Conformational state distribution and catalytically relevant dynamics of a hinge-bending enzyme...

Biophysical Journal Volume: 00 Month Year 1–37 1

SUPPORTING INFORMATION:

Conformational state distributions and catalytically relevant dynamics

of a hinge-bending enzyme studied by single-molecule FRET and a

coarse-grained simulation

Matteo Gabba‡, Simon Poblete†, Tobias Rosenkranz‡, Alexandros‡ Katranidis, Daryan Kempe$, TinaZuchner‡, Roland G. Winkler†, Gerhard Gompper†, Jorg Fitter‡,$

‡Institute of Complex Systems (ICS-5): Molecular Biophysics, and †Institute of Complex Systems(ICS-2): Theoretical Soft Matter and Biophysics, Forschungszentrum Julich, Julich, Germany; I.

Physikalisches Institut (IA), AG Biophysik, RWTH Aachen University, Aachen, Germany

1 SAMPLE PREPARATION

1.1 PGK Production and Labeling

A cysteine double mutant of the gene of Phosphoglycerate kinase (dmPGK) from Saccharomyces cerevisiae was generated as

described in Ref. 1. Briefly, the natural cysteine C97 was replaced by a serine and two cysteine residues were incorporated by

site-directed mutagenesis at positions Q135 and S290. Additionally, the corresponding single cysteine mutants (smPGK C97S

Q135C and smPGK C97S S290C) were prepared for control measurements. The mutated genes were integrated into the pET

15b expression system (Novagen, EMD Millipore, Merck KGaA, Darmstadt, Germany), thereby adding a hexahistidine tag

and a 6 amino acid long thrombin cleavage site to the N-terminus of the protein sequence for purification purposes. All PGK

variants were expressed and purified from the cytoplasm of Escherichia coli BL21-CodonPlus(DE3)-RIL (Stratagene, La

Jolla, California) by NiNTA affinity chromatography. Far UV circular dichroism spectroscopy (see below) and an enzymatic

activity assay (2) were performed to validate the secondary structure and the catalytic activity of the PGK variants. After flash

freezing in liquid nitrogen, proteins were stored at −80 ◦C.

The labeling strategy reported in Ref. 3 was followed. A detailed description is given in Refs.1, 4. Briefly, a 10mM PGK

solution was incubated in a reducing environment at 4 ◦C for 16 hours with 3-fold excess of the maleimide functionalized

acceptor dye (C2-Alexa647, Sigma Aldrich Co., St. Louis, USA). The labeled protein was separated from free dye by size

exclusion chromatography using a Sephadex G25 medium (Sigma Aldrich Co., St. Louis, USA). The single-labeled protein

fraction was isolated by anion exchange chromatography employing a 4 HiTrap DEAE FF 5 ml column (GE Healthcare

Life Science, Uppsala, Sweden) on an automated HPLC system (AKTA Explorer 10, GE Healthcare Life Science, Upssala,

Sweden). Afterwards, a second labeling reaction was performed as described above with a 10-fold excess of the maleimide

functionalized donor dye (C5-Alexa488, Sigma Aldrich Co., St. Louis, USA). Finally, double-labeled PGK was purified from

free dyes by means of size exclusion chromatography (see above).

1.2 Hybridization of Labeled DNA

Double labeled (double stranded) DNA (dlDNA) is employed to determine the detection efficiency ratio (g′ = gAgD

) of the

confocal microscope (5) and to calibrate the parameters employed for the calculation of the weighted accessible volumes. Two

dlDNA samples with the donor (C6-Alexa488) and the acceptor (C6-Alexa647) dyes separated by a different number of base

pairs (10bp and 17bp) were prepared by hybridization of the labeled single strands (purchased from PURIMEX, Grebenstein,

Germany). The sequences of the single strands are reported in Ref. 6 for the 10bp sample. For the 17bp sample, the following

single-strands were hybridized: 5’-GGA CTA GTC TAG GCG AAC GTT TAA GGC GAT CTC T(C6-Alexa488)GT TTA

CAA CTC CGA-3’ and 5’-TCG GAG TTG TAA ACA GAG ATC GCC TTA AAC GT(C6-Alexa647)T CGC CTA GAC TAG

© 2013 The Authors

0006-3495/08/09/2624/12 $2.00 doi: 10.1529/biophysj.106.090944

2 2 MEASUREMENTS

TCC-3’. To get a one-to-one ratio between the complementary labeled single strands, 1µl of each single strand solution (0.1

mM) was added to a total volume of 20µl of the annealing buffer (20 mM TRIS, 100 mM NaCl, 10 mM MgCl2, pH 7.5 (7)).

Then, the solution was heated up and kept at 98 ◦C for 3min and, finally, slowly cooled down to 25 ◦C with a temperature

gradient of 0.1◦Cs using a thermal cycler (PTC-200, Peltier Thermal Cycler, MJ Research, USA).

1.3 Silanization of the Cover Slips

The cover slips of the microscope were silanized with Sigmacote® (Sigma-Aldrich Co., St. Louis, USA) to prevent sticking

of PGK to the glass surface (8). First, the cover slips were immersed in aceton, and then in ethanol for ten minutes each.

After each step, they were rinsed with water and dried with nitrogen. Second, the glass surface was plasma cleaned (”Zepto”

plasma cleaner, Plasma Surface Technology, Diener Electronic GmbH, Ebhausen, Germany) for 3min at 60W , in order to

activate the silanol groups. Third, ∼ 100µl of Sigmacote® were deposited on top of the slide of (20×20)mm2 size and were

dried on a heating plate. Finally, the excess of Sigmacote® solution was rinsed with aceton and water. The obtained surface is

hydrophobic and prevents sticking of PGK for at least one hour.

2 MEASUREMENTS

2.1 smFRET Measurements

The smFRET measurements were performed with a MicroTime 200 confocal microscope (PicoQuant, Berlin, Germany)

equipped with a red (640nm) and a blue (470nm) diode lasers (LDH-D-C 640B and LDH-D-C 470B, PicoQuant, Berlin,

Germany), and with an UPLSAPO 60x/1.2NA objective from Olympus. The emitted photons were collected by the micro-

scope objective, passed through a dual-band dichroic mirror (470/640nm fitc/Cy5pc, AHF, Tubingen, Germany), focused on a

100 µm pinhole, and splitted into four detection channels by a further dichroic mirror (600dcrx, Chroma Technology, Bellows

Falls, USA) and by two polarizing beam splitter cubes (Linos Photonics, Gottingen, Germany). The red photons were filtered

by an emission filter (HQ 690/70M, Chroma Technology, Bellows Falls, USA) and focused on two SPAD detectors (SPCM-

CD3307M and SPCM-AGR-14, Perkin Elmer, Wood Bridge, Ontario, Canada). The blue photons were also filtered by an

emission filter (XF 3003 520DF40, Omega Optical Inc., Battlesboro, USA) and detected by two silicon avalanche photodi-

odes (τ -SPAD, PicoQuant, Berlin, Germany). The lasers were operated at 20 MHz with pulsed interleaved excitation (PIE)

by means of a computer controlled PDL828 ”Sepia-II” laser driver (PicoQuant, Berlin, Germany). The counts were processed

with a ”HydraHarp-400” time correlated single photon counting (TCSPC) aquisition unit (PicoQuant, Berlin, Germany). For

each detected photon, the arrival time (macro-time) was stored with nanosecond time resolution, and the time between the

excitation pulse and the photon detection (micro-time) was stored with a resolution of 16 ps.

The smFRET measurements were performed at ∼ 22 ◦C on double labeled PGK (dlPGK) to study the interdomain dynam-

ics, and on dlDNA to determine the detection efficiency ratio. The samples were excited with an optimal excitation power

that is the best compromise between high fluorescence emission rate and dye photostability (9). To determine the optimal

excitation power, the molecular brightness and the signal-to-noise ratio were measured as a function of the laser power (8).

