2.1.

Decay of Fluorescence Intensity and Its Associated Anisotropy

The time- and wavelength-resolved fluorescence spectroscopy system used in this study measures two orthogonal polarization components of fluorescence from samples. They are parallel $\left(I_p\right)$ and perpendicular $\left(I_s\right)$ with respect to the polarization of the excitation light. With these two components, the total fluorescence intensity decay and fluorescence anisotropy decay can be calculated by the following equations, respectively:^{11, 20}

Fluorescence intensity decay can be fitted by the following equation,

The intensity fraction of each term in the total fluorescence:

In this study, free and protein-bound NADH are regarded as different fluorophores, with each having its own distinct intensity and anisotropy decay. When there are two or more different fluorophores in the sample, the measured anisotropy decay is an average of the anisotropy weighted by its intensity fraction. The fluorescence associated anisotropy in Eq. 2 is then determined by the following equation:^{11, 20}

In practice, we fit the denominator,

2.2.

Experimental Setup and Sample Preparation

A schematic diagram of the time- and wavelength resolved fluorescence spectroscopy system is shown in Fig. 1 . The setup was based on a confocal system equipped with a polarizer in the excitation path and a pair of analyzers in the emission path. Briefly, the second-harmonic generation (SHG) of a femtosecond Ti:sapphire laser provided $360\text{-}\mathrm{nm}$ excitation, nearly to the excitation peak of NADH fluorescence. This ensured that the excited cellular fluorescence was dominated by NADH signal.^{21, 22} The expanded laser beam was polarized by a Glan-Taylor prism (Melles Griot 03PTA403) placed before a dichroic mirror. An objective lens (Leica $40\times$ , NA 0.75) focused the beam into the sample and collected the backscatter fluorescence signals. The excitation power on the sample is about $10\mu \mathrm{W}$ . To reduce the possibility of photobleaching in samples, the laser focus was scanned over a $100\times 100\text{-}\mu \mathrm{m}$ sampling area by a pair of galvo-mirror scanners, and the recorded signal was the integration of fluorescence over the sampling area.⁵ We found that photobleaching could be negligible, because the cellular autofluorescence spectra and time-decay remained the same after multiple scanning over the sampling area. The previous study demonstrated that the fluorescence signals integrated over the sampling area in living cell samples were dominated by the NADH fluorescence from mitochondria.²³

Fig. 1

Schematic diagram of time- and wavelength—resolved fluorescence system.

A $400\text{-}\mu \mathrm{m}$ optical fiber was used as a pinhole to collect the confocal fluorescence and to conduct the signals to a spectrograph. A grating with a blaze wavelength at $400\mathrm{nm}$ was used in the spectrograph. The detector of the spectrograph was a linear array of photomultiplier tubes (PMTs) connected with a time-correlated single photon counting (TCSPC) module to record time-resolved fluorescence signals in 16 consecutive spectral bands from $420\text{to}520\mathrm{nm}$ at $6.2\text{-}\mathrm{nm}$ intervals. Two orthogonal analyzers driven by a computer-controlled switcher were placed before the fiber. The orientation of each analyzer was adjusted carefully according to the polarization of the excitation beam. The parallel and perpendicular components of the time-resolved fluorescence emission, $I_p\left(t\right)$ and $I_s\left(t\right)$ were measured sequentially for equal amounts of exposure time of $60\mathrm{s}$ . The temporal response function of each wavelength channel $R_{\lambda }\left(t\right)$ was measured for accurate fitting of multiexponential decay of NADH fluorescence. In this study, the fluorescence of 2-[4-(dimethylamino)styryl]-1-methylpyridinium iodide (DASPI) dissolved in ethanol was used to measure the temporal response function of the system, since its fluorescence lifetime is significantly shorter than the response of TCSPC-based detection^{24, 25} and the responses of all the channels can be measured simultaneously. The spectral response of the system was calibrated by using a NIST-traceable tungsten light source [Ocean Optics (Dunedin, Florida) LS-1-CAL]. To test the performance of the system, we measured the time-resolved fluorescence of rhodamine 6G in ethanol and rose bengal in methanol, the well-known fluorescent dyes. After deconvolution of the system temporal response, the fluorescence lifetimes of rhodamine 6G in ethanol and rose bengal in methanol were 3.77 and $0.51\mathrm{ns}$ , respectively. The results are very consistent with those in the published literature.^{26, 27}

