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. 2017 Sep 7;121(35):8211-8241.
doi: 10.1021/acs.jpcb.7b03441. Epub 2017 Aug 28.

Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

Thomas-Otavio Peulen  1 , Oleg Opanasyuk  1 , Claus A M Seidel  1
Affiliations

Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

Thomas-Otavio Peulen et al. J Phys Chem B. .

Abstract

Förster resonance energy transfer (FRET) measurements from a donor, D, to an acceptor, A, fluorophore are frequently used in vitro and in live cells to reveal information on the structure and dynamics of DA labeled macromolecules. Accurate descriptions of FRET measurements by molecular models are complicated because the fluorophores are usually coupled to the macromolecule via flexible long linkers allowing for diffusional exchange between multiple states with different fluorescence properties caused by distinct environmental quenching, dye mobilities, and variable DA distances. It is often assumed for the analysis of fluorescence intensity decays that DA distances and D quenching are uncorrelated (homogeneous quenching by FRET) and that the exchange between distinct fluorophore states is slow (quasistatic). This allows us to introduce the FRET-induced donor decay, εD(t), a function solely depending on the species fraction distribution of the rate constants of energy transfer by FRET, for a convenient joint analysis of fluorescence decays of FRET and reference samples by integrated graphical and analytical procedures. Additionally, we developed a simulation toolkit to model dye diffusion, fluorescence quenching by the protein surface, and FRET. A benchmark study with simulated fluorescence decays of 500 protein structures demonstrates that the quasistatic homogeneous model works very well and recovers for single conformations the average DA distances with an accuracy of < 2%. For more complex cases, where proteins adopt multiple conformations with significantly different dye environments (heterogeneous case), we introduce a general analysis framework and evaluate its power in resolving heterogeneities in DA distances. The developed fast simulation methods, relying on Brownian dynamics of a coarse-grained dye in its sterically accessible volume, allow us to incorporate structural information in the decay analysis for heterogeneous cases by relating dye states with protein conformations to pave the way for fluorescence and FRET-based dynamic structural biology. Finally, we present theories and simulations to assess the accuracy and precision of steady-state and time-resolved FRET measurements in resolving DA distances on the single-molecule and ensemble level and provide a rigorous framework for estimating approximation, systematic, and statistical errors.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Fluorescence properties of the dyes Alexa488 and Alexa647 tethered to proteins are sample-dependent due to variations of the local dye environment. Average fluorescence lifetimes, ⟨τ⟩x, and residual anisotropies, r∞, of the fluorophores Alexa647 and Alexa488 attached via maleimide or hydroxylamine click chemistry to different amino acids of various proteins (human guanylate binding protein 1, T4 lysozyme, postsynaptic density protein 95, lipase foldase of Pseudomonas aeruginosa and the cyclin-dependent kinase inhibitor 1B). (A) For each sample, the species weighted averaged lifetime ⟨τ⟩x and r∞ are shown as dots overlaid by a Gaussian kernel density estimation. The fluorescence parameters are compiled in Table S1 for Alexa647 and in Table S2 for Alexa488 together with individual fluorescence lifetimes from a detailed decay analysis. Using radiative lifetimes of τF = 3.1 ns and τF = 4.5 ns for Alexa647 and Alexa488, respectively, the relative brightnesses, ⟨τ⟩x/τF, were calculated. The average values of all Alexa647 and Alexa488 samples are ⟨τ⟩x/τF = 0.43 ± 0.07 and ⟨τ⟩x/τF = 0.76 ± 0.11, respectively. The average residual anisotropies of Alexa647 and Alexa488 for all samples are ⟨r∞⟩ = 0.25 ± 0.07 and ⟨r∞⟩ = 0.18 ± 0.05, respectively. (B) The fluorescence intensity decays of the Alexa488 samples were formally resolved into two components τ1 and τ2 with the respective fractions x1 and x2 = 1 – x1. For each sample the lifetimes and fractions are shown as open circles overlaid with a Gaussian-kernel density estimation (green). The average lifetimes of the populations are τ1 = 3.9 ± 0.2 ns and τ2 = 1.0 ± 0.5 ns with species fractions of x1 = 0.8 ± 0.1 and x2 = 0.2 ± 0.1, respectively. The presented data are summarized in Table S2.
