Ultrafast Dynamics of Nonequilibrium Resonance Energy Transfer and

ARTICLE pubs.acs.org/JPCA

Ultrafast Dynamics of Nonequilibrium Resonance Energy Transfer and Probing Globular Protein Flexibility of Myoglobin Jeffrey A. Stevens, Justin J. Link,† Chen Zang, Lijuan Wang, and Dongping Zhong* Departments of Physics, Chemistry, and Biochemistry, OSU Biophysics, Chemical Physics, and Biochemistry Programs, 191 West Woodruff Avenue, The Ohio State University, Columbus, Ohio 43210, United States ABSTRACT: Protein structural plasticity is critical to many biological activities and accurate determination of its temporal and spatial fluctuations is challenging and difficult. Here, we report our extensive characterization of global flexibility of a globular heme protein of myoglobin using resonance energy transfer as a molecular ruler. With site-directed mutagenesis, we use a tryptophan scan to examine local structural fluctuations from B to H helices utilizing 10 tryptophan-heme energy transfer pairs with femtosecond resolution. We observed ultrafast resonance energy transfer dynamics by following a nearly single exponential behavior in 10
100 ps, strongly indicating that the globular structure of myoglobin is relatively rigid, with no observable static or slow dynamic conformational heterogeneity. The observation is against our molecular dynamics simulations, which show large local fluctuations and give multiple exponential energy transfer behaviors, suggesting too flexible of the global structure and thus raising a serious issue of the force fields used in simulations. Finally, these ultrafast energy transfer dynamics all occur on the similar time scales of local environmental relaxations (solvation), leading to nonexponential processes caused by energy relaxations, not structural fluctuations. Our analyses of such processes reveal an intrinsic compressed- and/or stretched-exponential behaviors and elucidate the nature of inherent nonequilibrium of ultrafast resonance energy transfer in proteins. This new concept of compressed nonequilibrium transfer dynamics should be applied to all protein studies by time-resolved F€orster resonance energy transfer (FRET).

I. INTRODUCTION Protein fluctuations have been considered an essential determinant in many biological activities,1
3 and conformation dynamics have been extensively studied recently, especially by single-molecule spectroscopy4,5 and molecular dynamics (MD) simulations.6,7 These conformation changes are usually ratedetermined steps, such as in DNA polymerases,8,9 and involve large amplitude motions on the length scale from Å to nm with relatively large free energy barriers from a few to 10s of kcals/ mol. These motions, presumably slaved by solvent (water) fluctuation through an R-relaxation process,10
12 are relatively slow on the time scales of longer than nanoseconds and typically result in (static or slow dynamic) heterogeneous kinetics.4,5 However, the true catalytic reactions in enzymes occur on the ultrafast time scales, typically less than nanoseconds.13
18 On such ultrafast time scales, proteins could switch among different substates19 coupled with hydration water fluctuations through a β-relaxation process.10
12 It has been challenging to directly monitor these ultrafast motions, especially in enzymatic reactions, as shown in a few systems of photosynthesis14,15 and photoenzymes.16
18 One significant advance recently is the observation of molecular recognition of heme proteins with diatomic ligands (CO, O2, and NO), and these ultrafast motions are critical to ligand binding and releasing.20
22 Meanwhile, MD simulations also predict significant fluctuations of various protein structural r 2011 American Chemical Society

elements of side chains, loops, turns and even small domains on the time scales from picoseconds to even microseconds.23
25 Thus, for a typical globular protein, we need to ask how fast the protein conformation fluctuates on the time scale of biological functioning, what about the protein plasticity relative to the static or dynamic heterogeneity, and how reliable the various protein motions predicted by MD simulations. To answer these critical questions, we choose the classic model protein of globular myoglobin to examine the global fluctuations by both experiment and MD simulations and thus directly compare the protein flexibility by two methods. The X-ray structure of sperm whale myoglobin (Mb) is shown in Figure 1.26 Myoglobin has eight R-helices (labeled A-H), with a total of 153 amino acids, two of which are intrinsic tryptophans (W7 and W14). In an earlier report,27 we systematically examined the local conformation fluctuations of the A-helix using a resonance energy transfer (RET) pair of intrinsic tryptophan with the prosthetic heme group as a molecular ruler. We observed a mobile W7 near the loose N-terminal and a rigid W14 buried inside the hydrophobic core. To examine the global flexibility of Mb, we designed 10 more tryptophan mutants, one Special Issue: Femto10: The Madrid Conference on Femtochemistry Received: June 28, 2011 Published: August 24, 2011 2610

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Figure 2. Normalized absorption and emission spectra of a typical holoMb mutant of A22W. Also shown is the emission of the corresponding apoMb mutant. Note that the emission peak of holoMb is bluer than that of apoMb. The downward arrow marks the pump wavelength (λpu), and the upward arrows mark typical gated fluorescence wavelengths (λfl).