A variety of NADH solutions and living cell cultures were used as samples in this study. To study the effects of cellular enzyme on the decays of NADH fluorescence intensity and anisotropy, pure NADH solution and the mixture solutions of NADH and lactate dehydrogenase (LDH), an enzyme present in a wide variety of organisms in living cells, were prepared for time- and wavelength-resolved fluorescence measurements. NADH powder and LDH solution were purchased from Sigma-Aldrich (Saint Louis, Missouri). The NADH solution was freshly prepared in $10\text{-}\mathrm{mM}$ tris(hydroxymethyl)aminomethane (Tris) buffer at pH 8. In the experiments, the $1000\text{-unit}∕\mathrm{ml}$ LDH solution was mixed in a 1:1 volume with the NADH solution. NADH concentration in the mixture was $500\mu \mathrm{M}$ .

SiHa and Ect1 cell lines were provided from the American Type Culture Collection (ATCC). The SiHa cell line was established from cervical cancer tissue, whereas the Ect1 cell line was developed from normal cervical tissue. SiHa cells were grown in Dulbecco’s Modified Eagle Medium (DMEM) containing 10% fetal bovine serum, and Ect1 cells were cultured in Keratinocyte-Serum-Free medium with $0.1\text{-}\mathrm{ng}∕\mathrm{ml}$ human recombinant EGF and $0.05\text{-}\mathrm{mg}∕\mathrm{ml}$ bovine pituitary extract. The cells were maintained in a 5% $\mathrm{C}{\mathrm{O}}_2$ incubator at $37°\mathrm{C}$ and cultured every $4\text{to}5\text{days}$ . On the day before the measurements, the cells were trypsinized from culture dishes and grown on microscope coverslips. Before the measurements, the cells were washed with phosphate buffered saline (PBS) solution twice to eliminate the fluorescence of the medium. The confluence of monolayer cells in the measurements was about 90%.

To disturb the redox potential of the cells, $5\text{-}\mathrm{mM}$ sodium cyanide (NaCN) and $100\text{-}\mu \mathrm{M}$ carbonyl cyanide 3-chloro phenylhydrazone (CCCP) were used. NaCN affects the mitochondrial transport by blocking the transfer of electrons from the electron donors, so the oxidation of NADH is prohibited and the free NADH is accumulated. CCCP reduces the proton gradient and thus increases particle exchange across the mitochondrial membrane. Free NADH in mitochondria is released to the cytosol and rapidly oxidized.²⁸ In this study, cell cultures were treated with NaCN or CCCP solution for five minutes then measured in PBS.⁵

2.3.

Global Fitting Analysis

The global analysis method described in Ref. 29 was used to fit Eq. 6 and obtain the parameters related to cellular metabolism and viscosity. Briefly, a vector $\mathbf{g}$ , including all the shared parameters and the independent parameters, was created. For example, rotational diffusion time and fluorescence lifetime in this study are independent of emission wavelength and considered the shared parameters. The rotational diffusion time reflects the rotational mobility of a fluorophore, which depends on its shape, size, or flexibility. The fluorescence lifetime indicates the dwell time of the electron in the lowest vibrational level of the excited state, and it is generally independent of emission wavelength.²⁰ We have measured the fluorescence lifetimes of several fluorophores, such as aqueous NADH, the mixture of LDH and NADH, rhodamine 6G, etc., and found that the lifetimes are all independent of the emission wavelength. However, the pre-exponential amplitudes at each wavelength are considered independent parameters, because they are a function of the fluorophore’s concentration and spectral line shape. Then the $\mathbf{g}$ -vector and the initial testing value of each fitting parameter were used to solve the Marquardt-Levenberg equation. The elements that were related to the shared parameters were processed by each curve, and the independent parameters were only restricted by their own decay curves.²⁹ The Marquardt-Levenberg nonlinear least-squares algorithm was used to search the global minima for all the curves. The details of the fitting algorithm can be found in Ref. 29.

