# Combined Fluorescence Fluctuation and Spectrofluorometric Measurements Reveal a Red-Shifted, Near-IR Emissive Photo-Isomerized Form of Cyanine 5

^{*}

## Abstract

**:**

## 1. Introduction

_{iso}), while the fluorescence quantum yield (Φ

_{f}) is relatively low compared to other fluorophore labels. Intersystem crossing to a triplet state typically competes with photo-isomerization and takes place with a low quantum yield (Φ

_{isc}), which often can be disregarded. The photo-isomerization is highly dependent on the local environment and is reduced by increased viscosity [3], increased viscous drag by head group substituents [22], and steric constraints upon binding to, e.g., proteins [23]. However, despite extensive research, many photophysical mechanisms of cyanine dyes remain elusive.

## 2. Results

#### 2.1. FCS and TRAST Experiments

#### 2.2. Photophysical Model Based on the FCS and TRAST Experiments

_{1}), this model also includes an emissive, double-cis conformation (P

_{2}), which is formed from P

_{1}. Such a P

_{2}state, formed with a two-step photo-induced process, is not typically found in (one-step) flash photolysis or transient absorption experiments but can be identified with, and has been inferred from, photokinetic steady-state fluorescence and absorption measurements [18]. In such a model, Cy5 can, in principle, reversely photo-isomerize between the N and P

_{2}states via two (mono-)cis states. For simplicity, however, we represent these two states as one mono-cis state in our model. The resulting three-state model of Figure 4B was then used as a basis for fitting the recorded FCS and TRAST curves (see the caption for a description and definition of fitted parameters). The effective rates and the differential equations governing the population of the N, P

_{1}, and P

_{2}states are described in Supplementary Information, Section S3 (Equations (S1)–(S8)).

#### 2.3. Experimental FCS and TRAST Data Fitted to the Photophysical Model

_{2}, Q, to 0. Likewise, with Q = 0, emission will only be detected following decay to the ground state of N. It should be borne in mind that FCS curves generally reflect the probability to detect a fluorescence photon from a molecule at correlation time, τ, given that a fluorescence photon was detected from the same molecule at τ = 0. The initial condition thus should reflect the probabilities of detecting a fluorescence photon from any of the states N, ${P}_{1}$, and ${P}_{2}.$ For the B-filter curves, Q = 0, and fluorescence photons can thus only be detected from N, and the initial condition is $\left[\left[N\right]\left(\overline{r},0\right),\left[{P}_{1}\right]\left(\overline{r},0\right),\left[{P}_{2}\right]\left(\overline{r},0\right)\right]=\left[1,0,0\right]$, as stated in Equation (S5). However, for FCS curves recorded with the R-filter, different initial conditions for the state populations across the FCS detection volume $\left[N\right]\left(\overline{r},t\right),\left[{P}_{1}\right]\left(\overline{r},t\right)$ and $\left[{P}_{2}\right]\left(\overline{r},t\right)$ apply. For FCS curves recorded with the R-filter, ${P}_{2}$ has a relative brightness of Q compared to N. The initial condition then reflects the probabilities that a detected fluorescence photon comes from N or P

_{2}and can be approximated by:

_{2}states, respectively, at a location $\overline{r}$ in the FCS detection volume. In the fitting of the FCS curves in Figure 2, we thus used the initial condition of Equation (1) as the initial condition for the state populations across the FCS detection volume for the R-filter curves and Equation (S5) for the B-filter curves. Since Q is included in the initial condition, Q was fitted globally (to the R-filter curves) in an iterative manner, with the initial condition of Equation (1) updated with each iteration until a stable Q-value was reached. For all FCS curves, given the relatively high ${\mathsf{\Phi}}_{exc}$ levels applied in the FCS experiments, the contribution from the thermal back-isomerization rates, ${k}_{biso1}^{Th}$ and ${k}_{biso2}^{Th}$, could be neglected compared to the excitation-driven contributions to the effective back-isomerization rates, ${k}_{biso1}\xb4$ and ${k}_{biso2}\xb4$. ${k}_{biso1}^{Th}$ and ${k}_{biso2}^{Th}$ could thus be fixed to 0 in the fit. Finally, in the fit, ${\sigma}_{N}$ was fixed to 6.2$\times {10}^{-16}$ cm

