) and distal (from 10-50 residues:
) tyrosinesMukopadhyay et al. 10.1073/pnas.0611503104. |
Fig. 5. Simulations with different thresholds NT and mean count rates N (slow case in dashed lines and fast case in solid lines).
Fig. 6. The g -parameter as a function of denaturant concentration.
Fig. 7. The Förster's distance (R0) of the Alexa Fluor 488 and Alexa Fluor 594 FRET-pair as a function of denaturant concentration.
Fig. 8. The effective Förster's distance (R0 eff) of the Alexa Fluor 488 and Alexa Fluor 594 FRET-pair as a function of denaturant concentration.
Fig. 9. The steady-state fluorescence anisotropy of the donor (Alexa Fluor 488) labeled NM as a function of denaturant concentration.
Table 1. Recovered parameters associated with FCS and the number of proximal (within 10 residues:) and distal (from 10-50 residues:) tyrosines
Residue position | Relative amplitude | tfast, ns | tslow, ns |
|
|
21 | 0.3 | 30 ± 10 | 200 ± 50 | 3 | 10 |
51 | 0.6 | 20 ± 5 | 210 ± 60 | 6 | 12 |
77 | 0.5 | 30 ± 10 | 220 ± 40 | 3 | 15 |
96 | 0.4 | 30 ± 10 | 230 ± 10 | 3 | 11 |
137 | 0.1 | - | 170 ± 30 | - | 4 |
184 | - | - | - | - | - |
Only the fluctuation components are shown. The diffusion component (≈ 0.3 ms) was similar for all of them. Relative amplitudes of the fluctuations with respect to the whole autocorrelation curves are presented. - , "not observed." and are the numbers of tyrosines within the neighboring 10 residues, and 10-50 residues, respectively.
SI Text
Fluorescence Labeling
Single-Cys mutants of NM were labeled using the thiol-reactive fluorescent dyes AlexaFluor-488 C5-maleimide, AlexaFluor-594 C5-maleimide (Molecular Probes, Eugene, OR) and Cy5 maleimide (Amersham Pharmacia Biosciences). The ethanol-precipitated protein was dissolved in 0.2 ml of 6 M GdmCl (pH 7.4, 10 mM Tris buffer) at a final conc. of 50 mM. To this, a solution of reactive dye (5-fold molar excess of protein) in DMSO (20 ml) was slowly added using a vortex stirrer. The mixture was left in the dark at room temperature for 4 h, after which an excess of DTT (20 ml of 1 M) was added to quench the reaction. The labeled protein was separated from free dye using a NAP 5 column (Amersham Pharmacia Biosciences) equilibrated with 8 M urea (10 mM Tris buffer, pH 7.4). The labeled protein was precipitated with 5 volumes of ethanol at - 80°C. Labeling efficiencies were estimated from relative protein/dye concentrations. For this measurement, the labeled protein was dissolved in 8 M urea, and protein and dye concentrations were calculated from absorbances measured at 276 nm (corrected for dye absorbance) and at the absorption maximum of the dye. 90-95% labeling efficiencies were obtained for all positions. For dual-labeling of the protein for FRET measurements, the double cysteine mutant (21/121) was first reacted with 1 equivalent of AlexaFluor-488 maleimide as described above. The mono-labeled protein was separated from unlabeled and doubly labeled protein by ion-exchange chromatography (MonoQ HR 5/5, Amersham Pharmacia). This singly labeled protein (label statistically distributed on either residue position 21 or 121) samples were used as donor-only control experiments. The fluorescence quantum yields at two positions (21 and 121) were nearly identical. The singly labeled protein was further reacted with AlexaFluor-594 C5-maleimide. The dual labeled protein was once again purified as mentioned above. Both singly and doubly labeled proteins were characterized by MALDI-TOF mass spectrometry. Thus, for dual labeled experiments the fact that the quantum yields is the same at both sites eliminates concerns about which site is labeled with which fluorophore.
