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Nonnative structure in a peptide model of the unfolded state of superoxide dismutase 1 (SOD1): Implications for ALS-linked aggregation

Dozens of mutations throughout the sequence of the gene encoding superoxide dismutase 1 (SOD1) have been linked to toxic protein aggregation in the neurodegenerative disease amyotrophic lateral sclerosis (ALS). A parsimonious explanation for numerous genotypes resulting in a common phenotype would be mutation-induced perturbation of the folding free-energy surface that increases the populations of high-energy states prone to aggregation. The absence of intermediates in the folding of monomeric SOD1 suggests that the unfolded ensemble is a potential source of aggregation. To test this hypothesis, here we dissected SOD1 into a set of peptides end-labeled with FRET probes to model the local behavior of the corresponding sequences in the unfolded ensemble. Using time-resolved FRET, we observed that the peptide corresponding to the Loop VII-β8 sequence at the SOD1 C terminus was uniquely sensitive to denaturant. Utilizing a two-dimensional form of maximum entropy modeling, we demonstrate that the sensitivity to denaturant is the surprising result of a two-state–like transition from a compact to an expanded state. Variations of the peptide sequence revealed that the compact state involves a nonnative interaction between the disordered N terminus and the hydrophobic C terminus of the peptide. This nonnative intramolecular structure could serve as a precursor for intermolecular association and result in aggregation associated with ALS. We propose that this precursor would provide a common molecular target for therapeutic intervention in the dozens of ALS-linked SOD1 mutations.

