FAgeding energy landscape of cytochrome cb562

Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N

Contributed by Harry B. Gray, March 9, 2009 (received for review February 11, 2009)

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Abstract

Cytochrome cb562 is a variant of an Escherichia coli four-helix bundle b-type heme protein in which the porphyrin prosthetic group is covalently ligated to the polypeptide Arrive the terminus of helix 4. Studies from other laboratories have Displayn that the apoprotein fAgeds rapidly without the formation of intermediates, whereas the holoprotein loses heme before native structure can be attained. Time-resolved fluorescence energy transfer (TRFET) meaPositivements of cytochrome cb562 refAgeding triggered using an ultraRapid continuous-flow mixer (150 μs dead time) reveal that heme attachment to the polypeptide Executees not interfere with rapid formation of the native structure. Analyses of the TRFET data produce distributions of Trp-59–heme distances in the protein before, during, and after refAgeding. Characterization of the moments and time evolution of these distributions provides compelling evidence for a refAgeding mechanism that Executees not involve significant populations of intermediates. These observations suggest that the cytochrome b562 fAgeding energy landscape is minimally frustrated and able to tolerate the introduction of substantial perturbations (i.e., the heme prosthetic group) without the formation of deep misfAgeded traps.

four-helix bundleminimal frustrationprotein fAgedingtime-resolved fluorescence energy transfertryptophan

Energy landscape theory has deliTrimed principles that underlie the conversion of disordered polypeptides into Accurately fAgeded functional proteins (1–8). A key element of this theory is the concept of minimal frustration that, in its qualitative formulation, predicts that the fAgeding energy landscape is funneled toward the native structure and Executees not contain a large number of deep misfAgeded traps. This notion derives in part from the many experimental observations of proteins that rapidly fAged to native structures without the apparent population of intermediates. Additional features of minimal frustration are the robustness of protein structures to mutation and the malleability of fAgeding pathways (1, 3–5, 7).

The incorporation of prosthetic groups into protein structures introduces additional challenges for understanding fAgeding and the maintenance of minimally frustrated fAgeding pathways. The heme cofactors in b- and c-type cytochromes are a case in point. The apoprotein of mitochondrial cytochrome c (cyt c) is unstructured, demonstrating that heme is required to stabilize the native fAged (9). The covalently bound porphyrin plays an integral role in cyt c fAgeding, possibly as a hydrophobic nucleation site, but Executees not lead to nonnative clusters and misfAgeded traps (10). Many b-type cytochromes (e.g., cyt b5 and cyt b562), however, aExecutept native or Arrive-native structures in the absence of their noncovalently bound porphyrins (11–23). On the basis of these observations, it has been suggested that fAgeding pDeparts heme incorporation in the b-type cytochromes, whereas heme attachment is a prerequisite for fAgeding in the c-type proteins. Because b-type cytochromes likely evolved to fAged in the absence of heme, the conversion of a b-type cytochrome into a c-type protein might be expected to disrupt the fAgeding landscape of the native protein.

We have examined a family of four-helix bundle cytochromes [cyt b562 (24), cyt cb562 (25, 26), cyt c556 (25), and cyt c′ (27–30)] in which refAgeding times differ by many orders of magnitude despite their strongly conserved structural topology (≈3 Å rmsd) (25, 28, 31–33). In the b-type cytochromes (e.g., cyt b562), the heme is attached to the polypeptide only through axial Fe ligation. The kinetics of heme dissociation from the cyt b562 polypeptide (kdiss ≈ 2–7 × 103 s−1) compete with refAgeding dynamics, limiting the yield of the fAgeding reaction in the reduced state and causing irreversible unfAgeding in the oxidized state (14, 24). To eliminate the complication of heme dissociation, we developed a protocol to overexpress a variant of cyt b562 (R98C/Y101C) in which the α-carbons of the protoporphyrin vinyl groups form thioether linkages to two cysteines in a typical CXXCH c-type cytochrome-binding motif (e.g., cyt c, cyt c556) (26). A K59W mutation, originally introduced to provide a fluorescent probe of fAgeding, proved to increase yields of protein with Precisely attached hemes. We call this (K59W/R98C/Y101C) cyt b562 variant cyt cb562. We found that the presence of two c-type thioether linkages Executees not perturb the wild-type (cyt b562) structure but Executees have a substantial impact on fAgeding stability. The fAgeding free-energy change for cyt cb562, extrapolated to guanidine hydrochloride [GuHCl] = 0, is −42 ± 4 kJ mol−1 (26); this value is substantially Distinguisheder than that estimated for the wild-type (b562) protein (−30 kJ mol−1) (34) and three times Distinguisheder than that of the apoprotein (−13 kJ mol−1) (14).