Figure 1. X-ray crystallography structure of myoglobin26 (PDB: 1MBD) shown with 10 tryptophan mutations at positions W22, W48, W57, W71, W74, W84, W95, W113, W125, and W144, displayed as yellow spheres. The prosthetic heme group is shown in pink.

at a time, using site-directed mutagenesis to cover all of the other helices, B
H (Figure 1). Thus, each mutant protein only has a single tryptophan-heme RET pair, with tryptophan as the energy donor and the heme as the energy acceptor. For all these mutant proteins, we have recently studied the hydration dynamics of each site-specific tryptophan by removing the heme group (apoMb) and observed two typical relaxation time scales in a few to 10s of picoseconds.28,29 These local relaxations are critical to the understanding of nonequilibrium RET dynamics,30
32 as we observed in our earlier study.27 In this report, we systematically characterize the RET dynamics of 10 mutant proteins at different positions and determine their actual time scales. With further measurements of all quantum yields and fluorescence lifetimes and calculations of time-resolved spectral overlap integrals, we can derive all orientation factors for the mutants. These results are directly compared with MD simulations to reveal the global protein flexibility, which is further examined with temperaturedependence studies. With all these results, the intrinsic nature of ultrafast nonequilibrium RET is evaluated and discussed.

II. EXPERIMENTAL SECTION A. Femtosecond Laser Setup. All of the femtosecondresolved measurements were carried out by using the fluorescence up-conversion method, and the integrated experimental setup has been described elsewhere.33 Briefly, the femtosecond pulse after the two-stage amplifier (Spitfire; Spectra-Physics) has a temporal width of 110 fs, centered at 800 nm, with energy of more than 2 mJ per pulse at a repetition rate of 1 kHz. Half of the laser energy was used to pump one optical parametric amplifier (OPA-800C; Spectra-Physics) to generate signal (1289 nm) and idler (2109 nm) beams. The latter was mixed with the residual fundamental (800 nm) in a 0.2 mm thick β-barium borate (BBO)

crystal (type I) to generate a femtosecond pulse at 580 nm. This femtosecond pulse was frequency-doubled to generate a pump wavelength at 290 nm by another 0.2 mm thick BBO crystal. The pump pulse energy typically was attenuated to 100
140 nJ per pulse before being focused into the motor-controlled rotating sample cell. The fluorescence emission was collected by a pair of parabolic mirrors and mixed with a gating pulse from the other half of the fundamental beam (attenuated) in a 0.2 mm BBO crystal (type I) through a noncollinear configuration. The upconverted signal, ranging from 223 to 253 nm, was detected by a photomultiplier coupled with a double-grating monochromator. The instrument response time under the current noncollinear geometry is about 400 fs, as determined from the up-conversion signal of Raman scattering of water at 320 nm. For all studies, the pump-beam polarization was set at a magic angle (54.7
) with respect to the acceptance axis (vertical) of the up-conversion crystal, and the polarization of the gating beam was set parallel to this axis through a half-wave plate. B. Sample Preparation. The mutant design and purification of Mb have been described in detail elsewhere.34,35 To achieve single tryptophan-heme RET, site-directed mutagenesis was used to place one tryptophan residue at a time for all ten mutants. The plasmid pMb122, containing the sperm whale myoglobin gene, was used to mutate two tryptophan residues to tyrosine at position 7 (W7Y) and to phenylalanine at position 14 (W14F) to create a double mutation of W7YW14F.36 This double mutant was used as a template for all 10 triple mutants with one more mutation of A22W, H48W, A57W, A71W, A74W, A84W, T95W, H113W, A125W, and A144W, a tryptophan scan of the protein surface. All of the mutants were expressed in E. coli with a reasonable yield. ApoMb was prepared by removing the prosthetic heme group according to the standard procedure,37 and all apoMb mutants were screened to determine each tryptophan’s lifetime and to ensure no ultrafast quenching from neighboring protein residues.38 All holoMb samples were dissolved in 20 mM Tris and 1 mM EDTA at pH 7.5, and apoMb was dissolved in a buffer of 10 mM sodium acetate at pH 6.1. The structures of apoMb mutants were examined by their CD spectra to verify the appropriate folding.28 Quantum yield measurements were performed at dilute concentrations of less than 10 μM in a 1 cm quartz cuvette. All time-resolved experiments used a protein concentration of about 200 μM in a 1 mm quartz rotation cell to avoid sample heating and degradation. All temperature-dependent measurements were performed in a 1 mm rotation cell that 2611

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Figure 4. Normalized, femtosecond-resolved transients of nine holoMb mutants gated at 350 or 360 nm with inserts at short-range time. Note the different time scales of two panels (A and B) and the tryptophan lifetime components were removed for clarity, with their relative percentages listed in Table 1. Figure 3. Normalized, femtosecond-resolved transients of the mutant W22 in holoMb (A) and apoMb (B) with a series of gated fluorescence emissions with inserts at short-range time. In holoMb, the long lifetime component (4%) was removed for clarity. Note the different time scales of the two panels, and the holoMb mutant transients decay much faster.