Measurements and Analysis
Ensemble fluorescence measurements
. Fluorescence experiments were performed using a SPEX-Fluoromax fluorimeter. For FRET experiments, 0.1 mM dual-labeled protein in 10 mM phosphate buffer (pH 7.4) containing 150 mM NaCl was used. The donor was excited at 488 nm, and spectra were recorded from 515 nm to 700 nm. Fluorescence anisotropies of the donor (lex 488 nm) and the acceptor (lex 594 nm) were 0.14 and 0.15, respectively, under refolding conditions. Significantly lower fluorescence anisotropy for both donor and acceptor compared to the fundamental anisotropy (0.4) revealed considerable depolarization due to the local rotational motion during the fluorescence lifetimes of both the dyes.Single-molecule FRET
. Single-molecule measurements were performed as described (1, 2). Briefly, fluorescence measurements were carried out using a home built laser confocal microscope system, using an Axiovert 200 microscope (Zeiss, Thornwood, NY). Excitation was achieved by focusing the 488 nm line of a 543-AP-A01 tunable argon-ion laser (Melles Griot, Carlsbad, CA) inside the sample solution, 20 mm from the glass cover-slip surface, using a water immersion objective (1.2 NA, 63X, Zeiss, Thornwood, NY). The fluorescence emission was collected using the same objective, separated from the excitation light using a dichroic mirror (Q495LP, Chroma Tech. Corp., Rockingham, VT), spatially filtered using a 100 mm pinhole, and separated into donor and acceptor components using a second dichroic mirror (630 DCXR, Chroma). The donor and acceptor signals were further filtered using an HQ 535/50M band-pass filter (donor, Chroma) and a 590 LPV2 long-pass filter (acceptor, Chroma), then detected using SPCM-AQR-14 avalanche photodiode (APD) photon counting modules (Perkin-Elmer Optoelectronics, Fremont, CA). Photon counts (number of photons per 0.5 ms) were recorded using a photon counting card (PCI 6602, National Instruments, Austin, TX) interfaced with a computer. The FRET efficiency histograms described in this paper were generated by using a two-channel data collection mode to simultaneously record donor and acceptor signals as a function of time, with a binning time of 0.5 ms. The donor-acceptor solutions used were ~ 100 pM in fluorophore concentration, ensuring that virtually all of the detected signals were due to single-molecules. The background counts (<1), leakage of donor into acceptor channel (~4%) and the direct excitation of acceptor (~5%) were estimated in separate experiments, and used to correct the signals before FRET analysis. A threshold of 30 counts (the sum of signals from the two channels) was then used to separate fluorescence signals from background, and FRET efficiencies were calculated for each accepted event using the equation E = (1+g ID/IA), and plotted in the form of a histogram. The g -parameter was obtained using a previously reported procedure (3 and see later). FRET-efficiency histograms were fit using bimodal Gaussian functions using Origin (OriginLab Corp., Northampton, MA), and the peak position obtained from the fitting parameters. At least four measurements were made for each sample.Single-molecule fluorescence coincidence measurements
. Single-molecule coincidence measurements were performed on the setup described above. Excitation was achieved by two-color (blue and red) overlapped laser beams: 488 nm line of a 543-AP-A01 tunable argon-ion laser and 633 nm line of a He-Ne laser (Melles Griot, Carlsbad, CA). The fluorescence was separated from the excitation light using a dichroic mirror (472-488-633PC, Chroma Tech. Corp., Rockingham, VT), and separated into two-color emission components using a second dichroic mirror (630 DCXR, Chroma). The signals were further filtered using an HQ 535/50M (green) and an HQ 670/50 band-pass filters (red) (Chroma) before focusing onto APDs. A threshold of 30 counts (the sum of signals from the two channels) was then used to separate fluorescence signals from background, and coincidence-ratios were calculated for each accepted event using the equation, S = (1+Iblue/Ired)-1, plotted in the form of a histogram and fitted using bimodal Gaussian functions using Origin. The excitation laser powers were adjusted to 250 (blue) and 70 mW (red) such that the coincidence-ratio was 0.5 for the standard-DNA sample. For experiments with protein samples, the laser powers were kept the same.FCS measurements and analysis.