The donor dye bound to PGK was excited with an average power of 73 µW , while the acceptor was excited with a power

of 26 µW . For DNA, the donor was excited at 106µW and the acceptor at 52 µW . The laser powers were measured at

the back focal plane of the microscope objective. The smFRET measurements were performed with an average number of

acceptor dyes within the detection spot of ∼ 0.03. For PGK, sets of 10 to 12 hours measurements were performed at each

experimental condition in the following buffer, 10 mM MOPS, 50 mM NaCl, 2 mM EDTA, pH 7.4 and 0.003 % Tween®20

(ROTH® GmbH, Karlsruhe, Germany), in order to collect from 15,000 to 25,000 single-molecule events. Experiments in the

presence of substrates were performed at concentrations ten times higher than the respective dissociation constant Kd (4). The

substrates were purchased from Sigma-Aldrich. The following substrates were used: D-(-)-3-phosphoglyceric acid disodium

salt (3-PG, purity ∼ 99.9%), adenosine 5’-diphosphate monopotassium salt dihydrate (ADP, purity ≥ 95%), and adenosine

5’-triphosphate magnesium salt (ATP, purity ≥ 95% from bacteria). For DNA, set of 4 hours measurements were performed

at ∼ 22 ◦C in the annealing buffer (20 mM TRIS, 100 mM NaCl, 10 mM MgCl2, pH 7.5)(7) including 0.001% Tween®20.

In this case, the cover slips were soaked in aceton and subsequently in ethanol for 10min each. In addition, after each of the

previous steps the cover slips were rinsed with Milli-Q water and dried with nitrogen.

Biophysical Journal 00(00) 1–37

2.2 FCS Measurements 3

2.2 FCS Measurements

The FCS measurements were performed with the same set-up employed for the smFRET experiments, except for the use of

two 50/50 beam splitters (Linos Photonics, Gottingen, Germany) instead of the polarizing cubes, and the use of single color

excitation at 40 MHz instead of 20 MHz, as used for PIE. The sample concentration was adjusted in order to have an average

number of fluorophores between 2 and 5 inside the detection volume. The data were recorded at ∼ 22 ◦C for (10− 20)min.

Prior to every measurement, the confocal detection volume was calibrated with FCS measurements of reference dyes with

known diffusion coefficient (10); Atto488-NHS for blue and Atto655-NHS for red (Atto-Tech GmbH, Siegen, Germany) were

used. The average dimension of the blue and the red detection spots were VB = 3.8 fl and VR = 7.9 fl, respectively. The

measurements with the substrates were peformed with solutions prepared as described in the previous subsection.

2.3 Fluorescence Lifetime Measurements

The ensemble lifetime measurements were performed as described in Ref. 11 with the same set-up employed for the smFRET

experiments, but the use of a single detector and single color excitation. Briefly, the sample concentration was adjusted in

order to have a total detection rate sf between 20 KHz and 50 KHz. The measurements were carried out at ∼ 22 ◦C for

∼ 10min until at least ∼ 105 counts at the maximum peak position of the TCSPC histogram were detected. The instrument

response function (IRF) was measured by collecting for ∼ 20min and without the emission filters the reflected signal from a

bare cover slip with a count rate of ∼ sf10 .

2.4 CD Measurements

Circular dichroism spectra of PGK were measured after each purification and before labeling to verify the protein secondary

structure. Measurements were performed at ∼ 22 ◦C using the J-810-Spectropolarimiter from JASCO (Groß Umstadt, Ger-

many) with a 1 mm path length cuvette after adjusting the sample absorption at 280 nm to an optimal value of ∼ 0.07.

Potential aggregates were removed prior to the measurement by filtering the solution with a 0.1µm pore filter (Whatman,

GE-Helthcare Bio-Sciences, Uppsala, Sweden). Samples were rejected if a deviation above ∼ 5% with respect to the spectra

of wild-type PGK was observed (see Fig.S1 for some examples).

3 DATA TREATMENT

3.1 Burst Selection

Data treatment was carried out with self-written MATLAB routines (v.R2012a, The MathWorks Inc.). The fluorescence pho-

tons from single-molecule events were selected with a burst search algorithm (12). To identify the start and the end of a burst, a

threshold of 160µs was applied to the inter-photon distance (IPD) trace of the PIE channel, previously smoothed by a moving

average filter (13, 14) with half-width m = 25. The edges of the burst were then used to select the donor (D) and the acceptor

(A) photons from time traces with a binning of 200µs. Only bursts with a total intensity F = FD +FA above a threshold NT

of 25 counts for dlPGK or 30 counts for dlDNA were selected for further analysis. For each burst, the fluorescence intensity

Ff (f = D, A), the molecular brightness ff , the donor lifetime in the presence of the acceptor τDA, and the FRET indicators

E and F ′ were calculated, and used to build up the efficiency histograms and the 2D-plots.

The donor (FD) and the acceptor (FA) fluorescence intensities were calculated with the following equations (5):

FD = SD − bgD · T (S1)

FA = SA − bgA · T − α · FD (S2)

where SD and SA are the total number of photons recorded by the donor and the acceptor detection channels, bgD and bgA are

the average background count rates[

countss

]

, T is the burst duration, and α is the fraction of donor emitted photons leaked into

the acceptor detection channel, which is called cross-talk (see Eq.S27). From the fluorescence intensities, the single-molecule

brightness ff was easily derived as follows

ff =Ff

T(S3)

The intensity averaged lifetime τj of a single-molecule event was calculated for an individual detection channel-j as the mean


4 3 DATA TREATMENT

delay time (δti = ti − texc) with respect to the excitation time (texc = 0) (8, 15, 16):

τj = 〈δt〉 = 1

Sj

Sj∑

i=1

δti (S4)

where Sj is the total number of photons detected in channel-j. The lifetime τDA of the donor was then calculated as a weighted

average of the parallel and perpendicular components (j =‖, ⊥) measured with two different detectors in the used set-up:

τDA =

∑

j wj · τj∑

j wj(S5)

Here, the weight wj of component-j is the inverse of the standard deviation σj of the delay times δti measured in channel-j:

wj =1

σj=

1

Sj·

Sj∑

i=1

(δti − 〈δt〉j)2

− 12

(S6)

The single-molecule lifetimes estimated with Eq.S5 for a set of free dyes were compared with the best values obtained from

ensemble lifetime measurements of six different samples with lifetimes between ∼ 0.8ns and ∼ 3.8ns. A relative deviation

between the best value and the single-molecule estimated lifetimes below 7% was observed.

The transfer efficiency E was calculated with the following equation:

E =FA

FA + γ · FD(S7)

with the fluorescence intensities (FA and FD) defined by Eq.S1 and Eq.S2, and γ defined as the product of two ratios (γ′ and

g′):

γ = γ′ · g′ = φA

φD· gAgD

(S8)

Finally, the FRET indicator F ′ was calculated as the ratio between the donor (FD) and acceptor (FA) fluorescence intensities

multiplied by the detection efficiency ratio (g′):

F ′ =FD

FA· g′ (S9)

To apply the previous equations a set of parameters (γ′, g′, and α) have to be known. These parameters were determined as

shown in Section 4.

3.2 Correlation Analysis

The intensity correlation functions

Gij(τ) =〈Ii(t)Ij(t+ τ)〉〈Ii(t)〉〈Ij(t)〉

(S10)

of the donor-donor GDD(τ) and donor-acceptor GDA(τ) intensity time-traces were calculated for logarithmically spaced lag

times τ (17). Only burst selected photons were employed for the analysis. From these two functions, the ratioGDD(τ)GDA(τ) was

calculated. In the main text, the normalized ratios are reported in Fig.3 for a better comparison.

3.3 Fitting of the Ensemble Fluorescence Decays

The ensemble fluorescence intensity decays were fitted in MATLAB (v.R2012a, The MathWorks Inc.) with a proper model

function after iterative reconvolution with the measured IRF (11, 18, 19). The weighted least-squared residuals, calculated

with the Neyman’s approach (20), were mimimized with FMINUIT (21). The goodness of fit was assessed from the χ2-

distribution (20). A 1% significance level was tolerated.

Fluorescence intensity decays in the absence of FRET were fitted with a multiexponential model function (19) to account for

local quenching and/or different conformers:

F (t) =

n∑

i=1

ai · e−tτi (S11)


3.4 Molecular Brightness 5

Here, the fitting parameters are the amplitudes ai at time zero, and the decay times τi of each exponential component.

The amplitude averaged lifetime 〈τ〉x and the intensity averaged lifetime 〈τ〉f (5, 19, 22) were determined from the fitting

parameters:

〈τ〉x =

∑

i ai · τi∑

i ai(S12)

〈τ〉f =

∑

i ai · τ2i∑

i ai · τi(S13)

Here, the sums run over the n-exponential components of the multiexponential decay (Eq.S11).