Table 1. Fitting Results of Ultrafast Fluorescence Transients of Nine Tryptophan Mutants mutant τRET (ps) A1

was heated and cooled with a VWR water-bath circulator. The absorption and emission spectra of each sample were verified before and after time-resolved measurements to ensure no changes of protein quality during the experiment. Figure 2 shows a typical absorption spectrum of ferric holoMb and tryptophan emission spectra of both ferric holoMb and apoMb of the W22 mutant. The holoMb emission is much weaker than that of apoMb with the emission peak at 335 nm, blue-shifted from 340.8 nm of apoMb, consistent with the ultrafast RET quenching of fluorescence emission.27,38

W71 W74

0.5 14.4

A2

0.28 0.04 0.12 0.03

A3

m τ3 (ps) τ4 (ps) τ5 (ps) A1 (%) 1.8 2.1

680 800

7950 3900

88 81

W95

23

0.12 0.02
0.09 2.8

185

1680

0.75

88

W48

45

0.18 0.002
0.13 1.7

300

3500

1.0

99

0.7

96

1.3

94

W22

51

0.15 0.01
0.05 2.3

410

4400

W84

53

0.15 0.01

400

3020

W144

120

0.02 0.001
0.05 21

1080

3140

W113a

140

0.10 0.16
0.05 0.83 350

3000

4.7

39

W57

205

0.09 0.03
0.07 3.3

2430

0.7

79

2.0

350

94

a

III. RESULTS AND DISCUSSION

The small A1 percentage (39%) of the RET component is due to the small m value, that is, the large contribution of the short lifetime component (350 ps) and the slow RET dynamics (140 ps).

A. Ultrafast Fluorescence Dynamics, Resonance Energy Transfer, and Local Dynamic Heterogeneity. A series of

transients (λfl = 350 or 360 nm) of holoMb as follows:

femtosecond- and wavelength-resolved fluorescence transients was taken from the blue to the red side of the emission spectra for 10 mutants in both apoMb and holoMb. Figure 3 shows several typical transients of W22 in both forms. In apoMb, the emission peak of W22 is 340.8 nm (Figure 2) and all the transients on the blue side of the peak in Figure 3B show two ultrafast solvation relaxations and two long lifetime decays. The two solvation dynamics are in 2.9 and 60 ps and the two lifetimes are 410 ps and 4.4 ns. At the red side of the emission peak, the transients decay by two long lifetime emissions. In ferric holoMb, all the transients become much faster, as shown in Figure 3A. Such changes must result from the RET from excited tryptophan to the heme group, not from any other protein side chain quenching. Similarly, at the blue side, the dynamics results from a mixture of solvation relaxation and RET. At the red side, the fast decay is dominant and is from the RET process. To extract the accurate RET times (τRET) from these fluorescent transients, we fit the red-side

IðtÞ ¼ A1 ðe
kRET1 t þ me
kRET2 t Þ þ A2 ðe
k3 t þ me
k4 t Þ þ A3 e
k5 t

ðIII:1Þ

where k3 = 1/τ3, k4 = 1/τ4, kRET1 = 1/τRET + 1/τ3, kRET2 = 1/τRET + 1/τ4, and τ3 and τ4 are the two lifetimes of fluorescence emission of apoMb. A1 and A2 are the relative contributions of RET and likely apoMb or disordered-heme Mb in the protein sample,27 and m is the relative ratio of lifetime components of τ4 to τ3 obtained from apoMb at the fixed red-side wavelength (350 or 360 nm).29 The last term of A3 (negative) and k5 (1/τ5) is the rise component, if necessary, due to solvation at the red side. Using eq III.1, we obtained τRET of 51 ps for W22, a single RET decay time and not a multiple- or nonexponential decay behavior. At the blue side, the transients exhibit multiple ultrafast decays due to solvation (see below). Thus, to study the RET 2612

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Table 2. Resonance Energy Transfer Times and Related Parameters for Nine Tryptophan Mutants J (10
14 cm3 M
1) mutant

τRET (ps)

QD

τRET

tss

orientation factor (k2)b

emission max (nm) ÆτDæa (ns)

r (Å)

Apo (τRET)

Apo (tss)

Holo (tss)

experiment

MD

W71

0.5

0.32

3.72

5.82

4.7

9.9 ( 0.4

323.8

336.8

334.3

2.54 ( 0.73

0.74 ( 0.56

W74

14.4

0.27

4.42

6.21

4.0

13.3 ( 1.7

327.8

338.3

333.2

0.47 ( 0.23

0.85 ( 0.30

W95

23

0.14

5.08

6.67

2.1

14.8 ( 0.5

329.7

338.6

332.9

0.48 ( 0.06

0.45 ( 0.28

W48

45

0.15

5.68

7.03

2.6

16.8 ( 0.4

335.8

342.4

337

0.57 ( 0.09

0.16 ( 0.07

W22

51

0.16

4.95

6.82

2.9

20.4 ( 0.6

330.2

340.8

335.3

1.82 ( 0.39

0.22 ( 0.23

W84

53

0.10

5.28

6.67

1.8

20.6 ( 0.9

335.0

341.7

340.8

1.75 ( 0.55

0.60 ( 0.49

W144

120

0.22

6.34

8.12

3.9

17.6 ( 1.0

335.0

344.8

336.6

0.25 ( 0.06

0.64 ( 0.31

W113 W57

140 205

0.18 0.20

4.86 5.72

5.70 6.25

2.6 3.0

17.2 ( 0.8 22.5 ( 0.3

330.7 335.1

335.6 338

334.7 336.1

0.20 ( 0.04 0.54 ( 0.05

1.09 ( 0.35 0.26 ( 0.10

a The average lifetimes are calculated by ÆτDæ = τradQD, as confirmed by our measurements for certain mutants. b The large one-standard deviations of experimental k2 are dominantly from the deviations of the simulated distance r. All other parameters have very small errors. The MD simulated k2 values have much larger one-standard deviations due to the significant fluctuations of orientations and distances.