^{2}(from [32], scaled by the absorption spectrum to obtain ${\sigma}_{N}$ at 638 nm) and ${\tau}_{F}$ to 1.0 ns, as obtained with TCSPC measurements (Figure S2). With these prerequisites, initial conditions, and fixed parameter values, global fitting based on Equation (10), and including both sets of FCS curves in Figure 2, could then successfully reproduce the experimental curves and yielded the following parameter values: ${k}_{iso}$ = 36 µs

^{−1}, ${\sigma}_{biso1}=0.25\times {10}^{-16}$ cm

^{2}, ${\sigma}_{iso2}=0.31\times {10}^{-16}$ cm

^{2}, ${\sigma}_{biso2}=0.25\times {10}^{-16}$ cm

^{2}, and $Q=0.46$.

^{2}and ${k}_{10}^{N}$ = 1/${\tau}_{f}$ − ${k}_{iso}$, with ${\tau}_{f}$ fixed to 1.0 ns. For the TRAST curves recorded with the B-filter, Q was fixed to 0 (for the same reasons as given before for the FCS fitting), while for the curves recorded with the R-filter, Q was fitted globally. For the fitting of the TRAST curves, and irrespective of the emission filter used, the same initial condition for the state populations could be applied (Equation (S5)). The fitting (to Equations (2)–(4)) resulted in curves that could successfully reproduce the experimental TRAST curves and yielded the following parameter values: ${k}_{iso}$ = 33 µs

^{−1}, ${\sigma}_{biso1}=0.26\times {10}^{-16}$ cm

^{2}, ${\sigma}_{iso2}=0.3\times {10}^{-16}$ cm

^{2}, ${\sigma}_{biso2}=0.25\times {10}^{-16}$ cm

^{2}, ${k}_{th1}$ = 0.015 µs

^{−1}, ${k}_{th2}$ = 0.08 µs

^{−1}, and $Q$ = 0.28 (for the TRAST curves recorded with the R-filter). The fitted parameter values are also in good agreement between the FCS and TRAST data. While $Q$ can be different in the FCS and TRAST experiments, due to possible differences in detection quantum yields between the setups used (Equation (2)), the fitted values indicate that such differences are small. It can be noted that the overall isomerization amplitudes show up differently in FCS than in TRAST experiments and with a larger contrast between the amplitudes in the FCS curves for the different emission filters used. This follows from the different initial conditions that apply in FCS versus TRAST experiments, the different weighting (by Q

^{2}for the FCS curves (Equation (10)), by Q only for the TRAST curves (Equations (2)–(4)), and different ${\mathsf{\Phi}}_{exc}$ levels applied in FCS and TRAST experiments.

_{1}, and P

_{2}state populations of Cy5 can evolve upon excitation, based on the fitted parameter values, and considering different excitation intensities applied, further illustrating how the underlying state population kinetics contribute to the observed relaxations in the TRAST experiments. Figure 4D shows how the N, P

_{1}, and P

_{2}state populations depend on ${\mathsf{\Phi}}_{exc}$ at CW excitation. It can be noted that for ${\mathsf{\Phi}}_{exc}$ < 5 kW/cm

^{2}, the populations are clearly ${\mathsf{\Phi}}_{exc}$ dependent, while for a higher ${\mathsf{\Phi}}_{exc},$ no major effects on the steady-state are found. At ${\mathsf{\Phi}}_{exc}$ approaching 100 kW/cm

^{2}, however, excited-state saturation effects set in, particularly in N (having the longest excited-state lifetime).