3.1.

Analyses of the Measurements from Reduced Nicotinamide Adenine Dinucleotide Solutions

Since there are folded and unfolded conformations of free NADH in aqueous environments which were first discovered from x-ray crystallographic data,³⁰ a biexponential function of Eq. 3 was used to describe the fluorescence intensity decay curves. 16 curves at consecutive emission wavelengths from $420\text{to}520\mathrm{nm}$ were globally analyzed by the method described in Sec. 2, where the lifetimes ${\tau }_1$ and ${\tau }_2$ are the shared parameters of all curves, and the pre-exponential amplitudes $a_{\lambda ,1}$ and $a_{\lambda ,2}$ , depend on their own curves. Excellent fitting was achieved with ${\chi }^2<2.5$ . The measured ${\tau }_1$ and ${\tau }_2$ are $0.252\pm 0.004$ and $0.583\pm 0.011\mathrm{ns}$ , respectively. The results agree well with reports in the literature.^{30, 31} By using the fitting results of lifetimes and pre-exponential amplitudes, the decay-associated spectra (DAS) of the folded and unfolded conformations of NADH were calculated based on Eq. 5. The results are displayed in Fig. 2 . As can be seen, the spectra of two different conformations of NADH are almost identical. The ratio of pre-exponential amplitudes $a_1∕a_2$ , averaged over all 16 channels, is $2.28\pm 0.19$ . Furthermore, we tested the fitting of free NADH fluorescence using a monoexponential model. The larger ${\chi }^2$ $(>10)$ indicated that the monoexponential model is not as accurate as the biexponential model in the description of the fluorescence decay of aqueous free NADH.

Fig. 2

Results of global fitting analysis of fluorescence signals from pure NADH solution. (a) The normalized decay associated spectra (DAS) of two conformations of aqueous NADH (a biexponential function was used to describe the fluorescence intensity decay curve, and 16 curves at consecutive emission wavelengths were globally analyzed). (b) The measured and fitted fluorescence anisotropy decay.

Next, the fluorescence anisotropy decay of free NADH in an aqueous solution was fitted using Eq. 6 with known parameters of the fluorescence intensity decay ( ${\tau }_1$ and ${\tau }_2$ , $a_{\lambda ,1}$ , and $a_{\lambda ,2}$ ). A monoexponential function was used to describe fluorescence anisotropy decay based on the assumption that two different conformations of free NADH contribute in the same way to the rotational diffusion of free NADH molecules. Excellent fitting results shown in Fig. 2 indicate that a monoexponential function is adequate to describe the fluorescence anisotropy decay of free NADH. The average rotational diffusion time $\left(\theta \right)$ and the average initial anisotropy $\left(r_{\mathrm{o}}\right)$ over the 16 wavelength bands are $0.128\pm 0.004\mathrm{ns}$ and $0.368\pm 0.029$ , respectively, which are consistent with the results of previous studies.^{30, 32}

Analysis of the time-resolved fluorescence anisotropy decay provides information on the rotational mobility of a molecule, and the rotational diffusion time sensitively reflects the volume of the molecule. This relationship is described by the Stokes-Einstein equation $\theta =\eta V∕kT$ , where $\eta$ is the viscosity, $T$ is the temperature in Kelvin, $k$ is the Boltzmann constant, and $V$ is the hydrodynamic volume of the rotating unit.²⁰ In the measurement, $T$ was controlled at $295\mathrm{K}$ ; the viscosity of water is known as $0.958\mathrm{cP}$ .³³ As a result, the volume of NADH was found to be about $544\pm 17{\mathrm{\AA }}^3$ , slightly larger than the previously reported $493{\mathrm{\AA }}^3$ that was theoretically calculated by using Van der Waals increments method.³⁴ The difference may be due to the complementary hydration volume.³⁰ For simplification, NADH is approximately regarded as spherically shaped molecules in this study.