dynamics and determine its time scale (rate) accurately, we must detect the time-resolved fluorescence dynamics at the emission peak or longer wavelengths. Similarly, we studied all of the other nine mutants, and the transients are shown in Figure 4, with removal of long components for clarity. The RET dynamics are obtained by gating the red-side emission at either 350 or 360 nm. All the transients basically exhibit a double-exponential decay with two distinct time scales, one major ultrafast component (RET) in picoseconds and one minor long component in nanoseconds. All fitting results are shown in Table 1 with relative percentages of RET contributions and long components. Specifically, for W71 located in E-helix, which is in proximity with the heme group, we obtained an ultrafast RET time of 0.5 ps. According to our MD simulations (see below), the center-to-center distance between the heme and W71 is about 10 Å but the shortest edge-to-edge separation is at van der Waals distance. At such a short distance, the energy transfer may not follow the conventional weakcoupling RET and other mechanisms39 (such as nonweak coupling or Dexter exchange interaction) are probably responsible for such ultrafast energy transfer, as observed in photosynthesis40 and recent polymer studies.41 For the nearby W74 in the E-helix and W95 in the F-helix, both donor
acceptor distances are similar, 13.3 and 14.8 Å, and the RET times are 14.4 and 23 ps, respectively. For W48 in the C
D loop and W84 in the F-helix, as well as the above W22 in the B-helix, the RET times are similar, 45, 53, and 51 ps, respectively. However, the distances of W84 and W22 to the heme acceptor, 20.6 and 20.4 Å, respectively, are significantly longer than that of W48, 16.8 Å. For another three mutants of W144 in the H-helix, W113 in the G-helix, and W57 in the D-helix, their RET times are 120, 140, and 205 ps with the energy-transfer distances of 17.6, 17.2, and 22.5 Å, respectively. For the W125 in the G-helix with the longest energy-transfer distance around 27 Å, we observed a long RET time of about 480 ps. The holoMb emission peak of W125 is 345 nm, but its apoMb emission peak is 341 nm, indicating that the local structure of apoMb is different from that of holoMb, and thus, W125 at the N-terminal of the G-helix probably rotates into the hydrophobic core during apoMb refolding. Thus, we cannot use eq III.1 to exactly extract the RET time due to the lack of lifetimes (τ3 and τ4) and relative ratio (m) of apoMb that has the same local structure of holoMb, but we can estimate to be about 480 ps from the fast decay transients at the red side.

With the precise measurements of these RET times, in the following we evaluate various parameters for determination of the RET time scales and examine the dynamic heterogeneity and related global flexibility and fluctuation of the protein. At the pointdipole approximation, the RET rate equation through dipole
dipole interaction at equilibrium state is expressed as eq III.2.42 kRET ¼


 1 R0 6 Q D k2 ¼ 8:79  1023 J τD r τ D n4 r 6

ðIII:2Þ

where QD and τD are the donor’s fluorescence quantum yield and lifetime in picoseconds without the energy acceptor, respectively, J is the spectral overlap integral of the normalized donor fluorescence spectrum (apoMb) and the acceptor’s absorption spectrum expressed by its extinction coefficient in units of cm3 M
1, n is the refractive index, which usually is about 1.33 in the protein,43,44 and r is the center-to-center distance of the donor and acceptor in Å. The orientation factor k2 is related to the relative alignments of the donor and the acceptor. Because each tryptophan mutant is from a triple mutation of the wild-type Mb, MD simulations were used to determine the distances of r in eq III.2. From the comparison of emission peaks between holoMb and apoMb, the local structure for the W125 mutant is changed from holoMb to apoMb, while for all other nine mutants the holoMb emission peaks are bluer than those of apoMb, and the local tryptophan’s structures seem unchanged. Thus, we will focus on our analyses and studies below only on these nine mutant proteins. The quantum yields (QD), lifetimes (τD), and fluorescence spectra for calculations of J are measured in apoMb without the acceptor heme group. Using tryptophan’s quantum yield of 0.14 in water as control,45 we obtained quantum yields (QD) between 0.10 and 0.32; see Table 2. It should be noted that caution must be taken when determining QD as measuring the apoMb concentration can be easily overestimated due to UV scattering in the absorption spectrum as previously noted.27 We noticed that the radiation lifetime, τrad (τD/QD), of tryptophan is about 14 ns in hydrophobic environments and about 20 ns in polar environments.46 Thus, we used τrad to be approximately 15 ns for apoMb, with the emission maxima of less than 339 nm and 18 ns with the longer emission maxima in eq III.2 and, if necessary, deduced the average lifetimes (ÆτDæ) of the mutants using ÆτDæ = τradQD, which were further confirmed by our measurements of lifetimes for certain apoMb mutants. 2613

