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A Fluorescence Approach for the Determination of Fluorescent Dissolved Organic Matter Chen Qian, Long-Fei Wang, Wei Chen, Yan-Shan Wang, Xiao-Yang Liu, Hong Jiang, and Han-Qing Yu Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b00324 • Publication Date (Web): 02 Mar 2017 Downloaded from http://pubs.acs.org on March 4, 2017

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Analytical Chemistry

A Fluorescence Approach for the Determination of Fluorescent Dissolved Organic Matter

Chen Qian, Long-Fei Wang, Wei Chen, Yan-Shan Wang, Xiao-Yang Liu, Hong Jiang, Han-Qing Yu* CAS Key Laboratory of Urban Pollutant Conversion, Department of Chemistry, University of Science and Technology of China, Hefei, 230026, China

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ACS Paragon Plus Environment


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Excitation-emission matrix (EEM) fluorescence spectroscopy coupled with parallel

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factor analysis (PARAFAC) has been widely applied to characterize dissolved organic

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matter (DOM) in aquatic and terrestrial systems. However, its application in

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environmental samples is limited because PARAFAC is not able to handle

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non-trilinear EEM data, leading to the overestimated number of components and

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incorrect decomposition results. In this work, a new method, Parallel Factor

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Framework-Clustering Analysis (PFFCA), is proposed to resolve this problem. First,

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simulated data with different signal to noise ratios and intensities of non-trilinear

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structure were tested to confirm the robustness of PFFCA. The residual sum of

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squares (RSS) of PARAFAC was significantly higher than that of PFFCA (P0.92) closer to actual EEM than PARAFAC (R2>0.81).

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Finally, to confirm the feasibility of PFFCA in analyzing natural samples,

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DOM-containing samples collected from both a polluted lake and river were tested,

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indicating that PFFCA provides a more precise estimation than PARAFAC. The

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results clearly indicate that PFFCA offers a robust approach for the unique

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decomposition of complex synthetic and natural samples, which is of great

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significance in understanding the characteristics of DOM in aqueous systems.

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INTRODUCTION

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Dissolved organic matter (DOM) is a mixture of complex and heterogeneous

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compounds with varying solubility and reactivity. Ubiquitous DOM plays critical

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roles in global biochemical/geochemical cycling and significantly affects the fate and

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transport of pollutants. Great efforts have been made to analyze and characterize

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DOM using multiple methods and instruments including infrared spectroscopy,1,

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nuclear magnetic resonance,1, 3, 4 and fluorescence spectroscopy.4-6 Among the various

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techniques, excitation-emission matrix (EEM) fluorescence spectroscopy coupled with

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parallel factor (PARAFAC) analysis can provide useful information regarding the

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fluorescence characteristics, especially for complex samples.7-9 It has been used as a

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powerful tool to characterize chromophoric DOM in environmentals due to its high

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rapidity, selectivity and sensitivity.9-11 PARAFAC analysis is a tensor decomposition

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method that decomposes the original data (intensity × emission × excitation) into

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trilinear components, with each component consisting of one score vector and two

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loading vectors (emission and excitation spectrums). The score vector of each

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component corresponds to its relative concentration. By using PARAFAC analysis,

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complex EEM fluorescence spectra can be separated into several components, usually

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indicating the compositions of tested samples.12, 13 This mathematical approach is of

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great significance because the overlapped spectroscopy of various contributors can be

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well separated, facilitating understanding of the behaviors of each component in

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environmental changes.9, 14

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When data are approximately low-rank trilinear and the fluorescent groups are

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independent, the general idea is that the components decomposed from the data

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correspond to the actual components in PARAFAC analysis. However, this concept is

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not valid in environmental samples because of the highly variant structure,

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conformation, and heterogeneity, as well as intra- and inter-molecular interactions of

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DOM.4, 15 Dissolved humic acid (HA), one of the most important types of DOM in

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aquatic environments, is a mixture of many molecules, some of which are based on a

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motif of aromatic nuclei with phenolic and carboxylic substituents linked together.16, 17

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The fluorescent groups in HA are not independent, suggesting that PARAFAC analysis

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may decompose HA into more than a single component, each representing merely a

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proportion of HA. This phenomenon has been observed in many previous studies, in

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which some components of HA derived from PARAFAC analysis showed a positive

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linear correlation (R2 > 0.8).18-23 Evidently, it is inappropriate to treat the highly

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correlated fluorophores as individual component. Component does not mean a certain

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substance but an identifiable unit, which has different fates or behaviors with each

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other. On one hand, if two substances come from the same source and change

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synchronously, correlation could not be used to identify which one is responsible for

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the changes. Although the impacts of substances can be inferred from their structure

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or chemical compositions, UV/visible humic acid-like or marine humic acid-like

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substances cannot provide useful information regarding their structure or chemical

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composition. Therefore, it is unnecessary to distinguish two substances with highly

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correlated concentrations. As a result, the number of components estimated by

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PARAFAC analysis might not be the actual component number (two examples are

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provided in Supporting Information to support this statement). The misestimate of the

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component number inevitably leads to totally different decomposition results, which

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remains one of the major defects of PARAFAC analysis.