We mixed LDH with NADH to validate our method for the extraction of free and protein-bound NADH signals. The following formula was used to describe the NADH fluorescence intensity decay:

Though bound NADH may have multiple decay channels, it was found that a biexponential model $(n=2)$ for the bound-NADH term was adequate to produce accurate fitting $({\chi }^2<2)$ of the time-resolved fluorescence signals measured from NADH and LDH mixtures. When $n$ was greater than 2, multiple local minima led to a series of fitting parameters without physical meaning. As a result, the decay time constants of bound-NADH fluorescence ( ${\tau }_1^{,}$ and ${\tau }_2^{,}$ ), the shared parameters in the global fitting, were found to be $1.03\pm 0.04$ and $2.51\pm 0.19\mathrm{ns}$ , respectively. The average ratio of two pre-exponential amplitudes $a_{\lambda ,1}^{,}∕a_{\lambda ,2}^{,}$ was $2.77\pm 0.11$ . The ${\chi }^2$ value was 1.88. Representative fitting results are shown in Fig. 3 . As can be seen, the decay-associated spectra of two components of bound-NADH are almost identical and the total fluorescence spectrum of NADH, and the LDH mixture was accurately fitted. The experimentally measured fluorescence intensity decay was also accurately fitted using Eq. 7, as shown in Fig. 3. It should be pointed out that the LDH purchased from Sigma-Aldrich was not purified, and only the unit of activity was provided. Therefore, the exact ratio of free to bound NADH in the mixture could not be accurately estimated.

Fig. 3

Representative results of global fitting analysis of fluorescence signals measured from the mixture solution of NADH and LDH. (a) The spectra of the measured and fitted NADH fluorescence signals. Open squares: experimentally measured total spectral signal. Solid line: the fitted total signal. Open circles: fractional decay associated spectrum (DAS) of free NADH. Up-triangles: fractional DAS of bound NADH1. Down-triangles: fractional DAS of bound NADH2. (b) The measured and fitted fluorescence intensity decay. (c) The measured and fitted fluorescence associated anisotropy decay.

To verify whether the free and bound NADH could be unambiguously distinguished based on Eq. 7, we analyzed the fluorescence anisotropy decay dynamics of the mixture. A typical fluorescence anisotropy decay curve measured from a NADH and LDH mixture is shown in Fig. 3. Unlike the result of aqueous NADH shown in Fig. 2, the anisotropy decay curve exhibited a quick decrease at first, followed by a small increase and then slow decay at longer times. This is a typical pattern of associated anisotropy decay with two fluorophores of different intensity and anisotropy decays in the mixture.^{11, 20} The fluorescence intensity decay of free NADH was quicker than that of bound NADH; its fractional intensity decreased progressively. As a result, the dominant contribution to the total anisotropy decay curve changed from free NADH at the start to bound NADH at the end. The associated anisotropy curve was fitted by the global analysis program using the following model based on the definition of $D_{\lambda }\left(t\right)$ in Eq. 6, as described in Sec. 2.1,

