about correlated binding of multiple proteins. For example, the slowly diffusing species containing protein S7 will reflect the sum of the binary complex S7·16S rRNA, two ternary complexes S7·S9·16S rRNA and S7·S19·16S rRNA, and the quaternary complex S7·S9·S19·16S rRNA (Fig. 1D). Correlated binding of two proteins can be measured using FCCS, but with three fluorophores it is not possible to unambiguously identify all species with FCS and FCCS data alone. In the example in Fig. 1, two different intermediates contain both S7 and S9, the ternary complex S7·S9·16S rRNA and the quaternary complex S7·S9·S19·16S rRNA (Fig. 1E). If the concentration of the quaternary complex can be measured using a three-color F3CS experiment, the combination of three single-color FCS datasets, three two-color FCCS datasets, and three three-color F3CS datasets will be sufficient to determine the populations of all 10 species.

An Experimental Triple Correlation Integral Insensitive to Double-Labeled Particles.

The central concept of F3CS (Fig. 2) is the use of a triple correlation integral to calculate correlation functions G(τ₁,τ₂) from raw fluorescence data obtained by a three-color microscope (23) (SI Appendix). The correlation curves are then fit to analytical functions that depend on the concentrations and the diffusion kinetics of the triple-labeled species. Within the microscope, optics route fluorescence such that each fluorophore is predominantly recorded in one of three intensity time-traces, i_α(t),i_β(t), and i_γ(t). The traces are recorded with single-molecule sensitivity and a time resolution faster than the timescale of the fluctuations that occur when molecules diffuse in and out of the focal volume. An experimental correlation integral takes the product of data from the three channels sampled at three sequential times, time t, time t + τ₁, and time t + τ₂, where τ₁ and τ₂ are each a logarithmic series of delay times centered around the timescale of the fluctuations:

[1]

Angled brackets indicate time averages that are later interpreted as ensemble averages. Two additional integrals are calculated by cyclic permutations of the time-traces to create a family of three unique datasets. The expression in Eq. 1 is a direct extension of established numerical methods for calculating both FCS curves (27) (SI Appendix, Eq. S1) and, at zero delay times, triple-color coincidence analysis values (23). However, the correlation in the numerator arises from signals for both double-labeled and triple-labeled molecules. As a result, the triple-labeled contribution is lost in the noise for all but the most dilute samples (SI Appendix, Fig. S1). A more useful experimental correlation integral uses δi(t) instead of i(t):

[2]

This choice of correlation integral adds complexity to a challenging numerical calculation, but has the important property that fluctuations present in only two of the three channels average to zero. As demonstrated in the SI Appendix, correlations calculated with Eq. 2 are only sensitive to molecules with all three labels, and Eq. 2 can thus resolve triple-labeled species against a background of double-labeled molecules. This property is a significant advantage over both coincidence methods and Eq. 1, in which the contributions from double-labeled molecules rapidly overwhelm the contributions from triple-labeled molecules as sample concentrations increase.

Fig. 2.

Conceptual basis of F3CS. (A) A sample containing a distribution of macromolecular complexes that differ by subunit stoichiometry. Each of three subunits are labeled with a distinct fluorophore (blue, orange, or magenta) and labeled subunits fluoresce when they diffuse through a microscope’s focal volume (red contours). (B) Fluorescence time traces contain fluctuations from ternary complexes (white traces), binary complexes and unbound subunits, but the identities of the contributors are lost in the bulk fluorescence signal. (C) The triple correlation integral (black box) analyzes fluctuations by converting them into correlation curves. Crucially, the integral is only sensitive to ternary complex fluctuations present in all three channels simultaneously. The height and shape of the correlation curves reflect concentrations and reaction dynamics of triple-labeled species.

Eq. 2 is the starting point for numerical methods that process raw data and the full theory predicting how F3CS data arise from the interplay of statistical mechanics and microscope optics (25). Two predictions of the theory must be tested here in order to validate F3CS: a relationship between the amplitudes of F3CS data and sample concentrations, and a relationship between the shape of the correlation curve and the rate of molecular diffusion.

The Amplitudes of F3CS Data Reflect Sample Concentrations.

