Quantitative Fluorescence Spectroscopy in Turbid Media - American

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Quantitative Fluorescence Spectroscopy in Turbid Media: A Practical Solution to the Problem of Scattering and Absorption Yao Chen, Zeng-Ping Chen,* Jing Yang, Jing-Wen Jin, Juan Zhang, and Ru-Qin Yu State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha, Hunan 410082, PR China S Supporting Information *

ABSTRACT: The presence of practically unavoidable scatterers and background absorbers in turbid media such as biological tissue or cell suspensions can significantly distort the shape and intensity of fluorescence spectra of fluorophores and, hence, greatly hinder the in situ quantitative determination of fluorophores in turbid media. In this contribution, a quantitative fluorescence model (QFM) was proposed to explicitly model the effects of the scattering and absorption on fluorescence measurements. On the basis of the proposed model, a calibration strategy was developed to remove the detrimental effects of scattering and absorption and, hence, realize accurate quantitative analysis of fluorophores in turbid media. A proof-of-concept model system, the determination of free Ca2+ in turbid media using Fura-2, was utilized to evaluate the performance of the proposed method. Experimental results showed that QFM can provide quite precise concentration predictions for free Ca2+ in turbid media with an average relative error of about 7%, probably the best results ever achieved for turbid media without the use of advanced optical technologies. QFM has not only good performance but also simplicity of implementation. It does not require characterization of the light scattering properties of turbid media, provided that the light scattering and absorption properties of the test samples are reasonably close to those of the calibration samples. QFM can be developed and extended in many application areas such as ratiometric fluorescent sensors for quantitative live cell imaging.

I

essentially restrict their wider application.5 Correction techniques using a ratio of fluorescence intensities at two emission wavelengths were also evaluated.11 It was discovered that there was a significant correlation between the ratio and factors other than the concentration of the target fluorophore, which indicating the ratio of fluorescence intensities at two wavelengths was not an effective approach for the correction of the effects of scattering and absorption. Measurement method-based techniques such as optimal fiber-optic design12 and the ratio of polarized fluorescence to reflectance13 have also been proposed to minimize the turbidity-induced fluorescence spectral variations by selectively recording fluorescence photons that have only traveled a relatively short distance through turbid medium. Compared with standard measurement techniques, these types of techniques measure only the fluorescence from the shallower depths of turbid medium and therefore may be restricted to the determination of fluorophores in upper tissue layers only. The modified Beer−Lambert law, Kubelka−Munk theory, and diffusion theory have been employed as theoretical bases for deriving a number of correction techniques. For example, Durkin et al.14 employed values of the Kubelka−Munk

n situ quantitative determination of exogenous/native fluorophores in tissue has the potential to aid medical diagnoses. However, elastic scattering and background absorption in turbid media, such as biological tissue or cell suspensions, are ubiquitous. The interplay of scatterers and absorbers can significantly distort the shape and intensity of fluorescence spectra of fluorophores. Such turbidity-induced fluorescence spectral variations introduce additional nonanalyte-specific variance into subsequent data analysis and, hence, greatly complicate the in situ quantitative determination of fluorophores in turbid media.1−4 The concentrations of fluorophores in turbid media can be accurately and reliably determined only when the effects of scattering and absorption are compensated by apposite correction techniques. There have been a number of techniques developed in recent years for correcting the effects of scattering and absorption on quantitative fluorescence spectroscopy.5,6 The most common techniques are based on a ratio of fluorescence to reflectance.5 However, early use of a ratio of fluorescence intensity to backscattered excitation light intensity yielded inconsistent results.7 Though a number of correction strategies, such as utilizing the spatial variations of fluorescence and reflectance,8 incorporating the diffuse reflectance at the emission wavelength9 and at both the excitation and emission wavelengths into correction factor,10 have been proposed in an attempt to improve the reproducibility of the results of techniques based on fluorescence-reflectance ratio, their intrinsic limitations © 2013 American Chemical Society

Received: September 27, 2012 Accepted: January 16, 2013 Published: January 16, 2013 2015

