# Determination of quantum yield of NADH and FAD in alcohol-water solutions:
the analysis of radiative and nonradiative relaxation pathways.

Ioanna A. Gorbunova  Marina K. Danilova  Maxim E. Sasin  Victor P. Belik
Dmitrii P. Golyshev  Oleg S. Vasyutinskii<EMAIL_ADDRESS>Ioffe Institute,
26 Polytekhnicheskaya, St.Petersburg, 194021 Russia  Peter the Great
St.Petersburg Polytechnic University, 29 Polytechnicheskaya, St.Petersburg,
195251, Russia

###### Abstract

Combined studies on fluorescence quantum yield in coenzymes NADH and FAD in
water-methanol, water-ethanol and water-propylene glycol mixtures and on time-
resolved fluorescence of the same molecules by means of the TCSPC method under
excitation at 450 and 355 nm have been carried out. A significant difference
in the behavior of NADH and FAD quantum yields in different alcohol-water
mixtures was observed. The dependence of quantum yield in NADH on alcohol
concentration was found to be similar in monohydric alcohols methanol and
ethanol and differed from that in polyhydric alcohol propylene glycol. In the
case of FAD, the behavior of quantum yield was almost independent of the type
of alcohol and exhibited a dramatic increase of 5–6 times with alcohol
concentration. The experimental results were analysed using a model based on
the quantum mechanical theory developed recently by the authors that took into
account radiative and nonradiative relaxation pathways. A generalised
expression for the fluorescence quantum yield containing contributions from
picosecond and nanosecond nonratiative decay processes in molecular excited
states was derived and used for clarification of the role of nanosecond and
picosecond relaxation channels in NADH and FAD in various water-alcohol
mixtures. The analysis of theoretical expression describing fluorescence decay
in polyatomic molecules excited by a short laser pulse resulted in a new
insight into the nature of the Decay Associated Spectra (DAS) phenomenon. The
contribution from the fast picosecond nonradiative decay in NADH to the
quantum yield in water-methanol and water-ethanol mixtures was found to be
practically independent of the alcohol concentration and hence of the NADH
conformation distribution. This result suggests that the picosecond decay in
NADH does not likely occur through electron transfer in the stacking
configuration of the nicotinamide and adenine moieties but through other
mechanisms. At the same time the contribution of the fast picosecond
nonradiative decay in NADH to the quantum yield in water-propylene glycol
solutions was found to depend on propylene glycol concentration, therefore the
sharp nonlinear increase of the measured quantum yield was associated with
decrease of both fast picosecond and relatively slow nanosecong quenching
nonradiative rates. In FAD, the contribution of the fast picosecond quenching
to the quantum yield was found to depend significantly on the alcohol
concentration in all alcoholes under study. This finding suggests that the
fast quenching gives a profound contribution to the rise of the measured
quantum yield with alcohol concentration and supports the established
mechanism of the fluorescence quenching in FAD through electron transfer
reaction in the $\pi$-stacked conformation between isoalloxazine and adenine
moieties.

###### keywords:

fluorescence quantum yield, NADH, FAD, solution, fluorescence quenching,
fluorescence decay times, picosecond relaxation, multiexponential decay,
alcohol-water mixture

††journal: Journal of LaTeX Templates

##  1 Introduction

Reduced nicotinamide adenine dinucleotide (phosphate) (NAD(P)H) and oxidized
flavin adenine dinucleotide (FAD) are essential biological coenzymes involved
in regulation of living cell metabolism that are actively used nowadays as
intrinsic fluorescent biomarkers for monitoring the respiratory chain activity
and cell metabolism [1, 2, 3]. A high potential of NAD(P)H and FAD
autofluorescence as biomarkers was highlighted in a series of seminal works by
Chance et al. [4, 5]. Chance et al. have demonstrated that NADH in its reduced
form exhibits autofluorescence at 400–500 nm, whereas its oxidized form, NAD+
does not fluoresce and developed spectroscopic ways to measure a redox ratio
NAD+/NADH for real-time monitoring of the metabolic state of a cell during
pathophysiological changes.

Reduced FAD (FADH2) and FAD are another redox pair largely associated with
respiration in mitochondria of eukaryotic cells. As known, the reduced form
FADH2 does not fluoresce while the oxidized form FAD can fluoresce under
excitation in the spectral region shorter than 420 nm [6]. Zhang et al. [7]
suggested a prominent way of determination the mitochondria redox state by
measuring the redox ratio HADH/FAD and shown that the measurement of the ratio
of fluorescence has important advantages over the absolute values.

Chance et al. [4, 8] suggested that the changes occurring in redox state in
cancer cells can be effectively studied by monitoring NADH fluorescence. This
approach was developed and widely used by many groups (see, e.g. [9, 10])
however further experiments elucidated a number of biological and technical
problems dealing with light scattering in tissue, absorption of the laser
light at 360 nm by other intracellular species, and the influence of a number
of factors on fluorescence intensity.

To overcome these problems Lakowicz et al. [11] employed the measurements of
NADH fluorescence lifetimes that are independent of light intensity and can be
used for separation of free and protein-bound NADH quantitatively. Moreover,
Bird et al. [12] reported that the ratio of free/protein-bound NADH is related
to changes in the NADH/NAD+ ratio. Therefore, quantifying NAD(P)H and FAD
fluorescence through fluorescence lifetime imaging allows in general to
determine the optical redox ratio with high sensitivity and therefore to
monitor small changes in metabolic activity [3]. Fluorescence lifetime imaging
microscopy (FLIM) is now widely used for monitoring of metabolic pathways
activated in cancer cells [2, 13, 14, 15].

As demonstrated in numerous studies mentioned above, FLIM in NAD(P)H and FAD
can be used for non-destructive determination of changes in cellular
metabolism. However, till now these changes are difficult to interpret [16].
The isotropic (polarization insensitive) part of the fluorescence signal
$I_{tot}(t)$ is usually presented as a sum of exponentials [17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27]:

$I_{tot}(t)=I_{0}\sum\limits_{i=1}^{n}a_{i}\,\exp\left(-\frac{t}{\tau_{i}}\right),$
(1)

where $I_{0}$ is a time-independent initial fluorescence intensity, $\tau_{i}$
are decay times, and $a_{i}$ are corresponding weighting coefficients that are
normalized to unity: $\sum_{i}a_{i}=1$.