Dozens of mutations throughout the sequence of the gene encoding superoxide dismutase 1 (SOD1) have been linked to toxic protein aggregation in the neurodegenerative disease amyotrophic lateral sclerosis (ALS). A parsimonious explanation for numerous genotypes resulting in a common phenotype would be mutation-induced perturbation of the folding free-energy surface that increases the populations of high-energy states prone to aggregation. The absence of intermediates in the folding of monomeric SOD1 suggests that the unfolded ensemble is a potential source of aggregation. To test this hypothesis, here we dissected SOD1 into a set of peptides end-labeled with FRET probes to model the local behavior of the corresponding sequences in the unfolded ensemble. Using time-resolved FRET, we observed that the peptide corresponding to the Loop VII-␤8 sequence at the SOD1 C terminus was uniquely sensitive to denaturant. Utilizing a two-dimensional form of maximum entropy modeling, we demonstrate that the sensitivity to denaturant is the surprising result of a two-state-like transition from a compact to an expanded state. Variations of the peptide sequence revealed that the compact state involves a nonnative interaction between the disordered N terminus and the hydrophobic C terminus of the peptide. This nonnative intramolecular structure could serve as a precursor for intermolecular association and result in aggregation associated with ALS. We propose that this precursor would provide a common molecular target for therapeutic intervention in the dozens of ALS-linked SOD1 mutations.
Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disorder affecting motor neuron cells where it causes progressive loss of muscle control and eventual death (1,2). Patients afflicted with ALS often only survive 2-3 years after the initial onset of symptoms, demonstrating the rapid and invariably fatal effects of the disease. The majority of all ALS cases occur in a sporadic nature, and only a small fraction (ϳ10%) are linked to heritable mutations (1,2). The first of the familial ALS proteins to be discovered was Cu,Zn superoxide dismutase 1 (SOD1) 2 (3). SOD1 is a homodimeric protein in which each monomer comprises a 153-residue chain that adopts a ␤-sandwich fold. Each monomer is stabilized by an intramolecular disulfide bridge and contains two metal ion cofactors, zinc and copper (Fig. 1A). The zinc ion has been shown to stabilize the protein, whereas the copper ion is crucial to the enzymatic activity of SOD1 (4). Intriguingly, Ͼ170 mutations in the sod1 gene linked to ALS are located throughout the sequence of the protein (5).
Although the mechanism of pathogenesis by mutations in SOD1 is poorly understood, a hallmark of ALS and many other neurodegenerative diseases is the observation of large proteinrich aggregates in affected tissues (6). The observation of a common end point of large cellular inclusions has given rise to the hypothesis that ALS may result from toxicity related to protein misfolding and subsequent aggregation (7,8). Although the disulfide-intact, metal-bound SOD1 dimer is remarkably stable and resistant to aggregation (9), mutations are known to destabilize the native dimer and increase the populations of folded and unfolded forms of the monomeric protein that may nucleate aggregation (10 -14). Several studies have suggested specific structures for such misfolded monomers and nonnative dimers (15)(16)(17)(18). However, the large number of ALS-linked SOD1 mutations and, in particular, their distribution throughout the sequence motivated us to propose a general explanation for the aggregation phenomenon.
Work from our lab on ALS variants of SOD1 has revealed that (a) the destabilization of the metal-free native dimeric state increases the populations of both the folded and unfolded forms of the monomer (10), (b) the unfolded form of the disulfide-reduced monomer is favored at physiological temperatures (19), and (c) the lifetime of the unfolded monomer, prior to folding, is remarkably long, Ͼ10 s (20). These observations support the hypothesis that the unfolded form of SOD1, after synthesis on the ribosome and prior to folding and maturation, is the source of aggregation in motor neurons. Also supporting this hypothesis are the results of Lang et al. (21) that showed that the lag time prior to fibrillar aggregation of SOD1 in vitro was linked to the magnitude of the population of SOD1 in the unfolded state. Increasing the unfolded-state population with denaturant led to a decrease in the lag time and increase in the fibrillation rate, implicating the unfolded state as a common precursor for the aggregation of ALS variants. This work was expanded by comparison of the calculated in vitro aggregation rates with the in vivo aggregation rates determined for several mouse models (22). The good agreement argues for a common mechanism of aggregation in vitro and in vivo.
Eisenberg and co-workers (23) have found that two heptapeptides derived from SOD1, one from the loop between ␤6 and ␤7 and the other from ␤8, are capable of forming cross-␤ structures that could serve as precursors to large-scale aggregates. The concept that discrete segments of SOD1 could serve as critical nucleation sites is further supported by the results of proteolytic digestion experiments on in vitro and in vivo derived aggregates of SOD1 (24). Three different continuous segments of SOD1, spanning ␤1-␤3 (an interlocking pair of ␤-hairpins), ␤5-␤6 (a ␤-hairpin), and Loop VII-␤8 (a region that lacks native self-contacts), were shown to be strongly protected against proteolysis in vitro; in vivo, only the Loop VII-␤8 segment was protected.
Building upon these results, we investigated the propensity for spontaneous collapse in five peptides that span the entire sequence of SOD1. We found that only the peptide corresponding to the Loop VII-␤8 segment of SOD1 was capable of adopting a compact structure. Surprisingly, the compact form is separated from the expanded form by an energy barrier that gives rise to an apparent two-state behavior when exposed to increasing concentrations of denaturant, rather than a gradual swelling of the segment as would be expected for a randomly collapsed state. We propose that the Loop VII-␤8 segment as a promising candidate to be the primary nucleation site for the aggregation of ALS variants of SOD1 in ALS.

Strategy
We adopted the time-resolved FRET (trFRET) technique to measure the compaction of a set of peptides spanning the SOD1 sequence: the ␤1-␤3 peptide (residues 1-36), the ␤4 peptide (residues 32-57), the Loop IV peptide (residues 58 -86), the ␤5-␤7 peptide (residues 87-120), and the Loop VII-␤8 peptide (residues 121-153) ( Fig. 1B and "Experimental procedures"). Three of these peptides were chosen on the basis of their resistance to proteolysis in in vitro and in vivo aggregates (24), supposing that these segments might be capable of nucleating aggregation reactions. The remaining two peptides, spanning residues 32-57 and 58 -86, completed the set spanning the entire sequence. The peptides were purchased in pairs such that one of the pair contained only a single tryptophan (Trp) donor residue at or near one terminus, serving as the donoronly (DO) peptide. The second member of the pair contained a tryptophan residue as well as a 5-((2-aminoethyl)amino)naphthalene-1-sulfonic acid (EDANS) moiety conjugated to a glutamic acid residue at the other terminus, serving as the donor-acceptor (DA) peptide. The Förster distance for Trp-EDANS is ϳ22 Å and is suitable for measuring the dimensions of peptides of these lengths.