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Technical Note

where xi represents the fluorescence spectrum of the ith sample, ci,j is the concentration of the jth fluorophore in the ith sample, the row vector fj denotes the intrinsic fluorescence spectrum of the jth fluorophore, and I is number of samples. But for turbid media, such as biological tissue or cell suspensions, things become more complicated. The fluorescence spectrum of a turbid sample is not only dependent on the concentrations of fluorophores but also greatly affected by the interplay of scatterers and absorbers in the sample. For simplicity, let us first assume that there is no absorber in the turbid sample under consideration. Then, the following model can be used to approximate the relationship between the measured fluorescence spectrum and the concentrations of fluorophores in the sample.

scattering and absorption coefficients, obtained from diffuse reflectance and transmission spectra, to predict the intrinsic fluorescence spectrum. The main disadvantage of this technique is the requirement to determine transmission and reflectance data as part of the experimental procedure, and it may only be feasible in vitro. Zhadin and Alfano15 derived a correction method from a one-dimensional diffusion model. But the technique seems to be limited to recovery of relative, rather than absolute, fluorescence intensities. Wu et al.1 introduced a photon migration model to fluorescence. The main disadvantage of the technique is that prior knowledge of a number of optical parameters is requisite. Monte Carlo simulation is increasingly being used to model the effects of scattering and absorption on the fluorescence spectra of fluorophores in turbid media, due to its applicability to any illumination-collection geometry, any tissue structure, and any range of optical properties. Kanick et al.16 and Stephen et al.17 utilized Monte Carlo simulations to characterize the effects of scattering and absorption on fluorescence intensity collected by single fiber fluorescence. One downside of Monte Carlo simulation is the long time to run simulations. Moreover, the choice of scattering phase function can greatly affect the accuracy of simulation results. Therefore, care must be taken to ensure the selected scattering phase function is as close an approximation as possible to that of the turbid medium under consideration. Otherwise, the simulations may produce significantly inaccurate results. The potential of multivariate calibration methods in alleviating the effects of scattering and absorption on quantitative fluorescence spectroscopy has also been evaluated. For instances, Na et al.18 and Sandby-Møller et al.19 investigated the relationship between autofluorescence and skin pigmentation and redness using multiple regression analysis. Durkin and Richards-Kortum20 explored the possibility of utilizing the partial least-squares (PLS) method to extract the concentrations of fluorophores from intensity measurements. Application of the conventional multivariate calibration methods to tissue fluorescence, however, is constrained by the characteristics of the training samples, which must have the same optical properties as the tissue under consideration.5 As discussed above, though a great effort of research has been devoted to the development of various correction techniques over the past several decades, the development of a successful and practical correction technique remains a considerable challenge. In this contribution, a simple but effective model was presented to describe the effects of scattering and absorption on the fluorescence spectra of fluorophores in turbid media. And then, a unique calibration strategy for the accurate quantitative determination of fluorophores in turbid media was deduced from the proposed model. Finally, the effectiveness of the technique developed in this contribution was evaluated by a model system (i.e., the determination of free calcium (Ca2+) in turbid media using fluorescent indicator Fura-2).

J j=1

Here, ai and pλ account for the multiplicative and wavelengthdependent effects of scatterers on the measured fluorescence spectrum of the ith sample, respectively. The symbol “◦” represents the Hadamard product. Please note that ai is different for different samples, while pλ is a constant term. When taking the effects of both scattering and background absorption into consideration, a more complex model is needed to approximately describe the relationship among the measured fluorescence spectrum of a turbid sample, the concentrations of fluorophores, and the effects of scattering and absorption. J

K

x i ≈ [giai∑ (ci , j·f *j )]◦exp[(hi ·qλ)◦(− ∑ zi . k ·sk )] j=1 K

= [bi∑ (ci , j·f *j )]◦exp[−hi ∑ (zi , k ·s*k )] j=1

k=1

s*k = qλ◦sk ,

bi = ai ·gi

(3)

where gi represents the background absorption effect at the excitation wavelength (or emission wavelength, if excitation spectra are measured), hi and qλ account for the multiplicative and wavelength-dependent effects of scatterers on the background absorption at emission wavelengths (or excitation wavelengths, if excitation spectra are measured), respectively, zi,k is the concentration of the kth absorber in the Ith sample, and sk denotes the intrinsic absorbance spectrum of the kth absorber. If the effects of background absorption at emission wavelengths are not very strong (i.e., hi∑kK= 1(zi,k·s*k ) < 0.7), eq 3 can be simplified as follows (the error induced by the simplification is less than 2%).