Nowadays using several supplementary fluorescence detection experimentalist
can measure a great number of fluorescence decay times $\tau_{i}$ describing
various aspects of the fluorescence dynamics. One of them is time correlated
single photon counting (TCSPC) technique allowing for determination of decay
times in the nanosecond and near sub-nanosecond time domain. The others are
femtosecond transient monitoring and up-conversion techniques that allow for
determination of the decay times in picosecond and sub-picosecond time domain.

In the nanosecond and near sub-nanosecond time domain free NADH in aqueous
solution is known to exhibit biexponential fluorescence decay with the
lifetimes of about 0.3 ns and 0.7 ns [28, 29, 18, 30] and in other solvents
the lifetimes and corresponding weighting coefficients depend strongly on
temperature and solvent type [31, 29, 28, 17]. The explanation of the nature
of the two observed fluorescence decay times in NADH for long time remained
controversial. In particular it was unclear if the two fluorescence lifetimes
either correspond to different geometric conformations of the whole molecule,
or they are intrinsic features of the NA ring [28, 32, 31, 33, 34, 17, 19].
Gorbunova et al. [35] suggested that the heterogeneity in the measured decay
times in NADH is due to different charge distributions in the _cis_ and
_trans_ configurations of the nicotinamide ring that results in different
electrostatic field distributions and different non-radiative decay rates
$(\tau^{\,nrad}_{l})^{-1}$ (see eq. (8)). This model was also shown to be
useful for elucidation of the single-exponential and relatively slow
fluorescence decay in NADH-alcoholedegidrogenase (ADH) complex [21] because as
known from the X-ray structure spectroscopy and NMR experiments, NAD(P)H
imbedded into the ADH binding site in a single unfolded _anti_ ” _trans_ -out-
of-plane” nuclear conformation [36, 37, 38]. Within the same model a
significant enhancement of the decay time value in the ADH-bounded NADH
compare with the free NADH in solution can be attributed [21] to a significant
decrease of charges separations in the nicotinamide (NA) ring in the
conditions of a typical apolar binding site environment in the ADH-NADH
complex [39, 40]. Similar reasons are likely responsible for significantly
different lifetime values observed in NADH bounded with various enzymes [16].

In the nanosecond time domain FAD in solutions and living cells demonstrates a
multiexponential fluorescence decay dynamics. At physiological pH and
temperature conditions in solution it is most common to fit FAD fluorescence
decay after excitation of the isoalloxazine moiety by two exponentials with
the lifetimes of about 2.3 ns and 3.5 to 4.5 ns [41, 42, 43, 44]. However, in
other solvents the number of lifetimes, their values and corresponding
weighting coefficients depend strongly on temperature, pH and solvent type
[45, 6, 22, 42, 41]. Despite numerous studies carried out the origin of the
two fluorescence nanosecond decay times in FAD still remains poorly
understood.

Multiexponential fluorescence decay was also observed in the picosecond time
domain by many groups using ultrafast fluorescence up-conversion and transient
monitoring methods. A very short decay time of about $\tau\simeq$ 1 ps that
was observed by several groups in NADH [26, 27, 46], FAD [25, 42, 22, 23, 47,
24], and many other molecules (see, e.g. [48, 49, 50]). It is commonly
attributed to water relaxation around the corresponding excited chromophore
moiety. A signature of this vibrational relaxation is Decay Associated Spectra
(DAS) that is characterised by the positive value of the corresponding pre-
exponential weighting coefficient $a_{i}$ in eq. (1) in the blue wing of the
fluorescence band and negative, or near zero coefficient $a_{i}$ in the red
wing of the fluorescence band [26, 46, 24, 50]. However, the understanding of
DAS still remained controversial [49].

Another typical picosecond decay times of about $\tau\simeq$ 26 ps observed in
NADH [26, 27] and of about $\tau_{d}\simeq$ 5-9 ps observed in FAD [23, 24,
42, 25] were associated with picosecond relaxation occurring between the
excited $S_{1}$ and the ground $S_{0}$ electronic states and resulting in fast
fluorescence quenching. These fluorescence decay is known as quasi-static-
self-quenching (QSSQ) [50] and results in decrease of the observed quantum
yield. In the case of NADH the routes of QSSQ are still not known exactly [26,
27, 46]. In particular, these can be either interactions of excited NADH
molecules with surrounding solvent molecules, or intramolecular internal
conversion to the ground electronic state, or intersystem crossing to the
triplet manifold [51]. In the case of FAD it is now well adopted that the
mechanism of the fluorescence quenching is an electron transfer reaction in
the $\pi$-stacked conformation [6, 52, 53, 22, 54].

A common way for determination of the fractional population of free and bound
species from the multiexponential expansion in eq. (1) is to assume that the
radiation decay rate $\gamma_{rad}=\tau_{rad}^{-1}$ remains constant and then
suggest that the weighting coefficients $a_{i}$ in eq. (1) are equal to the
fractional concentrations of the species associated with it and to use the
fraction of the total fluorescence signal generated by each species $i$ [40,
55, 16]:

$f=\frac{a_{i}\tau_{i}}{\sum_{j}a_{j}\tau_{j}}.$ (2)

However, the origin of the fluorescence decay times numbers and their values
in NADH and FAD bound to different enzymes still remains controversial.
Therefore, the relative number of coenzyme molecules bound to different
enzymes cannot be obtained without further characterization [55, 56, 21]. As
pointed out by Niesner et al. [55] in general $a_{i}$ and $f$ values are
influenced by the concentration, absorption cross-section, and fluorescence
quantum yield. Consequently, it is necessary to know the photophysical
properties of the fluorescing species in order to calculate their relative
concentration.