#### 2.4. Spectral-TRAST Experiments

## 3. Discussion

_{1}, and then from P

_{1}an additional, double-photo-isomerized state, P

_{2}, with both its excitation and emission spectra red-shifted compared to its all-trans state, N. Since P

_{2}is generated with a two-step photo-induced process, it is not expected to be clearly seen and has generally also not been reported from (one-step) flash photolysis or transient absorption experiments of pentamethine cyanine dyes. However, it has been implicated from a few photokinetic steady-state fluorescence and absorption studies [18]. From our experimental data and their analyses, we cannot fully exclude other photokinetic models of Cy5 than the three-state isomerization model of Figure 4B. Delayed fluorescence following triplet-state formation has been reported from Cy5 in deoxygenated ethanol solutions [9,39]. However, triplet states are effectively quenched with molecular oxygen under our experimental conditions, in air-saturated aqueous solutions. Moreover, the intersystem crossing yields of Cy5 are more than an order of magnitude lower than for isomerization and back-isomerization [32], and triplet state formation can thus be disregarded in our model. However, it is also possible to fit the experimental FCS and TRAST curves with a two-state isomerization model (Supplementary Information, Section S4) instead of the three-state model of Figure 4B. In such two-state model, with P

_{1}and P

_{2}merged into one photo-isomerized state, P, the merged P state may either indeed represent a single weakly fluorescent mono-cis state or a time average of one or several photo-isomerized forms and a double-photo-isomerized form of Cy5 (red-marked in Figure 4B). However, given that photo-isomerized, mono-cis conformations of pentamethine cyanine dyes typically have been found to exhibit low fluorescence [3,12,13,14,24], the three-state model of Figure 4B is the simplest model to incorporate such features. Moreover, irrespective of the underlying mechanisms and model, the implications of the experimental findings are in several aspects the same. Our data (Figure 4D) show that the formation of a red-shifted, emissive photo-isomerized state of Cy5 can take place at quite moderate excitation intensities (below kW/cm

^{2}), with a concomitant, red-shifted emission spectrum. This may have to be accounted for in multi-color imaging and spectroscopy experiments with Cy5, based on, e.g., linear unmixing, as well as in Förster resonance energy transfer (FRET) experiments, where the spectral shape of Cy5 also matters for a correct interpretation of the data. The added knowledge of Cy5 photo-isomerization provided in this work can also be useful for optimization of excitation conditions in SMS and SRM experiments. Moreover, knowledge of the photodynamics of Cy5, as presented in this work, can be used to design excitation strategies to specifically promote the formation of more red-shifted emission in Cy5. Cy5 with a more red-shifted, NIR emission may enable fluorescence measurements with lowered background and scattering, or the use of Cy5 as a NIR photosensitizer. From a methodological point of view, the parallel use of TRAST and FCS in this work makes it, on the one hand, possible to map the photodynamics of Cy5 with two independent techniques and, on the other hand, also to obtain complementary data. Particularly, with TRAST, lower excitation intensities can be applied, slower isomerization relaxation times can be studied (beyond the typical passage times of Cy5 through the FCS detection volume), and thermal back-isomerization rates can be determined. We showed how the relative brightness of the generated photo-induced states and the initial conditions for their populations come differently into play in FCS and TRAST analyses, also depending on the experimental conditions. This provides a framework for analyses of FCS and TRAST measurements, including photo-induced emissive states kinetics, in cyanine dyes as well as in other fluorophores. The fact that the FCS and TRAST curves could be fitted to the same photophysical model, and that fitting generated similar fitted parameters, gives further support to the experiments and these analyses.

^{−1}and 33 µs

^{−1}, respectively. This is close to previously reported FCS data (with ${k}_{iso}$ reported to be 25 µs

^{−1}[32]). As shown in this work, the lower the relative brightness difference between the switched states, the smaller the relaxation amplitudes in experimental FCS and TRAST curves. The formation rates and populations of partly emissive states will thus be underestimated in FCS and TRAST experiments if they are considered fully non-emissive. Additionally, the emissive photo-isomerized state, as found for Cy5 in this work, likely also needs to be taken into consideration in a broad range of SMS, SRM, FRET, and multi-color experiments in which Cy5 is used.