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J

K

x i ≈ bi∑ ci , j·f *j + bi∑ ci , j·f *j ◦[−hi ∑ zi , k ·s*k j=1

j=1 K

k=1 K

+ hi2(∑ zi , k ·s*k )2 /2! − hi3(∑ zi , k ·s*k )3 /3! ] k=1

J j=1

k=1

J

J

∑ ci ,j·f j,

f *j = pλ◦f j

j=1

(2)

THEORY Quantitative Fluorescence Model for Turbid Media. The fluorescence spectrum of a transparent sample containing J fluorophores can be expressed as a linear combination of the fluorescence contributions of all J fluorophores in the sample. xi =

J

x i ≈ (ai ·pλ)◦ ∑ (ci , j·f j) = ai∑ (ci , j·f *j ),

k=1

(4)

Assuming there is only one main absorber in the turbid samples under consideration, eq 4 can then be further simplified.

i = 1, 2, ..., I (1) 2016

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J

xi =

x i ≈ bi∑ ci , j·f *j + bi∑ ci , j·f *j ◦[−hizi·s* + hi2(zi·s*)2 /2! j=1 j=1 − hi3(zi·s*)3 /3! ] J

J

= bi∑ ci , j·f *j − bihizi∑ ci , j·f *j ◦s* + j=1

j=1

∑ ci , j·f *j ◦(s*)2 j=1

J

b h 3z 3 − i i i ∑ ci , j·f *j ◦(s*)3 3! j = 1

⎪

(5)

diag(b)c1 = α21 + X calβ2

k=1

= [bi*{[Ca 2 +]·f 1* + kd·f *2 )}◦ K

exp[−hi ∑ (zi , k ·s*k )] k=1

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EXPERIMENTAL SECTION Reagents and Chemicals. 20% Intralipid used to simulate the scattering properties of turbid media was purchased from Kelun Pharmaceutical Co., Ltd. (Sichuan, China). Fura-2 pentapotassium salt (fluorescent indictor) was obtained from Sigma-Aldrich (Shanghai, China). Hydroxyethl piperazine ethanesulfonic (HEPES) acid, ethylene glycol tetraacetic (EGTA) acid, basic fuchsion (BF) and β-nicotinamide adenine dinucleotide reduced disodium salt hydrate (NADH) were purchased from Aladdin Reagent (Shanghai, China). All of these products were of analytical grade and used without further purification. Direct-pure plus water system (Aquapro, Chongqing, China) was applied to produce ultrapure water used throughout the experiment. Sample Preparation. A total of 60 turbid samples (40 calibration samples and 20 test samples) containing various free Ca2+ concentrations ([Ca2+]) were prepared at 37 °C by mixing two solutions (solution A: 1 mM EGTA; solution B: 1 mM EGTA and 1 mM Ca2+; both containing 100 mM KCl, 10 mM HEPES, pH 7.00) in various ratios25 and adding appropriate amounts of intralipid, Fura-2, BF and NADH (Supporting Information, Table S-1). Each sample was then diluted with HEPES buffer (100 mM KCl and 10 mM HEPES) to 10 mL in a brown volumetric flask, and the pH is adjusted to 7.00 with KOH. All pH values were measured with a starter 3C pH meter (Ohaus instrument Co., Ltd. of Shanghai, China). The free Ca2+ concentrations in the turbid samples were calculated according to the method described by Harrison and Bers.26 Fluorescence Measurements of Turbid Samples. Fluorescence excitation spectra of turbid samples were acquired in a range of 270−450 nm at 1 nm intervals by an F-4500 fluorescence spectrophotometer (Hitachi, Japan) equipped with a Xenon lamp. The excitation and emission slit widths were both set to 5 nm. Emission wavelength was 510 nm. Each sample was analyzed three times by the spectrofluorometer. Data Analysis. The multiplicative parameter vector b* (b* = [b1*;b2*;···;bI*]) for the calibration samples were estimated from fluorescence spectra of the calibration samples by