Double correlation amplitudes are proportional to the inverse of the sample concentration (16),

[3]

where N₂ is the number of molecules observed in the focus of the microscope at any given time, and the effective volume 1/γ₂ is a contrast ratio reflecting both the size and shape of the microscope’s focal volume. Triple correlation amplitudes are predicted to be proportional to the inverse square of the sample concentration. N₃ is the number of molecules in the triple correlation focal volume and 1/γ₃ is the squared effective volume for triple correlations and certain high-order correlations (26, 28):

[4]

Since the effective volumes for double and triple correlations differ for most microscope geometries, it is convenient to express the triple correlation value N₃ in terms of the double correlation value N₂ to facilitate simultaneous analysis of double and triple correlation data:

[5]

The ratio can be computed from numerical models of the microscope point-spread function, and in practice the ratio must be calibrated for every microscope. Eq. 5 was verified with Rhodamine 6G in ethanol as a bright, mono-disperse reference sample. The microscope color-discriminating optics were removed such that fluorescence was evenly split between the three detectors and the single fluorophore appeared to be triple labeled. Amplitudes of both double and triple correlations were determined for a series of Rhodamine 6G samples of concentrations spanning 2 nM to 1 μM (Fig. 3), measured as the values of each correlation function extrapolated to zero delay times [G(0) and G(0,0) respectively]. (Fig. 3). As judged by the different slopes of the data in the log-log plot, double and triple correlation data obey different power laws as predicted, and data fit well to Eq. 5. Further, the ratio of effective volumes, is 1.65 ± 0.05 standard error of the mean (SEM), between the value of 1.54 predicted for a Gaussian focal volume and the value of 1.66 calculated using a numerical model of the point-spread function (25). Throughout this work, double and triple correlations are fit with the experimentally calibrated ratio . The data in Fig. 3 demonstrate that F3CS can readily measure the concentrations of analytes over the relatively high concentration range required for ribosome assembly reactions. The absolute concentration limits of F3CS are defined practically by signal to noise, which reaches a maximum when N₂ is near unity (SI Appendix, Fig. S3A). This usable concentration range can be shifted to higher or lower concentrations by contracting or expanding the microscope focal volume.

Fig. 3.

Verification of the relationship between triple-correlation amplitudes and sample concentrations. Background-corrected experimental amplitudes of double and triple correlations [G(0) and G(0,0) respectively] were measured for varying concentrations of the fluorescence standard Rhodamine 6G. While double correlations depend on the inverse of the sample concentration (16), triple correlation amplitudes depend on the inverse square of the concentration, reflected in the steeper slope. Focal volumes are determined by fitting each line to the equations shown. The calculated ratio of double to triple correlation focal volumes will later be used to fit both data simultaneously. F3CS can analyze samples across a large range of biochemically useful concentrations.

Delay-Time Dependent F3CS Data Measure Fluctuation Kinetics.

While the amplitudes of F3CS data measure concentrations of triple-labeled particles, the shape of the full F3CS dataset measures the kinetics with which the sample fluctuates. For freely-diffusing Rhodamine 6G (Fig. 4A), the sole source of fluctuations is diffusion of molecules in and out of the microscope’s focal volume. It is predicted that the delay time and slope of the correlation curve are determined by a combination of intrinsic molecular properties and the size and shape of the microscope’s focal volume,

[6]

[7]

where D is the diffusion constant of the molecule, and r₀ and z₀ are the 1/e² radii of the focal volume, in and normal to the focal plane, respectively. The expressions in Eqs. 6, 7 approximate the focal volume as a Gaussian ellipsoid, and the approximation is accurate enough that the analytical solution will rarely be inadequate for fitting routine data obtained with two-photon excitation. Since FCS and FCCS data also decay as a function of τ_D and ω (SI Appendix, Eqs. S4–S6), Eqs. 6, 7 were stringently tested by predicting the F3CS correlation function using values of τ_D and ω obtained by fitting FCCS curves calculated from the same dataset (Fig. 4B). The predicted curve (Fig. 4C) and data match very well and the magnitudes of the absolute residuals are small (SI Appendix, Fig. S3).

Fig. 4.