Figure 2
Figure 2
Set of rate constants for the excitation of the dyes, their de-excitation, and FRET that defines the time-dependent fluorescence decays. Definition of states and rate constants of a system composed of a single donor, D, and acceptor, A, excited by a single photon. The asterisk (*) indicates an excited fluorophore: D*A (excited donor, ground state acceptor), DA* (excited acceptor, ground state donor), and DA (ground state donor, ground state acceptor). kex is the rate constant of excitation; kD and kA are the rate constants of deactivation of the excited donor and acceptor state, and kRET is the rate constant of energy transfer from D to A. kD and kA are the sums of the respective radiative rate constant of fluorescence kF, internal conversion kIC, intersystem crossing kISC, and the quenching rate constant kQ. kQ depends on the local environments of the dyes. kF, kISC, and kIC are dye-specific and joined in the constants k0.
Figure 3
Figure 3
FRET-induced donor decay directly visualizes FRET rate constants and donor–acceptor distances. Fluorescence intensity decays of a donor fD|D(t) (top row) in the absence (green) and in the presence (blue, magenta, and orange) of FRET. The corresponding FRET-induced donor decays, εD(t)’s, are shown in the lower two rows. The fluorescence decays were calculated by eq 13 (single FRET-active species), eq 16 (mixture of FRET-active and FRET-inactive species), and eq 18 (mixture of FRET species and distribution of FRET species) (R0 = 50 Å and kD–1 = 4.0 ns). Information on FRET is obtained by comparing the fluorescence decay of the donor in the presence of an acceptor (blue or magenta) to its reference given by the fluorescence decay in the absence of FRET (green). εD(t) contains the reference implicitly. In the middle row, εD(t) is shown in linear scale. In the lower row, εD(t) is shown with a logarithmic time axis, and the time t between excitation and detection of fluorescence was converted into a critical donor–acceptor distance axis RDA,C by eq 15. This allows for the determination of the characteristic times of FRET kRET–1 and distances graphically at the point where εD(t) decayed to the value 1/e (shown as vertical lines). The time t corresponds to the DA distance of the FRET process. (A) Single distance of RDA = 40 Å (magenta) and RDA = 65 Å (blue), respectively. (B) Mixture of a FRET-active RDA = 40 Å (magenta) and RDA = 65 Å (blue) and a FRET-inactive species (fraction, xnoFRET = 0.1). (C) Mixture of two FRET-active species RDA(1) = 40 Å (50%) and RDA(2) = 65 Å (50%) (orange). The position and the height of the “steps” in the lowest plot relate to the FRET rate constant and the species fractions of the individual species. For comparison, the components (dotted blue and magenta lines) of the individual species are overlaid. (D) Normal distributed distance with a mean of ⟨RDA⟩ = 40 Å and a distribution width varying from 0 to 32 Å (black to magenta).
Figure 4
Figure 4
Experimental data can be visualized by the FRET-induced donor decay to reveal donor–acceptor distance distributions. Experimental fluorescence decays, FRET-induced donor decay, and maximum entropy analysis (MEM) of ensemble measurements of the human guanylate binding protein 1 dimer (hGBP1) singly labeled at amino acid Q577C by the donor, D (Alexa 488), and the acceptor, A (Alexa 647), respectively. The dimerization was induced by 500 μM GTPγS. (A) Donor fluorescence decays in the absence (τD(1) = 4.2, xD(1) = 0.94, τD(2) = 1.7 ns, xD(2) = 0.06) (green) and in the presence (orange) of an acceptor; the instrument response function (IRF) is shown as a gray line. The time axis measures the time between excitation and detection of donor photons. (B) Corresponding FRET-induced donor decay εD(t). The distance axis RDA,C(t) is given by the Förster relationship RDA,C = R0(ΦF,Dtk0,D)1/6 (k0,D–1 = 4.1 ns, R0 = 52 Å). The fluorescence decay was analyzed by a two component (N = 2) model (Supporting Information eq S1 in Note S1) using a width of w = 12 Å). The individual components with average distances of 38 and 58 Å are visualized by solid magenta and blue lines, respectively. (C) The DA distance distribution obtained by analyzing the fluorescence decays by the maximum entropy method (magenta high FRET, blue low FRET, dark-yellow experimental FRET-induced donor decay, orange fit).