(6)

(7)

(8)

2+

For the ith mixture of a Ca -bound indicator (denoted by f1) and a free indicator (denoted by f2) at concentrations of ci,1 and ci,2, respectively, its fluorescence spectrum (xi) can be decomposed as follows: i = 1, 2, ···, I

(9) 2+

(11)

Clearly, kd is a constant, satisfying the prerequisite of ci,j = ccons tan d (where i = 1, 2, ..., I; j≠1). The concentration of free Ca2+ in a turbid sample can be determined from the corresponding measured fluorescence spectrum using the quantitative model and the unique calibration strategy described in the above sections.

The Model System: Determination of [Ca ] in Turbid Media Using Fura-2. The effectiveness of the proposed quantitative model and the corresponding calibration strategy for fluorescence measurements of turbid media were evaluated by a model system (i.e., the determination of free Ca2+ in turbid media using fluorescent indicator Fura-2). Fura-2 is a ratiometric fluorescent dye which exhibits 1:1 binding stoichiometry with Ca2+.23 The equilibrium reaction is represented as24

x i = ci ,1f1 + ci ,2 f 2,

⎪

exp[(hi ·qλ)◦( − ∑ zi , k ·sk )]

2+

[Ca 2 +] + [Fura‐2] = [Fura‐2‐Ca 2 +]

(10)

K

α2 + x testβ2 α1 + x testβ1

i = 1, 2, ···, I

⎪

⎪

where Xcal = [x1;x2;...;xI], c1=[c1,1;c2,1;...;cI,1], diag(b) denotes the diagonal matrix in which the diagonal elements are the corresponding elements of b, and 1 is a column vector with its elements equal to unity. After the estimation of the model parameters α1, α2, β1, and β2, the above two calibration models can then be used to predict the content (ctest,1) of the target fluorophore in any test turbid sample from its measured fluorescence spectrum xtest, provided the light scattering and absorption properties of the test sample are reasonably close to those of the calibration samples. ctest,1 =

([Ca 2 +]·f1 + kd·f 2),

⎧⎛ ci ,2 ⎫ ⎞ x i ≈ ⎨⎜ ·bi ·pλ⎟◦([Ca 2 +]·f1 + kd·f 2)⎬◦ ⎠ ⎩⎝ kd ⎭

Calibration Strategy for Fluorescence Measurements of Turbid Media. Let us arbitrarily assume that the first fluorophore in eq 5 is the target constituent. When ci,1 + ∑j ∈ (2,3,···,J)ci,j = ccons tan d (i = 1,2,···,I) or the content of one fluorophore (it can be a real or an abstract fluorophore) does not vary over samples (i.e., ci,j = ccons tan d, where i = 1,2,···,I, j≠1), it is easy to prove that a linear relationship exists between xi and bi and also between xi and bici,1.21 Under such circumstances, the multiplicative parameters, bi (where i = 1, 2,..., I), for I calibration samples can be estimated from their measured fluorescence spectra by the modified optical path length estimation and correction (OPLECm) method.22 After the estimation of the multiplicative parameter vector b (b = [b1;b2;···;bI]) of I calibration samples, the following two calibration models can be built by multivariate linear calibration methods such as PLS. b = α11 + Xcalβ1 ;

kd

For turbid samples, when taking the effects of both scattering and background absorption into consideration, eq 10 should be replaced by the more complex eq 11.