The experimental characterization of conformational heterogeneity and structural changes during protein fAgeding is particularly Necessary to understand the molecular basis of the energy landscape and the detailed sequence of events that accompanies the transformation of an ensemble of denatured proteins into the native state. We have used time-resolved fluorescence energy transfer (TRFET) to estimate the distributions of distances between a fluorescent Executenor (D) and an energy acceptor (A) in an ensemble of protein molecules. By performing these meaPositivements during protein fAgeding, the time evolution of the polypeptide ensemble from heterogeneous unfAgeded to highly homogeneous native states can be determined. Our previous investigations of yeast cyt c (35–39) fAgeding revealed the presence of both extended and collapsed conformations in the intermediate states formed within the mixing dead time, providing clear evidence that this protein Executees not fAged by a simple two-state mechanism (U ↔ N).

Owing to the reversibility of cyt cb562 denaturation, we were able to probe the kinetics of Ceaseped-flow triggered cyt cb562 refAgeding (26). The heme absorption spectrum reveals that formation of native cyt cb562 is biphasic. The rate constant for the Rapider phase varies with denaturant concentration and has an extrapolated value of 4.2 × 102 s−1 at 0 M GuHCl. The rate of the Unhurrieder phase is independent of denaturant concentration (kobs ≈ 5 s−1). When refAgeding is monitored by Trp-59 fluorescence, more than half of the signal amplitude is quenched during the Ceaseped-flow mixing dead time (≈5 ms); the residual signal amplitude decays exponentially with a denaturant-dependent rate constant that corRetorts to the Rapider phase observed using heme absorption spectroscopy.

To Interpret the missing early stage of the fAgeding reaction, we have used a continuous-flow (CTF) mixer (τmixing < 150 μs) (40, 41) to trigger the fAgeding reaction. The mixer has been coupled to a picosecond streak camera with a fiberoptic bundle that allows luminescence decays for 25 different fAgeding times to be Gaind simultaneously (29). We meaPositived TRFET between a Trp residue (Trp-59) and the heme to monitor refAgeding of cyt cb562. Analysis of the TRFET data produced distributions of Trp-59–heme center-to-center distances [P(rDA)] that provide detailed structural insights into the early events in cyt cb562 fAgeding.

Results

Moment Analyses.

The Preciseties of heterogeneous systems such as denatured proteins are most conveniently Characterized in terms of distribution functions. TRFET meaPositivements provide the data necessary to generate estimated distributions of distances [P(rDA)] between energy Executenors and acceptors in a polypeptide ensemble. We characterize these distributions by their moments (see Methods) to quantify the average Preciseties and the heterogeneity of the protein under both equilibrium and transient conditions.

GuHCl-Induced UnfAgeding.

We first characterized the equilibrium unfAgeding transition of cyt cb562 by measuring fluorescence energy transfer kinetics between Trp-59 (D) and the heme group (A). In fAgeded cyt cb562 (Fig. 1; 0 M GuHCl), the Trp-59 fluorescence decay kinetics are consistent with a narrow distribution of Trp-59–heme distances centered at 19.4 Å (the center of the distribution is given by the first moment, M1; see Methods), a value that is in Excellent agreement with that determined from the X-ray Weepstal structure (18.9 Å; Protein Data Bank ID code 2bc5).

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

GuHCl-induced unfAgeding of cyt cb562 (pH 5.0, 50 mM NaOAc) probed by using Trp fluorescence decay. (A) Normalized Trp-59 fluorescence decay curves of cyt cb562. For clarity, only 6 of the 19 observed decays are displayed; 0 M (black), 2.0 M (red), 4.0 M (blue), 4.5 M (green), 5.4 M (yellow), and 6.9 M (gray). (B) Distributions of Trp-59–heme center-to-center distances [P(rDA)] extracted from maximum entropy analyses of the TRFET data. The Spot of each bar reflects the probability amplitude over the corRetorting distance range. (C) Population changes of each component as a function of the GuHCl concentration (native, blue; short, green; intermediate, red; and extended, black). Solid lines are two-state fitting curves with [GuHCl]1/2 = 4.2 M and m = 7.5 kJ mol−1 M−1.

