Microsecond protein dynamics observed at the single-molecule level

How polypeptide chains acquire specific conformations to realize unique biological functions is a central problem of protein science. Single-molecule spectroscopy, combined with fluorescence resonance energy transfer, is utilized to study the conformational heterogeneity and the state-to-state transition dynamics of proteins on the submillisecond to second timescales. However, observation of the dynamics on the microsecond timescale is still very challenging. This timescale is important because the elementary processes of protein dynamics take place and direct comparison between experiment and simulation is possible. Here we report a new single-molecule technique to reveal the microsecond structural dynamics of proteins through correlation of the fluorescence lifetime. This method, two-dimensional fluorescence lifetime correlation spectroscopy, is applied to clarify the conformational dynamics of cytochrome c. Three conformational ensembles and the microsecond transitions in each ensemble are indicated from the correlation signal, demonstrating the importance of quantifying microsecond dynamics of proteins on the folding free energy landscape.


Supplementary Note 1. Assignment of the peaks in the 2D lifetime correlation map:
Assignment of each diagonal peak in the 2D lifetime correlation map was made based on the pH and denaturant dependences of the fluorescence decay. Supplementary Figure   2 shows the full set of pH-and denaturant-dependent fluorescence decay data of Alexa546_cyt c measured in this study. As readily seen, the 70-ps lifetime component has the largest contribution at pH 5.5 where the native state is predominant. On the other hand, the 3-ns lifetime component is predominant in the data at pH 1.0 as well as those under a high denaturant condition in which cyt c is denatured. Therefore, it is reasonable to assign 70-ps (sp1) and 3-ns (sp4) lifetime components to the native state (N) and the unfolded state (U) of cyt c, respectively. As for the 280-ps and 1.7-ns components, the fluorescence decay under a high denaturant condition contains almost negligible contribution from the 280-ps lifetime component but substantial contribution from the 1.7-ns lifetime component. This implies the two distinct fluorescence lifetimes of sp3 do not stem from a single conformation that shows a biexponential decay, but result from two distinct emitting species. In other words, this result indicates that the equilibration process (i.e., conformational transition) between the substates exhibiting two fluorescence lifetimes in sp3 occurs within 1 μs. Therefore, the peaks in sp2 and sp3 can be assigned to three different folding intermediate states, that is, I 1 (sp2), I 2 (shorter lifetime component of sp3), and I 3 (longer lifetime component of sp3).

Supplementary Note 2. Equilibration process between N and I 1 recognized in the 2D emission-delay correlation map:
The 2D lifetime correlation maps shown in Fig. 3d-f clearly show the equilibration process between N and I 1 as an appearance of the cross peaks. This equilibration process can also be recognized in the 2D emission-delay correlation maps before ILT. Supplementary Figures 3a and b show the 2D emission-delay correlation maps at ΔT = 0.2 -4 μs and ΔT = 50-100 μs, respectively, for the microtime region of t = 0 ~ 0.93 ns.
The corresponding contour plots are also shown in Supplementary Figs. 3c and d for the microtime region of t = 0 ~ 0.5 ns. The key difference is that a "ridge" appears along the zero-time line in the 2D map at ΔT = 50 -100 μs (Supplementary Figs. 3b and 3d) whereas it is missing in the 2D map at ΔT = 0.2 -4 μs. This ridge is a typical feature that arises from the correlation between the short lifetime and long lifetime components 1,2 .
Because the experimental 2D emission-delay correlation maps also contain contributions other than those from N and I 1 , we simulated 2D maps assuming that only N and I 1 exists in the system to confirm that the above-mentioned difference surely reflect the equilibration process between N and I 1 . In this simulation, we first simulated 2D lifetime correlation maps for the two cases: one is the case that the equilibration process occurs slower than T (inset of Supplementary Fig. 3e), and the other is the case that the equilibration occurs faster (inset of Supplementary Fig. 3f). The relative population between the 70-ps and 280-ps lifetime components as well as the width of their peaks was set at the same values as those in the experimental data (sp1 and sp2 in Fig. 3d in main text). Then, the simulated 2D lifetime correlation maps were converted to 2D emission-delay correlation maps by Laplace transform. As seen in Supplementary   Figs. 3e and f, the simulated 2D emission-delay correlation maps reproduced essential features of the experimental 2D emission-delay correlation maps (i.e., the presence and absence of the ridge along the zero time line). This confirms that the equilibration process between N and I 1 is indeed recognizable even in the experimental 2D emission-delay correlation map. This also confirms the reliability of ILT using the 2D maximum entropy method to extract correct information about the fluorescence lifetime from experimental data.

