Supplementary Material

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1 Supplentary Material Three-Color Alternating-Laser xcitation of Single Molecules: Monitoring Multiple Interactions and Distances Nam Ki Lee, Achillefs N. Kapanidis, Hye an Koh, You Korlann, Sam On Ho, Younggyu Kim, Natalie assman, Seong Keun Kim, and Shimon Weiss. Theory of c-alx -A. Theoretical relations between 2-color and -color T. A three-probe syst creates three donor-acceptor pairs (-, -, and -; ig. A) characterized by three T efficiencies: (S) r T nr T (S2) r r T nr T nr T (S) T where is the T efficiency between X (donor) and Y (acceptor), the rate constant for T T between X and Y, X r the radiative decay rate constant of X, and X nr the non-radiative decay rate constant of X, respectively. Similarly, for a three-color syst where all probes are involved in T, the T efficiencies are: r nr T T T (S4) r nr T T T (S5) r T nr T (S6) where the measured is the T efficiency between X (donor) and Y (acceptor) in a triply-labeled species. In 2c-T, values are used to calculate distances ( ) between two probes using qs. S7-S8; S

2 ( / (S7) 6, ) ( ) Dκ n J ( ν ) Å (S8) where 2 D is the quantum yield of donor, κ the orientation factor, n the refractive index of the media, and J(ν) the integral of the spectral overlap (). When equals, (örster radius of a X-Y pair), is 5%. In 2c-T, since, is a constant independent of, directly reports on the distance. In c-t, however, does not directly report on the distance, because, is not necessarily constant for a threeprobe syst (2). or example, when is close to - pair, it quenches via T (from to ), reduces the quantum yield of, and changes,, (because is a function of the quantum yield of ; q. S8). As a result,, depends on (- distance). Similarly,, (- pair) can become a function of. In contrast,, is a constant, independent of the presence of. Therefore, we convert ( ) ( ) to using qs. S9-S in order to calculate three interprobe distances: (S9) (S). (S) -. -color ALX Detailed theory for 2c-ALX was described previously (). Here we describe the theory for c-alx measurent of three T efficiencies and three probe-stoichiometries values. c-alx produces nine distinct photon-ission streams (ig. S), corresponding to nine photon-counts for a single burst of fluorescence in solution. To describe photon-counts, we used the simple notation of Y X where X denotes itation laser, 477 nm, 52 nm, and 6 nm (each laser ites dominantly probes of,, and, respectively), and Y denotes photon detector, for nm, for nm, and for nm ission range (the ission wavelengths were selected by the combination of wavelength filters and dichroic mirrors, and each detector detects dominantly the ission of,, and, respectively). or typical T pairs, photon-counts induced by T for donor-acceptor species contains two types of crosstal: one is leaage, i.e., donor-ission detected at acceptor detection channel (ig. SA, L ), and the other is direct-itation, i.e., S2

3 direct itation of acceptor by donor-itation laser (ig. SA, Dir ). Accounting for these two crosstals is significant for accurate T measurents (). In case of c-t, additional crosstals are present (ig. S); we describe these crosstals using the advanced notation Z Y X, which represents the sub-photon-counts itted by fluorophore Z upon X laser-itation and detected by Y detector. In the case of the photons originating from T, we denote Z X Y to signify their T-induced origin. 2c-T contains three types of photon origin of D (donor), A (acceptor) and D A, while c-alx contains seven types of photon origins as,,,,,, and. Definitions for photon-counts of a fluorescence burst generated by c-alx. The first laser, iting dominantly, generates three types of fluorescence intensities (ig. S -6 µs ), and each of th is represented by the sum of the sub-photon-counts from the seven types of photon origin. or example, the photon count can be written as follows: L 2 ( Dir o L ) Dir ( L 2 o ) ( Dir o ) (S2) where Y X X Y denotes the photon-counts that contain crosstals to be corrected afterward ( is the photoncounts that do not contain crosstals or crosstals corrected one). The two main types of crosstals are written as L n and Dir n, (ig. S). Crosstals due to a combination of two crosstals, or a combination of crosstal and T are denoted by (A ). Similarly: (S) (S4) L Dir (S5) (S6) L 4 Dir (S7) (S8) (S9). (S2) Several of the photon-counts in q. S2-S2 are zero, because - and -itations by the -itation laser and -itation by the -itation laser are negligible, and because the ission of is not detected at -detector and the ission of is not detected at - and -detectors. The non-zero photon-counts in qs. S2 S2 can be written as a function of itation and ission properties, and T efficiencies: S