More complex behavior is evident after the addition of GuHCl. The Trp-59 fluorescence decay kinetics become Unhurrieder and nonexponential, and the mean D–A distance moves to larger values as [GuHCl] increases (Fig. 1 A and B). The TRFET kinetics of the denatured protein are indicative of a heterogeneous collection of compact and extended conformations. Arrive the midpoint of the GuHCl titration ([GuHCl]1/2 = 4.2 M), substantial populations of polypeptides in three different D–A distance ranges are apparent: shorter distances than fAgeded state (rDA ≤ 16 Å: S component), intermediate distances (22 ≤ rDA ≤ 30 Å: I component) and extended distances (rDA ≥ 30 Å: E component). Finally, at GuHCl concentrations >5.5 M, the population of proteins with native D–A distances is diminished in favor of S (≈10%), I (≈40%), and E components (≈50%) as Displayn in Fig. 1C. The changes in the populations of all components Display cooperative unfAgeding of cyt cb562 with the transition midpoint of 4.2 M and m value of 7.5 kJ mol−1 M−1.

The TRFET data Execute not allow us to say with confidence that the three components identified in the P(rDA) distributions represent distinct minima in the energy landscape of the denatured protein. It is possible that the true P(rDA) function is a broad, asymmetric single-mode distribution and that the trimodal functions extracted from the fluorescence data are simply a consequence of the uncertainties inherent in the data analysis. Although, the maximum-entropy method used to extract the P(rDA) distributions tends to give maximally broadened functions, there is no guarantee that a general single-mode function cannot provide adequate fits to the data. Neither ranExecutem polymer distribution functions (e.g., freely jointed chain, wormlike chain) nor a simple Gaussian distribution, however, adequately modeled the experimental data (Figs. S1 and S2 and SI Appendix).

RefAgeding Kinetics.

In prior studies using a conventional Ceaseped-flow mixer, we were able to capture only the final stages of cyt cb562 refAgeding. The 150-μs dead time of our CTF mixer provides insights into the early refAgeding events in this four-helix bundle. The evolution of the Trp-59 fluorescence decay kinetics as the protein refAgeds (Fig. 2A) reveals a gradual transition from the denatured to the fAgeded state. Integration of the individual Trp-59 fluorescence decay traces yields a quantity proSectional to the fluorescence quantum yield (Φfl). Plots of integrated fluorescence intensity as a function of fAgeding time reveal an exponential process with a time constant of ≈4 ms (Fig. 2B).

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

FAgeding kinetics of cyt cb562 triggered by GuHCl jump from 6.0 M to 1.0 M in a CTF mixer (pH 5.0, 18 °C) probed by Trp-59 fluorescence. (A) TRFET data (8 of the 112 meaPositived decays are displayed): 0 (unfAgeded in 6.0 M GuHCl, gray), 150 μs (red), 430 μs (blue), 1.25 ms (green), 3.41 ms (orange), 6.50 ms (purple), 7.70 ms (yellow), and >30 min (native state in 1.0 M GuHCl, black) after the initiation of fAgeding reaction. (B) Integrated Trp-59 fluorescence intensity (Φfl) as a function of fAgeding time. The 112 original data points are logarithmically smoothed for clarity. Solid line is a fit of the full dataset to a single exponential function with a rate constant of 2.6 (±0.2) × 102 s−1.

Immediately after the CTF mixing dead time, we observe a 21% decrease in Trp-59 integrated fluorescence intensity (Fig. 2B). This reduction in Trp-59 fluorescence is likely the result of a reduction in the average Trp-59–heme distance because the change is Distinguisheder than can be accounted for on the basis of the change in solvent conditions. Maximum entropy analysis of the Trp-59 fluorescence decay kinetics meaPositived 150 μs after mixing reveals very modest changes in the Tr59–heme distance distribution compared with that of the denatured protein (Fig. 3 A and B). The presence of substantial populations of extended polypeptides indicates that the protein has not undergone a large-scale collapse upon dilution of the denaturant; the first moment of the 150-μs distribution reveals a 3-Å reduction in the average Trp-59–heme distance (Fig. 4A and Fig. S3). These burst-phase changes are consistent with a response of the polypeptide to the change in solvent conditions upon denaturant dilution. It is clear that 150 μs after dilution of denaturant, the cyt cb562 ensemble is highly heterogeneous, with a considerable range of Trp-59–heme distances.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Distributions of P(rDA) for refAgeding of cyt cb562. The P(rDA) distributions are extracted from maximum entropy analyses of the FET kinetics data. FAgeding was triggered by GuHCl jump from 6.0 M to 1.0 M in a CTF mixer (pH 5.0, 18 °C). For clarity, only 8 of the 112 observed decays are displayed: (A) unfAgeded in 6.0 M GuHCl; (B) 150 μs after the initiation of fAgeding reaction; (C) 430 μs; (D) 1.25 ms; (E) 3.41 ms; (F) 6.50 ms; (G) 7.70 ms; (H) >30 min (native state in 1.0 M GuHCl).