FCS experiments were performed on the setup described for SM-FRET experiments, using a pseudocross correlation mode to allow sub-ms correlation measurements by eliminating the after-pulsing from the APDs (6) and with the following modifications. A 35-mm diameter pinhole was used, providing a 3-dimensional Gaussian confocal volume. The protein concentration used was 5-10 nM. To perform pseudo cross-correlation experiments, the sample fluorescence after filtering through a filter (HQ 535/50M, Chroma) was split using a 50:50 Beam splitter (10BC17MB.1, Newport) before focusing onto two APDs. The data were recorded using a digital autocorrelator (ALV-6010/160, ALV-GmbH, Langen, Germany). For FCS experiments with AlexaFluor-488, the blue laser power used was 150 mW, which is in the linear regime of <300 mW. For experiments with Cy5, red-laser power was kept very low (40 mW) to minimize the contribution of cis-trans photo-isomerization kinetics of the dye on the fast timescale (7). Data points from 12.5 ns to 10 ms related to fast fluctuations were fitted in Origin software using a three-exponential fit (Table S1) with the longest component being due to the triplet-state dynamics (ranging from 2-3 ms). For free AlexaFluor-488 in buffer no fast component (< 1 ms) was observed and the data could be fitted to a single exponential decay with the triplet-state time-constant (2 ms).The mean hydrodynamic radius of NM (4.5 ± 0.5 nm) was obtained (assuming a spherical shape) from its diffusion coefficient and using the Stokes-Einstein relationship (eq 1). The NM diffusion coefficient was calculated by comparison of its diffusion time with that of free Alexa Fluor-488 dye (with known diffusion coefficient) (10).
- (1)
Where k: Boltzmann constant; T: temperature; h: viscosity; D: diffusion coefficient.
The hydrodynamic radius was similar for NM labeled at different residue positions.
To establish that the observed fast decays are due to polypeptide chain dynamics and not due to other processes, we carried out additional experiments. First, no fast (< 1 m s) decay components were observed in FCS curves for free dye. Only a somewhat slower (2-3 ms) component common to all of the FCS curves is observed here. This component, whose amplitude is laser power dependent, is assigned to dye triplet dynamics, consistent with previous reports (8). In addition to ruling out the possibility that the fast ns decays are due to dye photophysics (including antibunching), the above result also rules out an imperfect confocal geometry as the origin of these decays. Additionally, we observed no nanosecond decay components for any labeling positions when Cy5 was used as a fluorophore in place of AlexaFluor-488. Previous work has shown that the fluorescence of Cy5 is not quenched significantly by amino acids (9). Additionally, we performed two-color cross-correlation experiments (analogous to coincidence experiments) under the same condition (10 nM total concentration of NM), which revealed no aggregation. We could also establish that the short component is not due to the rotational motion in the following way. Firstly, there are negative controls (Alexa-488 at 184 and Cy5 labeled NM), which do not show fast FCS decay components. Secondly, the average rotational correlation time of NM was estimated to be ~ 2 ns from the steady-state fluorescence anisotropy (using Perrin's equation). Therefore, rotational diffusion has no contribution in the fast FCS decay components (20-300 ns). Together, the above control experiments lead to the conclusion that the observed fast decays originate from fluctuations in AlexaFluor-488 quenching due to protein dynamics.
Simulation of the FRET-Histogram
According to Gopich and Szabo (4), the probability distribution for the FRET-efficiency E(r) = 1/[1+(r/R0)6] for slow fluctuations of a random coil (RCL) with a short observation time (i.e., conformational distribution is frozen on experimental timescale) is described by the following relationship:
- (2)
with 
being the mean squared end-to-end distance and R0 the Förster's distance.
For fast fluctuations leading to fast conformational averaging with respect to the observation time, the probability distribution becomes approximately a Gaussian centered at the mean efficiency
, and being 0.8 in our experiments [see ref. 3 for
]. Solving this for 
nm we calculate an end-to-end root-mean-squared distance 
4.1 nm. We used this value in the simulation for slow conformational averaging.
In our simulations, we took photon shot-noise into account for either of the two cases (slow or fast conformational fluctuations), following the work described in Gopich and Szabo (5) and calculating the following transfer efficiency distribution:
- (3)
With
, the distribution describing shot-noise with
) being the variance of the signal, 
, N the photon count rate, t the observation time, 
, a factor behaving approximately like a step function at 
equal to the threshold 
and the normalization factor:
- (4)
For the case of conformational averaging much faster then our observation time, the width of the distribution becomes very sharp so that we used a constant centered at the experimental FRET efficiency of 0.8 for 
in our calculation.
For the case of slow conformational averaging, we used
.