Under FRET coupling, the measured fluorescence intensity decay of the donor was fitted with the following model function

(7, 23):

F ′DA(t) = A · {xD · [(1− xD0) · FDA(t) + xD0 · FD0(t)]+

+ (1− xD) · e−t

τbg }(S14)

Here, the prefactor A is the amplitude at time zero of the decay, xD0 is the fraction of donor only molecules described by a

multiexponential decaying function FD0(t) (Eq.S11), and 1−xD = xbg is the fraction of background fluorescence represented

by a single exponential decay. The function FDA(t) represents the intensity decay of the donor quenched by FRET:

FDA(t) =

n∑

i=1

xi ·∫

pG(r) · e−[

tτD0,i

·(1+R0r )

6]

dr (S15)

where xi = ai∑

aiand τi are the amplitude fractions and the lifetimes of the multiexponential donor only decay FD0(t)

(Eq.S11), respectively. R0 is the Forster radius and pG(r) is a Gaussian distribution of inter-dye distances with a mean value

〈rDA〉 and standard deviation σDA:

pG(r) =1√

2π · σDA

· e−(r−〈rDA〉)2

2σ2DA (S16)

This function is a probability density function enclosing the information about the conformational space sampled by the two

dyes; for instance, 〈rDA〉 indicates the most probable inter-dye distance and σDA the extent of the fluctuations. Therefore,

the five fitting parameters of the model function F ′DA(t) (Eq.S14) are the following: the amplitude A, the fractions xD0 and

xD, and the Gaussian distribution parameters 〈rDA〉 and σDA. In fact, R0 and the set of values {xi} and {τi}, which were

measured from the single-labeled donor only samples, were fixed during the fit. The Gaussian distribution obtained from the

fits were used to calculate the corrected static line (Section 8), and to calibrate the parameters of the weighted accessible

volumes algorithm (Section 9.1).

3.4 Molecular Brightness

The ensemble molecular brightness ff[

countsms·molecule

]

(also called fluorescence detection rate) was determined by FCS

measurements using the following equation (24):

ff =sf − bgf〈N〉 (S17)

Here, sf[

countsms

]

is the total detection rate, bgf[

countsms

]

is the background count rate obtained from a measurement of buffer

only, and 〈N〉 is the average number of fluorescence molecule inside the detection volume corrected for background noise

effects (24).

3.5 Calculation of the Radius of Gyration

The radius of gyration Rg of freely diffusing PGK in the presence and in the absence of substrates was calculated from the

diffusion coefficient D [ cm2

s ] obtained from FCS measurements performed at ∼ 22 ◦C. The following empirical correlation

was used (25):

Rg = 5.78× 10−8 · T

η(T ) ·D (S18)


6 4 CHARACTERIZATION OF LABELED PGK

Here, T is the temperature in Kelvin, η(T ) is the temperature dependent viscosity of the solution in [cP], and 5.78 × 10−8

is an empirical constant in [ cm2·cP ·As·K ]. The viscosity of each solution was measured at ∼ 22 ◦C with the rolling ball method

(AMVn Automated Micro Viscometer, Anton Paar GmbH, Graz, Austria) employing a ball and a capillary with a diameter

of 1.5 mm and 1.6 mm, respectively. The density of the ball was ρB = 7.670 gcm3 and the density of the solution, as a first

approximation, was set to the value of water ρS = 0.99820 gcm3 . The experimental diffusion coefficient was corrected for the

bias due to mismatches between the refractive indexes of the measuring solutions with respect to water. This was done using

the measured refractive index (Abbe Refractometer AR3/AR4, A. Kruss Optronic, Hamburg, Germany) and the theoretical

relation D(n) reported in Ref. 26. The results are reported in Fig.S2 showing a reduction of the radius of gyration upon

substrate binding.

4 CHARACTERIZATION OF LABELED PGK

4.1 Determination of the Degree of Labeling

The degree of labeling (DOL) of single labeled PGK (slPGK) was determined using the following expression:

DOL =cdyecprot

(S19)

where the dye (cdye) and the protein (cprot) concentrations were calculated from the optical density ODmax

(

c = ODmax

ǫmax·ℓ

)

obtained from absorption spectra measured with a spectrophotometer (UV-2010-PC, Shimadzu, Duisburg, Germany). The

diffusion coefficient of the dye bound to PGK was also measured in order to assure complete removal of free dyes from the

measuring solution, as only under this condition, the DOL defines the average number of dyes bound to the protein. The

following values were obtained: DOLAl488Q135C = 0.33, DOLAl488

S290C = 0.56, DOLAl647Q135C = 0.24 and DOLAl647

S290C = 0.46. The

occupation probabilities ρi of the labeling sites (Q135C and S290C) of dlPGK were estimated from the measured DOLs of

slPGK considering that, (1) the labeling reaction is conducted with excess of dye, and (2) the affinities ζ of the dyes towards

one labeling site are similar for the single- and double-labeled samples (ζsl,i ≃ ζdl,i) (8):

ρi =DOLi

∑

i DOLi(i = Q135C, S290C) (S20)

The results are: ρAl488Q135C = 0.37, ρAl488

S290C = 0.63, ρAl647Q135C = 0.34 and ρAl647

S290C = 0.66. Since the occupation probabilities of

Alexa488-mal and Alexa647-mal towards one site are rather similar (ρAl488i ≃ ρAl647

i ), the average values (ρQ135C = 〈0.36〉and ρS290C = 〈0.64〉) were used to estimate a set of physical parameteres {ξ}, like the quantum yields φf , the donor only

intensity averaged lifetimes 〈τD0〉f , the cross-talk α, and the Forster radius R0 of dlPGK, by using the same parameters as

measured with slPGK. For this purpose, the following expression was employed:

ξ =∑

i

ρi · ξi (i = Q135C, S290C) (S21)

In the following, Eq.S21 will be used to determine the set of parameters {ξ} which are required to build the 2D-plots (Sec-

tion 8) and the efficiency histograms (Section 7) from smFRET experiments, and to analyze the ensemble lifetime FRET

measurements (Section 3.3). All the parameters were measured at ∼ 22 ◦C.

4.2 Quantum Yield Ratio

The quantum yield ratio γ′ of dlPGK was calculated as the ratio between the acceptor (φA) and the donor (φD) quantum

yields:

γ′ =φA

φD=

0.54

0.81= 0.67 (S22)

Since the quantum yields of dlPGK cannot be determined directly, they were calculated with Eq.S21 from experimental data

of slPGK. These quantum yields were measured with two independent comparative methods relying on either the lifetime or

the molecular brightness of well characterized reference dyes. Finally, the arithmetic mean of the obtained quantum yields

was used since static quenching was absent:

φ =φτ + φf

2(S23)


4.3 D-only Lifetime 7

The unknown quantum yield φτU was obtained with the ”lifetime method”:

φτU ≃ 〈τU 〉x

〈τR〉x· φR (S24)

Here, φR is the known quantum yield of a reference dye with a natural lifetime similar to the one of the unknown fluorophore

(τn,R ≃ τn,U ), and 〈τR〉x and 〈τU 〉x are the measured amplitude averaged lifetimes (Eq.S12) of the same dyes. This method

is only sensitive to dynamic quenching.

In addition, the unknown quantum yield φfU was also obtained with the ”brightness method”:

φfU ≃ gR,opt ·OD′

R(λex)

gU,opt ·OD′U (λex)

· fUfR

· φR (S25)

Here, three conditions must be fulfilled for Eq.S25 to hold: (1) The excitation intensity must be lower than the saturation

intensity (Ie ≤ Is), (2) similar excitation intensities (Ie,U ≃ Ie,R) are required, and (3) the electronic detection efficiencies

(gel,U ≃ gel,R) and the extinction coefficients (ǫU (λmax) ≃ ǫR(λmax)) have to be similar for the unknown and the refer-

ence. In Eq.S25, OD′(λex) is the normalized optical density at the excitation wavelength λex, gopt is the optical detection

efficiency (27), ff is the molecular brightness (Eq.S17), and φR is the reference quantum yield. This method is sensitive to

both, dynamic and static quenching. As a reference for both methods, free Alexa488-COOH (φR,D = 0.92 from Invitrogen

website) and Alexa647-COOH (φR,A = 0.33 from Atto-Tec product sheet) were used, after a cross calibration (28) with

Fluorescein (φ = 0.92 (29)), Atto488-NHS (φ = 0.80 from Atto-Tec product sheet), and Nile Blue (φ = 0.261 (30)).