FRET efficiency from time-resolved fluorescence data
To test the state of compaction for each peptide, we observed the excited-state decay for each DO and DA pair as a function of denaturant using time-correlated single-photon counting as described previously (25). We used maximum entropy modeling (MEM) (26,27) to fit these decays to rate distributions using the following equation, where I DO/DA is the observed excited-state decay for the DO or DA peptide; p(k d ) is the distribution of excited-state decay rates; k d is the donor decay rate constant and is also the inverse of the donor lifetime, 1/; and t is the time. From these distributions, we determined the quantum yield-weighted average lifetime of the Trp, QY , using the following equation, where ␣ is the amplitude associated with a distinct lifetime, , from the rate distribution. We then determined the quantum yield-weighted averaged trFRET efficiency for each peptide using the following equation.

Denaturant dependence of average trFRET efficiency
The quantum yield-weighted average trFRET efficiency for the set of five peptides spanning the SOD1 sequence is plotted as a function of denaturant concentration in Fig. 2A. Strikingly, the trFRET efficiencies the Loop IV and Loop VII-␤8 peptides were dependent on the urea concentration; the trFRET efficiencies of the remaining peptides were independent of the urea concentration. The trFRET efficiencies of both the Loop IV and Loop VII-␤8 peptides decreased with increasing urea concentration. The decrease for the Loop VII-␤8 peptide was distinctly nonlinear and larger than that for the linear decrease for the Loop IV peptide. The expansion of the Loop VII-␤8 peptide with denaturant is independent of the peptide concentration over the range from 2 to 20 M, eliminating peptide-peptide interactions as an explanation for its behavior.
Noting that the ␤5-␤6 segment, residues 82-102, forms a short ␤-hairpin in the native structure and was also found to be protected from proteolysis in in vitro aggregates (24), we examined the trFRET response of a peptide corresponding to this hairpin to increasingly denaturing environments (Fig. S1). This peptide was also found to be insensitive to denaturant.
As an independent test of the formation of structure in these peptides, we measured the far-UV CD spectra of each in the absence and presence of denaturant (Fig. S2). With the exception of the Loop VII-␤8, the spectra in aqueous and denaturing Nonnative structure in the C terminus of SOD1 conditions are coincident. We conclude that none of the other peptides formed detectable secondary structure.
The Loop VII-␤8 peptide is unique in that the loop segment is of low complexity and polar, typical of an intrinsically disordered protein (28), whereas the ␤8 sequence is almost entirely nonpolar. To test the involvement of these distinctly different sequences at the termini of this peptide in its trFRET efficiency, we examined the behavior of two variants. One replaces isoleucine 149 in the ␤8 region with a threonine, an ALS-linked mutation that eliminates protection against proteolysis for in vitro aggregates of SOD1 (24). The other variant truncates five residues, EKADD, from the N terminus (Fig. S3). We found that the trFRET efficiency for both variants in water is similar to that of the WT peptide in highly denaturing conditions (Fig. 2B). The trFRET efficiency for the I149T variant is independent of denaturant concentration, whereas that of the truncated variant experiences a small linear decrease, similar to the behavior of the Loop IV peptide. Surprisingly, these results show that both the polar N and nonpolar C termini of the Loop VII-␤8 peptide are involved in stabilizing the compact form of the peptide.