4 dec I η ( ) (S2) [ I η ( )] [ I η ( )] dec dec I η ( ) dec [ I η ( )] [ I η ( )] I η dec dec dec [ I η ( )] I η I η I dec dec dec η dec (S22) (S2) dec I η ( ) (S24) dec dec dec [ I η ( )] I η I η (S25) η dec I (S26) where I, I and Y I are -, - and -itation laser intensities, respectively; X is the absorption cross-section of Y (probe) upon X laser-itation;, and are quantum yields of, and, respectively; Ydec η X denotes the detection efficiency of X (probe)-ission by the Y detector; and denotes the T efficiency between X (donor) and Y (acceptor) of triply-labeled species. Crosstal corrections. It is essential to account for crosstals for accurate T measurents (). As in 2c-ALX, crosstals can be corrected in c-alx using the singly-labeled species. Among the six photon-counts,, and require crosstal corrections. i) Crosstal corrections for. contains two crosstals, L and Dir (q. S4). The L contribution can be defined on the basis of as: dec dec dec I η ( ) ( η / η ) l (S27) L where l is the leaage coefficient for -ission into -detection channel; l can be determined using the ratio / for -only species. The Dir contribution can be defined on the basis of as: Dir ( d (S28) dec I η ) [ I / I ] where d is the direct-itation coefficient for -itation by -itation laser; d can be determined using the ratio / for -only species. After the subtractions of L and Dir, contains only the photon-counts induced by the T from to : dec L Dir I η ( ). (S29) S4

5 ii) Using similar crosstal corrections for, we obtain: dec ( ) η I (S) iii) Using similar crosstal corrections for dec, we obtain: I η (S) (T efficiency) determination. After the corrections for crosstal terms, we obtain six photon-counts that are used (along with qs. S9 S) for determining the three T efficiencies of c-t, for example: I Similarly, I ( ) I ( )( dec dec η η (S2) η ( )( ) dec I η [ ( ) ( ) ] dec ) (S) (S4) dec I η ( ) (S5) I η (S6) dec I η. (S7) dec The three photon-counts induced by the itation of (qs. S2 S4) can be reduced to two T-related ratios: ( ) ( ) (S8; q. in text) ( { ( ) ( )} )( ) { ( ) ( )} (S9; q. 2 in text) where represents a proximity ratio (an approximate value of ) and denotes the detection-correction Ydec X dec factor (4) [ ( η ) /( η ) ]. Since all -factors for c-t can be measured using 2c-ALX Y Y X X sche(), they can be treated here as measurable constants. With all -factors nown, however, these two ratiometric- equations (qs. S8-S9) are insufficient to determine all three T efficiencies. or this reason, single-molecule T using single-laser itation cannot determine three T efficiencies from a single burst (5). In c-alx, the second laser ites that generates two types of photon-counts of and (qs. S5-S6); the ratio of these two photon-counts reports on as: S5

6 ( ) (S4; q. in text) Using qs. S8 S4, three accurate T efficiencies can be derived: ( )( ) (S4) (S42) ( ) ( ( ) [ ) (. (S4) )] The three are subsequently used for the calculation of three distances using q. S7. S6