The effect of PGK’s substrates on the quantum yields of slPGK was considered using the following equation:

φS ≃ 〈τS〉x〈τNS〉x

· φNS (S26)

where, φNS is the quantum yield measured without substrates (see above), 〈τS〉x and 〈τNS〉x are the amplitude averaged

lifetimes (Eq.S12) measured with and without substrates, and φS is the quantum yield in the presence of substrates. Since, the

deviations due to the substrates (±0.02) are smaller than the experimental error (±0.04), the quantum yields (φA = 〈0.54〉and φD = 〈0.81〉) averaged over the different experimental conditions were used for the calculation of γ′ (see Eq.S22).

4.3 D-only Lifetime

The intensity averaged lifetimes 〈τD0〉f of donor only samples were measured with and without substrates. The values

reported in Tab.S1 were used to calculate the static lines and the corrected static lines (see Section 8), which are shown

in the 2D-plots (see Main Text: Fig.2B and Fig.4).

4.4 Cross Talk

The cross talk α is the fraction of donor emitted photons sensed by the acceptor detection channel:

α ≃ fDA

fDD(S27)

where, fDA and fDD are the donor detection rates detected in the acceptor (DA) and the donor (DD) detection paths, respec-

tively. The cross talk of donor only slPGK were determined with Eq.S27 by measuring the two rates (fDA and fDD). A value

of α = 0.039 for dlPGK was obtained with Eq.S21 and used to calculate E and F ′.

4.5 Forster Radius

The Forster radius R0 = 51.0 A of dlPGK was obtained with the following equation (19):

R0[A] = 0.211 ·[

J(λ) · k2 · φD · n−4]

16 (S28)

Here, J(λ) =∫

f ′D(λ) · ǫA(λ) · λ4 dλ is the overlap integral between the corrected fluorescence emission spectrum of

the donor f ′D(λ) (19, 31) normalized to its area, and the absorption spectrum of the acceptor ǫA(λ) [

nm4

M ·cm ], k2 is the dye


8 7 EFFICIENCY HISTOGRAMS

orientation factor set to 23 for freely rotating dyes, φD is the quantum yield of the donor, and n is the refractive index

of the solution. The emission fD(λ) and the absorption ODA(λ) spectra were measured with a fluorimeter (QM-7, Pho-

ton Technology International, Birmingham, USA) and a spectrophotometer (UV-2010-PC, Shimadzu, Duisburg, Germany),

respectively. The absorption spectrum was calculated by multiplication of the molar absorption coefficient of Alexa647-mal

(ǫA(λmax) = 239, 000M−1cm−1) and the measured normalized absorption spectrum OD′A(λ). The refractive index of the

buffer n = 1.334 was measured with an Abbe analog refractometer (AR3/AR4, A. Kruss Optronic, Hamburg, Germany).

4.6 Rotational Mobility of PGK Bound Dyes

For both single-mutants (Q135C and S290C), labeled with the donor and with the acceptor fluorophore, time-resolved

anisotropy decay measurements were performed (11). Besides a slower rotational component representing whole molecule

rotation, the dominant component in these decays is caused by rotations of the attached dyes with rotational correlation times

below a nanosecond. Thus, the assumption of freely rotating dye made to calculate the Forster radius is justified and k2 was

set to 23 .

5 CHARACTERIZATION OF LABELED DNA

The set of parameters {ξ} = {φf , 〈τD0〉f , α, R0} was measured for dlDNA as described in Section 4 for dlPGK. For DNA,

the dye properties are independent from the labeling position. Therefore, Eq.S21 was not utilized because the measured phys-

ical quantities are equal in the single- and double-labeled samples. The following values were obtained and used for the

analysis of smFRET and ensemble lifetime FRET experiments: φA = 0.39, φD = 0.87, γ′ = 0.44, 〈τD0〉f = 3.91ns,

α = 0.053, and R0 = 51.1 A.

6 DETECTION EFFICIENCY RATIO

The reference detection efficiency ratio g′ = gAgD

of the confocal microscope was determined as described in Ref. 5 with a

smFRET calibration measurement performed with two double-labeled DNA samples having different transfer efficiencies.

The resulting 2D-plot is shown in Fig.S3. The measured reference value of g′ = 0.7 was corrected for daily fluctuations of

the detection efficiencies with the following relation:

g′U = g′ · δUδ

(S29)

Here, δf = fAfD

is the ratio between the fluorescence detection rates (fA and fD) of a dye (Rhodamine 101 from Molecular

Probes®, USA) emitting in both detection channels. The two ratios were measured at ∼ 22 ◦C: (i) δ = 31.82 the day of the

calibration, and (ii) δU the day of the actual smFRET measurements.

7 EFFICIENCY HISTOGRAMS

7.1 Multi-Gaussian Fit

The FRET efficiency histograms were fitted in MATLAB (v.R2012a, The MathWorks Inc.) using a weighted least squares

estimator (20). The weights wj were evaluated with a Poissonian error distribution (wj =√

Nj) (20). The employed model

was a sum of two Gaussian functions representing the compact (i = 1) and the expanded (i = 2) state

G(E) =∑

i=1,2

bi√2πσ2

i

· e−(E−〈Ei〉)

2

2σ2i (S30)

where, bi are the amplitudes, σ2i the variances, and 〈Ei〉 the mean FRET efficiencies of each population. The occupation

probabilities p1 and p2 = 1− p1 of the two states were calculated from the areas of the fitted Gaussian functions. The results

of the fits are reported in Tab.S2. These values were used to calculate the FRET averaged inter-dye distances (〈rDA〉E) in

Section 7.2 and the Gibbs free energy differences (∆Gij) in Section 7.6.

In order to test, if differences between the molecular brightness and/or the diffusion coefficient of the two states could affect

the occupation probabilities, two procedures were followed. Indeed, a longer diffusion time or a higher brightness of one of

the two populations would artificially increase the number of molecules above the threshold and consequentely the population


7.2 Correction of the Apparent Inter-Dye Distances 9

of this state. In a first approach, the threshold NT on the total intensity FA + FD was changed. In a second approach, the

burst were filtered with a threshold on the total brightness fA + fD. The resulting FRET efficiency histograms were then

normalized in order to detect changes in their shape. The results are reported in Fig.S13. From Fig.S13A, it can be seen that

the visibility of the low efficiency peak increases at high NT thresholds. Nevertheless, up to a threshold of 40 counts the shape

is almost unchanged meaning that the two states are equally visible. On the other hand, the histograms are not affected when

the threshold on the brightness is varied (see Fig.S13B). Altogether, these observation indicate that the two states have the

same brightness while the expanded state has a larger diffusion time. We can then conclude that, with the applied threshold of

25 counts, the two populations are equally visible and the occupation probabilities are not biased.

7.2 Correction of the Apparent Inter-Dye Distances

The apparent average inter-dye distance 〈r〉 was calculated from the fitted mean FRET efficiency 〈E〉 (see Eq.S30) using the

following equation:

〈r〉 = R0 ·(

1− 〈E〉〈E〉

)16

(S31)

To obtain the FRET averaged physical distance 〈rDA〉E , the apparent distance 〈r〉 was corrected for the bias due to variations

of the acceptor quantum yield φA as described in Ref. 6:

〈rDA〉E =〈r〉

〈φA〉16 · 〈φ− 1

6

A 〉(S32)

The two terms in the denominator of Eq.S32 were calculated as follows from ensemble lifetime measurements performed on

PGK (U) and on a reference dye (R):

〈φU 〉16 =

[ 〈τU 〉x〈τR〉x

· φR

]16

(S33)

〈φ− 16

U 〉 =n∑

i=1

xi,U ·[

τi,U〈τR〉x

· φR

]− 16

(S34)

The apparent and corrected physical distances (〈r〉 and 〈rDA〉E) obtained from the FRET histograms of ligand-free and

ligand-bound PGK are reported in Tab.S3, as well as the correction factors β = 〈φA〉16 · 〈φ− 1

6

A 〉. The relative deviation

between both distances is ∼ 1.7%. From the data (see Fig.S6), an increase of the mean inter-dye distance, which is in quali-

tative agreement with the values obtained by Haran and co-workers (32), is observed upon substrate binding. Here, it is worth

to mention that the FRET averaged inter-dye distance 〈rDA〉E obtained from smFRET measurements differs from the mean

inter-dye distance 〈rDA〉 acquired from ensemble lifetime FRET experiments (see Eq.S47 and Eq.S48) (7).