## 4. Materials and Methods

#### 4.1. Sample Preparation

#### 4.2. TRAST Experiments

_{0}= 20 µm (1/e

^{2}radius)). The fluorescence signal was collected with the same objective, passed through the same dichroic mirror and an emission filter (HQ720/150, Chroma, 680 nm blocking edge Brightline, Semrock, in combination with the last-mentioned filter or 710/40 Brightline, Semrock), and then fed to an sCMOS camera (Hamamatsu ORCA-Flash4.0 V3). The experiments were controlled and synchronized with custom software implemented in Matlab. A digital I/O card (PCI-6602, National Instruments) was used to trigger the camera and generate random excitation pulse trains sent to the AOM driver unit. For the spectral experiments, a function generator was used for AOM triggering and generation of the different pulse durations. The fluorescence signal was passed through an aperture (centered around the emission intensity maximum and with 23% of the fluorescence passing through, ensuring that only fluorescence from the center of the excitation volume is detected by the camera), passed through an emission filter (647 nm RazorEdge, Semrock ultrasteep long-pass-edge filter), and then focused into the multimode fiber (diameter 600 µm) of a fiber-coupled spectrometer (QEPro, Ocean Optics). The obtained emission spectra were corrected by normalizing them with the wavelength detection efficiency function and the grating efficiency for different wavelengths, since this is not completely uniform over the spectral width of the Cy5 emission spectrum.

#### 4.3. TRAST Analysis

_{2}, and with the two (mono-)cis states of Cy5 non-luminescent, and for simplicity represented as one state, P

_{1}. For a homogeneous solution sample, and from the rate equations of a Cy5 fluorophore subject to a rectangular excitation pulse starting at t = 0 (Supplementary Information, Section S3, Equations (S1)–(S8)), the fluorescence signal recorded in our experimental setup can be described by

_{2}compared to N, where ${}_{}{}^{1}q{}_{D}$ and ${}_{}{}^{2}q{}_{D}$ denote the overall detection quantum yield of the emission from the excited singlet state of N and P

_{2}, respectively, and ${}_{}{}^{1}q{}_{F}$ and ${}_{}{}^{2}q{}_{F}$ are the fluorescence quantum yields of these states. ${\sigma}_{N}$ and ${\sigma}_{{P}_{2}}$ denote the excitation cross section of the ground singlet state of N and P, respectively; $CEF\left(\overline{r}\right)$ is the collection efficiency function of the detection system; and $c$ is the fluorophore concentration.

_{0}before the onset of the next pulse. In the normalization step of Equation (4), several parameters used to calculate $F\left(t\right)$ in Equation (2) cancel out. The final expression for $\langle {F}_{exc}{\left(w\right)\rangle}_{norm}$ therefore becomes independent of $c$, as well as of the absolute ${q}_{D}$ and ${q}_{F}$ values for the two emissive species.

_{2}are accounted for in the relative brightness parameter, Q (Equation (2)), but could only be indirectly determined for P

_{2}(as part of a back-isomerization cross section, see the Results section). For N, an average singlet excitation rate, ${\widehat{k}}_{01}$, was calculated for each ROI using Equation (S9), as previously described [33,36,41,42] (see also Supplementary Information, Section S5 for details) using an excitation cross section of ${\sigma}_{N}=6.2\times {10}^{-16}{\mathrm{cm}}^{2}$ [32] (at 638 nm excitation).

#### 4.4. FCS Experiments

^{2}radius) of a 638 nm laser (LDH-D-C-640 from PicoQuant GmbH, Berlin, Germany) in continuous wave. The emitted fluorescence was collected back through the microscope objective (UPlanSApo 60x/1.2 w, Olympus, Tokyo, Japan), passed through a dichroic mirror (ZT405/488/635rpc-UF2, Chroma), an emission filter (HQ720/150, Chroma, 680 nm blocking edge Brightline, Semrock, in combination with last mentioned filter or 710/40 Brightline, Semrock), and focused onto a pinhole (50 µm diameter) in the back focal plane. The fluorescence signal was finally split and directed on two avalanche photodiodes (Tau-SPAD, PicoQuant GmbH, Berlin, Germany), whose signals were collected with a data acquisition card (Hydraharp 400, Picoquant, Berlin, Germany).