Again, accurate fitting was achieved as shown in Fig. 3. The ${\theta }_1$ of NADH and LDH mixture is $0.176\pm 0.009\mathrm{ns}$ , while the change of ${\chi }^2$ value becomes negligible when ${\theta }_2$ is greater than $30\mathrm{ns}$ in the fitting. In fact, accurate measurement of ${\theta }_2$ longer than $10\mathrm{ns}$ is impractical because of a limited measurement window determined by the repetition rate of the excitation laser $\left(78\mathrm{MHz}\right)$ and the fluorescence intensity decay of bound NADH $(\sim 2\mathrm{ns})$ . The results demonstrate that fluorescence anisotropy decay of the first term in Eq. 8 is at least two orders shorter that the second term. This provides solid evidence that the first term comes from free NADH and the second term is from bound NADH, because the LDH molecule $\left(27\mathrm{kDa}\right)$ is much larger than the NADH molecule $\left(709\mathrm{Da}\right)$ .

In addition, the rotational diffusion time of free NADH was increased compared with that of aqueous NADH solution. This is not surprising, because the diffusion time is proportional to the viscosity of the environment, and the viscosity of the mixture solution increased when LDH with much greater molecular weight was added. Based on the hydrodynamic volume of aqueous NADH measured previously and the Stokes-Einstein equation ${\theta }_1=\eta V∕kT$ , we obtained the viscosity coefficient of the NADH and LDH mixture at about $1.32\pm 0.06\mathrm{cP}$ . To verify the results, we measured the viscosity coefficient of the NADH and LDH mixture by using a microchannel viscometer. Details of the technology and measurement procedures were described in Ref. 35. The measured viscosity coefficient of $1.34\pm 0.02\mathrm{cP}$ was consistent with our results based on the analysis of NADH fluorescence anisotropy decay.

3.2.

Analyses of the Measurements from Living Cell Samples

When a fluorescent molecule presents in a solution of complicated chemical composition, the solvent effect will affect the fluorescence measurements. There are three major mechanisms that can cause changes in spectral and temporal fluorescence characteristics.²⁰ Binding with other molecules in the solution causes spectral shift, change of fluorescence lifetime, and decrease of mobility. The solvent shell effect shifts fluorescence emission, owing to stabilization of the excited state by the polar solvent molecules around the fluorescent molecule.³⁶ Finally, fluorescence quenching is another primary source of changes in fluorescence decay dynamics.

In a living cell, a large portion of NADH bind to a variety of enzymes and proteins in multistep metabolic pathways. When NADH binds to a large molecule, fluorescence lifetime and anisotropy will change significantly.^{11, 37} Free NADH signals can be differentiated from bound NADH based on their differences in temporal characteristics. Because 75 to 85% of intracellular fluid is water,³⁸ it is water molecules that mainly compose the solvent shell of free NADH. Thus it is reasonable to assume that the spectra of free NADH are the same both in aqueous solutions and in cells. According to the Stern-Volmer theory, fluorescence lifetime changes arising from quenching can be described by following equation,

Therefore, similar to the analysis of the NADH and LDH mixture, the fluorescence intensity decay of NADH fluorescence from living cells was fitted by Eq. 7, where the first and second terms were the contributions from free and bound NADH, respectively. To minimize possible interference of the flavoprotein (FAD) fluorescence peaking around $530\mathrm{nm}$ ,²² only 12 short-wavelength channels from $420\text{to}490\mathrm{nm}$ were used in the global analysis. Representative results obtained from monolayer SiHa cell culture are shown in Fig. 4 . As can be seen, excellent fittings to both the fluorescence spectrum and intensity decay were achieved. The spectral signal fitting showed that about three-quarters of total fluorescence intensity came from the bound NADH in living cells, and the spectral peaks of the bound NADH were blue shifted about $20\mathrm{nm}$ compared with the spectral peak of free NADH.

Fig. 4

Representative results of global fitting analysis of cellular NADH fluorescence signals from living SiHa cell samples. (a) The fluorescence spectra of the measured NADH signal, the fitted total signal, and the fractional decay associated spectra (DAS) of each component (free NADH, bound NADH1, and bound NADH2). (b) The measured and fitted fluorescence intensity decay. (c) The measured and fitted fluorescence associated anisotropy decay.