Fluorescence quantum yield is one of the most important parameter needed for
determination of the redox ratio and the ratio of free and protein-bound NADH
in biological solutions and living cells from fluorescence lifetime
measurement [3, 57] as it is known to be highly dependent on
solution/intracellular viscosity and polarity [58, 59, 32, 28, 60, 61, 17].
Scott et al. [59] studied fluorescence lifetime and quantum yield of NADH and
its derivatives in water and propylene glycol (PG) and revealed that the
excited state dynamics in NADH are mostly characterized by non-radiative
processes. This suggestion was supported in the following studies [32, 17, 28,
61, 60] where the dependence of fluorescence quantum yield and non-radiative
decay rates in NADH on temperature or solvent type was extensively studied.
Gafni et al [32], Fischer et al. [60], and Visser et al. [28] reported an
increase in the NADH quantum yield by an order of magnitude upon binding with
enzymes. Nakabayashi et al. [62] studied the effect of the local electric
field on NADH fluorescence in solutions and demonstrated an increase in
average fluorescence decay time due to the decrease in solvent polarity.
Blacker et al. [17] inquired time-resolved fluorescence in NADH in water-
glycerol solution and calculated non-radiative decay rate using Kramers-
Hubbard equation.

However, the origin of non-radiative pathways accounting for excited-state
dynamic in FAD and especially NADH still remain controversial. Also it is
unclear ether intermolecular quenching processes or intramolecular interaction
of nicotinamide and adenine can be account for the very low fluorescence
quantum yield in NADH [17, 59, 60].

Fluorescence quantum yield in FAD in solutions and proteins was intensively
studied during latest decades [6, 42, 54, 63]. Nakabayashi et al. [42]
observed rapid growth of fluorescence excited at 410 nm depending on alcohol
concentration increase in alcohol-water solutions and suggested that the
addition of a less polar solvent breaks the $\pi$-$\pi$ interaction in the
stacked conformation and produces the open FAD conformation which results in
the rise of fluorescence intensity. Radoszkowicz et al. [54] performed
molecular dynamics simulations of FAD in water-methanol mixtures and showed
that methanol affected the dynamics of FAD by enhancing the frequency of
unfolding events without any effect on the lifetime of unfolded states.

Despite a number of studies carried out the detailed physical interpretation
of experimental data in the form of multiexponential expansion in eq. (1) and
in the form of fluorescence quantum yields is still a challenging problem.

This paper aims to address this problem, at least partly. We carried combined
experimental studies including the determination of fluorescence quantum
yields in NADH and FAD dissolved in water mixtures with several alcohols:
methanol (MeOH), ethanol (EtOH), and propylen glycol (PG), and the time-
resolved fluorescence studies of the same molecules using TCSPC method under
excitation at 450 and 355 nm. The experimental results were analysed using a
new model taking into consideration radiative excitation and fluorescence
channels as well as nonradiative excited state relaxation pathways and based
on the quantum mechanical theory developed recently by the authors [64].

The main results obtained are as follows. A significant difference was
observed in the behavior of NADH and FAD quantum yields in alcohol solution.
In particular, the dependence of quantum yield in NADH on alcohol
concentration was similar for monohydric alcohols (methanol and ethanol) and
significantly different for polyhydric alcohol (propylene-glycol). In the case
of FAD, the behavior of quantum yield was almost independent of the type of
alcohol and exhibited a dramatic increase of 5–6 times with alcohol
concentration.

The analysis of general theoretical expression describing fluorescence decay
in a polyatomic molecule excited by a short laser pulse led to better
understanding of the nature of the DAS phenomenon. A generalised expression
for the fluorescence quantum yield that allowed to separate contributions from
the fast and slow nonratiative processes in molecular excited states was
derived and used for clarification of the role of nanosecond and picosecond
relaxation channels in NADH and FAD in various water-alcohol mixtures.

The contribution of the fast picosecond nonradiative decay in NADH to the
quantum yield in water-MeOH and water EtOH mixtures was found to be
practically independent of the alcohol concentration and hence of the NADH
conformation distribution. This result suggests that the picosecond decay in
NADH does not likely occur through electron transfer in the stacking
configuration of the nicotinamide and adenine moieties but through other
mechanisms. It also suggests that the known growth of NADH quantum yield at
high alcohol concentration occurs mostly due to relatively slow nanosecond
nonradiative mechanisms related with conformation distributions. At the same
time the contribution of the fast picosecond nonradiative decay in NADH to the
quantum yield in water-PG solutions was found to depend on PG concentration
and the sharp nonlinear increase of the measured quantum yield with PG
concentration was associated with decrease of both fast picosecond and
relatively slow nanosecong quenching nonradiative rates.

In FAD, the contribution of the fast picosecond quenching to the quantum yield
was found to depend significantly on the alcohol concentration in all MeOH,
EtOH. This finding suggests that the fast quenching gives a profound
contribution to the rise of the measured quantum yield with alcohol
concentration and supports the established mechanism of the fluorescence
quenching in FAD through electron transfer reaction in the $\pi$-stacked
conformation between isoalloxazine and adenine moieties.

##  2 Experimental Procedure

###  2.1 Materials

FAD disodium salt (98% purity, DIA-M) and $\beta$ – NADH (NADH disodium salt,
98 % purity, Sigma-Aldrich) were used in experiments. Unbuffered distilled
water (pH = 5.5), methanol (MERCK, extra pure), ethanol (extra pure),
propylene glycole and their mixtures with water were used as solvents. The 1.5
ml water-alcohol mixtures of various concentrations were preliminary prepared
and then 25$\mu$l FAD or NADH stock solutions were added to the water-alcohol
mixtures. Final FAD and NADH concentrations were equal to 60 $\mu$M and 15
$\mu$M respectively. These concentrations was chosen since similar FAD and
NADH concentration were used in earlier studies [41, 6, 44, 59] that allowed
to compare our experimental results with others in similar conditions. FAD and
NADH concentration used in the experiments was much less than its
solubility,therefore intramolecular interaction between dissolved molecules
and aggregate formation could be neglected. All solutions were prepared fresh
daily and used at the temperature of 20∘C.