7.3 Shot-Noise Variance

The shot-noise variance σ2SN was calculated for an average total intensity 〈N〉 = 〈FA + FD〉 in individual bursts higher than

the threshold NT = 25/30 used for the burst selection (〈N〉 > NT ) (33, 34):

σ2SN =

〈E〉 · (1− 〈E〉)〈N〉 (S35)

Here, the mean efficiency 〈E〉 was obtained from the fit of the FRET histogram (Eq.S30), and the ensemble average 〈N〉 was

calculated from the measured distribution p(N) = hist(N) of the total burst intensities (N = FA + FD):

〈N〉 =∑

N · hist(N)∑

hist(N)(S36)

The calculated σ2SN values are reported in Tab.S4 for each Gaussian population.


10 7 EFFICIENCY HISTOGRAMS

7.4 Acceptor Quantum Yield Variance

To calculate the variance σ2φA

due to variations of the acceptor quantum yields, first, the variance of the apparent distance

distribution p(r) was calculated (6):

σ2r = 〈rDA〉E · 〈φA〉

13 ·

[

〈(φ− 16

A )2〉 − 〈φ− 16

A 〉2]

(S37)

Here, the average quantum yields of the acceptor were obtained in analogy with Eq.S33 and Eq.S34, and the FRET averaged

distance 〈rDA〉E was calculated with Eq.S32. Second, the variance σ2φA

was calculated with the following equation, assuming

that the function E(r) (Eq.S39) is antisymmetric 〈[E(〈r〉+ δr) = −E(〈r〉 − δr)〉] for small fluctuations δr around the mean

apparent distance 〈r〉 previously obtained (Eq.S31):

σ2φA

≃ 1

2· [E+ − E−]2 (S38)

Here, the upper and lower values E± = 〈E〉 ±∆E were obtained by plugging the distances r∓ = 〈r〉 ∓ σr in the following

equation:

E(r) =

[

1 +

(

r

R0

)6]−1

(S39)

The calculated σ2φA

values are reported in Tab.S4 for each Gaussian population

7.5 Conformational Variance of the Expanded State

The conformational variance σ2c of the expanded state of ligand-free and ligand-bound PGK was calculated as the difference

between the measured total variance σ2 (Eq.S30), and the sum of the shot-noise variance σ2SN (Eq.S35) and the variance due

to variations of the acceptor quantum yield σ2φA

(Eq.S38), that are reported in Tab.S4 with i = 2:

σ2c = σ2 − σ2

SN − σ2φA

(S40)

Then, the definition reported in Ref. 33, which is valid for inter-dye fluctuations slower than the average observation time

(τc << 〈T 〉), was used to analytically express the measured conformational variance σ2c as a function of measurable quantities

and the unknown standard deviation σDA of the inter-dye distance distribution:

σ2c ≃

∫

[E(r)− 〈E〉]2 · pG(r) dr (S41)

Here, an empirical Gaussian distribution of distances pG(r) (Eq.S16) with fixed mean 〈rDA〉E = 55.5 A and unknown stan-

dard deviation σDA was used to approximate the static distribution of distances p(r) due to PGK interdomain motions. The

mean efficiency was set to 〈E〉 = 0.35 and the Forster radius to R0 = 51.0 A. The graphical solution of Eq.S41 was obtained

by changing σDA until the calculated integral reached the measured value of σ2c = 0.051 for ligand-free and ATP-/ADP-

bound PGK (black line in Fig.S4), and the value of σ2c = 0.038 for 3-PG-/3-PG*ADP-bound PGK (blue line in Fig.S4).

Values of σDA ∼ 9.7 A and ∼ 8.1 A were obtained, respectively.

7.6 Gibbs Free Energy Differences

The Gibbs free energy differences ∆Gij = Gj − Gi [J

molecule ] between the compact (j) and the expanded (i) state of PGK

were calculated as follow assuming a 2-state model (i ⇀↽ j):

∆Gij = −ln

(

pj

pi

)

β(S42)

Where, pj and pi are the occupation probabilities of the compact and the expanded state, calculated by normalizing to one the

areas of the two Gaussian populations (Eq.S30), and β = 1kBT = 2.45× 1020 1

J . The equilibrium constant Kij between both

states was also calculated from the occupation probabilities:

Kij =pjpi

(S43)

The calculated values at ∼ 22 ◦C are given in Tab.S5 and show that substrate binding shifts the equilibrium towards the

compact state of PGK.


7.7 Average Burst Duration 11

7.7 Average Burst Duration

The average burst duration 〈T 〉 for a set of bursts generated by the expanded or the compact state of the PGK domains was

calculated with the following equation:

〈T 〉 =∑

T · hist(T )∑

hist(T )(S44)

Here, hist(T ) = p(T ) is the experimentally determined distribution of the burst duration T [ms] (see Fig.S11 and S12). The

sum runs over bursts with transfer efficiency < 0.4 (expanded state) or > 0.7 (compact state) in order to avoid averaging over

both populations. The obtained values are plotted in Fig.S5 showing the larger spatial extension of the exapanded state with

respect to the compact state.

8 2D-PLOTS

8.1 Static Line

The static line defines the expected correlation between F ′ and τDA for a static system (5) and was calculated as follows:

F ′ =1

γ′· τDA

〈τD0〉f − τDA(S45)

Here, 〈τD0〉f is the intensity averaged lifetime (Eq.S13) of the donor only sample measured at ensemble level, and γ′ is the

measured quantum yield ratio (Eq.S22). Deviations below the static line indicate inter-dye distance fluctuations occurring on

the same timescale or faster then the observation time T .

8.2 Corrected Static Line

The corrected static line accounts for inter-dye distance fluctuations much faster than the observation time (τc << ms).Possible origins of fast dynamics are dye linker dynamics or protein dynamics. The corrected static line was calculated with

an empirical polynomial transformation f(τDA) applied to the static line as described in Ref. 35. To do so, the transformed

lifetimes τ ′′DA:

τ ′′DA =

4∑

i=0

ci · τ iDA (S46)

were employed in Eq.S45. The parameters used for the calculations of the corrected static lines are reported in Tab.S6. Here,

an important parameter is the standard deviation σDA of the inter-dye Gaussian distribution (Eq.S16), which was retrieved

from the fit of the ensemble intensity decays with the model function F ′DA(t) (Eq.S14).

9 COARSE-GRAINED MODEL

Our model of PGK is composed of a set of point particles located at the positions of the Cα-atoms of a reference crystal struc-

ture (pdb:1QPG). An Elastic Network force field (36, 37) is imposed between the particles. The actual particle displacements

depend on the details of the force field, which can be adjusted to reproduce the experimental inter-dye distance distributions

(Eq.S16) obtained from our ensemble-lifetime FRET measurements. Such adjustment requires to consider the effect of the

linker dynamics in the distance distribution between the dyes. This was implemented by using the weighted Accessible Vol-

ume (wAV) algorithm on each of the protein configurations produced by a simulation run using the aforementioned force

field.

9.1 Weighted Accessible Volume

Initially, the Accessible Volume (AV) algorithm (7) generates for each fluorophore a cloud of accessible points around the

labeled group from a given macromolecule configuration. Thus, the distance between the dyes can be obtained by averaging

over the clouds corresponding to both donor and acceptor. In this work, two different distances (7) were calculated from the

sets of possible donor and acceptor positions, {rD(i)} and {rA(j)}, in order to compare the simulations with the experiments.


