Frequency-domain phase fluorometry in the presence of dark states: A numerical study

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Abstract

Fluorescence anomalous phase advance (FAPA) is a newly discovered spectroscopy phenomenon: instead of lagging behind the modulated light, fluorescence signal can exhibit FAPA as if it precedes the excitation source in time. While FAPA offers a promising technique for probing dark state lifetime, the underlying mechanism is not fully elucidated. Herein we investigate frequency-domain phase fluorometry as a result of intricate interplay between a short-lived fluorescent state and a long-lived dark state. In particular, the quantitative dependence on modulation frequency, excitation intensity, nonradiative decay, intersystem crossing and dark-state lifetime are explored respectively. A comprehensive view of phase fluorometry emerges consequently.

Highlights

► Fluorescence anomalous phase advance arises due to dark state hysteresis. ► Phase fluorometry quantitatively depends on multiple properties of dark state. ► Dark states enrich the behaviors of classical frequency-domain phase fluorometry.

Introduction

Fluorescence spectroscopy is one of the most widely used spectroscopic tools in various areas of science and technology [1], [2]. Unlike fluorescence intensity, the fluorescence lifetime of the fluorophore reflects its intrinsic photophysical properties that are independent of fluorophore concentration, photobleaching and excitation condition. More importantly, fluorescence lifetime is extremely sensitive to the surrounding environment including molecular binding, excited-state quenching, local viscosity, solvent polarity, ion strength, refractive index and energy transfer [3], [4], [5], [6]. As such, complementary to the popular fluorescence-intensity-based measurements, fluorescence lifetime spectroscopy has played a unique and important role in providing valuable information about the local physicochemical environment of fluorophores [1], [2], [3], [4], [5], [6], [7], [8]. For example, fluorescence lifetime imaging microscopy (FLIM) has flourished as a powerful tool in optical imaging [4], [5], and fluorescence lifetime of individual fluorophore/protein complex has been monitored in real time to reveal conformational fluctuation dynamics [8].

Commonly, there exist two distinct approaches to measure the fluorescence lifetime: the time domain and the frequency domain methods. The time domain measurement makes use of a train of short pulses of light (normally femtoseconds or picoseconds) to excite the sample repeatedly and then records the time-dependent fluorescence decay profile that follows the pulsed excitation, from which the fluorescence lifetime can be deduced. To the contrary, in frequency domain fluorescence lifetime measurement, commonly referred to as phase fluorometry, the sample is excited by a sinusoidally modulated continuous wave light source and the resulting modulated fluorescence is subsequently monitored and analyzed. The present study mainly deals with the frequency domain phenomenon.

The conventional wisdom about phase fluorometry is that, owing to the finite and non-vanishing fluorescent lifetime τ of the fluorophore, the modulated fluorescence emission exhibits a reduced modulation depth and is always delayed in time relative to the original excitation. Quantitatively, the reduced modulation depthm=1/(1+ω2τ2)and the delayed phase angleϕ=arctan(ωτ)where ω is the circular modulation frequency in radians per second. Both m and ϕ contain the lifetime information about the excited state of the sample [1]. Obviously, a high modulation frequency will lead to a more negative phase delay that is closer to −90°, whereas a slow modulation will result in a small but still negative phase delay according to Eq. (2). It is crucial to note that under no circumstances could the phase shift become positive in the conventional phase fluorometry.

Most recently, our group reported an experimental observation of frequency-domain fluorescence anomalous phase advance (FAPA) [9], which is opposite to the expected phase delay in conventional fluorescence lifetime phase fluorometry. When fluorescent molecules flavin adenine dinucleotide (FAD), Rhodamine 6G (Rh6G) and fluorescein isothiocyanate (FITC) are excited by a sinusoidally modulated laser around MHz, instead of detecting a negative phase shift between the emitted fluorescence and the excitation laser, the measured phase shift is actually positive which suggests that the fluorescence is emitted “ahead” of the laser source. Further experiment showed that FAPA is pronounced only within a narrow range of modulation frequencies that are outside quasi-static and quasi-equilibrium conditions [9].

FAPA is believed to be induced by the dynamical hysteresis of long-lived dark state of fluorescent molecules, as the FAPA signal is found to be strongly dependent on the concentrations of a series of known triplet state quenchers and promoters [9]. Dark state, which universally exists for almost all fluorescent molecules, refers to the long-lived non-fluorescent state of fluorophores [10]. It is interesting to note that dark states of fluorescent molecules have recently attracted considerable attentions in a number of microscopy applications. First, the dark state lifetime is typically much longer than the fluorescence lifetime, rendering it to be highly sensitive to a certain class of weak environmental properties [11]. Second, by exploiting the stochastic switching or blinking of fluorophores or fluorescent proteins, fluorescence imaging can circumvent the diffraction limit in terms of spatial resolution [12], [13], [14], [15]. Third, triplet relaxation microscopy leads to a major increase in total fluorescence signal and photo-stability of fluorescent molecules under imaging [16], [17]. Considering FAPA is tightly related to the dark states of fluorescent molecules, FAPA provides a promising technique to study the dark states dynamics and also imaging dark states lifetime distributions in complex biological samples [9].

Although our earlier experimental report provides evidence of the photo-physical effects of dark states underlying FAPA, the coherent picture and the quantitative characterization are not available. In particular, under the interplay between the fluorescent state and the dark state, how the phase fluorometry behaves in the entire modulation frequency range, how the phase shift turns over from the conventional negative value to the positive, how the conventional phase delay and the new FAPA are different from each other, and how phase fluorometry can be used to probe the changes of the relevant photophysical rates are still unknown. In this study, we seek to comprehensively investigate the role of dark state in phase fluorometry, which to our best knowledge has not been studied in the literature before. Various aspects of phase fluorometry will be separately examined including the dependence on light modulation frequency, excitation light intensity, nonradiative decay rate, intersystem crossing rate and dark-state lifetime, respectively.

Section snippets

Method

We use a simplified three-level kinetic model: the ground state (G), the singlet excited state (E) and the dark state (D) as shown in Fig. 1. The dynamic transitions of molecular population on these three states under excitation of a sinusoidally modulated laser could be described by the following system of ordinary differential equations:NG(t)+NE(t)+ND(t)=1;dNG(t)d(t)=-kGE(t)NG(t)+(kEG+kEG)NE(t)+kDGND(t);dNE(t)dt=kGE(t)NG(t)-(kEG+kEG)NE(t)-kEDNE(t);dND(t)dt=kEDNE(t)-kDGND(t);kGE(t)=I0(sin(2πν

Results

To have a global view of phase fluorometry, the phase shift is calculated as a function of a broad range of modulation frequencies (from 50 kHz to 325 MHz) of the excitation source with and without the involvement of a dark state. As shown in Fig. 2A, the phase shift curve from a three-level kinetic model in the presence of a dark state is not exactly the same as the one produced by the conventional two-level model in the absence of a dark state. The net difference between the above two phase

Conclusion

Dark states appear to enrich the behaviors of the classical frequency-domain phase fluorometry. In the present study, we have systematically investigated various aspects of phase fluorometry in the presence of dark states, in light of the recently observed fluorescence anomalous phase advance (FAPA). It is shown that FAPA exists in a narrow range of modulation frequency that is resonant with the intrinsic time scale of dark-state lifetime, outside both the quasi-static and the quasi-equilibrium

Acknowledgment

We are grateful to Evangelos Gatzogiannis, Ya-Ting Kao, Louis Brus, Kenneth Eisenthal, Rafael Yuste, Nicholas Turro and Sijia Lu for helpful discussions. W.M. acknowledges the start up funds from Columbia University.

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