Note that the variance also depends on the threshold that we used to distinguish burst from background (5). The threshold in all experiments was set to 30 counts. From FCS experiments and the actual burst distribution we estimated N to be around 30 counts. Fig. 5 shows simulations for a different thresholds NT and mean count rates N to illustrate how the distributions vary with these parameters.
Estimation of Intradye Distances from Single-Molecule FRET
The observed FRET-efficiency (Eobs) is calculated in a ratiometric manner from the counts in donor (D) and acceptor (A) channels from eq. 5 (1, 2). The corrected FRET-efficiency (Ecorr) related to intra-dye distance involves a factor (g)which is dependent on the sample (the ratio of fluorescence quantum yields, fA/f D) and the optical geometry (the ratio of detection efficiencies, eA/e D), as given in equations 6 and 7. The quantum yield component of the g -parameter is measured from independent experiments by measuring relative quantum yields of D and A. The ratio of the detection efficiencies are measured as described previously (3). The g -parameter is plotted as a function of denaturant concentration (Fig. 6).
- (5)
- (6)
- (7)
The Förster's distance (R0) of the dye pair in (Å) is related to the donor quantum yield (FD), index of refraction (h), orientation factor (k2) (2/3 for dynamically averaged orientation) and overlap integral (J) as given by Eq. 8. The effective Förster's distance (R0 eff) in single-molecule experiments, which incorporates the g -parameter, is given in Eq. 9. The variations in R0 (and in R0eff) under different conditions is determined from emission spectra of donor, absorption spectra of acceptor, quantum yield of donor, refractive index of the medium and plotted in Figs. 7 and 8. The modifications in R0 eff can be used to estimate the mean distance as expressed in Eq. 10 and 11.
- (8)
- (9) Where 
- (10)
- (11)
The fluorescence anisotropy of the donor is plotted as a function of denaturant (Fig. 9). Under native conditions, the measured anisotropies (0.14 and 0.15 for donor and acceptor, respectively) are appreciably greater than 0, and hence the orientation factor k 2 could deviate from 2/3, thus contributing to deviations in the estimated distance. Given that NM is relatively unstructured and that flexible C5-linkers are used for the dye attachments, it is very reasonable to assume that relative orientations of the donor and acceptor fluorophores are randomized during the integration time of the SM-FRET measurements. Such an assumption is supported by the significant chain flexibility deduced from our observed ns-timescale fluctuations. Additionally, rapid randomization of different orientations is also supported by the close to shot-noise limited FRET peak shape. Under these conditions, an upper limit on the deviation of the estimated distance can be calculated using the "static averaging" limit for k 2 (11). The measured E in this case is lower than the E that would be measured for the same distance, but where k 2 is 2/3, i.e., the "dynamic averaging" limit. For the case of native NM, this would result in a corrected E of 0.95, corresponding to a distance of 33 Å. Because our measured anisotropy values indicate that we have significant dye reorientation during the donor excited state lifetime, the true value will lie between these two numbers (33 Å and 43 Å). In other words, 43 Å should be considered an upper limit on the inter-dye distance in native NM, and the protein may in fact be even more collapsed than indicated by this value.
Estimation of the Expected Intrachain Distances of a Gaussian Chain
The random-coil behavior of a polymer chain can be described by a power-law relationship between the ensemble averaged radius of gyration (RG) and polymer length:
R
G = R0 Nn - (12)Where N is the number of residues, R0 is a constant (function of the persistence length of the polymer). n is an exponential scaling factor which is a function of the nature of the solvent: n = 3/5 (for good solvent); 1/2 (for Flory's theta solvent) and 1/3 (for poor solvent).
For unfolded random-coils, R0 is estimated to be ~ 1.93 (12).
Therefore, for a 100-residue separation, RG = 30 Å (good solvent) & 19 Å (theta solvent).
Assuming a Gaussian chain, RG can be converted to a mean squared distance <r2> with the following relationship:
R
G 2 = <r2>/6 - (13)Therefore, the root mean square distance for a 100-residue separation is 74 Å (good solvent) & 47 Å (theta solvent). It is expected that R0 in a theta solvent or in the EV-limit will be somewhat higher than for simple random-coil approximation and this will result in an increase in the expected distance (> 47 Å). Therefore, the distance estimated from our FRET experiments is likely to be somewhat lower that the expected distance under any of these conditions.
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