###  2.2 Quantum yield measurements

The procedure of the absolute fluorescence quantum yield determination in NADH
and FAD molecules in water-alcohol solutions was similar to that used in
previous studies (see, e.g. [42, 54, 60, 59]). In brief, the experimental
procedure was as follows. An excitation laser beam propagated through a quartz
cuvette (10x10 mm) containing the molecular solution. All experiments were
carried out in the low absorption condition when the absorption in the
experimental sample was less than 15% to avoid saturation and photobleaching
effects. The laser beam intensity transmitted through the cuvette with the
molecular solution $\langle I_{tr}^{mol}\rangle$ and with pure solvent
$\langle I_{tr}^{sol}\rangle$ was recorded by a phododiode to determine
absorption in the molecular sample. Molecular fluorescence was collected at
the right angle to the laser beam propagation, then it passed through the
glass optical filter for damping the scattered excitation light, and was
focused onto a photodetector. The absolute quantum yield was determined using
the expression:

$Q=NG\frac{\langle I_{fl}\rangle}{\langle I^{sol}_{tr}\rangle-\langle
I^{mol}_{tr}\rangle},$ (3)

where $\langle I_{fl}\rangle$ is the fluorescence intensity, angle brackets
mean time averaging, $N$ is a constant taking into account the photon energy
of the excitation and fluorescence light, and G is the geometry factor
calculated as the ratio of the solid angle within fluorescence detection area
to the total emission solid angle.

As known, FAD has two low laying wide absorption bands with maxima at 450 and
370 nm and NADH has a wide absorption band with a maximum at 340 nm. A pulsed
Nd:YAG laser (SNV-40P, Teem Photonics) with output at 355 nm, pulse duration
of 400 ps, and repetition rate of 2 KHz was used in our experiments for
excitation of NADH and for excitation of FAD through the second absorption
band, and a pulsed semiconductor laser with output at 450 nm, pulse duration
of 30 ps, and repetition rate of 20 MHz was used for excitation of FAD through
the first absorption band. Only the time-averaged laser intensities were
recorded by the photodetector. Each laser intensity at the cuvette was kept at
about 40 mW. The fluorescence intensities were recorded in NADH and FAD within
whole their fluorescence bands without spectral resolution. The molecular
fluorescence and laser beam intensities transmitted through the cuvette were
detected by a photodiode photodetector PD300-SH (Ophir Optronics) with the
sensitivity spectral range of 350–1100 nm. The photodetector was calibrated
taking into account its wavelengths sensitivity.

In most of the experiments for increasing of the signal-to-noise ratio the
laser beam was modulated at the frequency of 114 Hz by a chopper installed in
front of the cuvette. An amplitude-modulated electric signal from the
photodetector was separated and detected by a narrow-band lock-in amplifier
and then collected and analysed with a computer. An intensive fluorescence
signal in FAD in aqueous solution was recorded in a wide-band frequency regime
without laser beam modulation and then used for determination of the absolute
quantum yield with respect to eq. (3). This signal was used for calibration of
all other signals. Having in mind that the time-averaged fluorescence
polarization was relatively low in all our experiments (less than 14% in NADH
and less than 4% in FAD) no special corrections of the fluorescence amplitude
due to polarization effects were made as these corrections were smaller that
the quantum yield experimental error bars shown in Figs. 1 and 2 below.

###  2.3 Lifetimes measurements

The procedure of determination of the fluorescence decay times was similar to
that described in detail in our recent publications [65, 66, 67, 35, 21].
Briefly, the pulsed lasers with output at 450 nm and 355 nm described above
were used in this paper for one-photon excitation of FAD via the first and the
second absorption bands. Two orthogonally polarized fluorescence components
$I_{\|}(t)$ and $I_{\bot}(t)$ were recorded in experiment using time
correlated single photon counting (TCSPC) technique. The polarization
components $I_{\|}(t)$ and $I_{\bot}(t)$ was fitted with the multiexponential
function in eq. (1) using a global fit procedure with a least square
differential evolution algorithm with convolution [35]. The polarization-
insensitive part of the fluorescence intensity $I_{tot}(t)$ was calculated
according to:

$I_{tot}(t)=I_{\|}(t)+2I_{\bot}(t).$ (4)

##  3 Experimental results

Fluorescence quantum yield in FAD determined upon excitation at 450 nm and 355
nm in three different water-alcohol solutions of various concentrations are
presented in Figs. 1a–c as a function of the alcohol concentration.

---
Figure 1: Fluorescence quantum yield in FAD upon excitation at 450 nm and 355
nm in three water-alcohol solutions: propylene glycole (a), methanol (b), and
ethanol (c) as a function of alcohol concentration. Symbols in plots a–c are
experimental data and red curves in represent the corresponding alcohol
viscosities.

According to Figs. 1a–c the absolute quantum yield in FAD in pure water under
excitation at 450 nm and 355 nm was found to be $Q$=3.33$\pm$% and
$Q$=1.87$\pm$%, respectively. The quantum yield in pure water at 450 nm in
Figs. 1a–c agrees perfectly with that reported earlier by Islam et al. [6] and
Sengupta et al. [63]. To the best of our knowledge the quantum yield in FAD
under excitation at 355 nm was determined in this paper for the first time.

As can be seen in Fig. 1 the fluorescence quantum yield in FAD rose
dramatically with alcohol concentration in all solutions under study at each
excitation wavelength. In water-propylene glycol solutions fluorescence
quantum yield in Fig. 1a increased practically linearly with propylene glycol
concentration and in pure propylene glycol reached the values of $Q$=17% and
$Q$=9% under excitation at 450 and 355 nm, respectively. In water-methanol
solutions the quantum yield in Fig. 1b also increased linearly up to the
methanol concentration of about 80% and reached the values of $Q$=15% and
$Q$=10% under excitation at 450 and 355 nm, respectively. At higher methanol
concentrations the quantum yield decreased somehow by 2–3% at both excitation
wavelengths. In water-ethanol solutions the quantum yield in Fig. 1c increased
almost linearly with alcohol concentration up to the concentration of about
70% and then increased more slow at higher concentrations reaching the maxima
of 19% and 11% under excitation at 450 and 355 nm, respectively.

Quantum yields in NADH determined upon excitation at 355 nm in water–propylene
glycol, water-methanol, and water-ethanol solutions as a function of alcohol
concentrations are shown in Figs. 2a–c.

---
Figure 2: Fluorescence quantum yield in NADH upon excitation at 355 nm in
three water-alcohol solutions: propylene glycole (a), methanol (b), and
ethanol (c) as a function of alcohol concentration. Black symbols in plots a–c
are experimental data and red curves in represent the corresponding alcohol
viscosities.