Verification of the triple-correlation fit function describing the kinetics of diffusion across two delay times. Experimental (A) F3CS and (B) FCCS curves from the same sample of freely-diffusing Rhodamine 6G molecules. FCCS data alone were fit to standard fit parameters (N, τ_D, ω). The latter two parameters dictate curve shape, and were used with Eqs. 6, 7 to calculate the (C) predicted triple correlation function, scaled to match the data. The prediction and data differ by < 1% on average, confirming the validity of the triple-correlation fit functions and establishing that data from the three different FCS methods of the ribosome identification scheme can be fit simultaneously to the same parameters.

The F3CS data are readily interpretable using Eqs. 6, 7, confirming the general theory of F3CS (25). The expression for F3CS in Eq. 6 is conveniently written to allow simultaneous fitting of three color data to FCS, FCCS, and F3CS curves using the same fit parameters. In this way, the populations of complex mixtures of binary, ternary, and quaternary complexes can be resolved, making F3CS a suitable approach for analysis of ribosome assembly, as outlined in Fig. 1.

Simultaneous Quantitation of ten Species Populated During 30S Ribosome Assembly.

The assembly of the head domain of the 30S ribosomal subunit was monitored by partial reconstitution of full length 16S rRNA and six proteins (S7, S9, S10, S13, S14, S19). Three proteins (S7, S9, S19) were labeled with different fluorophores, in accordance with the 30S identification scheme (Fig. 1 D–F). In order to monitor substoichiometric intermediates formed by any of the potential assembly pathways illustrated in Fig. 1B, a long time-point assembly reaction (+16S rRNA) was compared against an otherwise identical no-rRNA control (−16S rRNA). All three autocorrelation functions (Fig. 5A) exhibit longer decay times in the presence of the 16S rRNA, indicating that all three proteins bound the rRNA to various extents. Proteins S7 and S9 are the most tightly bound, while only 38 ± 2% of S19 bound the rRNA, as determined by fitting auto correlations to SI Appendix, Eq. S4 with one bound and one free species. The amplitudes of cross-correlation data (Fig. 5B) all increased in the presence of 16S rRNA, indicating that ternary and/or quaternary species formed. Uniformly long decay times of FCCS data indicate that all colocalized proteins were bound to rRNA, consistent with structural data (29) indicating that each protein independently interacts predominantly with the rRNA.

Fig. 5.

30S ribosome assembly intermediates quantified. An assembly reaction with labeled S7, S9, and S19 and unlabeled S10, S13, S14, and 16S rRNA, was allowed to proceed to completion (96 h). A second reaction lacking 16S rRNA was run for comparison. (A) Autocorrelations of both datasets showed a lengthening of decay times in the +16S rRNA reaction, indicative of binding. Curves are normalized and gray lines demark 0% and 100% binding. S19 bound to a lesser extent than S7 and S9. (B) Cross-correlation amplitudes rose with the +16S rRNA reaction, indicating the formation of multiply-labeled species. (C) F3CS data for the −16SrRNA control showed excellent rejection of contamination from single-labeled proteins, even at high concentration. (D) F3CS data for the +16SrRNA reaction contained positive amplitude and long decay kinetics indicative of triple-labeled complexes in the reconstitution. Quantitation of ten 30S assembly intermediates was achieved by fitting (A–D) globally (SI Appendix, Eqs. S4–S9), and errors were estimated from 9 sequential measurements that were fit independently. (E) The +16S rRNA reaction contained significant populations of eight out of ten possible intermediates, including two intermediates that were not predicted by classical assembly maps (10). Bars indicate standard error. (F) The −16SrRNA reaction contained only unbound S7, S9, and S19, consistent with the inability of most ribosomal proteins to bind together in the absence of rRNA. Errors for the −16SrRNA control only were enlarged five times for clarity.