#### 4.5. FCS Analysis

_{0}and S

_{1}, together with ${\sum}_{i=1}^{n}\left[{A}_{i}\left(\overline{r}\right)\right]$, equals 1.

_{1}) state, and assuming uniform excitation conditions within the FCS detection volume, the recorded autocorrelation curves (FCS curves) can be expressed as [32,43]

_{1}in the detection volume upon excitation, and ${\tau}_{iso}$ is the average isomerization relaxation time. For recorded FCS curves fitted to Equation (8),${N}_{m}$, ${A}_{iso}$, ${\tau}_{iso}$, ${\tau}_{D},$ and $S={\omega}_{z}/{\omega}_{0}$ were used as fitted parameters, with the fitting based on a non-linear least squares optimization routine written in Matlab.

_{1}) and an emissive double-cis (P

_{2}) conformation, as described by the model of Figure 4B, Equation (7) changes into:

_{1}, and P

_{2}for i = 1, 2, and 3, respectively, and ${\lambda}_{i}\left(\overline{r}\right)$ are the corresponding relaxation rates/eigenvalues. $W\left(\overline{r}\right)$ refers to the molecular brightness of N, and Q is the relative brightness of P

_{2}compared to N, as defined in Equation (2). With the population probabilities for N, P

_{1}, and P

_{2}after onset of constant excitation, ${\mathsf{\Phi}}_{exc}\left(\overline{r}\right),$ at time $t=0$, $\left[N\right]\left(\overline{r},t\right),\left[{P}_{1}\right]\left(\overline{r},t\right)$, and $\left[{P}_{2}\right]\left(\overline{r},t\right)$, defined as in Supplementary Information, Section S1 (Equations (S1)–(S8)), Equation (9) can be written as:

_{2}(also denoted ${A}_{1}\left(\overline{r}\right)$ and ${A}_{3}\left(\overline{r}\right)$ before), respectively. The fitting of photophysical rate parameters was then performed with a program written in Python, simulating theoretical FCS curves using Equation (10) and comparing them to the experimental data. Similar to the fitting of the experimental TRAST curves, the set of rate parameter values best describing the experimental data was then found using non-linear least squares optimization. In the fit, the excited-state lifetimes, ${\tau}_{f}$, of N and P

_{2}were fixed to fitted values determined with TCSPC measurements (see the Results section). In the fits, the ratio of $S={\omega}_{\mathrm{z}}/{\omega}_{0}$ was fixed to 6.8 and ${\tau}_{D}$ was fitted as an individual parameter to the separate curves.

#### 4.6. Fluorescence Lifetime Measurements

## Supplementary Materials

**Section S1:**FCS curves recorded with excitation at different wavelengths;

**Section S2:**Fluorescence decay measurements of Cy5 with time-correlated single-photon counting (TCSPC);

**Section S3:**Electronic state model equations for Cy5 (with Equations (S1)–(S8));

**Section S4:**TRAST and FCS data fitted to a two-state photo-isomerization model;

**Section S5:**Spatial distribution of excitation rates and calculation of average rates in the TRAST experiments (with Equation (S9)).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Experimental FCS curves (thin lines) recorded at 638 nm excitation (mean ${\mathsf{\Phi}}_{exc}$ 21 kW/cm

^{2}), with the emission filter used as specified in the legend. The curves were individually fitted to a two-state model (one dark state; thick solid lines) using Equation (8). Fitted amplitudes decreased with more red-shifted emission filters used (0.61, 0.54, 0.44), while the relaxation times did not significantly change (isomerization relaxation time, ${\mathsf{\tau}}_{iso}$, 0.6 µs). Fitting residuals are shown in the lower subplot.