We conducted cellular-based measurements to exhibit the capabilities of our measurement system and global-fitting analysis. The results of all parameters obtained from SiHa and Ect1 cell samples before the treatments with a mitochondrial inhibitor and uncoupler are summarized in Table 1 . SiHa cells are well-known ectocervical cancer cells, whereas the Ect1 cells are established from normal ectocervical epithelium immortalized by HPV-16 E6/E7 transformation.⁴⁰ As can be seen, the ratio of the fractional intensity of free NADH signal to bound NADH signal were 0.45 and 0.32 for SiHa cells and Ect1 cells, respectively. The Warburg hypothesis suggests that cancer cells mainly generate energy by anaerobic glycolysis, whereas normal cells mainly generate energy from oxidative phosphorylation. Since more types of enzymes participate in oxidative phosphorylation compared with glycolysis, there are more binding sites in oxidative phosphorylation.³⁷ This may provide an explanation why SiHa cells had a greater fraction of intracellular free NADH compared with Ect1 cells.

Table 1

Analysis of fluorescence intensity decays from cell samples. Maximal χ2 value in all fittings was not more than 2. n is the number of cell samples, and five measurements were conducted from different sites in each sample. The free/bound values reflect the ratio of the fractional intensity defined in Eq. 4.

To further demonstrate the correlation of the ratio of free to bound NADH with the cell’s metabolic state, the redox potential of cells were disturbed by the mitochondrial inhibitor NaCN and mitochondrial uncoupler CCCP, respectively.^{4, 5, 28} The results of the cell samples after the treatments of NaCN and CCCP are also listed in Table 1. The values of free to bound NADH increased with NaCN treatment and decreased with CCCP treatment in both SiHa and Ect1 cells, which were consistent with previous studies.^{4, 5} However, the amplitudes of these changes were different. The changes in Ect1 cells were more significant compared with those in SiHa cells. For example, with NaCN treatment, the ratio increased by 23% in SiHa cells, whereas it increased by 131% in Ect1 cells. With CCCP treatment, the ratio decreased by three times more in Ect1 cells than in SiHa cells. Reasons for these differences between SiHa and Ect1 cells are currently undetermined. It should be noted that the measurement of FAD/NADH to estimate the redox state of cells was not evaluated in this study, because the signal of FAD fluorescence is extremely weak at the excitation wavelength of $360\mathrm{nm}$ .

To investigate viscosity of small solutes in cells, we analyzed the cellular fluorescence anisotropy decay of cell samples. Because NADH is a small molecule, the microviscosity for small molecules rather than the macroviscosity for large proteins or organelles could be probed by measuring NADH rotational mobility. A typical fluorescence anisotropy decay curve measured from a SiHa cell sample is shown in Fig. 4. Similar to the analysis of fluorescence anisotropy decay in the NADH and LDH mixture, the model based on Eq. 8 was used to fit the associated anisotropy decay. A typical fitting result for SiHa cells is shown together with the experimentally measured curve in Fig. 4. $r_{\lambda ,1}^{\prime }$ and $r_{\lambda ,2}^{\prime }$ were 0.36 and 0.25, respectively. ${\theta }_1$ was $0.204\mathrm{ns}$ , and ${\theta }_2$ was more than $30\mathrm{ns}$ . Again, the uncertain large ${\theta }_2$ value meant that bound NADH in cells was rotationally immobile in the time scale of our measurement window, which was limited by the repetition rate $\left(78\mathrm{MHz}\right)$ of our Ti:sapphire laser system and fluorescence lifetime of bound NADH.