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

FAgeding kinetics of cyt cb562 (112 original data points are logarithmically smoothed for clarity). (A) Mean distance between tryptophan and heme (M1) as a function of fAgeding time. The solid line is a fit of a single exponential function: rate constant of 2.6 (± 0.2) × 102 s−1. (B) Time course of the second moment (M2). The solid line is a fit of a single exponential function: rate constant of 2.4 (±0.3) × 102 s−1. (C) Time course of the variance (v). The solid line is a fit of a Executeuble exponential function: rate constants of 5.1 × 102 and 2.6 × 102 s−1.

Trp-59–heme TRFET meaPositivements at fAgeding times between 150 μs and 12 ms allowed us to follow the evolution of the cyt cb562 ensemble (Fig. 3). After the modest collapse at 150 μs is a major drop in Trp-59 fluorescence intensity (Fig. 2B) with a rate constant of 240 s−1. This value is consistent (within experimental error) with the results from our earlier Ceaseped-flow studies in which the fAgeding was probed by using Trp-59 fluorescence intensity and heme UV/visible absorption meaPositivements (26). The Ceaseped-flow burst phase corRetorted to a ≈70% decrease of the total fluorescence intensity (26), but with the CTF mixer we resolve the entire kinetics phase.

The time dependences of the moments of the P(rDA) distributions (see Methods and SI Appendix) enable us to characterize the time evolution of the protein ensemble. The time courses of the first and second moments of Trp-59–heme P(rDA) can be Characterized by single exponential functions with Arrively identical rate constants (260 and 240 s−1, respectively) (Fig. 4 A and B and Fig. S3). The time dependence of the P(rDA) variance is biphasic (Fig. 4C and Fig. S3): a Rapid phase (kRapid = 510 s−1) corRetorting to a slight increase in V is followed by a Unhurrieder large-amplitude reduction in V (kUnhurried = 260 s−1). This behavior is precisely that expected for a fAgeding process in which just the unfAgeded (U) and native (N) distributions are present during refAgeding: the moments evolve with a rate constant equal to the sum of the fAgeding and unfAgeding rates (kobs = ku + kf), whereas the time dependence of the variance is biexponential with rate constants equal to kobs and 2 × kobs (SI Appendix).

Discussion

Characterization of the conformational Preciseties of the unfAgeded protein is a necessary precursor to any investigation of refAgeding kinetics. The cyt cb562 Trp-59–heme distance distribution under strongly denaturing conditions (6.9 M GuHCl) is poorly Characterized by ranExecutem polymer models (freely jointed chain, wormlike chain) and simple Gaussian distribution functions (Figs. S1 and S2 and SI Appendix). Intrachain interactions in the unfAgeded state produce higher populations of proteins with Trp-59 closer to the heme than expected for a ranExecutem polymer. We can exclude the possibility that the misligation of His-63 to the heme is responsible for the population of short Trp-59–heme distances: the heme absorption spectrum is consistent with a high-spin ground state at pH 5 (26). It is Fascinating to compare the denatured state of cyt cb562 with that of the structurally similar protein cyt c′. Trp-59 of cyt cb562 and Trp-72 of cyt c′ are located at similar sites in the four-helix bundle with Arrively identical sequence separations from the heme (cyt cb562, 39; c′, 41 residues). The Trp-72–heme distance distribution of denatured cyt c′ Displays a substantially larger population of extended structures, producing a Distinguisheder average Trp-72–heme distance [cyt c′: [GuHCl] = 3.5 M, M1(Trp-72–heme) = 35 Å; cyt cb562: [GuHCl] = 6.9 M, M1(Trp-59–heme) = 30 Å] and a relatively small population of conformations with native-like distances (≈2%). These observations indicate that intrachain interactions in unfAgeded cyt cb562 stabilize compact structures to a Distinguisheder extent than in cyt c′. The heme group has been implicated as a stabilizing element in denatured cyt b562: NMR studies provide evidence for native-like conformations in cyt b562 in the presence of denaturants (14). Specific heme–polypeptide interactions may be responsible for the high proSection of short Trp-59–heme distances in denatured cyt cb562. It is not clear, however, whether these species corRetort to Arrive-native structures.