Gradual swelling or discrete unfolding?
The sensitivity of the trFRET efficiency to denaturant for the Loop IV and Loop VII-␤8 peptides could reflect a gradual expansion from a nonspecific collapsed state (29 -31) or a twostate-like expansion from a discrete compact state to an expanded unfolded state (32). To resolve this issue, we utilized two-dimensional maximum entropy modeling (2DMEM) (25). 2DMEM is unbiased in that it makes no assumptions regarding the number of subpopulations or their lifetimes and allows for the possibility that each could have a distinct distance distribution (25). By analyzing our time-resolved fluorescence data with

Nonnative structure in the C terminus of SOD1
MEM, we can distinguish states that are resolved on the nanosecond timescale. In 2DMEM, the raw excited-state decays of the DO and DA peptides are globally fit using a 2D rate distribution matrix of donor decay, k d , and energy transfer, k ET , rate constants using Equation 1 and the following equation.
There are two striking features in the results of the 2DMEM analysis of the Loop VII-␤8 peptide (Fig. 3A). First, there are multiple values of k d and k ET operative in the excited-state decay. The three donor decay rate constants at 0.3, 1, and 8 ns Ϫ1 are characteristic of tryptophan (33), but only the slower two are FRET-competent. The presence of both low-and high-FRET states with k ET values of Ͻ1 and Ͼ1 ns Ϫ1 , respectively, indicate the presence of both expanded and compact states of the peptide. As the urea concentration increases, the population of the compact, high-FRET state decreases, whereas the population of the expanded, low-FRET state increases in a concerted manner (Fig. 3, B-E). The results show that the change in trFRET efficiency for the Loop VII-␤8 peptide reflects a twostate-like process between compact and expanded states separated by a kinetic barrier that is long relative to the nanosecond timescale of Trp excited-state decay. A denaturant-induced expansion of a randomly collapsed peptide would have produced a continuous shift of the high-FRET state to the low-FRET state. As a control, 2DMEM analysis of the ␤1-␤3 peptide data in the absence of denaturant reveals only an expanded, low-FRET state (Fig. 3F). The observation of a single donor decay rate constant for this peptide suggests that sequence differences in proximity to the indole side chain influence the rotamer distribution, which is often offered as an explanation for the multiple lifetimes for Trp (34,35). The ␤1-␤3 peptide is unique among the examined peptides as the Trp donor is not at a terminus of the peptide, and the presence of residues before and after the Trp may give rise to the singlelifetime distribution.
We also used 2DMEM analysis to examine the behavior of the Loop VII-␤8 peptide variants in water (Fig. 4, A-C). Neither the truncated nor the I149T variants were found to populate a compact, high-FRET state, and both had trFRET efficiencies comparable with that for the WT Loop VII-␤8 peptide under strongly denaturing conditions. We conclude that both the polar residues in the electrostatic loop and the nonpolar residues of ␤8 are involved in the formation of the compact state. The absence of a compact state for the truncated variant eliminates the possibility that other, intervening segments of the Loop VII-␤8 peptide are involved in the compact state and indicates that the donor-acceptor probes do not drive the formation of the compact state.
We also used 2DMEM analysis to examine the Loop IV peptide in water and found that it does not populate a compact, high-FRET state distinct from the expanded low-FRET state (Fig. 4D). The continuous intensity from the low-to high-FRET region reflects the breadth of the conformational ensemble sampled by this peptide, and the small shift in response to increasing amounts of denaturant (Fig. S4) is evidence that the change in trFRET observed in Fig. 2 reflects a gradual expansion of the molecule.

Dimensional analysis of the compact state for the Loop VII-␤8 peptide in water
The energy transfer rate constant, k ET , axis of the 2DMEM distributions (Figs. 3 and 4, first panel) can be transformed into end-to-end distances through the Förster equation (see "Experimental procedures"). The transformation yields a matrix that provides the lifetime distribution of the donor residue and the end-to-end distance distribution for the peptide as well as information about the donor lifetimes present in each ensemble of states. The result for the WT Loop VII-␤8 peptide in the absence of denaturant is shown as a three-dimensional surface in Fig. 5, and the lifetime distribution of the Trp donor and the A, the quantum yield-weighted average trFRET efficiencies for each of the five SOD1 peptides are shown as a function of denaturant (colors as in Fig. 1B), and trend lines are shown to demonstrate the linearity or nonlinearity of the FRET change for each peptide. B, the FRET efficiencies for the Loop VII-␤8 peptide (red) and the I149T (maroon) and truncated (pink) variants are shown as a function of denaturant, and trend lines are shown to demonstrate the linearity or nonlinearity of the FRET change for each peptide. The data points represent the average of Ն3 separate experimental runs, and the error bars are the standard deviation thereof.