The results of all measurements of SiHa and Ect1 cells before and after the treatments with NaCN and CCCP are listed in Table 2 . As described before, the rotational diffusion time of free NADH ${\theta }_1$ is proportional to the environmental viscosity. As a result, the cellular microviscosity could be calculated from the rotational diffusion time. Based on Stokes-Einstein equation ${\theta }_1=\eta V∕kT$ , we found that the cellular microviscosity was about 1.6 times higher than water. This result is consistent with previous reports.^{14, 19} It should be pointed out that the Stokes-Einstein equation holds only for spherically shaped molecules. Therefore, the values determined by this equation should be regarded as estimates. Furthermore, we found that the treatment with NaCN caused obvious decrease of the rotation diffusion time of free NADH, while the treatment with CCCP did not cause the same effect. It is known that NaCN interrupts the electron transport chain and causes hypoxia. Previous studies have demonstrated that hypoxia caused osmotic swelling of mitochondria.⁴¹ A recent study based on real-time microscopy further pointed that the mitochondria of fibroblasts swelled when treated with rotenone or antimycin A, which caused hypoxia in cells, whereas the morphology of the mitochondria did not change when treated with CCCP.⁴² The dilution of intramitochondrial fluid by swelling will reduce the viscosity in mitochondria, which are the sources of most of cellular NADH fluorescence.²³ These may explain the changes in the rotation diffusion time of free NADH when cells were treated with NaCN.

Table 2

Analysis of associated anisotropy decays from cell samples. Maximal χ2 value in all fittings was not more than 1.2. Viscosity was estimated from the rotational relaxation time of free NADH.

3.3.

Single Wavelength Fitting Versus Global Fitting Analyses

In principle, the parameters in $I_{\lambda ,c}\left(t\right)$ and $D_{\lambda ,c}\left(t\right)$ models can be obtained by fitting the experimental curve recorded in a single wavelength band. However, this approach does not take advantage of the relationship between individual decay curves recorded in different wavelength bands to reduce the local minima and improve fitting accuracy. Global analysis facilitates the analysis of multiple measurements simultaneously in terms of internally consistent sets of fitting parameters. Previous study has demonstrated that global analysis can significantly improve accuracy compared with individual analysis.⁴³ In this study, we found that in the global fitting analysis, it was crucial to make use of the time-resolved fluorescence signals recorded from all 16 (12 for cells) emission wavelengths to effectively reduce multiple local minima and produce accurate fitting results. As an example, the cellular fluorescence measured at a single emission wavelength from controlled SiHa cells was fitted based on Eq. 6 using the method described in Ref. 11. As shown in Table 3 , multiple minima were found, and three sets of parameters that produced the best fitting $({\chi }^2=1.1)$ were significantly different from each other, making it difficult to identify which set of parameters holds true physical meaning. However, the fitting results based on global analysis of 12 wavelengths presented in Tables 1, 2 always converged to one single set of parameters. In addition, we also used the measurement result from the mixture solution of NADH and LDH to compare the fitting based on the signal at the single wavelength band, with the global fitting using signals recorded at 16 wavelength bands. As shown in Table 4 , four sets of parameters that were significantly different from each other produced the best fitting $({\chi }^2=1.2)$ , indicating that multiple local minima occurred in fitting the data from the mixture NADH solutions with simpler chemical composition in comparison with living cells. In contrast, the results based on global fitting converged to a single set of parameters again. These results demonstrated that global analysis provided more accurate fitting and physical meaning than the fitting based on a single wavelength band.

Table 3

Fitting results based on the same fluorescence signal from cells at single wavelengths of NADH fluorescence peaks. With the same measured fluorescence data, three sets of results were achieved, and χ2=1.1 for each fitting. Parameters in this table were defined in Eq. 6, and the fitting method was defined in Ref. 11.

Table 4

Fitting results based on the same fluorescence signal from the NADH and LDH mixture solution at single wavelengths of NADH fluorescence peaks. With the same measured fluorescence data, four sets of results were achieved, and χ2=1.2 for each fittings. Parameters in this table were defined in Eq. 6, and the fitting method was defined in Ref. 11.