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The overlap integral, J, is generally expressed as eq III.3.42 Z FðλÞεðλÞλ4 dλ Z ðIII:3Þ J ¼ FðλÞdλ where F(λ) represents the emission spectrum in the absence of the acceptor and ε(λ) is the absorbance molar extinction coefficient, in units of cm
1 M
1. Typically, the steady-state fluorescence spectrum is used to calculate J. However, if the RET time is on a similar time scale of the local hydration dynamics, we must carefully consider the nonequilibrium RET process due to the local relaxation,27,31 and the resulting spectrum shifting toward the red side. Figure 5A shows the shifting spectra at the different times for the W74 mutant with the time-zero spectrum peaked at 321.8 nm. Such spectrum shifting results in changing of the J value, and thus, using the steady-state spectrum would produce a bigger J value. Figure 5B shows the comparison of two local relaxation times (τ1 and τ2) reported by our early studies29 with the current RET time for all nine mutants. Notably, all RET times except for W71 are on similar time scales as the local hydration, and for W71, the RET time is even much shorter than the first relaxation time of 2.5 ps. Thus, F(λ) and J should be represented more accurately as a function of time, F(λ,t) and J(t). Figure 5C shows the time dependence of J values for W74 calculated by eq III.3 with the femtosecond-resolved emission spectra (FRES), F(λ,t). Thus, eq III.3 should be written as follows: Z Fðλ, tÞεðλÞλ4 dλ Z ðIII:4Þ JðtÞ ¼ Fðλ, tÞdλ In Figure 5C, we marked several values of J at t = t0, τ1, τRET, τ2, tsc, and tss; tsc and tss are times when the solvation is completed and the FRES reaches the steady-state emission maximum, respectively. If we use the conventional eq III.2 to calculate kRET with J(tss), 6.21  10
14 cm3 M
1, instead of J(τRET), 4.42  10
14 cm3 M
1, the resulting rate would be larger by 40%. For all nine mutants, the time-zero emission maxima are about 320
323 nm,29 much bluer than the steady-state peaks of 335
345 nm. With all reported hydration dynamics for nine mutants,29 we can calculate all FRES as shown in Figure 5A and thus derive J(t), as shown in Figure 5C, and finally obtain J(τRET). The final results of J(τRET) and J(tss) are shown in Table 2. It should be pointed out that all emission maxima at τRET are bluer than the steady-state emission peaks of holoMb, and these holoMb peaks are bluer than those of apoMb (Table 2). Even for t = 3τRET, the calculated emission maxima are mostly bluer than those of holoMb, indicating the long component contributions with a redder emission like apoMb, as observed in our ultrafast fluorescence transients (Table 1). B. Orientation Factors, Local Fluctuations, and MD Predictions. Knowing the RET rates, kRET, and all parameters of τrad (τD/QD), r (MD average, see below), and J(τRET), as summarized in Table 2, we can use the F€orster equation (eq III.2) to derive the orientation factor k2. For our eight mutants, except for W71, we obtained k2 values between 0.20 for W113 and 1.82 for W22 (Table 2). These values are much less or far greater than the average value of orientation factor (0.67),42 which is widely used for RET studies, indicating again that, for RET in proteins, the donor and acceptor can be highly restricted, and using the

Figure 5. (A) Absorbance of the W74 mutant holoMb shown with the emission of apoMb at six different times: t0, time zero; τ1, the first hydration time; τRET, the RET time; τ2, the second hydration time; tsc, solvation completed; and tss, reaching steady state. (B) RET times (green) compared with the first (blue) and second (orange) hydration times for nine mutants. Note the log scale for the times. (C) Overlap integral changes with time including the typical values at six special times in (A). Inset is shown with the early time. The emission profile was kept the same with time in calculation. The corresponding emission maxima are shown at the top of (C).

average value (0.67) would lead to a significant error for accurate determination of the distance r. For W71, although the energy transfer probably proceeds through a different mechanism, using the center-to-center donor
acceptor distance of 9.9 Å, we would obtain a k2 value of 2.54 for the ultrafast RET in 0.5 ps, still less than the maximum value of 4.0. With MD simulations using initial X-ray structure for mutations,25 we can estimate the k2 values of nine mutants with all atomic coordinates by the following equation.42 k2 ¼ ðcos θDA
3cos θD cos θA Þ2

ðIII:5Þ

All angles of θDA, θD, and θA are relative orientations, as shown in Figure 6A. The transition dipole moment of tryptophan is taken from the 1La transition, 38
from the major axis of the tryptophan ring.47 The heme transition moment is taken to be in the interval of 50
60
relative to the R
γ-meso axis of the porphyrin ring.48 These transition directions are also shown in Figure 6A. Thus, the orientation factors between the dipoles can be determined from their relative dipole’s geometry (Figure 6A). Figure 6B,C 2614

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Figure 6. (A) Relative directions of transition dipole moments of the heme and tryptophan and all related angles used to calculate the orientation factor. (B) Calculated orientation factor and (C) center-tocenter distance of the tryptophan-heme energy transfer pair from a 14 ns MD trajectory simulation for mutants of W48, W57, W74, and W84. (D) Orientation factors of experimental results and MD calculations for nine mutants. Error bars represent one standard deviation from the calculated values. Note the dramatic differences between experiment and MD simulations.

shows typical k2, calculated from eq III.5 with the normal heme configuration, and r changes with time from several MD trajectories for W57, W84, W48, and W74 of a 15 ns simulation with the first 1 ns as the initial equilibrium. Clearly, W74 and W84 have large fluctuations of k2 and r values and W48 and W57 show smaller changes. The W74 and W84 are close to the ends of termini of the E and F helices, and the E
F loop could be very flexible, as shown in our early MD simulations.25 Thus, we take the average MD values of k2 and r, and the derived values are listed in Table 2. For k2, it ranges from 0.16 for W48 to 1.09 for W113 and these values are very different from the experimental ones, except that for W95 the MD value is 0.45 and the experimental one is 0.48. All other eight mutants show significant