Supplementary Note 3. Existence of I 1 and I 2 :
The I 1 and I 2 states give two distinct peaks at 280 ps and 300 ps in the 2D lifetime correlation maps at ∆T = 0.2-4 μs (Fig. 3d), whereas they are converged and become indistinguishable in the 2D maps at longer delay times (Figs. 3e and 3f). This is due to the limited accuracy of lifetime determination of the MEM-based analysis. However, this convergence does not affect our argument about the existence of the I 1 and I 2 states that have fluorescence lifetimes of ~300-ps. As clearly seen in the 2D map for ∆T longer than 10 μs, the cross peaks between 70 ps and 280 ps and those between 280 ps and 1.7 ns are clearly observed. On the other hand, no cross peak is observed between 70 ps and 1.7 ns components. This feature cannot be rationalized with a single state having ~300-ps lifetime because, if so, the cross peak between 70 ps and 1.7 ns must be observed. Thus, we can conclude that there are two independent states having ~ 300-ps lifetimes, and one state (I 1 ) is in equilibrium with N (70 ps) state while another (I 2 ) is in equilibrium with I 3 (1.7 ns) state, within 10 μs.

Supplementary Note 4. Autocorrelation and cross-correlation of each substate:
Fluorescence autocorrelation functions of N, I 1 , I en , and U as well as the cross-correlation function between N and I 1 were obtained from After an explanation about the concept of the component-specific correlation function, the actual procedure is described.

Concept of component-specific correlation function
The relationship among the ordinary fluorescence intensity correlation function (G I (T)), 2D emission-delay correlation map ( ) is written as follows 1 : (1) When the sample contains different fluorescent species and the observed fluorescence decay consists of multiple fluorescence lifetime components, the component-specific correlation function (G I;i,j (T)) can be written in an analogous way: When j = i, the resulting correlation function ) (  Fig. 3d-f and Supplementary Fig. 4 were calculated, and the substate-specific autocorrelations of N and U, and cross-correlation between N and I 1 were obtained.

Autocorrelation of I 1
The diagonal peak corresponding to I 1 is overlapped with that of I 2 in I en . Therefore, it is not possible to extract the peak intensity of I 1 directly from the 2D lifetime correlation map. However, the contributions of I 1 and I 2 in the overlapped peak can be evaluated using independent lifetime distributions (α(ΔT;τ)) shown in Fig. 3g-i where K is the number of independent lifetime distributions at each ΔT. The independent lifetime distribution containing I 1 is easily distinguishable from that including I 2 , because I 2 is always associated with I 3 to form a single independent lifetime distribution I en (i.e., I 2 and I 3 are already in equilibrium at the shortest ΔT).
Furthermore, I 1 and I 2 always appear in different independent lifetime distribution because no equilibration process between I 1 and I en is observed through whole ΔT.
Therefore, the intensity of the diagonal peak of I 1 (i.e., the correlated part for calculating the autocorrelation of I 1 ) can be evaluated from corresponding independent lifetime distribution (i.e., sp2 in the data for ΔT = 0.2 -4 μs) by the following way; ( where α k;I1 (ΔT;τ) and K' correspond to the independent lifetime distribution and the number of independent lifetime distributions that I 1 is contained, respectively. K' needs to be set at 2 for the data at ∆T = 2 -6, 4 -8, 6 -10 and 8 -12 µs when the equilibration process with N is in progress because I 1 appears in the two independent lifetime distributions. For other ∆Ts, K' was set at 1.