7 2. nsble measurent. The quantum yields for Alexa 488, TM and Alexa 647 were measured as described (6) using singly-labeled DNA in single-molecule buffer ( mm HPS-NaOH ph 7, 5 mm NaCl, µg/ml SA, mm mercaptoethylamine, and 5% glycerol); the values were.9,.5 (or.25), and.2 for Alexa 488, TM and Alexa 647, respectively (see Table below). The quantum yield of TM was sensitive to the labeling positions, while those of Alexa 488 and Alexa 647 are not. The steady-state fluorescence anisotropy values of Alexa 488, TM and Alexa 647 in dsdna were measured to be.5,.2 (or.8) and.9, respectively (see Table); these values are low compared to the anisotropies of the immobile probes (.6-.4), indicating substantial rotational freedom of the probes, and justifying the assumption κ 2 2/. Using the κ 2 approximation, the örster radius for the Alexa 488-TM, TM-Alexa 647, and Alexa 488-Alexa 647 pairs were calculated to be 62 Å, 66 Å (62 Å for TM.25), and 56 Å, respectively. Dye Position QY a r b Alexa 488 C bot.9.5 C2 top.9.5 TAMA C top.25.8 C2 bot.25.8 C-a bot.5.2 Alexa 647 C bot.2.9 C-a bot.2.9 a Quantum yield b Steady-state fluorescence Anisotropy S7

8 . -determination. or calculation of accurate-t (S4-S4), measurents of -factors (detection-correction factors (4)) are necessary (). -factors for c-t can be defined (using the notation of Theory of c-alx ) as: η dec, dec η η dec, dec η η dec. (S44) dec η Since by definition:, (S45) two -factors are sufficient for accurate-t measurents. Since TM has a different quantum yield depending on the labeling positions in dsdna (see 2. nsble measurent ), we divided the five dsdna constructs into two groups: group (C-a and C-c, TM.5) and group 2 (C, C2 and C-b, TM.25); for group, we experimentally determined the -factors using two sets of T pairs, and for group 2 we used the standard pair method (ref.). i) roup : using the two sets of T pairs (for, - of C-a and C-c; for, - of C-a and C-c), and the method described in ref. (in section of Calculation of ), we obtained.74±.4 (mean ± standard deviation of 4 individual experiments), and using q. S45,.2..9±.7 and ii) roup 2: when identical probes are used for the different D-A pairs, -factors can be determined using nown - factor as standard (see section of Determination of for various D-A pairs using a standard pair in ref ). mploying this method, -factors of group 2 were determined using the -factors for group as standard. Since the difference between group and group 2 is only the quantum yield of TM, we could obtain the three values as.88,.4, and.9. eferences for Supporting Information. Clegg,. M luorescence resonance energy transfer and nucleic acids. Methods nzymol. 2: Liu, J. W. and Y. Lu. 22. T study of a trifluorophom-labeled DNAzyme. J. Am. Ch. Soc. 24: Lee, N. K., A. N. Kapanidis, Y. Wang, X. Michalet, J. Muhopadhyay,. H. bright, and S. Weiss. 25. Accurate T measurents within single diffusing biomolecules using alternating-laser itation. iophys. J. 88: Ha, T. J., A. Y. Ting, J. Liang, W.. Caldwell, A. A. Deniz, D. S. Chla, P.. Schultz, and S. Weiss Singlolecule fluorescence spectroscopy of enzyme conformational dynamics and cleavage mechanism. Proc. Natl. Acad. Sci. U. S. A. 96: Clamme, J. P. and A. A. Deniz. 25. Three-color single-molecule fluorescence resonance energy transfer. Chphysch 6: S8

9 6. Kapanidis, A. N., Y. W. bright,. D. Ludescher, S. Chan, and. H. bright. 2. Mean DNA bend angle and distribution of DNA bend angles in the CAP-DNA complex in solution. J. Mol. iol. 2: S9

10 A 4 µs rest continuous 6 µs (2 µs period) 4 µs rest 4 µs rest 4 76 µs (2 µs period) 8 6 µs (2 µs period) 52 nm 477 nm 52 nm 6 nm 477 nm 52 nm 6 nm 477 nm 52 nm 6 nm Dir DA Dir Dir 2 Dir D A L L 2 L L L 4 APD APD2 APD APD APD2 APD APD APD2 APD APD2 APD D D A D IU S. Schatic of alternating itation, observable photon issions, and crosstals of c-alx. (A) Conventional single-molecule 2-color T (2c-T) using single-laser itation. 52-nm laser ites D directly, and A indirectly via T, results in photon issions and. Two crosstals are present in 2c-T syst; Dir denotes direct itation, i.e., the direct itation of A by D itation laser, and L denotes leaage, i.e., the ission of D detected by APD2 (A ission detection channel). () c-alx. The 477-nm laser mainly ites and gives rise to non-zero photon-counts,, and ; the 52-nm laser mainly ites and gives rise to, ; and the 6-nm laser mainly ites and gives rise to. The ratios based on the six photon-counts report on three proximity-ratios ( ( S ). c-alx results in three Dir crosstals and four L crosstals. ) and three probe-stoichiometries S