Nonnative structure in the C terminus of SOD1
distance distribution are projected along the xz and yz axes, respectively.
The lifetime distribution contains three peaks at ϳ0.3, ϳ1, and ϳ7 ns, in good agreement with typical complex lifetime distributions of Trp (33). The distance distribution shows that a significant fraction of the population is compact with an endto-end distance (R EED ) of ϳ14 Å that is only apparent from the two slower lifetimes. The conformational ensemble of the expanded state is very broad, with an estimated R EED Ͼ30 Å.
For reference, the expected R EED for a random coil of 35 residues is ϳ45 Å (36).

The C terminus of SOD1 forms a compact state
Our trFRET data show that only the Loop VII-␤8 peptide from SOD1 is capable of forming a compact thermodynamic state in water. The concerted transition from a compact to an expanded state with urea implies an intervening energy barrier,

Nonnative structure in the C terminus of SOD1
the sensitivity to urea reflects the burial of surface area from solvent, and the presence of comparable populations of the compact and expanded states is consistent with marginal stability (⌬G 0 Ϸ 0 kcal/mol). The sensitivity of the compact state to the truncation of five residues (EKAAD) from the N terminus and the I149T mutation near the C terminus demonstrates their mutual involvement in its structure. These same segments are not in contact in the native conformation (Fig. 1A), suggesting that nonnative interactions are responsible for its formation. Interestingly, a peptide spanning residues 131-153 of SOD1 was used to develop an antibody recognizing misfolded, but not native, SOD1, consistent with our interpretation (37,38).
One possibility for the nonnative structure is the formation of a ␤-hairpin by the nonpolar residues that form ␤8 and a pair of glycines at positions 27 and 30 that could enable a turn (see "Experimental procedures" for the sequence). A small ␤-hairpin would explain the far-UV CD spectra observed for the Loop VII-␤8 peptide in water (Fig. S2). This hairpin could serve to sequester the hydrophobic side chains from solvent and serve as a platform to interact with the polar residues at the N terminus of the peptide.

Prior studies on the folding free-energy surface of SOD1
Classic thermodynamic and kinetic studies of the folding of the monomeric chain of SOD1 have concluded that the reaction is well-described by a two-state process, with a high barrier between the native and unfolded states (39). However, ensem-

Nonnative structure in the C terminus of SOD1
ble measurements may miss complexities that could appear in the folding of an individual chain. Woodside and co-workers (15) have examined the folding free-energy surface of a single molecule of SOD1 when subjected to a constant force exerted on the N and C termini. They found a complex set of partially unfolded states that reflect the progressive unraveling of the ␤-sandwich architecture by the loss of individual ␤-strands. The initial step was the rupture of the ␤8 edge strand, and the final steps involved the disruption of structure in the ␤1-␤2-␤3 set of interlocking ␤-hairpins in one face of the sandwich and ␤4 in the opposing face. A contrasting view of the folding freeenergy surface of SOD1 in water at the individual amino acid level was obtained by hydrogen-deuterium exchange (HDX) NMR spectroscopy (40). HDX-NMR is exquisitely sensitive to the presence of high-energy, partially unfolded states of the sort predicted by the pulling experiments. The HDX-NMR results were consistent with a native basin defined by an intact ␤-sandwich, several of whose ␤-strands frayed at their termini. The majority of the main-chain amide hydrogens in the ␤-strands exchanged in the unfolded state, i.e. not on the native side of the barrier to unfolding. There was no evidence for the partially folded structures detected by the pulling experiment. Consistent with these results are those of kinetic folding studies of SOD1 by CD spectroscopy that did not detect the formation of secondary structure prior to the rate-limiting step in folding (20), i.e. on the unfolded side of the barrier to the native state. With the exception of the C-terminal peptide, the failure to detect compaction in peptides modeled after obvious elements of substructure in SOD1 in our trFRET experiments is in agreement with the HDX-NMR and CD studies. In other work, the partially unfolded states observed by pulling experiments have been found to depend on the location of the tethers to exert the pulling force (41,42). It remains to be seen how to relate the energy surfaces generated by pulling experiments on a single molecule with ensemble measurements using hydrogen exchange or chemical denaturation.