Autocorrelation of I en
The correlated parts of the autocorrelation of I 3 and the cross-correlation between I 2 and I 3 can be extracted directly from the relevant isolated peaks in 2D lifetime correlation maps, whereas the correlated part of the autocorrelation of I 2 is obtainable in a similar manner as I 1 . However, I 2 and I 3 are in equilibrium even for the shortest T, and I 2 and I 3 behave identically as one single substate I en . Therefore, we evaluated the correlated part of the autocorrelation of I en as a substate that intrinsically exhibits two distinct lifetime components as follows.
Suppose the substate S consists of two lifetime components (τ 1 and τ 2 ) that are already in equilibrium. Then, the substate-specific autocorrelation function (G I ;S,S (ΔT)) can be written as; Numerator of the last expression in equation (7) can also be written using independent lifetime distribution of substate S (α S (ΔT;τ)); Therefore, the correlated part for the autocorrelation of substate S can be evaluated using corresponding independent lifetime distribution. Using equation (8), the correlated part of the autocorrelation of I en was evaluated from the corresponding independent lifetime distribution.

Uncorrelated part
The uncorrelated part (i.e., the denominator of equation (2) and (8)) can be evaluated from the amplitude of each substate in the ensemble-averaged fluorescence decay that was calculated from all photon data because they have the following relationship (see also equations (4)-(7) in Methods); where A(τ i ) is the amplitude of τ i component in the ensemble-averaged fluorescence decay, T 0 is the total measurement time, ΔT is macrotime delay and ΔΔT is the width of temporal window. In case of I en , denominator in equation (8) can be written as; , (   I3  I3  uncor  I3  I2  uncor  I2  I2 In equation (10) To evaluate the amplitude of each substate in the ensemble-averaged fluorescence decay, the fluorescence decay curve of each substate was first calculated by Laplace transform of the corresponding independent lifetime distributions (sp1, sp2, sp3 and sp4 in Fig. 3g, which correspond to N, I 1 , I en and U, respectively). After the amplitude at the time origin is normalized to 1, the normalized decay curves were used to fit the ensemble-averaged fluorescence decay curve for obtaining the absolute amplitude of each substate. In the fitting, the ratio between N and I 1 was kept to 0.25 which was determined from the intensity ratio of the diagonal peaks of N and I 1 in The obtained amplitudes were used for calculating the uncorrelated parts using equation (9) or (10).

Supplementary Note 5. Origin of the dark states and validity of the Scheme involving them:
The highly quenched state, which is also called the dark state, has already been reported for some organic dyes attached to proteins 3,4 . The quenching mechanism has also been studied, and it was suggested that the ground-state complex is formed and that photo-induced electron transfer occurs between the dye and aromatic residues such as tryptophan or tyrosine. In fact, cyt c has one tryptophan and five tyrosines in its sequence. Therefore, it seems possible that cyt c takes conformations in which specific interaction between Alexa546 and these aromatic residues is significant and it quenches fluorescence very efficiently. The fluorescence lifetimes of such highly quenched states have been reported to be several ps 4 , which is too short to be detected with the TCSPC system employed in the present study.
We modify simple Scheme 1 (Fig. 4) and propose Scheme 2 (Fig. 6)  Alexa546_cyt c, the two correlation curves are very close, reflecting that the contribution of the unfolded state (U) is predominant and that the system is quite homogeneous at pH 1.0. The small difference recognized between two correlation curves is due to minor contributions from intermediate states as shown in Supplementary Fig. 2b. However, the two correlation curves of Alexa546_cyt c exhibit a steep slope in the short ∆T region, which is completely missing in the correlation curves of Alexa546_DTT. This marked difference clearly shows that the correlation curves of Alexa546_cyt c at this pH cannot be described only by translational diffusion.
Because the system is quite homogeneous from a view point of the fluorescence lifetime but there is a feature indicating chemical reactions, the reaction should be a reaction between the fluorescent state and the dark state.
In Supplementary Figure 6b, pH dependence of the fluorescence decay of Alexa546_cyt c is shown. For this data set, the experimental conditions such as the protein concentration, excitation intensity, and data accumulation time are all the same.
Therefore, we can directly compare their time-resolved fluorescence intensities.
Remarkably, the intensity at t = 0 decreases drastically by changing pH from 5.5 to 3.5, and then increases by further shifting pH to 2.5. The fluorescence intensity at t = 0 directly reflects the total population of the emissive Alexa546 that is detectable with the TCSPC system. Thus, if the intensity at t = 0 changes, it means that the total population of emissive Alexa546 changes with change of pH. Because the total population of Alexa546 is the same, it implies the involvement of highly quenched states in the folding scheme. This also supports Scheme 2 shown in Fig. 6.