Because the ribosomal proteins do not interact with each other, the −16S rRNA sample should not contain any protein-protein complexes and accordingly the F3CS data are zero within error (Fig. 5C). Spectroscopically, these data also demonstrate excellent rejection of crosstalk from noninteracting proteins. F3CS data from the +16S rRNA sample (Fig. 5D) have substantial amplitudes, demonstrating successful detection of the fully assembled quaternary complex containing S7, S9, and S19 bound to 16S rRNA. Long decay times of the triple correlation (τ_D = 1.05 ± 0.04 ms) indicate that quaternary complexes diffuse slower than free proteins by a ratio of 5.2 ± 0.2, consistent with the notion of a compact, folded 16S rRNA as the substrate for protein binding (free protein data from autocorrelations, SI Appendix). At short delay times, the triple correlation data are lower in precision than the Rhodamine 6G data (Fig. 4A) because of lower fluorophore brightness and very high concentrations (SI Appendix, Fig. S3A), but a combination of long diffusion times, a large number of data points in the triple correlation and nine repeated measurements yield data that are quite amenable to fitting, and the amplitude G(0,0) was determined to within 2% standard error.

Concentrations of the ten 30S species were extracted from the global dataset of three autocorrelations, three cross-correlations, the three permutations of the triple correlation, and three fluorescence intensities. Nonlinear least-squares methods fit data to SI Appendix, Eqs. S4–S9 using twenty variables: one apparent concentration N_j for each of ten species, three fluorophore emission rates and one infinite-time asymptote, G(∞) or G(∞,∞), per each FCS, FCCS, or F3CS curve, which compensates for instrument drift and is typically zero. Previously determined values were used for microscope focal volume dimensions, optical losses in the detection pathway, molecular diffusion constants and relative fluorophore brightness changes between free and bound states (SI Appendix). To combine FCS, FCCS, and F3CS data that were each obtained with varying degrees of precision, data were weighted with experimental error estimates. Concentrations (Fig. 5 E–F) of the ten 30S intermediates were calculated from fitted N_j values, and errors were estimated from 9 independent measurements and fits. The main source of error was covariation amongst the ten N_j values. Errors estimated for the −16S rRNA sample were lower, presumably because the lack of bound species lowered the potential for covariation, and these errors were enlarged fivefold for visibility in Fig. 5F.

The observed 30S intermediates (Fig. 5E) contain two “forbidden” species lacking S7: the binary S9·16SrRNA complex and ternary S9·S19·16SrRNA complex. These two species cannot be explained by photobleached or partially labeled S7 alone (SI Appendix). The presence of S9·S19·16SrRNA and the absence of S19·16S rRNA suggest that S9 can recruit binding of S19 in the absence of S7. These interactions were verified by single-color FCS titrations of S9 in the presence of S19 alone (SI Appendix, Fig. S4), confirming thermodynamic cooperativity between S9 and S19 and confirming that these particles can form at the present concentrations in the absence of S7. Thus, using F3CS measurements, there is direct evidence for populations of novel ribosome assembly intermediates.

Discussion

Two specific predictions of the thermodynamic assembly maps (Fig. 1C) were not borne out by the F3CS data: S7 was not essential for S9 and S19 binding and S9 and S19 did not bind independently of each other. This different pattern of interactions arises in part because F3CS data were recorded under equilibrium conditions and are sensitive to much weaker interactions. Analogous differences are found between kinetic data obtained at equilibrium conditions with time-resolved hydroxyl radical foot-printing (6, 8) and kinetic data of stable interactions probed with isotope pulse-chase experiments (5, 7). In this context, F3CS data support the view that ribosomal proteins initially bind weakly, and that binding is stabilized cooperatively as assembly proceeds. Weak interactions have physiological relevance since assembly takes place in vivo at approximately 1 μM concentrations of free ribosomal proteins (30), and induced-fit (8) and weak binding modes have been previously characterized for the primary binding proteins S4 and S7 (6, 31).

Eight of ten intermediate species were populated along the possible assembly pathways shown in Fig. 1B. The presence of each intermediate in this equilibrium distribution is not enough to imply that the pathway it is on is sampled during assembly reactions, but more intermediates are possible than the Nomura map predicts, questioning the assumption that assembly pathways are pruned by strong thermodynamic interdependencies. The relative amounts of each intermediate suggest an energetic bias towards an assembly pathway with S7 first, S9 second, and S19 last, which when viewed as a statistical average would be consistent with kinetic evidence of ordered assembly obtained by bulk averaging (2, 5, 6). If the thermodynamics predict the kinetics of assembly, then a small energetic bias between on- and off-pathway states would give rise to hallmarks of both parallel and ordered assembly. The reaction rates of individual assembly steps must now be determined using F3CS to monitor reconstitutions in real time and determine the flux through each parallel assembly pathway. If the moderate degree of parallelism implied by the present thermodynamics is found throughout the entire ribosome assembly landscape, the long-standing goal of writing a definitive reaction mechanism would be unobtainable, and kinetic models of assembly would require statistical treatment of a large number of intermediates and pathways.

