Supplementary Information Programming Light-harvesting Efficiency Using Dna Origami

The remarkable performance and quantum efficiency of biological light-harvesting complexes has prompted a multidisciplinary interest in engineering biologically inspired antenna systems as a possible route to novel solar cell technologies. Key to the effectiveness of biological “nanomachines” in light capture and energy transport is their highly ordered nanoscale architecture of photoactive molecules. Recently, DNA origami has emerged as a powerful tool for organizing multiple chromophores with base-pair accuracy and full geometric freedom. Here, we present a programmable antenna array on a DNA origami platform that enables the implementation of rationally designed antenna structures. We systematically analyze the light-harvesting efficiency with respect to number of donors and interdye distances of a ring-like antenna using ensemble and single-molecule fluorescence spectroscopy and detailed Förster modeling. This comprehensive study demonstrates exquisite and reliable structural control over multichromophoric geometries and points to DNA origami as highly versatile platform for testing design concepts in artificial light-harvesting networks.

: Details of the fluorescent dye attachment sites on the DNA origami platform and sequences of the corresponding modified DNA strands. The origami coordinate n denotes the nucleotide number and h the helix number with respect to the origin (0, 0) as defined by the position of A1.  Normalised intensity / a.u.
We first characterised the spectroscopic properties of the antenna components without donor-to-acceptor energy transfer (see Supplementary Methods for absorption measurements). In Fig. S2a Figure S3: Single-molecule measurements. Energy transfer efficiencies obtained using single-molecule fluorescence measurements for the single donor-acceptor pairs a) A-D1 and b) A-D2 representing the two possible next-neighbour distances on the DNA origami platform.
The origami coordinates (see Table I) can be translated into theoretical distances between the dyes by assuming a nucleotide-to-nucleotide distance of 0.34 nm along the helix and an average helix-to-helix distance of 2.6 nm. 1,2 This yields theoretical next-neighbour separations of ∼5.2 nm in a perpendicular and ∼6 nm in a diagonal orientation with respect to helix direction. Using single-molecule fluorescence measurements, we quantified the energy transfer efficiency E (γ-corrected, see Supplementary Methods) between the acceptor dye and the donor dyes D1 (Fig. S3a) and D2 (Fig. S3b), respectively, representing the two possible inter-dye distances in our design. Assuming a Cy3-Cy5 Förster radius of R 0 = 5.4 nm, 3 we could estimate the next-neighbour distances experimentally, yielding    measured. The stoichiometry parameter S describes the ratio between donor and acceptor dyes of the sample and is defined as Antenna effect in dependence of number of donors obtained from single-molecule (red, AE sm tot ) and ensemble (black, AE tot ) measurements. We determined the slopes with a linear fit, yielding m ens = 0.31 for the ensemble and m sm = 0.12 for the single-molecule measurements, respectively. The error bars correspond to the standard error of the mean.
The values for AE sm tot (single-molecule) are consistently lower than for AE tot (ensemble) (Fig. 3). This can be largely explained by the dependence of the antenna effect on the excitation wavelength; in the two techniques, different excitation wavelengths were used for the acceptor molecule (λ sm A =640 nm in single-molecule and λ ens A =600 nm in ensemble measurements, respectively), see Fig. 2c. As Cy5 absorbs ∼2.8× more at λ sm A than at λ ens A (Fig. S2a), the extinction coefficient of Cy5 under the conditions of the single-molecule measurements can be written as Ξ A (λ sm A ) = 2.8 Ξ A (λ ens A ). The difference in absorptivity for Cy3 at the donor excitation wavelength (λ sm D =532 nm in single-molecule and λ ens D =521 nm in ensemble measurements, respectively) is negligible (Fig. S2a), hence we can assume Ξ D (λ sm D ) = Ξ D (λ ens D ).
The antenna effect for the single-molecule measurements can be expressed as (see Eq. (4) in and , the relationship between AE sm tot and AE tot can thus be written as The ratio between the slopes is thus expected to be We verified this by determining the slopes experimentally, as shown in Fig. S6.3. We get a ratio of m ens /m sm = 2.6, which is in very good agreement with the expected value in Eq. 3.
We can thus conclude that the antenna effect is equivalent in both measurement techniques following the correction accounting for the different excitation wavelengths. Minor sources of errors not taken into account here might arise from differences in set-up parameters such as relative light intensities and detector efficiencies. Figure S6.4: Direct comparison between single-molecule and ensemble fluorescence measurements. a) Energy transfer efficiency (E * ) obtained from single-molecule measurements. We analysed 1-donor (blue), 2-donor (green) and 6-donor (red ) samples (Fig. 1b). We screened several thousand molecules for each sample type, and used a Gaussian fit to determine the E * (data not shown). The error bars correspond to the standard deviation of the Gaussian fit. b) Energy transfer efficiency (E * ) obtained from ensemble measurements. We analysed 1-donor (blue), 2-donor (green) and 6-donor (red ) samples (Fig. 1b). Each sample was prepared in three independent replicates. The error bars correspond to the standard error of the mean.
We have determined the energy transfer efficiency E * from both single-molecule and ensemble measurements. The energy transfer efficiency is defined as where where ω D 0 (ω A 0 ) is the resonant frequency of the donor (acceptor). In the main text (see From the linear fit we obtainedα = Φ D /Φ A = 0.606 and q = 0.006 (see Model in the main text).
We now study the relation AE tot = AE tot (N ) without using any fitting parameter, evaluating the ratio Φ D /Φ A using experimental values for the molar extinction coefficients. The Exciting both dyes at their maximum absorption wavelengths (λ 0