The fluorescence quantum yield in aqueous solution was determined to be
$Q$=2.1$\pm$0.2 that agrees perfectly with the value reported earlier by Scott
et al. [59] and Gafni et al. [32]. As can be seen in Fig. 2a in water-
propylene glycol solutions, fluorescence quantum yield in NADH exhibited a
nonlinear behavior with propylene glycol concentration and reached the maximum
of $Q$=8% in pure propylene glycol. This result is also in agreement with the
earlier result reported by Scott et al. [59]. The quantum yield dependence in
Fig. 2a almost perfectly follows the propylene glycol viscosity dependence,
also the quantum yield value in pure propylene glycol was about 4 times larger
than in water. As can be seen in Figs. 2b,c in the case of water-methanol and
water-ethanol solutions fluorescence quantum yield in NADH increased
practically linearly with alcohol concentration and reached the maxima of
about 3.2 % in the pure alcoholes. As can be seen in Figs. 2b,c fluorescence
quantum yield in NADH was about 1.5 times larger in pure alcohol than in
water.

The dependence of FAD and NADH quantum yields on ethanol and methanol
concentrations was studied earlier by several groups [42, 54, 60, 59]. Our
results presented in Figs. 1 and 2 are at least in qualitative agreement with
them. The increase of fluorescence intensity in FAD in water-ethanol and
water-glycerol solutions was observed early by Nakabayashi et al [42] who
observed an almost 5 times increase of FAD fluorescence intensity upon
excitation at 445 nm in 50% ethanol solution compared with pure water. The
dependence of FAD quantum yield on methanol concentration shown in Fig. 1b is
consistent with the result reported earlier by Radoszkowicz et al [54]. In the
case of NADH, an 1.5 times increase of fluorescence intensity upon excitation
at 360 nm in methanol solution compared with water was reported by Freed et
al. [58]. Moreover, the same increase in fluorescence intensity and relative
quantum yield in dihydronicotinamide in ethanol and methanol was observed by
Fischer et al [60]. At the same time, the complete quantitative data on
fluorescence quantum yields in NADH and FAD in Figs. 1 and 2 are presented in
this paper at the first time.

The experimental results shown in Figs. 1 and 2 can be briefly summarized as
follows. A significant difference was observed in the behavior of NADH and FAD
quantum yields in alcohol solution. In particular, the dependence of quantum
yield in NADH on alcohol concentration was similar for monohydric alcohols
(methanol and ethanol) and significantly different for polyhydric alcohol
(propylene-glycol). In the case of FAD, the behavior of quantum yield was
almost independent of the type of alcohol and exhibited a dramatic increase of
5–6 times with alcohol concentration.

The fluorescence decay times and corresponding weighting coefficients are
given in Tables 1 and 2 for NADH and FAD in water-alcohol solutions,
respectively. The data in Table 1 were obtained in our recent publication [68]
and the data in Table 2 were obtained in this paper experiments. As can be
seen in Tables 1 and 2 the fluorescence decay in both molecules was double
exponential with decay times $\tau_{1}$ and $\tau_{2}$.

Table 1: Fluorescence decay times $\tau_{i}$ in NADH determined upon two-photon excitation at 720 nm [68]. Solvent |  $\tau_{1}$, ns ($a_{1}$) |  $\tau_{2}$, ns ($a_{2}$)
---|---|---
H2O | 0.26 (0.74) | 0.62 (0.26)
MeOH 98% | 0.30 (0.41) | 0.72 (0.59)
EtOH 98% | 0.38 (0.33) | 0.93 (0.67)
PG 98% | 0.56 (0.44) | 1.23 (0.56)

Experimental data in Table 1 for aqueous solution are in agreement with our
recent results [30, 35] and with those those reported earlier in NADH under
one-[61, 31] and two-photon [19] excitation within experimental error bars.
Also, both decay times shown in Table 1 in pure methanol agree roughly with
those reported earlier [31, 33] where a three-exponential model was used.

Table 2: Fluorescence decay times $\tau_{i}$ in FAD determined upon excitation at 355 nm and 450 nm. | 355 nm | 450 nm
---|---|---
Solvent |  $\tau_{1}$, ns ($a_{1}$) |  $\tau_{2}$, ns ($a_{2}$) |  $\tau_{1}$, ns ($a_{1}$) |  $\tau_{2}$, ns ($a_{2}$)
H2O | 2.17 (0.68) | 4.46 (0.32) | 2.40 (0.69) | 4.52 (0.31)
MeOH 80 % | 2.22 (0.32) | 4.05 (0.68) | 3.23 (0.61) | 4.58 (0.39)
EtOH 80 % | 2.51 (0.11) | 4.13 (0.68) | 2.57 (0.13) | 4.51 (0.87)
PG 80 % | 2.20 (0.11) | 4.97 (0.89) | 3.01 (0.15) | 5.30 (0.75)

The existence of two excited state lifetimes in FAD obtained in this paper is
in agreement with the results reported by Sengupta et al. [63] and Esposito et
al. [69], however contradicts to the conclusions given by Nakabayashi et al.
[42], where the existence of four lifetimes have been reported under similar
experimental conditions. The decay time $\tau_{1}$ and $\tau_{2}$ values in
Table 2 obtained in aqueous solution are in perfect agreement with those
reported earlier [63, 69, 44].

##  4 Discussion

###  4.1 A model of the excited state relaxation dynamics

We consider a simplified model taking into consideration radiative excitation
and fluorescence channels as well as nonradiative excited state relaxation
pathways. A generalized scheme of optical excitation in NADH and FAD via the
first excited state $S_{1}$ and following relaxation pathways is shown in Fig.
3, where $R$ is the reaction coordinate and $S_{0}$ and $S_{1}$ are the PESs
of the electronic ground and the first excited states, respectively.

---
Figure 3: A generalized scheme of excitation and relaxation pathways in FAD
and HADH.

According to Fig. 3 an ultrashort laser pulse resonantly promotes ground state
molecules to the highly excited vibrational energy levels of the first
electronic excited state and then two fast picosecond nonradiative relaxation
processes occur shown with black dashed lines with arrows. One of them is the
vibrational relaxation (VR) within the excited state manifold that results in
the population of the lowest vibrational levels of the state $S_{1}$. This
relaxation can be associated with the relaxation decay time of about
$\tau_{v}\simeq$ 1 ps that was observed by several groups in NADH [26, 27, 46]
and FAD [25, 42, 22, 23, 47, 24]. This fast vibrational relaxation is
schematically shown in Fig. 3 with a black dashed line with arrow denoted
$nr1$.