11 Assigned species Photon counts Time (s) IU S2. Time-traces generated by c-alx ( ms binning; C-c of ig 2 A). represents photon counts, Y X where X denotes itation laser, 477 nm, 52 nm, and 6 nm, and Y denotes photon detector, for APD, for APD2, and for APD. APD detects dominantly the ission of, APD2 of, and APD of, respectively. The bacground noises are <.7 Hz for each detection channel. T efficiencies between and, and, and and of C-c, are approximately 42%, 4%, and 24%, respectively. ive bursts are assigned representatively in the time-traces; -- denotes triply-labeled species, while - and - denote doubly-labeled species. S

12 A C 5 C-c 5 C-b 5 Number of bursts C Number of bursts D Number of bursts IU S. -D histograms of :: mixture of C, C-c, and C-b (ig. 7 ). (A) Schatic description of three triply-labeled species. (-D) -D histograms, obtained after collapsing the burst points of -D histogram in ig. 7 to each axis. reen, lue, and ed lines represent individual aussian fits of C, C-c, and C-b, respectively, and lac lines, sum of the three aussian fits. Individual aussian fits of C, C-c, and C-b were obtained from the -D histogram; the molecules (burst points) of C, C-c, and C-b were selected graphically, respectively, and mean proximity-ratios for each species were obtained using aussian fitting. The measured proximity-ratios agree well with those measured from solutions containing a single triply-labeled species, and the ratio of molecules is.:.:.2, consistent with the initial mixing ratio. However, the three species are hardly discriminated in -D histograms, and thereby the proximity-ratios of each species and the mixing ratio are not accessible in -D histograms. S2

13 TAL S. Crosstals factors: leaage and direct itation. Crosstals L factors a l.9 l 2. l, l 4.4 Dir b d.9~.5 d 2.~.2 d.~.8 a or definition of each factor, see ig. S and Theory of c-alx. b Dir depends on the itation laser powers of three lasers. S

14 TAL S2. T efficiencies and distances in 2-color and -color ALX a -color ALX 2-color ALX b dsdna T pair (Å) ( ) c (Å) ( ) c (Å) C ±..5 ±. 8 ± 2. ±..4 ±. 84 ± ±.2.42 ±.2 68 ± 2.46 ±..45 ±. 66 ± ±..4 ±. 98 ± 5. ±. d. ±. d 5 ± 6 d C2-62. ±.. ±. 88 ± 2. ±..2 ±. 87 ± ±..5 ±. ± 4.6 ±..6 ±. 99 ± ±..22 ±. 69 ±.2 ±..22 ±. 69 ± C-a ±.2.47 ±.2 6 ±.47 ±..42 ±. 65 ± ±..2 ±. 75 ±.28 ±..4 ±. 74 ± ±..6 ±. 5 ±.57 ±.2.59 ±.2 5 ± C-b ±.. ±. 85 ± 2. ±.. ±. 88 ± ±..9 ±. 92 ± 2.9 ±.2.9 ±.2 92 ± ±..6 ±. 52 ±.58 ±..6 ±. 52 ± C-c ±.2.42 ±.2 65 ±.48 ±.2.42 ±.2 65 ± ±.. ±. 9 ±. ±..5 ±. 89 ± ±..26 ±. 67 ±.2 ±..22 ±. 69 ± a All the averages and the standard deviations were obtained from more than four individual measurent. b Three independent 2-color ALX measurents were carried for the doubly-labeled species. c : simple proximity ratio d is too small to give meaningful distance value. S4