S8 Detailed model
We model the energy transfer from the antenna complex to the common acceptor core using a set of rate equations governing the dynamics of the populations of the donor and acceptor chromophores, under external laser excitation and hetero-FRET interaction. This treatment assumes that only one particle (i.e. one excitonic quasiparticle in this case) is present in the system at any time, which is valid for the low excitation conditions under which the experiments have been carried out.
Let then ρ A , ρ D be the populations of the excited states of the acceptor (A) and the donor (D), respectively. For a single donor-acceptor pair, the temporal evolution of the exciton population is then described by the following rate equations: where Γ DA is the pairwise hetero-FRET rate constant between the donor and the acceptor dyes, and Γ D (Γ A ) the radiative recombination rats of the donor (acceptor), respectively.
The FRET rate Γ DA depends on the lifetime of the donor excited state (τ D = 1/Γ D ) and the donor-acceptor separation (R): where R 0 is the Förster radius, i.e. the donor-acceptor separation corresponding to a FRET efficiency E(R) equal to 50%: where κ 2 is the dipole orientation factor, which is equal to 2/3 for quasi-random dipole orientations, n is the refractive index of the medium, QY D is the fluorescence quantum yield of the donor and J is the spectral overlap integral between the emission spectrum of the donor and the absorption spectrum of the acceptor.  to findρ A,A * . Such a pump term can be written as

The antenna effect is given by AE
where α(ω) is the absorption coefficient, ω 0 the resonant frequency of the donor/acceptor molecule, and I inc = 1 2 ε 0 cE 2 0 is a cycle averaged intensity of the incident radiation driving the oscillator ω 0 .
We then get:ρ The antenna effect can be written in terms of the molar extinction coefficient Ξ(ω), where α = c mol Ξ, c mol being the molar concentration: This is the most general expression of the antenna effect. If one assumes equal incident photon fluxes (F = I inc / ω) for the excitation of donors (at wavelength λ D ) and acceptors (at wavelength λ A ), F D (λ D ) = F A (λ A ) and thus I D inc (λ D )/I A inc (λ A ) = λ A /λ D , which yields When more than one donor is present, as in the ring antenna system examined here, the system Eqs. (8)(9) scales up with total number N of donor dyes D i (i = 1, ..., N ): In the case of identical donors (Γ D i = Γ D ∀ i) located at a same distance from the acceptor , the cumulative antenna effect (AE tot ) simply scales with N , In the analysis developed above we have not considered the homo-FRET interaction between the donor dyes. We have assumed that the (identical) donor dyes are (i) equally spaced within the ring, so that the homo-FRET rates between a dye and its first nearest neighbours are Γ DD being the homo-FRET rate. For the ring structure, we assume that all the donors D i are (i) located at the same distance R from the acceptor A, so that Γ D i A (R i ) = Γ DA (R) ∀i (see Fig. S8) and (ii) equally spaced on the ring so that Γ D i D i+1 = Γ D i−1 D i = Γ DD ∀i. The ring-shaped antenna assembled on the DNA origami plate is a good approximation of such an idealised geometry.
For the wire configuration, we consider again equally spaced dyes with inter-dye sep-aration equal to R. In this case the separation between each i−th dye and the acceptor is R i = iR, i = 1, ..., N (see Fig. S8), and the hetero-FRET decay rates are given by   Figure S9: Theoretical model. Difference between the averaged AE tot (R) and the exact expression AE(R 1 )+AE(R 2 ) for increasing differences δR between the single donor-acceptor separations R 1 and R 2 (δR = R 2 − R 1 ).
To analyse the cumulative antenna effect (AE tot ) in the two-donor configuration (see Model in Methods) we introduced the average donor-acceptor separationR, where R 1 = R + δR R 2 =R − δR. Then, we approximated AE tot = AE(R 1 ) + AE(R 2 ) with AE tot (R), see Eq. (5) in Methods. Figure S9 shows how the averaged AE tot (R) differs from the exact expression AE(R 1 )+AE(R 2 ) for increasing differences δR between the single donor-acceptor separations R 1 and R 2 (δR = R 2 − R 1 ). In this simulation we considered a Förster radius

Absorbance measurements in bulk
Absorbance measurements were performed using a Cary 300 Bio UV-Visible Spectrophotometer (Agilent Technologies). The Cy3-and Cy5-labelled staple strands were diluted to a final concentration of ∼ 500 nM in 1 × TE in a low volume cuvette (∼100 µl) (Sigma-Aldrich). Absorbance spectra were recorded over a wavelength range of 350-700 nm and normalised with the blank solution (1 × TE).

Data analysis of single-molecule fluorescence measurements
The data received from the fluorescence measurements are analysed by using a burst search algorithm. 7 We subtracted the background signals from the photon counts and extracted the leakage value from the donor only population and the direct excitation factor from the acceptor-only population according to N. K. Lee et al. 8 The E-values are corrected with the detection correction factor γ to take into account differing detection efficiencies and quantum yields of the dyes. The E-S-histograms are further filtered by using ALEX-2CDE and FRET-2CDE filters. 9