Figure 5
Figure 5
In a general framework for the analysis of time-resolved FRET experiments, a conditional probability matrix relates the acceptor to the donor states. Schematics illustrating the meaning and relation of the parameters in the eq 23. The donor states, indicated by green shades, are characterized by sets of variables {QD, RD}(i), defining corresponding rate constants kD(i), and their fractions xD(i). The acceptor FRET states are characterized by sets of variables {QA, RDA}(j), defining corresponding FRET rate constants kRET(i), and are indicated by red shades. The gray frame outlines the fraction matrix [xDA(i,j)] of FRET pairs where the donor is in state i and the acceptor in state j. This matrix is presented implicitly by the row product of the donor fraction vector xD and conditional probability matrix [ξ(i,j)] (shades of gray). The gray shades of the protein picture shown in the top left edges illustrate different correlation between donor and acceptor-FRET parameters and indicate corresponding values of the [xDA(i,j)] matrix (the darker shades correspond to the higher fractions). Note that the structure of matrix [xDA(i,j)] and [ξ(i,j)] is not the same. (A) The general case. (B) The homogeneous case. In this case the donor fluorescence decay can be factorized in form of eq 11 and the matrix [ξ(i,j)] has special, uniform-row shape. (C) Case of the full correlation between donor and acceptor states. In this case the number of FRET states is reduced to the number of donor or acceptor states, and the conditional probability matrix turns into an identity matrix.
Figure 6
Figure 6
Uncertainties of the condition probability matrix may propagate to errors of the donor–acceptor distances in particular for minorly populated states. Limitations of the homogeneous approximation illustrated by simulations of a typical time-resolved experiment with three discrete FRET states. (A) Simulated time-resolved fluorescence decay histograms with 100 000 photons in peak (bin width 14.1 ps) using an experimental recorded IRF with a fwhm of 250 ps of a system with three discrete donor states 4 ns (80%), 2.5 ns (14%), and 0.5 ns (6%), and three discrete FRET states 40 Å (30%), 45 Å (50%), and 60 Å (20%) (R0 = 50 Å, k0–1 = 4 ns). The 40 and 45 Å state are associated with the donor lifetime of 4 ns; the 60 Å state is associated with the donor lifetimes 2.5 and 0.5 ns. The conditional probability matrix [ξ(i,j)] and the corresponding values of the [xDA(i,j)] matrix are shown as numbers in the tables. (B) The analysis result using the correct model and the inappropriate homogeneous model are shown on the top and bottom, respectively. The weighted residuals (w.res.) of both models are indistinguishable. To the right the recovered distances and fractions are plotted in a bar diagram.
Figure 7
Figure 7
Coarse-grained BD simulations describe the dye’s spatial distribution, dynamics, and the quenching by amino acids. (A) Effect of a quencher (orange) on the fluorescence lifetime distribution of a donor (green) in the absence (left) and presence (right) of FRET. The donor is located within its sterically accessible volume (AV) shown as a half-circle. The lines in the half-circles are isolines for the donor fluorescence lifetimes in the absence of FRET kD–1 (left), the characteristic times of FRET kRET–1 (middle), and the donor fluorescence lifetimes in the presence of FRET (kD + kRET)−1 (right), respectively. Histograms of the corresponding lifetimes are shown below. Experimentally, the lifetime distributions in the absence (left) and presence (right) of FRET are accessible (highlighted by gray dotted boxes). (B) Illustration of relevant simulation parameters of the coarse-grained Brownian dynamics (BD) simulations. The donor dye Alexa488 (shown in black) is approximated by a sphere (green) with a radius Rdye and is connected to the protein by a flexible linker (blue) of the length Llink and diameter Lwidth. The green mesh outlines the AV of the dye and limits all possible conformational states ΛD. The quenching amino acids Q are approximated by spheres of radius RQ located at their respective centers of mass. On the basis of the distance RDQ between the dye and Q and the radiation boundary Rrad, the fluorescence lifetimes of ΛD are calculated by eq 28 considering all quenching amino acids. This assigns fluorescence lifetimes kD–1 to all ΛD which are either unquenched kD = τ0–1 or quenched τ0–1 + kQ. Quenched states are highlighted in orange. To each state a diffusion coefficient D is assigned on the basis of its distance to the molecular surface. Dyes close to the molecular surface within the accessible contact volume ACV (magenta) diffuse more slowly. The ACV is determined by a critical distance Rsurface and the distances RCβ to all Cβ-atoms. For fast simulations, the conformational space Λ of the dye is discretized, and ΛD(i), a diffusion coefficient D(i), and 1/kD(i) are associated to each state. In each iteration of the BD simulations with time steps Δt the location of the dye is randomly changed to generate a trajectory of states Λ(t) and fluorescence lifetimes 1/kD(t). (C) The used simulation parameters are summarized in the shown tables.