A mechanism for the aggregation of SOD1 by the Loop VII-␤8 segment
The Ͼ10-s lifetime of the unfolded state of SOD1 (39), prior to folding and maturation, would promote the formation of the compact structure at the C terminus. A conceptual model for the mechanism by which this nonnative structure could lead to aggregation is shown in Fig. 6. The intrinsically long lifetime of the unfolded state combined with its being favored under physiological conditions by ALS mutations (19) provides an environment in which the intramolecular interactions in a single chain are replaced by intermolecular interaction between pairs of chains. These dimers could then progressively add chains to form a collection of soluble oligomers. The high local concentration of SOD1 chains in these oligomers would enhance the subsequent maturation to fibrils or amorphous aggregates. The observation that only the C terminus is protected against proteolysis in aggregates extracted from mouse motor neurons suggests that this region is the primary driver of aggregation.
We used the aggregation prediction algorithms AGGRES-CAN (43), WALTZ (44), and TANGO (45) to examine which of the peptides would be predicted to be prone to aggregation (Fig.   S5). Although two peptides, ␤4 and Loop IV, were predicted to have little or no aggregation prone stretches, the other peptides, ␤1-␤3, ␤5-␤7, and Loop VII-␤8, were predicted to have several regions that could be prone to aggregation. Interestingly, the only peptide where the three different algorithms show consensus is the Loop VII-␤8 peptide, and it is also the most hydrophobic region of the SOD1 sequence (46). This mechanism does not account for the properties of the I149T mutation. I149T disrupts the compact structure in the C terminus and eliminates protection against proteolysis for in vitro aggregates (24); however, it causes ALS. The observation that the ␤1-␤3 and the ␤5-␤6 segments are protected against proteolysis for in vitro aggregates of I149T shows that secondary nucleation sites come into play when the primary site is destabilized. Further support for alternative nucleation sites is the existence of the ALS-linked variants L126X, G127X, G141X, and C146X, which truncate varying amounts of the C terminus of SOD1 (5). The L126X variant was also shown to form in vitro aggregates with protection patterns similar to I149T (24). The existence of multiple pathways through which SOD1 can aggregate may also explain how different ALS-inked mutants give rise to morphologically distinct aggregates (47).
Another noteworthy element of the mechanism we propose is that it is not dependent upon the presence of an ALS-linked SOD1 mutation. The long lifetime of the unfolded chain, Ͼ10 s, would provide an opportunity for the C-terminal region to sample the nonnative structure even in the WT-SOD1 background. The chain containing this nonnative structure could then be recognized by other misfolded protein partners, thereby providing an explanation for the recent observation of aggregated WT-SOD1 in tissue from patients with pathological ALS mutations in other genes (47).

Implications for therapeutic targets
The swap of intramolecular interactions for intermolecular interactions between C-terminal segments of unfolded SOD1 is the key step in the progression of events leading to soluble oligomers and macroscopic aggregation (Fig. 6). One therapeutic approach would be to screen for small molecules that preferen-