J bihi2zi2

2!

ci,2

2+

Since the concentration of free Ca ([Ca ]) in the ith sample can be expressed as [Ca2+] = kd × ci,1/ci,2 (kd is the effective dissociation constant of the Ca2+-bound indicator), eq 9 can be rewritten as 2017

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addition of scatterer primarily affects the intensity rather than the shape of the fluorescence spectra. As shown in Figure 2, the existence of the absorber (BF) also has significant effects on the intensity of the fluorescence

OPELCm (Supporting Information). Subsequently, two calibration models: b* = α11 + Xcalβ1 and diag(b*)c[Ca2+] = α21 + X cal β 2 were established using PLS method. With the fluorescence spectra of the test turbid samples being recorded, the free Ca2+ concentrations ([Ca2+]) in the test turbid samples can then be obtained by dividing the prediction of the second calibration model by the corresponding prediction of the first calibration model. For the convenience of presentation, the above calibration procedure is simply referred to as quantitative fluorescence model (QFM) method. The performance of QFM was compared with those of PLS calibration models with and without data preprocessing methods such as multiplicative signal correction (MSC),27 standard normal variate (SNV)28 and extended inverted signal correction (EISC)29 in terms of root-mean-square error of prediction (RMSEP) and average relative error (ARE). The optimal models were determined by cross validation (Figure S-1 of the Supporting Information).

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RESULTS AND DISCUSSIONS Effects of Scattering and Absorption on Fluorescence Measurements. For Fura-2-Ca2+ system without background interferences and scattering and absorption effects, the free calcium concentration is linearly related to the measured fluorescence intensity by a ratio-metric model.23,30 [Ca 2 +] = βkd(R − R min)/(R − R max )

Figure 2. The effects of absorber BF on the fluorescence spectra of both Fura-2 and Fura-2-Ca2+.

spectra. It fully verifies the appropriateness of introduction of the multiplicative parameter b*i in eq 11. The presence of the scatterer (intralipid) and absorber (BF) and the fluorescence interference (NADH) significantly distorted the linear relationship between [Ca2+] and (R − Rmin)/(R − Rmax) (Figure 3) and make it rather difficult to infer [Ca2+] from the measured fluorescence spectra of turbid samples.

(12)

where R is the ratio of fluorescence intensities at the emission wavelength, 510 nm, when the excitation wavelength is set at 340 and 380 nm, respectively, Rmin is the measured fluorescence ratio in the absence of Ca2+, Rmax is the measured fluorescence ratio of the Ca2+-saturated dye, β is the ratio of the fluorescence intensities at the wavelength chosen for the denominator of R (e.g., 380 nm excitation for Fura-2) in zero and saturating [Ca2+], and kd is the dissociation constant of Fura-2 for Ca2+. Obviously, a linear relationship exists between [Ca2+] and the ratio-metric measurement, (R − Rmin)/(R − Rmax), for transparent solutions (see Figure S-2 of the Supporting Information). But, for turbid media (Fura-2-Ca2+-BF-NADHintralipid emulsion system), the measured fluorescence intensity is not only dependent on the concentrations of fluorophores but also greatly affected by the presence of a scatterer (e.g., intralipid) and an absorber (e.g., BF). As can be seen in Figure 1, the fluorescence intensities of both Fura-2 and Fura-2-Ca2+ solutions decrease significantly as the amount of added intralipid increases. Interestingly, it seems that the

Figure 3. [(R − Rmin)/(Rmax − R)] vs [Ca2+] for the calibration turbid samples.

Accurate Determination of [Ca2+] in Turbid Media by QFM. As demonstrated above, the effects of scattering and absorption on fluorescence spectra of turbid media can cause significant systematic errors on the quantitative determination of [Ca2+], if they are not being appropriately modeled or corrected. With a view to achieving accurate quantitative determination of [Ca2+] in turbid media, QFM was applied to mitigate the effects of scattering and absorption on the fluorescence spectra. The application of QFM requires the estimation of the multiplicative parameter vector b* for the calibration samples. Figure 4 shows the multiplicative parameter vector b* for the calibration samples estimated by OPLECm. It can be seen from Figure 4 that the calibration turbid samples with different amounts of intralipid, BF, and/or free Fura-2 have significant different multiplicative parameters.