Figure 8
Figure 8
Coarse-grained model captures the diffusion and dynamic quenching of Alexa488 and correlates with experimental data. Simulation of donor fluorescence decays by Brownian dynamics (BD) simulations: (A) BD simulation of the donor, D, Alexa488-C5-maleimide attached to the human guanylate binding protein 1 (PDB-ID: 1F5N). The attachment atom (on amino acid Q18C) is shown as a blue sphere, and quenching amino acids (His, Tyr, Met, and Trp) are highlighted in orange. D states close to the surface are shown in magenta. The green dots represent a subset of potential fluorophore positions of an 8 μs BD simulation. In the upper-right corner a contiguous part of a trajectory is displayed (colored from white to dark green). (B) Comparison of simulated donor fluorescence decays for various diffusion coefficients D. The analysis result of the corresponding experimental fluorescence decay, formally analyzed by a biexponential relaxation model (x1 = 0.82, τ1 = 4.15, x2 = 0.18, τ2 = 1.35), is shown in magenta. The decay of the unquenched dye with a fluorescence lifetime of 4.1 ns is shown in black. (C) Simulated fluorescence quantum yields of fluorescent species ΦF,D(sim) for a diffusion coefficient D = 15 Å/ns vs experimentally determined quantum yields ΦF,D(exp) for a set of variants of the proteins T4L, hGBP1, PSD-95, and HIV-RT. The black line shows a 1:1 relationship. ΦF,D(exp) was determined by ensemble TCSPC (hGBP1, T4L, PSD-95) or single-molecule measurements (HIV-RT). The data point highlighted by the red arrow corresponds to the experiment shown in panel B. The crystal structures used to simulate the donor fluorescence decays are listed in Table S3.
Figure 9
Figure 9
Fast translational diffusion of the donor and acceptor dyes affects the recovered apparent donor–acceptor distribution due to averaging during their fluorescence lifetime. Effects of dye diffusion on apparent DA distance distributions, x(Rapp). (A) Apparent DA distance distributions, x(Rapp) recovered from a fluorescence decay of a donor with a lifetime of 4 ns attached to amino acid F379C and an acceptor attached to amino acid D467C of the hGBP1 protein structure (PDB-ID: 1F5N) in dependence of the diffusion coefficients of the donor DD and the acceptor DA = 1/2DD without interaction of the dyes (left) and with interaction of the dyes (right) with the protein surface. Interacting dyes close to the protein surface diffused 10 times slower. (B) Apparent distances of a two-state system in dynamic exchange. The equally populated discrete states RDA(1) = 40 Å and RDA(2) = 60 Å (R0 = 52 Å) are in dynamic exchange with a rate constant kdyn. The resulting biexponential FRET-induced donor decay was converted to yield two apparent distances (orange lines). Using these apparent distances, the average distance (black) was calculated. The gray line is the static average of the two distances.