These measurements of triply labeled 30S intermediates were a difficult first challenge for F3CS that required design and construction of an instrument capable of acquiring fast multichannel data, derivation of the F3CS theory, and implementation of numerical algorithms for calculating the correlation integrals. The need to integrate FCS, FCCS, and F3CS data required a complete rederivation of FCS theory, and the need to work at high concentrations prompted a reevaluation of the way the experimental triple correlation integral is calculated. The resulting F3CS method is much more accurate and useful than triple-color coincidence or high-order correlation data. This enhanced utility is partly due to the two delay times of F3CS, which provide a means to avoid optoelectronic artifacts and the statistics of shot noise (32) at zero delay times, and correlation amplitudes are much better estimated by fitting the entire two-tau dataset than by using a single zero-delay datapoint. Joint delay times also open up new possibilities for exploring the kinetics of multiple linked conformational changes in both freely diffusing and immobilized molecules, and the three measurements at the core of F3CS enable conditional probabilities (33) to be calculated with fast time resolution and thorough statistical sampling. The 30S identification scheme combining FCS, FCCS and F3CS can be readily adapted to other fluorescently-labeled biochemical systems. Since fluorescence resonance energy transfer (FRET) is not required, the design of constructs and placement of fluorophores is greatly simplified and intact macromolecular assemblies can be investigated without size restrictions. Here, using full length 16S rRNA revealed complicated interactions that were not seen using minimal RNAs. More generally, F3CS provides a statistical framework for ternary complex quantitation that can be adapted for confocal microscopy and diverse analytical instrumentation.

Conclusions

The pattern of interactions observed at high concentrations with F3CS differs from the Nomura map, suggesting that it is overly simplistic to consider 30S ribosome assembly as a series of one-step binding events. Given the general agreement between the Nomura map and the gross order of kinetic rates, at least the kinetic rates of stable interactions, the Nomura map should be more narrowly interpreted as a guide to the conformational changes that lock each protein into place, essentially describing the end game of ribosome assembly. In the strictest sense, the map would not necessarily describe the order of binding. The separation between initial weak binding and final locking interactions depicts ribosome assembly as a supramolecular collapse followed by slow rearrangements, analogous to the fast compactions observed in protein folding, and one can not but wonder what effect weakly bound proteins have on RNA that is undergoing conformational rearrangements. Studying weak interactions in real time will remain a challenge, but both here and in general realm of macromolecular assembly and function, F3CS will be valuable for directly probing the subunit composition of complex macromolecules.

Materials

F3CS experiments were performed using a microscope (SI Appendix, Fig. S5) that was loosely based on the instrument for triple-color coincidence analysis (23). Multiphoton excitation of three spectrally distinct fluorophores using a single laser guarantees focal volume overlap across all colors. Fluorescence was detected simultaneously in three channels with 800 ns resolution and photon counts were recorded for off-line correlation analysis. The experimental triple-correlation function was calculated as described (25). The suite of software written to acquire data, calculate correlation integrals, and fit data will be reported elsewhere and made freely available.

Global fitting of FCS, FCCS, and F3CS data took into account multiple species and microscope calibration parameters. Generalizing standard practices in FCS (22, 34), SI Appendix, Eqs. S4 and S5 consider the contribution of every species and background noise to every FCS and FCCS curve, and SI Appendix, Eq. S8 extends these concepts to F3CS. The final model for F3CS data contains contributions from each species, in the form of Eqs. 6, 7. The contributions are weighted by the number N_j of molecules of each species j per double-correlation focal volume and the effective brightness Υ_α,j of species j at detector α. Each brightness term is calculated using a matrix method that consistently accounts for fluorophore brightness, labeling schemes, fluorophore behavior such as quenching upon binding and FRET, optical losses, and detector cross-talk (SI Appendix, Fig. S2). Methods are further described in the SI Appendix.