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For a given sample with fixed compositions, a unique decomposition of the

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fluorophores is essential to make fair comparisons. Nevertheless, a unique

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decomposition cannot always be acquired when performing PARAFAC on complex

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environmental samples. The decomposition result of one sample may change when it is

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decomposed with different sample series, which is another major limitation for

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PARAFAC applications. A unique decomposition in PARAFAC analysis can be

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acquired if all spectra and concentration profiles are linearly independent.14 A

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non-unique result will result in misunderstanding sample compositions and

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fluorophore changes, which may notably affect or alter some previous conclusions.

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The main reason for these two barriers is that the PARAFAC approach can only

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be applied in treating linearly dependent fluorophores, and the analysis of

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non-trilinear structure is beyond the limits of PARAFAC. In other words, sloping peak

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in the EEM landscape destroys the independence of excitation and emission spectra.

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Therefore, the acquisition of a unique decomposition result from data sets that do not

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conform to trilinear structure should be of great concern. It was observed that the use

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of more components in Diltiazem contributed to a more correct and robust

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concentration estimation.24 Consequently, a new separation method is required with an

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aim at accurately determining the actual component number by eliminating the

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PARAFAC limitation of requiring trilinear results. To date, there is no such

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information about how to determine the number of components and combine the

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collinear components to estimate the actual components in the samples.

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In this work, a new method, called Parallel Factor Framework-Clustering

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Analysis (PFFCA), is proposed, which includes two steps: data decomposition and

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component formation. First, 24 simulated data sets with different intensities of

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non-trilinear structure and signal to noise ratios (SNR) were tested to investigate the

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robustness when handling non-trilinear data. Second, synthetic and environmental

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samples were tested with the PFFCA approach. One mixture of HA and bovine serum

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albumin (BSA) was used to test the feasibility of PFFCA in processing synthetic

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samples. Finally, two environmental sample series from a polluted lake and river were

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examined in an attempt to test whether the decomposition could provide a unique

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result for environmental samples. For all of the above cases, PARAFAC analysis with

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a core consistency diagnostic and split-half analysis was also examined for

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comparison. The reason why the core consistency diagnostic is used is given in SI.

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To avoid confusion of the components decomposed from the data and the actual

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components in the samples, in the following sections, the components decomposed

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from the data will be called “factors”, and the actual components in the samples will

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be called “components”.

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MATERIALS AND METHODS

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Principles of PFFCA. Theoretically, excitation and emission wavelengths are

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independent, and PARAFAC is thus a reasonable tool. However, when dealing with

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complex samples such as DOM, the presupposition is no longer valid, and the only

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way to distinguish different components is the derived scores. The PFFCA method

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principally assumes that all of the components are independent and that the dataset is

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decomposed into many factors. Afterwards, the factors whose scores are highly

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correlated should be combined into one component because they individually

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represent only a proportion of the component. Two steps make up the basic idea of

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PFFCA showing in Supporting Information. PFFCA modeling was carried out in

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MATLAB 7.10.0 (Mathworks, Natick, MA, USA) with the N-way toolbox 3.1.25

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PFFCA is available on via the Internet at http://pubs.acs.org/.

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Simulated Fluorescence Data Acquisition. Two peaks (Peaks A and B)

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conformed to trilinear structure were defined to simulate fluorescent peaks (Figure 1a).

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Peak C did not conform to trilinear structure and was designed to simulate the first or

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second Rayleigh scatterings or complex fluorescent substances, e.g., HA. All of these

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peaks were simulated by a two-dimensional Gaussian function:

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f, = · exp −

+

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(1)


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where the coefficient M is the amplitude indicating the “concentration” of each peak,

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(xo, yo) is the center, and σx and σy represent the standard deviations of the

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concentrations in the x and y dimensions, respectively. The coefficients of Peaks A, B

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and C are listed in Table S1. The data were composed of 20 EEM landscapes, each

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with a size of (70 × 60). We presume that x and y represent the emission wavelength

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(Em) from 300 nm to 359 nm and excitation wavelength (Ex) from 280 nm to 349 nm,

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respectively. Peaks A and B were both Gaussion peaks with the amplitudes (M)

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changing sinusoidally and cosinoidally, respectively, while the Peak C was a 45o

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rotated Gaussian peak with a constant amplitude in each EEM. The amplitude of Peak

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C was kept constant in the 20 samples to eliminate the influence of rate-of-change of

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Peak C. To examine the influence of Peak C, the amplitude of Peak C was tested from

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0.2 to 1.7 with a 0.3 step increase in different datasets. To simulate the actual EEM

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data as closely as possible, random noise was added to the EEM spectra and SNR

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values at 10, 15, 20 and 50 were tested. The EEM matrixes of these three peaks were

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added together to generate the combination EEMs. Therefore, 24 datasets with

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different Peak C intensities and SNR were simulated, each with a size of (20 ×70 × 60)

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(Table S2).