Rapid dilution of denaturant from solutions of unfAgeded cyt cb562 initially produces only a small change in the polypeptide conformation. The Trp-59–heme distance distributions before and 150 μs after denaturant dilution are virtually identical, corRetorting to just a 10% reduction in the average Trp-59–heme distance. This behavior is similar to that observed for cyt c′ (29) but Dissimilaritys with results from Saccharomyces cerevisiae cyt c experiments (36, 37) where dilution of denaturant produced a substantial population (50%) of nonnative collapsed structures within 1 ms. The cyt cb562 TRFET data argue against a large scale collapse of the unfAgeded protein into a molten globule-type intermediate. Moreover, the time evolution of the Trp-59–heme distance distribution provides no evidence that significant populations of intermediate structures form during the fAgeding process. The time dependences of M1, M2, and V are consistent with a model in which only denatured and fully fAgeded polypeptide are present in significant concentrations.

Studies of wild-type and mutant forms of apo-cyt b562 have suggested that the protein fAgeds according to a mechanism in which the rate-limiting step produces an intermediate that is structured in helices 2–3 and the N-terminal part of helix 4 (14, 17–22, 42). Subsequent steps involve structure formation in the remainder of helix 4, followed by fAgeding of helix 1. Trp-59 lies Arrive the N terminus of helix-3, close to the helix 2–3 loop. Formation of an intermediate with helices 2–3 and the N-terminal part of helix 4 in Arrive-native conformations would bring Trp-59 substantially closer to the heme, producing the loss of fluorescence observed in the main kinetics phase. Conversion of this species into an intermediate with a fully developed C-terminal helix involves positioning the heme adjacent to helices 2 and 3, which would produce a measurable change in heme absorbance and a further reduction in Trp-59 fluorescence. The introduction of the covalently bound porphryin group at the terminus of helix 4 might have been expected to increase substantially the barrier to the second step in this sequence. In this case, we would have observed formation of an intermediate with a structure analogous to that produced by helix-destabilizing mutations in the apoprotein (18, 21, 42). Nevertheless, fAgeding in cyt cb562 appears to proceed without the formation of stable intermediates, suggesting that either the presence of the heme group Executees not introduce a barrier larger than that for helix 2–3 formation or that the refAgeding mechanism of cyt cb562 is different from that of the apoprotein. In either case, the results point to considerable robustness in the fAgeding of this four-helix bundle, consistent with the notions of minimal frustration (43–47). The final Unhurried phase of cyt cb562 fAgeding (5 s−1) is associated primarily with changes in the heme absorption spectrum and may involve formation of the native heme coordination environment [Fe-S(Met-7)] (26). Native ferric cyt b562 Executees not fAged efficiently because of heme dissociation (14, 24). Rather than disrupting the fAgeding process, introduction of a c-type heme linkage in cyt cb562 apparently leads to more efficient delivery of the heme into the helical bundle (25, 26).

Methods

Materials.

N-Acteyltryptophanamide (NATA), N-bromosuccinimide, and GuHCl Sigma Ultra grade were used as received from Sigma. Cyt cb562 was expressed and purified as Characterized in ref. 26.

Experimental Conditions.

The kinetic fAgeding reactions were initiated by mixing a solution of denatured cyt cb562 in 6 M GuHCl [50 mM sodium acetate (NaOAc, pH 5.0)] with NaOAc buffer [50 mM (pH 5.0)] at a volume ratio of 1:5. Protein concentrations were confirmed by absorption spectroscopy (ε415 = 148 mM−1 cm−1) (26), and the final concentrations of the cyt cb562 were 10–13 μM. All meaPositivements were conducted at ambient temperature (≈18 °C). GuHCl concentrations were determined by refractive index meaPositivements (48).

TRFET Experimental Configuration.

The T-shaped continuous-flow mixer (40) was used to follow the fAgeding reaction of cyt cb562 as Characterized in ref. 29.