12 9 COARSE-GRAINED MODEL

The mean inter-dye distance 〈rDA〉 was calculated with the following definition:

〈rDA〉 = 〈|rD(i) − rA(j)|〉i,j =1

nm·

n∑

i

m∑

j

|rA(j) − rD(i)| (S47)

The FRET averaged inter-dye distance 〈rDA〉E was calculated with the following equations:

〈rDA〉E = R0 ·[

1

〈E〉 − 1

]16

(S48)

〈E〉 = 1

nm·

n∑

i

m∑

j

1

1 +(

|rA(j)−rD(i)|

R0

)6

(S49)

The parameters used in this calculation were chosen according to the work of Sindbert et al. (38), due to the similarity of the

linkers and fluorophores used. Each dye is characterized by three radii (RA,Ddye(i)) which account for its anisotropic geometry,

while the length of its corresponding linker (LA,D) is taken as the distance between the labeled atom (Cα of the labeled

aminoacid in PGK, and the carbon at position 5’ of thymine in DNA) and the center of the dye with the linker in an extended

conformation. However, for a partially flexible linker, the probability that a point inside a cloud is visited by a dye is not

necessarily uniform. A further step is given by the weighted accessible volume (wAV) approach, where the sets of donor and

acceptor positions are weighted by a Gaussian function

P (r) =1

∫

AVe−|r−rl|2/(2σ2

AV)· e−|r−rl|

2/(2σ2AV ) (S50)

Here, rl is the labeled atom position. Consequently, each adding term in the averages of Eqs. S47 and S49 must be weighted

by its corresponding probability at rA(j) and rD(i). The parameter σAV has been calibrated from ensemble lifetime FRET

measurement of the inter-dye distance distribution (see Eq.S16) performed with a double-labeled DNA strand on which

two points separated by 17 base pairs were labeled with C6-Alexa488 and C6-Alexa647 (see Fig.S8). The parameters used

for the calculation are: RDdye(1) = 5.2 A, RD

dye(2) = 4.2 A and RDdye(3) = 1.5 A for C6-Alexa488, and RA

dye(1) = 9.9 A,

RAdye(2) = 7.7 A, RA

dye(3) = 1.5 A for C6-Alexa647, with linker lengths of LD = 19.3 A and LA = 24.6 A, respectively.

The width of the linker is of 4.5 A, the allowed sphere radius is 2.25 A and the grid spacing is 0.4 A. This calibration

penalizes the fully extended conformations of the linker due to its hydrophobicity (39) and entropic effects (7). The value

of σAV is scaled for each dye according to the length of its linker. To avoid an excessive dependence on the linker model,

we have performed the analysis assuming two scenarios: a rigid linker, where σAV ∝ LA,D and a Gaussian chain linker,

assuming σAV ∝√LA,D. This setup requires only one fit parameter. The arithmetic mean between these two limiting cases

(σDAV = 3.7 A and σA

AV = 4 A) were used to calculate the average distance 〈rDA〉wAV between the dyes, and the extension

of the fluctuations σwAVDA . The error bars (δσD

AV = ±0.2 A and δσAAV = ±0.4 A) corresponding to the half of the difference

between the limiting cases were used to determine the confidence intervals δ〈rDA〉wAV and δσwAVDA on the calculated values.

The results shown in Tab.S7 for a 17bp distance are in good agreement with the experimental values. The procedure was also

tested for a shorter inter-dye distance, showing reasonably well agreement too, while the uncorrected AV algorithm gives an

overestimated standard deviation σAVDA ∼ 10 A. However, the average distance 〈rDA〉wAV is underestimated by the corrected

wAV procedure for the shorter inter-dye distance (10bp). This is can be attributed to a possible repulsive interaction between

the dyes, which is neglected in the current approach.

For the calculation of the wAV in PGK (see Fig.S9), where C2-Alexa488 and C5-Alexa647 were used for the measure-

ments, the dye parameters are kept, but the lengths of the linkers are 18.9 A and 21.4 A, considering their shorter contour

lengths. It is also assumed that the dye-macromolecule interaction is not relevant, or averaged out. The calculated values of

σDAwAV are shown in Tab.S8. The comparison between the calculated standard deviations σwAV

DA (see Tab.S8) with the value

obtained from ensemble lifetime FRET experiments σDA = (8.8 ± 0.4) A clearly demonstrates that protein dynamics is

required to describe the experimental results. This means that rigid-body interdomain motions contribute to the variance

of the measured inter-dye distance distribution (Eq.S16) in addition to linker dynamics. Finally, the amplitude of motion

FWHMCC = 2.355 · σCC = (12.3± 0.5) A (see Tab.S8) of the labeled Cα-atoms agrees with the value of 13.0 A obtained

by the MD simulations in Ref. 40.


9.2 Simulation Details 13

9.2 Simulation Details

The interaction potential between two particles i and j of the elastic network separated by a distance rij smaller than a cut-off

distance rc is (41):

U(rij) =1

2K(R0

ij)(rij −R0ij)

2 (S51)

where R0ij is the reference distance of the crystal structure. The elastic constant K(R0

ij) is the restitution constant for each

pair of particles given by:

K(r) = Ce−r2/r20 . (S52)

The constant C, which is directly related to the flexibility of the model, has been adjusted to agree with the interdye distance

distribution provided by the ensemble lifetime FRET data. The rest of the parameters were set to r0 = 7 A and rc = 12 A.

This adjustment is performed over a set of short simulations at constant temperature, and calculating the wAV as mentioned

above for a set of at least 2000 independent configurations. This yields C = 89 ± 5 kJmol·nm2 at a temperature of 300K. For

the analysis of the distances of the Cα and the phosphates, representations containing the atomistic details of each of the

three rigid domains (C-terminal, N-terminal and hinge), previously identified with DomainFinder (36, 37) (with paremeters

deformation threshold 1000 and domain coarseness 40 for mode 7), were superimposed over the trajectory of the protein.

Once the amplitude of the motion has been adjusted, the protein is embedded in a solvent simulated by the Multiparticle Colli-

sion Dynamics approach (42, 43). This method has proven to correctly produce hydrodynamic interactions in the system (43),

and it has been successfully applied to several soft matter systems such as colloids, polymers and vesicles (43). The equations

of motion of the model protein were solved using the Velocity Verlet algorithm. In terms of the parameters of MPC, such as

solvent particle mass m, temperature kBT and collision cell size a, we have performed eight simulations of 107 collisions

(5× 108 integration time steps) with collision time h = 0.1√

ma2/kBT , collision angle α = 130o, solvent particle density

ρ = 10 a−3 and solute particle mass M = 10m. The cell size a corresponds to 5.7 A, while the box size was of L = 80a.

For the comparison with experiments, simulation results are expressed in terms of the characteristic time t0 = 6πηR3g/kBT ,

where Rg is the radius of gyration and η is the viscosity. The autocorrelation function of the squared distance between the

centers of mass of the C- and N-terminal domains reported in Fig.S10 shows an exponential decay with a characteristic time

of 1 ns. This characterizes the interdomain dynamics with a FWHM of 12.3 A found in the model.

9.3 Normal Mode Analysis

The displacements of the atoms with respect to their position in the reference crystal conformation was obtained from the

normal modes calculated with the MMTK package (41), using the Cα force field for vibrational modes with a cut-off radius

of 12 A. The first three modes after translations and rotations were hinge-bending, propeller twist and rocking motions. The

hinge-bending is a Pacman-like motion of the two domains that closes and open the cleft (see Fig.1 in the Main Text). The

propeller twist motion is a twisting of the domains around the axis that goes through the substrates. The rocking motion is

an anticorrelated rotation of the domains around the axis perpendicular to the cleft. The trajectory was projected onto these

modes according to Ref. 44 taking into account that all the particles that compose the coarse-grained model have the same

mass. Finally, the radius of gyration and the FRET averaged inter-dye distances, that are shown in Fig.6 (see Main Text), were

calculated for each protein conformation.



FIGURES

Figure S1

Figure S1: Collection of representative CD spectra of single and double cysteine mutants of PGK. The gray shaded area

represents the ±5% tolerance region with respect to the reference spectra of wild type PGK shown in black. An example of

a rejected sample is shown in violet.


9.3 Normal Mode Analysis 15

Figure S2

Figure S2: Radii of gyration (Rg) of dlPGK calculated from the diffusion coefficients D measured by fluorescence correlation

spectroscopy (FCS) in the presence and the absence of substrates. A reduction of the radius of gyration is observed upon

substrate binding.



Figure S3

Figure S3: 2D-plot of the dlDNA smFRET calibration measurement. The two populations, which correspond to the two

dlDNA samples used for the calibration, are shown together with the corrected static line (red continuous line), which con-

siders the presence of linker dynamics. The static line is also shown (red dashed line). The parameters ({ci}, 〈τD0〉f , and γ′)

used for the calculation of the corrected static line are shown in the insets, as well as the detection efficiency ratio g′ = 0.7obtained from the calibration measurement. The polynomial coefficients {ci} (see Eq.S46) were calculated using a standard

deviation σDA of 6.0 A for the Gaussian distribution of the inter-dye distances (Eq.S16). The cross-talk α used to determine

F ′ is also given.