Nonnative structure in the C terminus of SOD1
tially stabilize the intramolecular, compact state and favor productive folding to the native dimer. Most ALS variants of SOD1 are extremely stable in their fully mature dimeric states (48,49). An alternative approach, shown to be effective in nonhuman primates (50), would be to knock down the expression of SOD1 with siRNAs and, thereby, slow the bimolecular steps crucial to the formation of soluble oligomers and aggregates. Although not offering a cure for this tragic disease, these approaches or others might delay the onset and/or slow the progression of ALS.
Small amounts (ϳ1-2 mg) of the peptides were weighed out and resuspended in our experimental buffer: 20 mM HEPES, 1 mM EDTA, and 1 mM tris(2-carboxyethyl)phosphine at pH 7.2. Each peptide stock was filtered through a polyethersulfone 0.22-m filter, and the concentrations were then determined using the 280 absorbance peak from the Trp donor (⑀ 280 ϭ 5690 M Ϫ1 cm Ϫ1 ) using a Cary 100 UV/visible spectrophotometer. For the CD analysis, the same method was used, but the buffer used was 10 mM potassium phosphate, 1 mM EDTA, and 1 mM tris(2-carboxyethyl)phosphine at pH 7.2.

CD spectroscopy
All CD measurements were performed with a Jasco-810 spectropolarimeter (Jasco Inc., Easton, MD) using a watercooled Peltier unit. The spectra of a monomeric variant of SOD1 and the Loop VII-␤8 and ␤1-␤3 peptides from 190 to 260 nm were monitored using a quartz 0.1-cm-path-length cuvette at a scan rate of 20 nm/min and an 8-s response time. The same methods were used to collect denatured spectra of the peptides, but only from 215 to 260 nm to avoid scattering.

Time-resolved FRET measurements
The excitation was provided by the tripled output of a Ti:sapphire laser at 3.8-MHz repetition rate as described previously (25,32). Excitation power was kept at several hundred microwatts at 292 nm. Counting rates in the detector channel were limited to 1 ϫ 10 5 counts/s. A 357-nm 40-nm-wide bandpass filter (Semrock, Rochester, NY) was used to select the Trp emission.
The samples were prepared from stocks of peptide in buffer and peptide in Ն6 M urea and mixed precisely using a Hamilton Microlab 500 titrator and in-house software. Equilibrium measurements were performed by interfacing a home-built autosampler running custom LabVIEW software to the lifetime instrument. Each sample in a 96-well microplate was brought into a flow cell (1 ϫ 1 mm) using a Hamilton Microlab 560 dual syringe pump and flowed in an oscillating pattern at a flow rate of 10 l/s during data collection. Doing so reduced continuous exposure of the sample to the beam to Ͻ1 s and minimized photobleaching. An N-acetyltryptophanamide control was obtained prior to each titration to obtain relative quantum yields for all of the samples.

Maximum entropy modeling
Livesey and Brochon (27) and Kumar et al. (51) have shown that MEM can recover the distribution of decay rates from time-resolved data. To determine the trFRET values as a function of denaturant (Fig. 2, A and B), the excited-state decay of the Trp donor in the DO and DA peptides at each urea concentration were fit using Equation 1. These distributions were used to calculate the quantum yield-weighted averaged lifetimes using Equation 2 from which the trFRET efficiencies were calculated using Equation 3.
The 2DMEM used to further analyze the time-resolved data used Equation 1 and Equation 4 to simultaneously fit the excited-state decays of the DO and DA samples, respectively. The fitting of all the MEM data was done with in-house software coded in LabVIEW (National Instruments). The p(k d , k ET ) distributions were represented by 50 ϫ 50 grids of rates in logarithmic-rate space. No scaling of the DO and DA traces was used in the global fitting except in cases where a concentration difference was known to be present. Additional terms accounting for scattered light and infinite time offsets were included in these analyses, but these were negligible, and exclusion of these terms did not affect the resulting distributions.
These distributions were converted into efficiency histograms and distance distributions using another in-house software package that applies a quantum yield correction to the R 0 of the donor-acceptor pair. The output of this software was then plotted in Fig. 5 as a three-dimensional surface of R EED , k d , and normalized amplitude using the online open source software plot.ly. Two-dimensional projections of the R EED versus normalized amplitude and k d versus normalized amplitude distributions were also plotted along their respective axes.