ARTICLE

Figure 7. (A) Schematic model of nonequilibrium resonance energy transfer with S1 and S1† for excited and hot excited states, respectively. Also shown is the energy stabilization by solvation of the excited donor with typical times, corresponding to different RET rates. (B) The calculated transients under different conditions of orientation factors, distances, or spectral overlap integrals from MD simulations and experimental results; see text. (C) The nonequilibrium resonance energy-transfer transients with the exact solution of nonequilibrium spectral overlap integrals J(t) and two kinds of its decomposition into two terms with the first term either using J0 at t0 or Jss at tss; see text.

deviation of MD k2 values from the experimental ones. For W71, W57, W22, W84, and W48, their MD values of 0.74, 0.26, 0.22, 0.6, and 0.16 are much smaller than the experimental ones of 2.54, 0.54, 1.82, 1.75, and 0.57, respectively. However, for W113, W74, and W144, the MD values of 1.09, 0.85, and 0.64 are significantly larger than those experimental ones of 0.2, 0.47, and 0.25, respectively. Figure 6D shows the comparison of these values from our experiment and MD simulations and all error bars represent calculated one-standard (1σ) deviations. We also calculated the disordered-heme49 RET times and found that their time scales are mostly on the same order of the normal-heme RET dynamics in 10s to 100s of picoseconds. Because the disordered-heme Mb usually has a minor population in the protein solution, we believe that the observed long components in nanoseconds are probably not from the disordered-heme RET contributions. It is striking that eight experimental k2 values among nine mutants in B
H helices are drastically different from MD 2615

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The Journal of Physical Chemistry A simulations. This observation clearly indicates that the local structures under room temperature in solution are different from the local MD simulated structures, even though a long nanosecond relaxation process has been performed from the mutated X-ray structure by gradually raising low temperature of the crystal structure to room temperature of a protein solution. Furthermore, we observed that nearly all RET dynamics follow a singleexponential decay, indicating less fluctuating local structures but MD simulations predict very dynamic behaviors of local structures, especially near the loops or terminals, leading to at least a double-exponential or nonexponential decay behavior. Clearly, even with tens of nanoseconds equilibrium, the “equilibrium structure” in MD simulations under room temperature in solution is still a serious issue, as observed here. C. Nonequilibrium Energy Transfer, Global Conformation Rigidity, and MD Simulations. We recently have systematically studied protein surface hydration28,29,34,50
52 and binding/ active-site solvation53,54 and observed local relaxation on the time scales from subpicoseconds to subnanoseconds. For a chromophore such as tryptophan with the lifetime of a few nanoseconds, the relaxation basically occurs together with the fluorescence emission.55 Thus, the observed dynamic heterogeneity, J(t) (eq III.4), is a general phenomenon and reflects the intrinsic nature of ultrafast nonequilibrium RET in proteins. The molecular mechanism is depicted in Figure 7A. At each moment of t0, τ1, τ2, or tsc, the energy level is different and the resulting RET dynamics by coupling to the acceptor energy levels would be different. For tryptophan-heme energy transfer pair, the RET rates become larger with time due to the strong coupling with the Franck
Condon allowed absorption region (Figure 2). If tryptophan has multiple rotamers,56 a set of such nonequilibrium RET processes occur, leading to more heterogeneous dynamics. Thus, the ultrafast RET dynamics intrinsically is a nonequilibrium process with variable kRET(t), which changes with time. We can write the general RET dynamics, IRET(t), by the following equation. Rt
kRET ðt 0 Þdt 0 , IRET ðtÞ  e 0 k2 ðtÞ QD JðtÞ, c ¼ 8:79  1023 ðIII:6Þ kRET ðtÞ ¼ c 6 r ðtÞ τD n4 The final nonequilibrium dynamics of ultrafast RET with time could be expressed as follows. R t k2 ðt0 Þ 0 0
c Jðt Þdt ðIII:7Þ IRET ðtÞ  e 0 r6 ðt0 Þ Figure 7B shows a series of simulated ultrafast RET dynamics under different conditions for W74. Curve a is the fitted result of averaging more than 12000 transients calculated from eq III.7 by taking different time zeros in MD simulations of k2 and r in Figure 6B. J(t) was taken from Figure 5C for each IRET(t) calculation and for a given t, we took k2 and r from Figure 6B as constants and only integrated J(t0 ) function from 0 to t. Clearly, the fluctuations of k2 and r and nonequilibrium of J(t) result in the multiple-exponential decay dynamics of curve a, which could be fit by triple exponential decays (5.0 ps, 62%; 27 ps, 31%; and 384 ps, 7%). Curve b is calculated from eq III.7 using J(t) in Figure 5C, but we first averaged k2 and r over 14 ns MD simulations in Figure 6B, and thus, k2 and r values are treated as constants in eq III.7. The nonequilibrium behavior of the RET dynamics is completely from J(t0 ) in eq III.7 and this case could be the real situation when the local structure is