Figure S4

Figure S4: Graphical solutions of Eq.S41. The red line represents the integral on the right hand side of Eq.S41 as a func-

tion of the unknown standard deviation σDA. The black and blue lines represent the measured conformational variances

σ2C ≃ 0.051 and σ2

C ≃ 0.038 for ligand-free and ADP-/ATP-bound PGK, and 3-PG-/3-PG*ADP-bound PGK, respectively.

The two intersections between the lines are the desired solution: σDA ∼ 9.7 A and σDA ∼ 8.1 A.



Figure S5

Figure S5: Average burst durations 〈T 〉 of the expanded (cyan) and compact (yellow) conformations of PGK obtained by

means of smFRET experiments performed with and without substrates. A larger spatial extension of the expanded state with

respect to the compact one can be seen.



Figure S6

Figure S6: Comparison of the mean inter-dye distance obtained by smFRET (our data in red) and time-resolved ensemble

FRET measurements (Haran and co-workers (32) in green and Lillo and co-workers (45) in yellow).



Figure S7

Figure S7: Black trace: fluctuations of the distance rPP between the 3-PG phosphate group and the γ−phosphate of ATP

along the 500 ns trajectory obtained from the MPC simulation. Colored traces: projections of rPP trace along the three slow-

est modes; the hinge bending motion (blue), the rocking motion (red), and the propeller twist motion (green). The red dashed

line represents the minimal distance of ∼ 4 A required for a successful phosphate transfer reaction.



Figure S8

Figure S8: The isosurfaces of the wAVs at a distance of FWHM = 2.355 · σAV with respect to the labeled atom (the carbon

at position 5’ of thymine) are represented for C6-Alexa488 in green and for C6-Alexa647 in red. The labeling positions are

separated by 17bp. The DNA structure was generated on the ”3D-DART” webserver by uploading the single strand sequence.

The representation is in scale with Fig.S9 and was created with VMD (v.1.9) (46).



Figure S9

Figure S9: The isosurfaces of the wAVs are shown for PGK (pdb:1QPG) at a distance of FWHM = 2.355 ·σAV with respect

to the labeled Cα. The donor cloud (C5-Alexa488) is here represented at position Q135 and the acceptor cloud (C2-Alexa647)

at position S290. The representation is in scale with Fig.S8 and was created with VMD (v.1.9) (46).



Figure S10

t (ns)

C(t)(A

2)

43.532.521.510.50

1000

100

10

1

Figure S10: Autocorrelation function C(t) of the distance between the center of mass of the N- and C-domains. An exponential

decay with a correlation time of 1 ns is obtained.



Figure S11

Figure S11: (A) Burst duration distribution, and (B) calculated ratioGDD(τ)GDA(τ) for ligand-free PGK.



Figure S12

Figure S12: For ligand-bound PGK are shown: (A) the measured burst duration distributions, (B) the apparent FRET efficiency

histograms at different bin widths, and (C) the calculated ratiosGDD(τ)GDA(τ) .



Figure S13

Figure S13: Efficiency histograms of PGK obtained (A) by increasing the threshold NT on the total number of photons

FA + FD per burst, and (B) by selecting bursts above a choosen molecular brightness per burst fT . Color code: NT = 25

(black), 30 (red), 40 (yellow), 50 (blue), 60 (green) and 100 (orange/brown) counts; fT = 0 (black), 5 (red), 10 (yellow), 15

(blue), 20 (green) and 30 (orange/brown) counts per milliseconds.



TABLES

Table S1

Table S1: Decay times τD0,i and amplitude fractions xi of donor only dlPGK. The intensity averaged lifetimes 〈τD0〉f are

also reported. For dlPGK, the reported values were calculated using Eq.S21 from values measured with slPGK. Different

substrates were added to the PGK buffer solution (ATP and ADP at 13 mM, 3-PG at 42 mM).

substrates τD0,1 [ns] τD0,2 [ns] x1 x2 〈τD0〉f [ns]

none 1.65 3.98 0.17 0.83 3.80

ATP 1.46 3.88 0.17 0.83 3.71

ADP 1.52 3.90 0.16 0.84 3.74

3-PG 1.93 4.05 0.15 0.85 3.91

3-PG*ADP 1.70 3.94 0.17 0.83 3.75



Table S2

Table S2: Set of parameters obtained from the fit of the 1D efficiency histograms of dlPGK in the ligand-bound and the

ligand-free forms. For each Gaussian, the mean 〈Ei〉, the variance σ2i , and the occupation probability pi =

bi∑

i biare reported.

The subscripts refer to the compact state population (i = 1) and the expanded state population (i = 2).

substrate 〈E1〉〈E2〉 σ21 σ2

2 p1 p2 χ2r

none 0.78 0.35 0.011 0.063 0.57 0.43 6.047

ATP 0.70 0.36 0.013 0.067 0.70 0.30 2.343

ADP 0.74 0.35 0.011 0.066 0.69 0.31 2.415

3-PG 0.76 0.35 0.010 0.050 0.77 0.23 5.011

3-PG*ADP 0.73 0.35 0.012 0.053 0.78 0.22 5.002



Table S3

Table S3: The apparent mean inter-dye distances 〈ri〉 and the FRET averaged inter-dye distances 〈rDA〉Eiare reported for

each population and for the different substrates, as well as the correction factors β = 〈φA〉16 · 〈φ− 1

6

A 〉. The following lifetime

and quantum yield were used as reference values to apply Eq.S33 and Eq.S34: 〈τR〉x = 1.38ns and φR = 0.58.

substrate β 〈r1〉 [A] 〈rDA〉E1[A] [A] 〈r2〉 [A] 〈rDA〉E2

[A]

none 1.0176 41.3 40.6 56.5 55.5

ATP 1.0167 44.3 43.6 56.2 55.3

ADP 1.0179 42.8 42.1 56.6 55.5

3-PG 1.0168 42.2 41.5 56.5 55.5

3-PG*ADP 1.0165 43.4 42.7 56.5 55.5



Table S4

Table S4: Calculated variances of the compact state population (i = 1) and the expanded state population (i = 2). The shot

noise variance (σ2SN,i), the variance due to variations of the acceptor quantum yield (σ2

φA,i), and the sum of both contributions

(σ2tot,i = σ2

SN,i + σ2φA,i

) are reported in efficiency units.

substrate σ2SN,1 σ2

φA,1σ2tot,1 σ2

SN,2 σ2φA,2

σ2tot,2

none 0.0024 0.0063 0.009 0.0032 0.0111 0.014

ATP 0.0034 0.0086 0.012 0.0037 0.0102 0.014

ADP 0.0027 0.0079 0.011 0.0032 0.0112 0.015

3-PG 0.0030 0.0067 0.010 0.0037 0.0104 0.014

3-PG*ADP 0.0029 0.0077 0.011 0.0033 0.0102 0.014



Table S5

Table S5: Occupation probabilities of the compact (p1) and the expanded (p2) state with PGK in the ligand-free and the ligand-

bound form. The Gibbs free energy difference ∆Gij = Gj − Gi (see Eq.S42) and the equilibrium constants Kij =pj

pi(see

Eq.S43) were calculated at ∼ 22 ◦C from the occupation probabilities (pj and pi) obtained from the fit of the 1D efficiency

histograms.

substrate p1 p2 K21 ∆G21

[

kcalmol

]

none 0.57 0.43 1.3 -0.17

ATP 0.70 0.30 2.3 -0.50

ADP 0.69 0.31 2.2 -0.47

3-PG 0.77 0.23 3.4 -0.71

3-PG*ADP 0.78 0.22 3.6 -0.74



Table S6

Table S6: Parameters used for the calculation of the ”corrected” static lines and the 2-state dynamic lines.

substrate R0 [A] 〈τD0〉f [ns] σDA [A]

none 51.0 3.80 8.8

ATP 51.0 3.71 8.1

ADP 51.0 3.74 8.2

3-PG 51.0 3.91 8.7

3-PG*ADP 51.0 3.75 8.8



Table S7

Table S7: The mean inter-dye distance 〈rDA〉 and the amplitude of fluctuations about the mean σDA are reported in A as

obtained from ensemble lifetime FRET experiments and wAV calculations performed on two DNA samples. The experimen-

tal errors were estimated with the support plane analysis as described in ref.(19). The confidence intervals on the calculated

values were estimated considering two limiting case for the linkers flexibility (see Section 9.1).