**Figure 2.**FCS curves recorded under different mean ${\mathsf{\Phi}}_{exc}$ (638 nm excitation) and using two different emission filters: 645–680 nm (B-filter, data: thin solid lines; fitted curves: dim thick lines) and 690–750 nm (R-filter, data: dotted lines; fit: thick dashed lines). The FCS curves were fitted globally, as described in the main text. Fitting residuals are shown in the lower subplot.

**Figure 3.**TRAST curves recorded under different mean ${\mathsf{\Phi}}_{exc}$ (638 nm excitation) and using two different emission filters: 645–680 nm (B-filter, data: dim circles; fitted curves: dim thick lines) and 690–750 nm (R-filter, data: circles; fit: thick dashed lines). The TRAST curves were globally fitted, as described in the main text. Fitting residuals are shown in the lower subplot.

**Figure 4.**(

**A**) Potential energy curve diagram for photo-isomerization of Cy5, where the energies of the ground and excited singlet states are represented as functions of the total torsion angle ($\mathsf{\Theta}$) and which includes an all-trans (N), a mono-cis (P

_{1}), and a double-cis (P

_{2}) conformation. N is excited with a rate ${\sigma}_{N}{\Phi}_{exc}$ from the singlet ground state ${S}_{{0}_{}}$ to the singlet excited state ${S}_{{1}_{}}$. The ${S}_{{1}_{}}$ state of N can decay back to the ${S}_{{0}_{}}$ state with a rate ${k}_{10}^{N}$, with a fluorescence quantum yield of ${\Phi}_{f}^{N}$, or it can transfer to a twisted intermediate state ${T}_{{W}_{1}},$ with a yield of ${\Phi}_{1{T}_{{W}_{1}}}$. The effective isomerization rate is then given by ${k}_{iso1}={\Phi}_{1{T}_{{W}_{1}}}{k}_{10}^{N}\alpha $, where $\alpha $ is the branching ratio of the ${T}_{{W}_{1}}$ state to go into P

_{1}(and 1- $\alpha $ the corresponding branching ratio to go back to N). Similarly, P

_{1}is excited with a rate ${\sigma}_{{P}_{1}}{\Phi}_{exc}$ from its ${S}_{{0}_{}}$ state to its ${S}_{{1}_{}}$ state. The ${S}_{{1}_{}}$ state can decay back to the ${S}_{{0}_{}}$ state with a rate ${k}_{10}^{{P}_{1}}$, with a fluorescence quantum yield of ${\Phi}_{f}^{{P}_{1}}$, or it can transfer to any of the twisted intermediate states ${T}_{{W}_{1}}$ and ${T}_{{W}_{2}}$ and undergo back-isomerization to N or a second isomerization to P

_{2}, with rates ${k}_{biso1}={\Phi}_{2{T}_{{W}_{1}}}{k}_{10}^{{P}_{1}}\left(1-\alpha \right)$ and ${k}_{iso2}={\Phi}_{2{T}_{{W}_{2}}}{k}_{10}^{{P}_{1}}\left(\beta \right)$, respectively, where $\beta $ is the branching ratio of the second twisted intermediate state ${T}_{{W}_{2}}$. Finally, P

_{2}is excited with a rate ${\sigma}_{{P}_{2}}{\Phi}_{exc}$ from its ${S}_{{0}_{}}$ state to its ${S}_{{1}_{}}$ state, ${k}_{10}^{{P}_{2}}$ denotes the decay rate back to ${S}_{{0}_{}}$, and ${\Phi}_{f}^{{P}_{2}}$ is the fluorescence quantum yield of P

_{2}. From its ${S}_{{1}_{}}$ state, P

_{2}can transfer to the twisted intermediate state ${T}_{{W}_{2}}$ and undergo back-isomerization to P