Figure 1. The effects of intralipid on the fluorescence spectra of both Fura-2 and Fura-2-Ca2+. 2018

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Table 1. The Predictions of [Ca2+] in the Test Turbid Samples Obtained by Different Methods

method QFM PLS PLS_MSC PLS_SNV

Figure 4. The multiplicative parameter vector b* for the calibration turbid samples estimated by OPLECm with the number of underlying components taking a value of 5.

PLS_EISC

no. of samples

true concentration (nM)

mean predicted concentration (nM)

SEa (nM)

AREb (%)

10 10 10 10 10 10 10 10 10 10

54.12 177.5 54.12 177.5 54.12 177.5 54.12 177.5 54.12 177.5

56.43 175.8 106.4 180.9 87.71 213.5 59.42 205.3 71.35 203.6

6.226 10.63 55.47 25.38 49.65 41.93 15.19 31.52 25.66 29.08

7 54 44 19 26

a SE: standard error, SE = [∑iI = 1(ci − cture)2/(I − 1)]1/2 bARE: average relative error: ARE = (1/I)∑i I= 1(|ci − cture|/cture)100%

These results are in excellent agreement with the QFM model in eq 11, which says: bi* varies with ai (the multiplicative effects of scattering), gi (the background absorption effect at the excitation wavelength), and ci,2 (the concentration of free Fura2). The high consistency between the theory and the experimental results at least partially demonstrates the effectiveness of QFM in modeling the effects of scattering and absorption. After the estimation of the multiplicative parameter vector b*, two calibration models, b* = α11 + Xcalβ1 and diag(b*) c[Ca2+] = α21 + Xcalβ2, were established using PLS method and used to predict the free Ca2+ concentrations ([Ca2+]) in the test turbid samples from their measured fluorescence spectra. For the purpose of comparison, PLS calibration models with and without data preprocessing methods such as MSC, SNV, and EISC were also constructed. Figure 5 compared the predictive

average relative error of about 54%. The application of MSC, SNV, or EISC had improved the predictive performance of PLS calibration model to some extent. However, as an empirical preprocessing method, the capability of MSC, SNV, or EISC in mitigating the effects of scattering and absorption on fluorescence spectra is still not strong enough to provide predictions with acceptable accuracy. In contrast, the concentration predictions given by QFM are quite close to the actual values. Its average relative error is about 7%, 2.7−7.7 times smaller than the corresponding values of various PLS models. To the best of our knowledge, these results might be the best results achieved so far for turbid media without the use of advanced optical technologies. Considering the high consistency between the theory and the experimental results about the multiplicative parameter vector b* and the capability of QFM to provide accurate concentration predictions for fluorophores in turbid samples, one can conclude that QFM is an effective and reliable technique to remove the effects of scattering and absorption on fluorescence spectroscopy and therefore provide a promising and convenient entry to monitor the concentrations of fluorophores in turbid media.

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CONCLUSIONS The presence of scatterers and absorbers affects the fluorescence spectra of fluorophores in turbid media, significantly distorting the linear relationship between the concentrations of fluorophores and their fluorescence measurements and making it rather difficult to infer the concentrations of fluorophores from the measured fluorescence spectra. With a view to achieve accurate quantitative determination of fluorophores in turbid media, a quantitative fluorescence model (QFM) was proposed in this contribution to explicitly model the effects of scattering and absorption. Under some mild conditions, a unique calibration strategy was deduced from the proposed model. The effectiveness of the proposed model and the calibration strategy was evaluated by a model system: the determination of free calcium ([Ca2+]) in turbid media using Fura-2. The obtained experimental results are highly consistent with the proposed theoretical model. Furthermore, QFM succeeded to provide accurate concentration predictions for [Ca2+] in turbid samples with an average relative error of about 7%, probably the best results achieved so far for turbid media. The implementation of QFM is rather simple too. Aside

Figure 5. The RMSEP values (nanomolar) of the predictions for [Ca2+] in the calibration and test turbid samples obtained by different methods.