System 〈rDA〉exp σexpDA 〈|rDA|〉wAV σwAV

DA

17bp 58.4± 0.4 5.3± 0.6 61.3± 0.1 5.9± 0.110bp 41.6± 0.2 6.4± 0.2 34.9± 0.2 5.9± 0.1



Table S8

Table S8: The mean inter-dye distance 〈rDA〉 and the amplitude of fluctuations about the mean σDA are reported in A, as

obtained from wAV calculations for the rigid crystal structure of PGK (pdb:1QPG) and along the simulated trajectory. The

same parameters are also shown for the distance between the labeled positions (Q135 and S290). The confidence intervals on

the calculated values were estimated considering two limiting case for the linkers flexibility (see Section 9.1).

Model 〈|rDA|〉wAV σwAVDA 〈rCC〉 σCC

Rigid 39.1 6.9± 0.3 39.0± 0.1 -

Flexible 36.9± 0.1 9± 0.1 37.2± 0.2 5.2± 0.2

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List of Figures

S1 Collection of representative CD spectra of single and double cysteine mutants of PGK. The gray shaded area

represents the ±5% tolerance region with respect to the reference spectra of wild type PGK shown in black.

An example of a rejected sample is shown in violet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

S2 Radii of gyration (Rg) of dlPGK calculated from the diffusion coefficients D measured by fluorescence corre-

lation spectroscopy (FCS) in the presence and the absence of substrates. A reduction of the radius of gyration

is observed upon substrate binding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

S3 2D-plot of the dlDNA smFRET calibration measurement. The two populations, which correspond to the two

dlDNA samples used for the calibration, are shown together with the corrected static line (red continuous

line), which considers the presence of linker dynamics. The static line is also shown (red dashed line). The

parameters ({ci}, 〈τD0〉f , and γ′) used for the calculation of the corrected static line are shown in the insets,

as well as the detection efficiency ratio g′ = 0.7 obtained from the calibration measurement. The polyno-

mial coefficients {ci} (see Eq.S46) were calculated using a standard deviation σDA of 6.0 A for the Gaussian

distribution of the inter-dye distances (Eq.S16). The cross-talk α used to determine F ′ is also given. . . . . . 16

S4 Graphical solutions of Eq.S41. The red line represents the integral on the right hand side of Eq.S41 as a func-

tion of the unknown standard deviation σDA. The black and blue lines represent the measured conformational

variances σ2C ≃ 0.051 and σ2

C ≃ 0.038 for ligand-free and ADP-/ATP-bound PGK, and 3-PG-/3-PG*ADP-

bound PGK, respectively. The two intersections between the lines are the desired solution: σDA ∼ 9.7 A and

σDA ∼ 8.1 A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

S5 Average burst durations 〈T 〉 of the expanded (cyan) and compact (yellow) conformations of PGK obtained

by means of smFRET experiments performed with and without substrates. A larger spatial extension of the

expanded state with respect to the compact one can be seen. . . . . . . . . . . . . . . . . . . . . . . . . . . 18

S6 Comparison of the mean inter-dye distance obtained by smFRET (our data in red) and time-resolved ensemble

FRET measurements (Haran and co-workers (32) in green and Lillo and co-workers (45) in yellow). . . . . . 19

S7 Black trace: fluctuations of the distance rPP between the 3-PG phosphate group and the γ−phosphate of

ATP along the 500 ns trajectory obtained from the MPC simulation. Colored traces: projections of rPP trace

along the three slowest modes; the hinge bending motion (blue), the rocking motion (red), and the propeller

twist motion (green). The red dashed line represents the minimal distance of ∼ 4 A required for a successful

phosphate transfer reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

S8 The isosurfaces of the wAVs at a distance of FWHM = 2.355 · σAV with respect to the labeled atom (the

carbon at position 5’ of thymine) are represented for C6-Alexa488 in green and for C6-Alexa647 in red. The

labeling positions are separated by 17bp. The DNA structure was generated on the ”3D-DART” webserver by

uploading the single strand sequence. The representation is in scale with Fig.S9 and was created with VMD

(v.1.9) (46). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

S9 The isosurfaces of the wAVs are shown for PGK (pdb:1QPG) at a distance of FWHM = 2.355 · σAV

with respect to the labeled Cα. The donor cloud (C5-Alexa488) is here represented at position Q135 and the

acceptor cloud (C2-Alexa647) at position S290. The representation is in scale with Fig.S8 and was created

with VMD (v.1.9) (46). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

S10 Autocorrelation function C(t) of the distance between the center of mass of the N- and C-domains. An

exponential decay with a correlation time of 1 ns is obtained. . . . . . . . . . . . . . . . . . . . . . . . . . . 23

S11 (A) Burst duration distribution, and (B) calculated ratioGDD(τ)GDA(τ) for ligand-free PGK. . . . . . . . . . . . . . 24

S12 For ligand-bound PGK are shown: (A) the measured burst duration distributions, (B) the apparent FRET

efficiency histograms at different bin widths, and (C) the calculated ratiosGDD(τ)GDA(τ) . . . . . . . . . . . . . . . 25

S13 Efficiency histograms of PGK obtained (A) by increasing the threshold NT on the total number of photons

FA + FD per burst, and (B) by selecting bursts above a choosen molecular brightness per burst fT . Color

code: NT = 25 (black), 30 (red), 40 (yellow), 50 (blue), 60 (green) and 100 (orange/brown) counts; fT = 0

(black), 5 (red), 10 (yellow), 15 (blue), 20 (green) and 30 (orange/brown) counts per milliseconds. . . . . . . 26



List of Tables

S1 Decay times τD0,i and amplitude fractions xi of donor only dlPGK. The intensity averaged lifetimes 〈τD0〉fare also reported. For dlPGK, the reported values were calculated using Eq.S21 from values measured with

slPGK. Different substrates were added to the PGK buffer solution (ATP and ADP at 13 mM, 3-PG at 42 mM). 27

S2 Set of parameters obtained from the fit of the 1D efficiency histograms of dlPGK in the ligand-bound and

the ligand-free forms. For each Gaussian, the mean 〈Ei〉, the variance σ2i , and the occupation probability

pi =bi

∑

i biare reported. The subscripts refer to the compact state population (i = 1) and the expanded state

population (i = 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

S3 The apparent mean inter-dye distances 〈ri〉 and the FRET averaged inter-dye distances 〈rDA〉Eiare reported

for each population and for the different substrates, as well as the correction factors β = 〈φA〉16 · 〈φ− 1

6

A 〉.The following lifetime and quantum yield were used as reference values to apply Eq.S33 and Eq.S34:

〈τR〉x = 1.38ns and φR = 0.58. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

S4 Calculated variances of the compact state population (i = 1) and the expanded state population (i = 2). The

shot noise variance (σ2SN,i), the variance due to variations of the acceptor quantum yield (σ2

φA,i), and the sum

of both contributions (σ2tot,i = σ2

SN,i + σ2φA,i

) are reported in efficiency units. . . . . . . . . . . . . . . . . . 30

S5 Occupation probabilities of the compact (p1) and the expanded (p2) state with PGK in the ligand-free and the

ligand-bound form. The Gibbs free energy difference ∆Gij = Gj − Gi (see Eq.S42) and the equilibrium

constants Kij =pj

pi(see Eq.S43) were calculated at ∼ 22 ◦C from the occupation probabilities (pj and pi)

obtained from the fit of the 1D efficiency histograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

S6 Parameters used for the calculation of the ”corrected” static lines and the 2-state dynamic lines. . . . . . . . . 32

S7 The mean inter-dye distance 〈rDA〉 and the amplitude of fluctuations about the mean σDA are reported in A as

obtained from ensemble lifetime FRET experiments and wAV calculations performed on two DNA samples.

The experimental errors were estimated with the support plane analysis as described in ref.(19). The confi-

dence intervals on the calculated values were estimated considering two limiting case for the linkers flexibility

(see Section 9.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

S8 The mean inter-dye distance 〈rDA〉 and the amplitude of fluctuations about the mean σDA are reported in A,

as obtained from wAV calculations for the rigid crystal structure of PGK (pdb:1QPG) and along the simulated

trajectory. The same parameters are also shown for the distance between the labeled positions (Q135 and

S290). The confidence intervals on the calculated values were estimated considering two limiting case for the

linkers flexibility (see Section 9.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34


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