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relatively rigid with a constant distance (r) and fixed orientation (k2) on the ultrafast time scale. The resulting curve b cannot be fit precisely by a single exponential decay but instead can be fit β with a compressed-single-exponential decay, e
(t/τ) , with τ = 6.3 ps and β = 1.05. Note that the parameter β is larger than 1. Clearly, curves a and b are very different, and besides, the J(t) heterogeneity of the fluctuations of k2 and r on the ultrafast time scale cause significant multiple-exponential behaviors and the RET times could cover continuously from a few to 10s and 100s of picoseconds, as shown here for W74. Our experimental observation clearly shows a single exponential decay, similar to curve b, indicating constant k2 and r on the ultrafast RET time scale and implying a relatively immobile globular structure on this time scale. Curve c shows our observed experimental RET dynamics with a single exponential decay of τRET = 14.4 ps. Curve d is the corrected result of curve c by J(t) heterogeneity in Figure 5C using kRET(t0 ) = ((J(t0 ))/(J(τRET)τRET)) in eq III.6. Similarly, the curve d is not a single exponential decay any more and could be fit by a compressed-single-exponential decay with τ = 15.2 ps and β = 1.06. Such correction of heterogeneity of curve d is the same as curve b due to using the same J(t) and, thus, both give the similar β values. Finally, curve e is the simulated result using the steady-state J(tss), that is, kRET(t0 ) = ((J(tss))/(J(τRET)τRET)), in eq III.6, and curve e is a single exponential decay with τ = 10.3 ps, clearly faster than the true RET dynamics (14.4 ps) due to the overestimated J value. To understand why the parameter β is larger than 1, not less than 1, we can further analyze eq III.7 assuming constant k2 and r. For a chromophore in proteins with two relaxation times (τ1 and τ2), we can express the function of J(t) as follows: JðtÞ ¼ Jss
J1 e
t=τ1
J2 e
t=τ2

ðIII:8Þ

where Jss is the steady-state J(tss) and J1 and J2 are the changes of J values in relaxation of τ1 and τ2, respectively. Jss
J1
J2 is the J value at time zero, J0. Thus, we only need to evaluate the integration of J(t) from 0 to t. The final result could be written in the following two terms. Z t Jðt 0 Þdt 0 ¼ Jss t
½J1 τ1 ð1
e
t=τ1 Þ 0

þ J2 τ2 ð1
e
t=τ2 Þ

ðIII:9Þ

We can also use the Taylor expansion of the exponential terms and rewrite the integration in another two terms. Z t Jðt 0 Þdt 0 ¼ ðJss
J1
J2 Þt 0 
 
 J1 J2 J1 J2 2 3 þ þ þ t
t þ ::::: 2!τ1 2!τ2 3!τ21 3!τ22 ðIII:10Þ
14


14

Assuming that Jss, J1, and J2 are 6  10 , 2  10 , and 2  10
14 cm3 M
1, respectively, and τ1 and τ2 are 4 and 150 ps, similar to the values of W74, we simulated a series of curves in Figure 7C. Curves a and b in Figure 7C are plotted from the first and second terms in eq III.9. The first term is a single exponential decay and the time constant (5.7 ps) is determined by the steadystate Jss, an overestimated RET dynamics. The second term generates a rise curve that has all values larger than 1 to correct the first overestimated single-exponential term. Curve c is the 2616

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Figure 9. Normalized, femtosecond-resolved fluorescence transients at three different temperatures for W84 with the insert at short-time range. Transients are gated at 350 nm on the red side of the emission peak. Note no significant change in RET at different temperatures.

Figure 8. Simulations of RET dynamics with three different J(t) functions of (a) complete rise, (b) complete decay, and (c) rise and decay. The corresponding RET dynamics show dramatic different behaviors with compressed-, stretched-, compressed/stretched-exponential behaviors with averaged RET times of 52, 112, and 60 ps, respectively. The schematic of the donor emissions at t0 and tsc and the acceptor absorption is also shown.

product of the two curves a and b and is plotted by the exact solution in eq III.9. Curve c does not follow a single-exponential decay anymore and can be fit by a compressed-single exponential decay of τ = 10.1 ps and β = 1.17. We also plotted the first and higher order terms of eq III.10 of curves d and e, respectively, in Figure 7C. The first term is a single-exponential decay (16.0 ps) and the time constant is determined by the J value at time zero (J0). This term underestimates the RET dynamics. Curve e is a decay function with a first Gaussian term (t2) to correct the underestimated RET dynamics and curve c is also the product of the two curves d and e. Clearly, the final exact RET dynamics is not a single exponential decay and it can be represented by a compressed-single-exponential decays with a compressed parameter of larger than 1. The observed compressed-single-exponential RET behavior must result from the exponential increase of J(t) with time, that is, the FRES moving toward the absorption maximum (Figure 8a) that is a general case. Figure 8 shows three typical scenarios of J(t) changes with time by assuming that J(t) follows double exponential behaviors in 5 and 50 ps, mimic to the typical relaxation dynamics.29 With all other parameters together to be 5.67  1011 cm
3 M ps
1 in eq III.6 (except J(t)), we simulated the RET dynamics for these three cases in Figure 8. In case b, J(t) decays with time as the FRES moving away from the absorption maximum and the RET dynamics follow stretched-exponential decays (β2 is extremely close to 1 for the second component). In case c, J(t) initially rises and then decays as the FRES moving across the absorption maximum and the RET dynamics first follow the compressed-exponential and then stretched-exponential behaviors. Clearly, if J(t) decays with time, the RET dynamics must follow stretched-exponential behavior(s). Thus, with different