The model suggested in this paper is based on the quantum-mechanical
expressions describing transient absorption signals and fluorescence decay
after one-, or two-photon excitation of a polyatomic molecule by an ultrafast
laser pulse reported recently by Gorbunova et al. [64] According to ref. [64],
the contribution from the fast vibrational relaxation $nr1$ to the
fluorescence decay reflects fast rearrangement of the molecular nuclear
configuration in the molecular excited state after ultrashort laser excitation
and depends on both internal molecular interactions and interactions with
solute molecules. The corresponding contribution to the isotropic fluorescence
decay can be approximated in the form [64]:

$\displaystyle R^{fl}_{0}(t)\approx
A^{iso}_{1}+(A^{iso}_{0}-A^{iso}_{1})e^{-{t/\tau_{v}}},$ (5)

where time-independent terms $A^{iso}_{0}$ and $A^{iso}_{1}$ specify the
values of the term $R^{fl}_{0}(t)$ at the nuclear configurations that refer to
the initial molecular state $S_{0}$ and to state $S_{1}$, respectively:
$A^{iso}_{0}=R^{pr}_{0}(t)|_{S_{0}}$, $A^{iso}_{1}=R^{pr}_{0}(t)|_{S_{1}}$,
and the term $\tau_{v}$ is the vibrational relaxation time.

###  4.2 Decay associated spectra (DAS)

The term $A^{iso}_{0}$ is proportional to the fluorescence intensity from the
excitation point (blue arrow in Fig. 3) and the term $A^{iso}_{1}$ is
proportional to the excitation intensity from the excited state equilibrium
point (red arrow in Fig. 3). Depending on the conditions
$A^{iso}_{0}>A^{iso}_{1}$, or $A^{iso}_{0}<A^{iso}_{1}$, eq. (5) describes
positive, or negative DAS. Also, the terms $A^{iso}_{0}$ and $A^{iso}_{1}$ are
proportional to the corresponding Frank-Condon factors of the excited (_e_)
and ground (_g_) electronic states: $A^{iso}_{0}\sim\langle
v_{e}|v_{g}\rangle^{2}|_{t=0}$, $A^{iso}_{1}\sim\langle
v_{e}|v_{g}\rangle^{2}|_{t\rightarrow\infty}$, where $v_{g}$ and $v_{e}$ are
vibrational wave functions.

The scheme illustrating the fluorescence decay during the fast vibrational
relaxation $nr1$ in given in Fig. 3. As can be seen in Fig. 3 Frank-Condon
integrals $\langle v_{e}|v_{g}\rangle$ depend significantly on the radiative
transition energy. In particular, if the photon energy exceeds the transition
energy shown with a red arrow and denoted as $h\nu_{red}$, the fluorescence
intensity from the condition $A^{iso}_{0}>A^{iso}_{1}$ is fulfilled and
therefore the blue wing of the fluorescence band is characterized by positive
DAS. When the fluorescence photon energy decreases the factor $A^{iso}_{1}$
increases having its maximum at 0-0 transition, while the factor $A^{iso}_{0}$
decreases monotonously due to more and more unfavorable relationship between
the vibrational wave functions $v_{g}$ and $v_{e}$. Therefore the condition
$A^{iso}_{0}\leq A^{iso}_{1}$ can be fulfilled and the red wing of the
fluorescence band can be characterized by near zero, or negative DAS. The
conclusions made are in qualitative agreement with experimental observations
[25, 26, 27, 46, 42, 22, 23, 47, 24]. The detailed description of DAS as
function of the fluorescence photon energy depends on the actual PESs of the
ground and excited states that as not known. Note that the vibration
relaxation occurs within the excited state and therefore does not contribute
to the measured fluorescence quantum yield.

###  4.3 Picosecond quenching dynamics

Another type of picosecond relaxation occurs between the excited $S_{1}$ and
the ground $S_{0}$ electronic states and results in fast fluorescence
quenching that results in decrease of the observed quantum yield. This
relaxation is shown in Fig. 3 with a black dashed line with arrow denoted
$nr2$. This relaxation can be associated with the picosecond decay times of
about $\tau_{d}\simeq$ 26 ps observed in NADH [26, 27] and of about
$\tau_{d}\simeq$ 5-9 ps observed in FAD [23, 24, 42, 25]. In the case of NADH
the routes of the quenching are still not understood in detail and in the case
of FAD it is now well adopted [6, 52, 53, 22, 54] that the mechanism of the
fluorescence quenching occurs through an electron transfer reaction in the
$\pi$-stacked conformation.

We suggest that irrespectively of the quenching mechanism the excited state
population $N(t)$ in the course of QSSQ can be approximated by the expression:

$\displaystyle N(t)\approx N_{1}+N_{2}e^{-{t/\tau_{q}}},$ (6)

where concentrations $N_{2}$ and $N_{1}$ characterize the excited molecular
conformations that are affected and not affected by QSSQ, respectively and
$\tau_{q}$ is the quenching characteristic time.

In the case of FAD the concentration $N_{2}$ can be associated with the
stacked conformations and the concentration $N_{1}$ can be associated with the
unstacked conformations. Equation (6) describes the simplest case of
interaction between two molecular states. In case of an exchange reaction
between them, or if the number of interaction states is more that two,
additional exponentials can appear in eq. (6).

According to the model shown in Fig. 3 when the fast picosecond relaxations is
over and all remained conformations of excited molecules populate the lowest
vibrational levels of the $S_{1}$ electronic state, much slow nanosecond
radiative and nonradiative relaxations occur in the nanosecond and near
subnanosecond time range.

###  4.4 Time-resolved fluorescence decay in polyatomic molecules

A general theoretical expression describing fluorescence decay in polyatomic
molecules excited by a short laser pulse can the approximated in the form:

$\displaystyle I^{iso}_{fl}(t)$ $\displaystyle=$
$\displaystyle\frac{I_{X}+2I_{Y}}{3}\approx{I_{0}}R^{fl}_{0}(t)N(t)\sum_{l}\,a_{l}\,e^{-t/\tau_{l}}.$
(7)

where the term $R^{pr}_{0}(t)$ given in eq. (5) describes a contribution to
the fluorescence signal from the fast vibrational relaxation, the term $N(t)$
given in eq. (6) describes QSSQ, $N(0)=N_{1}+N_{2}$, and the term under the
sum with $l=1,2$ describes the fluorescence decay due to relatively slow
nanosecond relaxation processes with decay times $\tau_{1}$ and $\tau_{2}$.