Figure 10
Figure 10
Average donor–acceptor distance and the recovered average distance systematically deviate on a small scale. The effect of the quencher location on the mean apparent distance between the donor, D, and acceptor, A , ⟨Rapp⟩ is illustrated using a crystal structure (PDB-ID: 1F5N) of the human guanylate binding protein 1. A set of 23 simulations (quencher located at amino acid number: 156, 158, 299, 313, 317, 321, 325, 326, 329, 336, 329, 336, 374, 378, 382, 387, 390, 393, 524, 532, 538, 539, 542) was performed. The simulations consider dye diffusion and D quenching. The relative distance difference between the average distance ⟨RDA⟩ (52 Å) and the average apparent distance ⟨Rapp⟩ was mapped on the Cβ-atom of the respective quencher. The D and A accessible volume are shown as green and red mesh, respectively. The blue spheres mark the attachment points of D (F379C) and A (D467C).
Figure 11
Figure 11
Relative error of a normalized donor–acceptor distance, δ(RDA/R0), depends on the normalized donor–acceptor distance, RDA/R0, and a number of experimental parameters. Estimated relative uncertainties δ(RDA/R0) of the DA distance, RDA, for a given number of detected photons, N, with dependence of the distance RDA/R0 for time-correlated single photon counting (TCSPC), intensity-based measurements by multiparameter fluorescence detection (MFD) with one-color excitation (OCE), and pulsed-interleaved excitation (PIE). On the top the contributions of the shot noise and the relevant calibration/correction parameters (colored solid lines) are shown. The resulting total uncertainty is shown as a dotted line. On the bottom, the distance-dependent scaling of the total uncertainty is shown for a different number of photons. The uncertainties for TCSPC were estimated by eqs 46–51 using a radiative rate constant of kF,D = 0.25 ns–1 and a relative error corresponding to the donor fluorescence variation among different protein samples in Figure 1 (τD(0) = 3.9 ± 0.2 ns). The time-window, T = 16 ns, of the fluorescence decay histogram was separated into 53 detection channels resulting in a detection channel width of 0.3 ns (the typical width of an instrument response function in single-molecule (sm) detection). The uncertainties of the MFD-OCE and MFD-PIE measurements were calculated by eqs 35–45. In both cases the fluorescence quantum yield of the donor and acceptor were ΦF,D = 0.8 and ΦF,A = 0.3, respectively. In the MFD-OCE and MFD-PIE plots, α = 0.02 ± 0.005, γ′ = 0.8 ± 0.05, and ΦF,A = 0.3. The relative fractions of the nonfluorescent background were BG|G/IG|G = 0.02 and BR|G/IR|G = 0.01. In MFD-PIE, BR|R/IR|R = 0.02, η = 0.02 ± 0.01, and β = 0.3 ± 0.1. In MFD-OCE, ΔΦF,A = 0.05.
Figure 12
Figure 12
Expected relative error, δ, of the recovered average donor–acceptor distance, ⟨Rapp⟩, which was estimated from simulated FRET experiments of diffusing dyes tethered to proteins. This validates the homogeneous FRET model for the analysis of fluorescence decays of flexibly coupled quenched dyes. Fluorescence decays for the currently best-resolved protein structures were simulated using coarse-grained BD simulations and parameters of the donor–acceptor (DA) pair Alexa488/Alexa647 (see Figure 7). FRET rate constants were calculated using a donor fluorescence lifetime of τD = 4.0 ns and a Förster radius of R0 = 52 Å assuming an orientation factor κ2=2/3. The average apparent DA distances ⟨Rapp⟩ were determined by the FRET-induced donor decay εD(t) by solving eq 20. (A) The obtained ⟨RDA⟩ values are compared to the recovered ⟨Rapp⟩ values. The cyan line corresponds to a 1:1 relationship. The red line describes the empirical relation ⟨Rapp⟩ and ⟨RDA⟩ given by eq 53. On the top, the relative deviation δ = (⟨RDA⟩ – ⟨Rapp⟩)/⟨RDA⟩ is shown. For better comparison, binned deviations are shown. (B) The dependence of the absolute difference Δ = ⟨RDA⟩ – ⟨Rapp⟩ on the simulated fluorescence quantum yield of the donor ΦF,D is shown. This dependence was characterized by a linear model shown in the inset of the figure. To reduce the noise, the data were binned. The circles and error bars correspond to the average and the standard deviation of each bin, respectively.