_{1}, with a rate ${k}_{biso2}={\Phi}_{3{T}_{{W}_{2}}}{k}_{10}^{{P}_{2}}\left(1-\beta \right)$. From both P

_{1}and P

_{2}, thermal back-isomerization from their ${S}_{{0}_{}}$ states can take place with the rates ${k}_{biso1}^{Th}$ and ${k}_{biso2}^{Th}$, respectively. In the model, and in our studies of Cy5, intersystem crossing from any of the ${S}_{{1}_{}}$ states of N, P

_{1}, and P

_{2}to a triplet state can be neglected. Given the short (1.0 ns) excited-state lifetime of Cy5, excited singlet-state populations will be low for the ${\Phi}_{exc}$ applied, particularly in the TRAST experiments. Consequently, the effective rates of intersystem crossing will be low compared to typical triplet-state decay rates found in air-saturated aqueous solutions (~0.5 µs

^{−1}) [31,32]. Moreover, intersystem crossing will also be effectively outcompeted by the higher isomerization and back-isomerization rates of the N, P

_{1}, and P

_{2}states. (

**B**) Simplified three-state photo-isomerization model based on the model in Figure 4A and used to fit the recorded FCS and TRAST curves in Figure 2 and 3. In the TRAST and FCS experiments, the transitions between the N, P

_{1}, and P

_{2}states occur on a timescale of µs or longer, much longer than the equilibration between the ground and excited singlet states within the N, P

_{1}, and P

_{2}states upon onset of excitation light (their anti-bunching times), which takes place in the ns time range. Hence, in the model, we only need to consider the effective rates of isomerization and back-isomerization, with ${k}_{iso1}\u2019={k}_{iso1}{\sigma}_{N}\xb7{\Phi}_{exc}/{k}_{10}^{N}$ and ${k}_{iso2}\u2019={\sigma}_{iso2}{\Phi}_{exc}$ denoting the isomerization rates from N to P

_{1}and from P

_{1}to P

_{2}, respectively, and ${k}_{biso1}\xb4={\sigma}_{biso1}{\Phi}_{exc}+{k}_{biso1}^{Th}$ and ${k}_{biso2}\xb4={\sigma}_{biso2}{\Phi}_{exc}+{k}_{biso2}^{Th}$ denoting the back-isomerization rates from P

_{1}to N and from P

_{2}to P

_{1}, respectively. Here, ${k}_{iso1}$ is the isomerization rate from the excited singlet state of N to P

_{1}, and ${\sigma}_{iso2}$, ${\sigma}_{biso1}$, and ${\sigma}_{biso2}$ represent cross sections for P

_{1}-to-P

_{2}isomerization, P

_{1}-to-N back-isomerization, and P

_{2}-to-P

_{1}back-isomerization, respectively, as defined in Supplementary Information, Section S3 (Equations (S3)–(S4)). ${k}_{biso1}^{Th}$ and ${k}_{biso2}^{Th}$ denote the thermal back-isomerization rates from P

_{1}to N and from P

_{2}to P

_{1}, respectively. Here, given that most cyanine dyes are in an all-trans (N) conformation at thermodynamic equilibrium [1,24,32], we neglect any thermal isomerization within Cy5 and thus assume that it fully returns to its N state in the absence of excitation. Finally, in the fitting of the parameter values of the model of Figure 4A to the experimental TRAST and FCS curves, the fluorescence quantum yields, as given in Figure 4A, are set to ${\Phi}_{f}^{N}={}_{}{}^{1}q{}_{F}$, ${\Phi}_{f}^{{P}_{2}}=0$ and ${\Phi}_{f}^{{P}_{2}}={}_{}{}^{2}q{}_{F}$, i.e., with P

_{1}non-emissive, and with the relative fluorescence brightness of P

_{2}compared to N given by $Q=({}_{}{}^{2}q{}_{F}{}_{}{}^{2}q{}_{D}{\sigma}_{{P}_{2}})/({}_{}{}^{1}q{}_{F}{}_{}{}^{1}q{}_{D}{\sigma}_{N})$, Equation (2), and where Q also was included as a fitting parameter in the fitting of the FCS and TRAST curves in Figure 1 and Figure 2. As a possible model, we also discuss a two-state model, with P