The sum in eq. (7) contains two exponentials with decay times $\tau_{1}$ and
$\tau_{2}$ and weighting coefficients $a_{1}$ and $a_{2}$. The heterogeneity
in the measured decay times in the nanosecond time domain in NADH and FAD in
solutions and cells was well documented over a long period of time from the
time-resolved fluorescence studies. Most of the authors agree that the
heterogeneity in the measured fluorescence decay times in the nanosecond time
domain in NADH and FAD contain contributions from radiative and nonradiative
decay channels. Particular routes of the nanosecond nonradiative relaxation in
NADH and FAD are not known. These can be either ro-vibronic interactions in
excited FAD molecules and interactions with surrounding solvent molecules, or
rapid conformational fluctuations with intramolecular internal conversion to
the ground electronic state. The former is shown in Fig. 3 by a with a black
dashed line with arrow denoted $nr3$ and the latter can occur in non-stacked
conformations due to electron transfer reaction in the vicinity of CI. Anyway,
each of the measured decay times: $\tau_{1}$ and $\tau_{2}$ can be presented
as a combination of the radiative $\tau^{\,rad}$ and nonradiative
$\tau^{\,nrad}$ decay times:

$\frac{1}{\tau_{l}}=\frac{1}{\tau^{\,rad}}+\frac{1}{\tau^{\,nrad}_{l}},$ (8)

where the radiative decay time $\tau^{\,rad}$ in eq. (8) is assumed to be the
same for all excited conformations.

###  4.5 Fluorescence quantum yield

The fluorescence quantum yield $Q$ obtained by time-averaging of eq. (7)
taking into account eqs. (5) and (6) can be presented in the form:

$Q=Q_{0}\frac{a_{1}\tau_{1}+a_{2}\tau_{2}}{\tau^{\,rad}},$ (9)

with

$Q_{0}=\frac{N_{2}}{N(0)},$ (10)

where $a_{1}\tau_{1}+a_{2}\tau_{2}$ is proportional to the total fluorescence
intensity, $\tau^{\,rad}$ is proportional to the fluorescence intensity that
could be measured in the absence of the nanosecond nonradiative relaxation,
and the condition $a_{1}+a_{2}=1$ was taken into account.

The partial quantum yield $0\leq Q_{0}\leq 1$ in eqs. (9) and (10) is a ratio
between the number of molecules remaining in the bottom of the first excited
electronic state $S_{1}$ after the picosecond dynamics is finished and the
total concentration of the molecules excited by the laser pulse
$N(0)=N_{1}+N_{2}$.

###  4.6 Experimental data analysis

The terms $Q$, $Q_{0}$, and $(a_{1}\tau_{1}+a_{2}\tau_{2})$ in eq. (9) were
assumed to be the function of alcohole concentration, while the radiative
decay time $\tau^{\,rad}$ is assumed to be a constant. All three terms were
determined from the experimental data presented in sec. 3. Using the quantum
yield experimental values in Figs. 1 and 2 and the experimentally determined
delay times $\tau_{1}$, $\tau_{2}$, and weighting coefficients $a_{1}$,
$a_{2}$ the ratio $Q_{0}/\tau^{\,rad}$ was determined from eq. (9) as a
function of alcohole concentrations for all three alcohols used: MeOH, EtOH,
and PG. The radiative time $\tau^{\,rad}$ and the partial quantum yield
$Q_{0}$ were determined separately from the ratio $Q_{0}/\tau^{\,rad}$ using
the the boundary condition $Q_{0}=1$ for the highest value of the ratio at the
highest alcohol concentration. The boundary condition $Q_{0}=1$ was more sound
in the case of FAD as it is well known that at high alcohole concentration
fast picosecond fluorescence quenching in stacked FAD conformations give
small, or negligible contribution to excited state dynamics [42, 54, 25]. In
the case of NADH this boundary condition was less sound because although the
dynamics of the fast picosecond fluorescence quenching in this molecule is
known [26, 27] its mechanisms are so far pure understood. Anyway, this
approach gives correct behavior of $Q_{0}$ as a function of the alcohol
concentration however can only result in some vertical shift in Fig. 4a below.

The obtained partial quantum yields $Q_{0}$ for NADH and FAD are presented in
Figs. 4a–c as a function of the alcohol concentration for three solutions: PG,
MeOH, and EtOH. The determined radiative decay times $\tau^{rad}$ are as
follows. Fig. 4a: HADH excitation at 355 nm, $\tau^{rad}$=10.6 ns, Fig. 4b:
FAD excitation at 450 nm, $\tau^{rad}$=21.9 ns, and Fig. 4c: FAD excitation at
355 nm, $\tau^{rad}$=29.6 ns. The former value can be compared with the
theoretical value of the radiative decay time in NADH $\tau^{\,rad}=20.6$ ns
reported by Scott et al. [59]. Therefore, in both NADH and FAD the estimated
radiative decay times $\tau^{rad}$ were found to be much longer than the
measured fluorescence decay times $\tau_{1}$ and $\tau_{2}$ in Tables 1 and 2.

---
Figure 4: Partial quantum yield $Q_{0}$ in NADH and FAD as a function of the
alcohole concentration in solution for three solutions: PG, MeOH, and EtOH.

This result supports the well adopted conclusion [59] that nonradiative decay
rate dominates over the radiative one,
$(\tau_{i}^{\,nrad})^{-1}\gg(\tau^{\,rad})^{-1}$. Therefore the first term in
the _rhs_ in eq. (8) can be neglected compare with the second term meaning
that the measured fluorescence decay times are mostly relate with nanosecond
nonradiative decay.