performance of QFM and various PLS models for both the calibration and test turbid samples. Obviously, QFM far outperformed various PLS models in terms of RMSEP. The RMSEP values of QFM for the calibration and test turbid samples are 8.5 and 8.0 nM, respectively, which are less than one-third of those of various PLS models. For more detailed comparisons, the predictions of QFM and various PLS models for the concentrations of free Ca2+ in the test turbid samples are listed in Table 1. Due to the effects of scattering and absorption, PLS calibration models built on the raw fluorescence spectra could not provide satisfactory concentration predictions for the test turbid samples with an 2019

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from the fluorescence spectra of the calibration samples and the concentrations of the target fluorophore in the calibration samples, no other prior knowledge of the system under consideration is needed. Though the preliminary results demonstrated the effectiveness of the proposed method in quantitative fluorescence spectroscopy for turbid media, further research is needed to explore its full potential. Our future work will be focused on the extension of the proposed method to more complex systems such as ratiometric fluorescent sensors for quantitative live cell imaging.

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(16) Kanick, S. C.; Robinson, D. J.; Sterenborg, H. J. C. M.; Amelink, A. Biomed. Opt. Express 2012, 3 (1), 137−152. (17) Stephen, C. K.; Dominic, J. R.; Henricus, J. C. M. S.; Arjen, A. Opt. Lett. 2012, 37 (5), 948−950. (18) Na, R.; Stender, I. M.; Henriksen, M.; Wulf, H. C. J. Invest. Dermatol. 2001, 116, 536−540. (19) Sandby-Møller, J.; Poulsen, T.; Wulf, H. C. Photochem. Photobiol. 2003, 77 (6), 616−620. (20) Durkin, A. J.; Richards-Kortum, R. Lasers Surg. Med. 1996, 19 (1), 75−89. (21) Chen, Z. P.; Morris, J.; Marin, E. Anal. Chem. 2006, 78 (22), 7674−7681. (22) Jin, J. W.; Chen, Z. P.; Li, L. M.; Steponavicius, R.; Thennadil, S. N.; Yang, J.; Yu, R. Q. Anal. Chem. 2012, 84 (1), 320−326. (23) Grynkiewicz, G.; Poenie, M.; Tsien, R. Y. J. Biol. Chem. 1985, 260 (6), 3440−3450. (24) Van den Bergh, V.; Bones, N.; De Schryver, F. C.; Ameloot, M.; Steels, P. Biophys. J. 1995, 68 (3), 1110−1119. (25) McGuigan, J. A.; Luthi, D.; Buri, A. Can. J. Physiol. Pharmacol. 1991, 69 (11), 1733−1749. (26) Harrison, S. M.; Bers, D. M. Am. J. Physiol.: Cell Physiol. 1989, 256 (6), C1250−C1256. (27) Geladi, P.; McDougall, D.; Martens, H. Appl. Spectrosc. 1985, 39 (3), 491−500. (28) Barnes, R. J.; Dhanoa, M. S.; Lister, S. J. Appl. Spectrosc. 1989, 43 (5), 772−777. (29) Pedersen, D. K.; Martens, H.; Nielsen, J. P.; Engelsen, S. B. Appl. Spectrosc. 2002, 56 (9), 1206−1214. (30) Takahashi, A.; Camacho, P.; Lechleiter, J. D.; Herman, B. Physiol. Rev. 1999, 79 (4), 1089−1125.

ASSOCIATED CONTENT

S Supporting Information *

MATLAB code for the modified OPLEC method, experimental design for the Fura-2-Ca2+-BF-NADH-Intralipid emulsion system, RMSEP values from cross validation obtained by QFM and various PLS calibration models with different numbers of latent variables built on the raw and preprocessed fluorescence spectra by MSC, SNV, and EISC, and the linear relationship between [Ca2+] and the ratio-metric measurement (R − Rmin)/(R − Rmax) of transparent solutions containing Fura-2 and calcium calibration buffer. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (+86) 731 88821989. Fax: (+86) 731 88821989. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support of the National Natural Science Foundation of China (Grants 21075034, 21275046, and 21035001) and the Program for New Century Excellent Talents in University (NCET-12-0161).

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REFERENCES

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dx.doi.org/10.1021/ac302815e | Anal. Chem. 2013, 85, 2015−2020