choice of energy transfer pairs, the RET dynamics will follow different nonexponential behaviors (Figure 8). Our experimental results show all single-exponential RET dynamics, which is extremely close to a compressed-single-exponential decay as shown by curves d and e in Figure 7B due to the fact that the β value is very close to 1. By knowing J(t) function, we can use eq III.9 or III.10 to estimate the parameter β and thus build the corresponding compressed or stretched model in data analyses. From our extensive studies of nine mutants with MD simulations and our early report of A-helix,27 it strongly indicates that, at least for myoglobin, the globular protein conformation is relatively rigid from examination of the A
H helices. The single exponential decay of ultrafast RET dynamics is strongly against the large fluctuations of k2 and r from the MD simulations (Figure 5B), not like others57 claiming the observation of structural fluctuations by simply examining the constituted tryptophan-coumarin 153 energy transfer in apoMb without considering the nonequilibrium RET dynamics. Our results indicate that the MD simulations give too flexible protein structures and suggesting that the force fields used in simulation need improvement.58 Finally, we further performed temperature dependent studies at 6, 21, and 40
C, and Figure 9 shows the results for W84. Clearly, with temperature changes, the RET dynamics for the mutants do not show significant temperature dependence from 6 to 40
C. Consistently, it shows again that the globular conformation of myoglobin is relatively rigid. The global RET dynamics and temperature studies show that for myoglobin there is no significant static heterogeneity or slow dynamic heterogeneity. On the ultrafast time scale, the heterogeneous RET dynamics is from the ultrafast local relaxation, energetically but not structurally. The local protein structures could fluctuate on the very small length scale, as observed by small wobbling angles of tryptophan residues from anisotropy studies,29 and probably slaved by the local solvent (water) molecules.10
12,28,29,55

IV. CONCLUSION We reported our global characterization of the globular protein conformation flexibility using resonance energy transfer as a molecular ruler with 10 tryptophan-heme transfer pairs by placing an intrinsic tryptophan among the B
H helices in myoglobin using site-directed mutagenesis. With spatial site specificity and femtosecond resolution, we observed much less fluctuating local structures and all energy transfer dynamics show a single-exponential decay on the ultrafast time scales from 2617

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The Journal of Physical Chemistry A subpicoseconds to subnanoseconds. With our early study of A-helix dynamics, the globular myoglobin exhibits a relatively rigid structure, less flexible than expected, with no observable static or slow dynamic heterogeneity. However, molecular dynamics simulations give an opposite trend and show significant local structural fluctuations, especially side chain (tryptophan) orientations, resulting in multiple exponential decays of energy transfer dynamics which were not observed by experiment. Thus, this study raises a serious issue on globular protein flexibility simulated by molecular dynamics and indicates that the force fields used in simulations need significant attention and improvement. The ultrafast resonance energy transfer occurs on the similar time scales as the local relaxation upon donor (tryptophan) excitation, as recently observed in many proteins. Thus, the resonance energy coupling changes with time and the ultrafast transfer dynamics is an intrinsic nonequilibrium process. The spectral overlap integral is no more a constant and changes with time due to the spectral shifting induced by the local environment relaxation (solvation). From our analyses (Figures 7 and 8), the ultrafast resonance energy transfer intrinsically follows a compressed- and/or stretched-exponential dynamics and such nonexponential dynamic behaviors result from local energy relaxation (mainly hydration), not from local protein structural fluctuation. These results reveal a new concept of compressed and/or stretched dynamics and elucidate the nature of nonequilibrium in ultrafast protein resonance energy transfer.

’ AUTHOR INFORMATION Corresponding Author

*Phone: (614) 292-3044. Fax: (614) 292-7557. E-mail: dongping@ mps.ohio-state.edu. Present Addresses †

Department of Physics, Xavier University, Cincinnati, OH 45207.

’ ACKNOWLEDGMENT We thank Prof. Stephan Sligar (University of Illinois at Urbana
Champaign) for generously providing us the myoglobin plasmid (pMB122). Also thanks to Dr. Ya-Ting Kao for the help with experiment, Tanping Li for the help of MD simulations in Figure 6, and Zheyun Liu for the discussion of Figure 8. This work was supported in part by the National Science Foundation (Grant CHE0748358) and the Camille Dreyfus Teacher-Scholar (to D.Z.). ’ REFERENCES (1) Henzler-Wildman, K.; Kern, D. Nature 2007, 450, 964–972. (2) Smock, R. G.; Gierasch, L. M. Science 2009, 324, 198–203. (3) Frederick, K. K.; Marlow, M. S.; Valentine, K. G.; Wand, A. J. Nature 2007, 448, 325–329. (4) Yang, H.; Luo, G.; Karnchanaphanurach, P.; Louie, T.-M.; Rech, I.; Cova, S.; Xun, L.; Xie, X. S. Science 2003, 302, 262–266. (5) Hanson, J. A.; Duderstadt, K.; Watkins, L. P.; Bhattacharyya, S.; Brokaw, J.; Chu, J.-W.; Yang, H. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 18055–18060. (6) Karplus, M.; McCammon, J. A. Nat. Struct. Biol. 2002, 9, 646–652. Karplus, M.; Kuriyan, J. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 6679–6685. (7) Klepeis, J. L.; Lindorff-Larsen, K.; Dror, R. O.; Shaw, D. E. Curr. Opin. Struct. Biol. 2009, 19, 120–127.

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