Figure 4 manifests a significant difference between the behavior of the
reduced quantum yield $Q_{0}$ in NADH and FAD as a function of the alcohol
concentration. $Q_{0}$ in NADH in Fig. 4a is almost constant at all
concentrations of MeOH and EtOH, and at moderate concentrations of PG. Only at
the PG concentrations larger than 70% the reduced quantum yield $Q_{0}$
increases but not much. Having in mind that the change of alcohol
concentration in solution results in the change of conformation distribution,
in particular toward the increase of the unfolded conformations number, the
data in Fig. 4a suggest that fast picosecond quenching processes in the
molecular excited states in NADH do to actually depend on the conformation
distribution at least in metanol-water and ethanol-water solutions. This means
that the picosecond decay in NADH does not likely occur through electron
transfer in the stacking configuration but through other mechanisms. The same
is likely true in PG solutions where a moderate increase of the reduced
quantum yield at high PG concentrations may be due to slowdown of the fast
quenching processes in high viscosity conditions.

Therefore, the linear growth of the measured quantum yield $Q$ in NADH in MeOH
and EtOH solutions in Figs. 2b and c with alcohol concentration can be
explained by relatively slow nanosecond nonradiative processes described by
the term $a_{1}\tau_{1}+a_{2}\tau_{2}$ in eq. (9). As reported recently by
Gorbunova et al. [35] and shown in Table 1 the measured decay times $\tau_{1}$
and $\tau_{2}$ in NADH in water-MeOH solutions only slightly depend on the
methanol concentration, while the weighting coefficient $a_{2}$ that refers to
the longer lifetime increased in about 1.6 times from pure aqueous to pure
methanol conditions. It should be noted however, that we do not associate the
longer time $\tau_{2}$ with the unfolded NADH conformation. As shown in ref.
[35] $a_{2}$ was practically constant and equal to $a_{2}$= 0.24 at MeOH
concentrations below 70% and rose up to 0.4 only at higher concentrations. At
the same time, the contribution of the folded conformation $N_{fol}$ is known
to decrease dramatically with MeOH concentration and approaches zero value at
about 70-80% MeOH [70, 18, 35].

Similar conclusions can be made about the behavior of the quantum yield $Q$ in
NADH in water-ethanol solutions in Fig. 2c based on Fig. 4c, Table 1, and the
dependence of the parameters $\tau_{1}$, $a_{1}$, $\tau_{2}$, $a_{2}$ on EtOH
concentration reported in ref. [20].

As can be seen in Fig. 4a the reduced fluorescence quantum yield $Q_{0}$ of
NADH in propylene glycol remains almost constant at small and middle PG
concentrations smaller than 70% and increases by about 1.6 times at larger PG
concentrations. According to eq. (9) sharp nonlinear increase of the measured
$Q$ with PG concentration in Fig. 2a can be associated with decrease of both
fast picosecond and relatively slow nanosecong quenching nonradiative rates.

As can be seen in Figs. 4b and c the behavior of the reduced quantum yield
$Q_{0}$ in FAD as a function of the alcohol concentration differs from that in
NADH. $Q_{0}$ rises almost linearly with alcohol concentration and increases
at the concentration of 80% by a factor of 3–4 under excitation at 450 nm and
by a factor of 2.5–5 under excitation at 355 nm. This sharp increase of
$Q_{0}$ manifests the decrease of fast picosecond quenching rate in FAD
excited states. The mechanism of the picosecond fluorescence quenching in FAD
is well established [6, 52, 53, 22, 54], it occurs through an electron
transfer reaction in the $\pi$-stacked conformation. The probability of the
electron transfer reaction depends dramatically on FAD conformation: it is
very high in $\pi$-stacked conformations where the adenine and isoalloxazine
rings are parallel in close proximity to each other and is practically zero in
unfolded conformations [23, 24, 42, 25]. Therefore, the sharp increase of
$Q_{0}$ with alcohol concentration in Figs. 4b and c reflects the dramatic
decrease of the contribution of $\pi$-stacked conformations in solution.

Having in mind eq. (9), the comparison of the fluorescence reduced quantum
yield $Q_{0}$ in FAD in Fig. 4b,c with the measured total quantum yield $Q$ in
Fig. 1 suggests that the fast picosecond dynamics gives the major contribution
to the fluorescence signal intensity change with MeOH concentration, however
there is a minor influence from the slow nanosecond dynamics.

##  5 Conslusions

The studies of the quantum yield and the dynamics of fluorescence decay in
NADH and FAD excited at 355 nm and 450 nm in water- methanol, ethanol, and
propylen glycole mixtures have been carried out. The global fit procedure was
used for determination of the fluorescence parameters from experimental data.
A significant difference was observed in the behavior of NADH and FAD quantum
yields in alcohol solution. In particular, the dependence of quantum yield in
NADH on alcohol concentration was similar for monohydric alcohols (methanol
and ethanol) and significantly different for polyhydric alcohol (propylene-
glycol). In the case of FAD, the behavior of quantum yield was almost
independent of the type of alcohol and exhibited a dramatic increase of 5–6
times with alcohol concentration. The contribution of the fast picosecond
nonradiative decay in NADH to the quantum yield in water-MeOH and water EtOH
mixtures was found to be almost independent of the alcohol concentration. The
contribution of the fast picosecond nonradiative decay in NADH to the quantum
yield in water-PG solutions was found to depend on PG concentration. The
contribution of the fast picosecond quenching to the quantum yield in FAD was
found to depend significantly on the alcohol concentration in all MeOH, EtOH.
The experimental results were analysed using a new model based on the quantum
mechanical theory developed recently by the authors. The analysis of general
theoretical expression describing fluorescence decay in polyatomic molecules
excited by a short laser pulse gave a new insight of the nature of DAS
phenomenon. An expression for the fluorescence quantum yield that allowed to
separate the contributions from the fast and slow nonratiative processes in
molecular excited states was derived and used for clarification of the role of
nanosecond and picosecond relaxation channels in NADH and FAD in various
water-alcohol mixtures. A sharp increase of the measured quantum yield with PG
concentration was associated with decrease of both fast picosecond and
relatively slow nanosecong quenching nonradiative rates. As was shown the fast
quenching gives a profound contribution to the rise of the measured quantum
yield with alcohol concentration. The results obtained were compared with the
results reported by other authors.

## Acknowledgement

The experiments were carried out under the support of Russian Science
Foundation, grant No 18-53-34001. Calculations and models developed were
performed under the financial support of BASIS Foundation, grant no.
19-1-1-13-1. The authors are grateful to the Ioffe Institute for providing the
equipment used in experiments.

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