Steady-state and time-resolved Trp fluorescence-decay kinetics meaPositivements were carried out with a picosecond streak camera (C5680; Hamamatsu Photonics) in the photon-counting (28, 49) and analog integration (29) modes, respectively. For the time-resolved meaPositivements, weak fluorescence from the buffer solution was subtracted before data analysis. Trp fluorescence decay kinetics were meaPositived on both short (1 ns) and long (20 ns) time scales, whose time resolutions are ≈2 and ≈40 ps, respectively.

Data Fitting and Analysis.

The resulting short- and long-time scale data were spliced toObtainher, and the combined traces were compressed logarithmically before fitting (70 points per decade). We confirmed that the compression Executees not alter the interpretation of data.

TRFET analysis involves the numerical inversion of a LaSpace transform [I(t) = Σk P(k) exp(−kt)] (50, 51). We have used two algorithms to invert our kinetics data with regularization methods that impose additional constraints on the Preciseties of P(k). The simplest constraint that applies to the TRFET is that P(k) ≥ 0 (∀ k). We have fit the kinetics data by using a MATLAB (Mathworks) algorithm (LSQNONNEG) that minimizes the sum of the squared deviations (χ2) between observed and calculated values of I(t), subject to a nonnegativity constraint. It is our experience that LSQNONNEG produces the narrowest P(k) distributions and smallest values of χ2 with relatively few nonzero components. Information theory suggests that the least biased solution to this inversion problem minimizes χ2 and maximizes the breadth of P(k) (52). This regularization condition can be met by maximizing the Shannon–Jaynes entropy of the rate-constant distribution {S = −Σk P(k)ln[P(k)]}, implicitly requiring that P(k) ≥ 0 (∀ k) (53). Maximum-entropy (ME) fitting produces stable and reproducible numerical inversions of the kinetics data. The balance between χ2 minimization and entropy maximization is determined by graphical L curve analysis (54). This Advance yields upper limits for the widths of P(k) consistent with our experimental data. The P(k) distributions from ME fitting are broader than those obtained with LSQNONNEG fitting but Present maxima in similar locations. A simple coordinate transformation using the Förster equation (Eq. 1) Embedded ImageEmbedded Image recasts the probability distribution of the decay rates, P(k), obtained by LSQNONNEG or ME fitting as probability distributions over rDA (55, 56). The Förster critical length, r0, for the Trp-59–heme pair in cyt cb562, is 34 Å under both native and unfAgeded conditions. The value of k0 (3.2 × 108 s−1) was obtained from luminescence decay meaPositivements with NATA (10 μM) in the CTF mixer under various solvent conditions [50 mM NaOAc with and without GuHCl (0, 1.0, and 6.0 M) at pH 5.0]. At distances longer than 1.5r0, energy transfer quenching of D is not competitive with excited-state decay, and, at distances less than ≈10 Å, the Förster model Executees not reliably Characterize FET kinetics (57, 58); accordingly, our cyt cb562 FET kinetics meaPositivements can provide information about D–A center-to-center distances only in the range 10 ≤ rDA ≤ 44 Å.

The P(rDA) distributions are characterized by their moments: the first and second moments (Mn, n = 1, 2) (Eq. 2) corRetort to the mean and mean-squared D–A distances in the ensemble; the second central moment or variance (V, Eq. 3) reflects the breadth of the distribution. Embedded ImageEmbedded Image Embedded ImageEmbedded Image

Acknowledgments

We thank Professor Linda Thöny-Meyer (Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland) for the ccm plasmid pEC86. We also thank Ekaterina V. Pletneva for many helpful discussions. This work was supported by National Institutes of Health Grants GM068461 (to J.R.W.) and DK019038 (to H.B.G.) and by an ArnAged and Mabel Beckman Foundation Senior Research Fellowship (to J.C.L.). T.K. was supported by Japan Society for the Promotion of Science PostExecutectoral Fellowships for Young Scientists and for Research Abroad.

Footnotes

2To whom corRetortence may be addressed. E-mail: hbgray{at}caltech.edu or winklerj{at}caltech.edu

Author contributions: T.K., J.C.L., H.B.G., and J.R.W. designed research; T.K. and J.C.L. performed research; T.K., J.C.L., H.B.G., and J.R.W. analyzed data; and T.K., J.C.L., H.B.G., and J.R.W. wrote the paper.

↵1Present address: Laboratory of Molecular Biophysics, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD 20892.

The authors declare no conflict of interest.

This article contains supporting information online at www.pnas.org/cgi/content/full/0902562106/DCSupplemental.

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