_{1}and P

_{2}merged into one photo-isomerized state, P (marked with a red-dotted square in the figure). The merged P state may represent either a single, weakly fluorescent mono-cis state or a time average of one or several photo-isomerized forms and a double-photo-isomerized form of Cy5. See also Supplementary Information, Section S4, and the main text for discussion. (

**C**) Calculated populations of N, P

_{1}, and P

_{2}over time after onset of excitation at 638 nm, and based on the fitted parameters, as specified in the main text. The color (see legend) indicates which state is calculated; increasing color intensities represent a higher ${\mathsf{\Phi}}_{exc}$ applied. The ${\mathsf{\Phi}}_{exc}$ values used in the calculations were 1.2, 2.4, 3.6, and 4.7 kW/cm

^{2}. Black curves represent the resulting weighted normalized fluorescence contribution from the fluorescent states N and P

_{2}. (

**D**) Calculated steady-state populations within Cy5 upon CW excitation, based on rates and cross sections, as obtained from fitting of the experimental FCS and TRAST curves in Figure 2 and Figure 3 to the model in Figure 4B. The steady-state populations are plotted versus ${\mathsf{\Phi}}_{exc}$. Colors in the legend indicate which state population is calculated. The steady-state is affected by thermal rates in the ${\mathsf{\Phi}}_{exc}$ range typically used in TRAST experiments (<5 kW/cm

^{2}), but for the ${\mathsf{\Phi}}_{exc}$ range used in the FCS experiments (≥4 kW/cm

^{2}), they have a small impact on the steady-state populations of N, P

_{1}, and P

_{2}.

**Figure 5.**Spectral-TRAST measurements of Cy5 in PBS solution (12 mM, pH 7.2) at 638 nm excitation. The spectra in (

**A**–

**B**) are measured at ${\mathsf{\Phi}}_{exc}$ = 3.9 kW/cm

^{2}using excitation pulse trains with a constant duty cycle of 0.002 and with different pulse widths, w. (

**A**) Emission spectra obtained for different w (specified in legend), normalized with the emission maximum retrieved at 100 ns. (

**B**) Emission spectra obtained for different w (specified in legend), normalized with the emission maximum for each curve. (

**C**) TRAST curves generated from fluorescence within different spectral windows of the spectra in (

**A**) and with the different spectral windows specified in the legend. The TRAST curves were normalized so that the fluorescence intensity recorded with w = 100 ns within the different spectral windows (blue curve in (

**A**)) was set to unity.

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## Share and Cite

**MDPI and ACS Style**

Sandberg, E.; Piguet, J.; Liu, H.; Widengren, J.
Combined Fluorescence Fluctuation and Spectrofluorometric Measurements Reveal a Red-Shifted, Near-IR Emissive Photo-Isomerized Form of Cyanine 5. *Int. J. Mol. Sci.* **2023**, *24*, 1990.
https://doi.org/10.3390/ijms24031990

**AMA Style**

Sandberg E, Piguet J, Liu H, Widengren J.
Combined Fluorescence Fluctuation and Spectrofluorometric Measurements Reveal a Red-Shifted, Near-IR Emissive Photo-Isomerized Form of Cyanine 5. *International Journal of Molecular Sciences*. 2023; 24(3):1990.
https://doi.org/10.3390/ijms24031990

**Chicago/Turabian Style**

Sandberg, Elin, Joachim Piguet, Haichun Liu, and Jerker Widengren.
2023. "Combined Fluorescence Fluctuation and Spectrofluorometric Measurements Reveal a Red-Shifted, Near-IR Emissive Photo-Isomerized Form of Cyanine 5" *International Journal of Molecular Sciences* 24, no. 3: 1990.
https://doi.org/10.3390/ijms24031990