Figure 13
Figure 13
Deviation of the distance distribution between a donor, D, and an acceptor, A, for the two possible combinations DA and AD was studied to assess the error of a random labeling. The effect of labeling symmetry on the expected distance distributions evaluated by the accessible volume (AV) simulations (see Supporting Information, Note S3). (A) AVs of Alexa488/Alexa647- and BodipyFL/Alexa647-dye pairs attached to the amino acids Q344C/A496C of a hGBP1 protein structure (PDB-ID: 1DG3). (B) The resulting distance distributions x(RDA) and mean distances ⟨RDA⟩. (C) Comparison of both possible average distances for a set of large protein structures (with more than 360 amino acids). The average distances ⟨RDA⟩ = 1/2(⟨RDA(DA)⟩ + ⟨RDA(AD)⟩) are plotted vs their deviation Δ = ⟨RDA(DA)⟩ + ⟨RDA(AD)⟩ in a two-dimensional histogram for a random set of fluorophore pairs for Alexa488/Alexa647 (red). The histograms to the side and the top are the projections of the respective axes. For the dye pair BodipyFL/Alexa647 only a histogram of Δ is shown (green).
Figure 14
Figure 14
Considering the simplest bimodal model with two discrete distances, the distance resolution of time-resolved fluorescence measurements is limited by the shot noise of the experiment. Statistical error estimates of a two-distance model described by eq 56 with distances formula image and formula image, fluorescence lifetime τD(0) = 4 ns, and a time-window of 12.5τD(0). (A) Relative standard error δ per 106 photons of the distances formula image (blue, left), formula image (green, middle), and their difference ΔRDA (red, right). White lines are isolines δ = 0.5 (also shown at panel D). (B) Isolines of δ(formula image)) = 0.5 (blue line), δ(formula image) = 0.5 (green line), and δ(ΔRDA)=0.5 (red line) for 106 counted photons (the same as white lines at panel A). The isolines partition the parameter space in four regions: (i) All three parameters are resolved. (ii) The distances formula image, formula image can be reliably determined while the relative standard error of their difference δ(ΔRDA) increases above value 0.5. (iii) Only the shorter distance formula image is reliably estimated. The distance distribution is only partially resolved, and the species with small FRET rate constant cannot be distinguished from non-FRET species. (iv) None of the parameters is resolved. The vertical lines indicate limiting distances formula image of the region i (red) and formula image of the region ii (green). (C) Dependence of the limiting distances formula image and formula image on the number of detected photons.
Figure 15
Figure 15
Distances estimated by time-resolved fluorescence measurements for the simplest bimodal model of two discrete distances are highly correlated. (A) Correlation coefficients formula image. (B, left) The 2D probability distribution function (counterfeit normal) of observed estimates of parameters formula image, formula image for expectations formula image, formula image. (B, right) The marginal (1D projections) probability distribution functions of estimations of formula image (blue), formula image (green), and the probability distribution functions of ΔRDA estimation (red, shifted for comparison) for 4 sets of expected parameters marked by circles in Figure 14A,B and here in panel A. Indices (i, ii, iii) correspond to the regions defined in Figure 14B.
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References

    1. Förster T. Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Phys. 1948, 437, 55–75. 10.1002/andp.19484370105. - DOI
    1. Stryer L.; Haugland R. P. Energy transfer: A spectroscopic ruler. Proc. Natl. Acad. Sci. U. S. A. 1967, 58, 719–726. 10.1073/pnas.58.2.719. - DOI - PMC - PubMed
    1. Hochstrasser R. A.; Chen S. M.; Millar D. P. Distance distribution in a dye-linked oligonucleotide determined by time-resolved fluorescence energy transfer. Biophys. Chem. 1992, 45, 133–141. 10.1016/0301-4622(92)87005-4. - DOI - PubMed
    1. Klostermeier D.; Millar D. P. Time-resolved fluorescence resonance energy transfer: A versatile tool for the analysis of nucleic acids. Biopolymers 2002, 61, 159–179. 10.1002/bip.10146. - DOI - PubMed
    1. Muretta J. M.; Jun Y.; Gross S. P.; Major J.; Thomas D. D.; Rosenfeld S. S. The structural kinetics of switch-1 and the neck linker explain the functions of kinesin-1 and Eg5. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, E6606–E6613. 10.1073/pnas.1512305112. - DOI - PMC - PubMed

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