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Fluorescence Data of an HA and BSA Mixture. HA and BSA were purchased

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from Sigma-Aldrich Co., USA. Deionized water with resistivity higher than 18.2

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MΩ/cm at 25 °C was used. The tested concentrations were from 0 to 25 mg/L for HA

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and from 0 to 50 mg/L for BSA. Three-dimensional EEM fluorescence spectra were

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recorded using an Aqualog spectrometer (Horiba Co., Japan). An orthogonal testing

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with a total number of 36 EEM landscapes was produced (Table S3). The measured

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emission spectra ranged from 211 to 618 nm with a 3.8-nm step increase, while the

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excitation wavelength increased sequentially from 230 to 600 nm with a 3-nm step.

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Inner filter effect (IFE) was corrected by the Aqualog software. To test the impact of

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second-order Rayleigh scattering, each sample was measured with and without a low

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pass filter with a 290-nm cutoff. The resulting data cube had a size of (36 × 125 × 124).

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The EEM landscape of a sample containing 15 mg/L HA and 40 mg/L BSA is shown in

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Figure 1b.

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Fluorescence Data of Natural Water Samples. Two sample sets from natural

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sources with different contamination degrees were tested. Samples from Chaohu Lake,

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Anhui Province, China, representing low-contamination natural water, were collected

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monthly from East Chaohu Lake (31°32.081’ N, 117°38.845’ E) and West Chaohu

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Lake (31°38.341’ N, 117°21.416’ E) from March 2014 to January 2015. The second

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sample series was collected from the Nanfeihe River, Anhui Province, China (with a

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spatial distribution from 31°53.178' N, 117°13.074' E to 31°43.050' N, 117°24.246' E)

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in a single sampling day, and was selected to represent highly contaminated natural

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water.26, 27 Each sample of 500 mL was collected with polyethylene terephthalate

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bottle and filtered with 0.22-µm cellulose acetate membrane immediately after

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sampling. All samples were kept in a 4 oC refrigerator and tested in 48 h. The pH

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values were 7.45±0.28 for the Lake samples and 6.93±0.21 for the River samples.

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Considering no significant difference in pH for each sample, the sample pH value was

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not adjusted before measurements to reveal the spectroscopic characteristic of each

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sample as close to natural environment as possible. The two sample series are

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respectively referred to as the Lake sample and the River sample in the following

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discussion (Figure S1). Each sample was tested with an emission spectrum ranging

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from 211 to 618 nm with a 3.8-nm step increase and an excitation wavelength

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increasing sequentially from 264 to 600 nm with a 3-nm step. IFE was corrected by

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the Aqualog software. For each sample, the analysis was conducted in triplicate. The

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resulting data cube of the East Lake sample (dataset E) and the West Lake sample

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(dataset W) had a size of (10 × 125 × 113). A dataset (dataset EW) including both the

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East and West Lake samples (20 × 125 × 113) was also tested to validate whether the

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PFFCA method can provide a unique decomposition result when decomposing

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different sample series. The resulting data cube of the River sample (25× 125 × 113)

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was divided into two sub-datasets (one with a size of 12× 125 × 113 containing all of

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the even-numbered samples and the other with a size of 13× 125 × 113 containing all

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of the odd-number samples).

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RESULTS AND DISCUSSION

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Robustness in Treating a Non-trilinear Dataset. Simulated data (the amplitude of

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Peak C and SNR were 0.8 and 15, respectively) were first analyzed to test the

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feasibility of dealing with non-trilinear data. After decomposition by PFFCA analysis,

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8 factors were determined. The scores of these factors and the locations of these

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factors in the EEM landscape are respectively shown in Figures S2a and S2b. F2

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represents Peak A, F1 represents Peak B, and the combination of F3 to F8 is the

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representation of Peak C. PARAFAC was also checked as a comparison. As shown in

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Figure S3a-b, the number of factors determined by the core consistency diagnostic

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was 3. Split-half analysis indicates that 3-factor model is valid. A paired samples t-test

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was used to reflect the significance level between the actual and estimated

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concentrations (Table 1). The p values of both methods were over 0.05, suggesting

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that the estimated concentrations were not significantly different from the actual

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concentrations. However, the average residual of the estimated concentrations and the

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actual concentrations of PFFCA were less than that in PARAFAC analysis for Peaks A,

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B and C, and p values were less than 0.05, suggesting that the residual of the PFFCA

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method was significantly less than that of PARAFAC.

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Although the t-test results indicate that the estimated and actual concentrations

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were not significantly different in the PARAFAC method, the estimated

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concentrations versus the actual concentrations of Peak A seemed to be an oval,

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indicating that the series of Peak A had a slight phase-shift (Figure S3c-d). This result

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shows that two samples with the same actual concentration may generate different

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estimated concentrations simply because the location in the test sequence is different.

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This might result from the interference of the non-trilinear structure. Thus, when

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PARAFAC is applied in quantitative analysis, the potential risk of the interference of

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non-trilinear structure should be strongly noted.

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The residuals of actual and estimated landscapes are shown in Figure 2. As more

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factors were used in PFFCA, the color bar in Figure 2 shows that the residuals of

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PFFCA were smaller than those of PARAFAC by five to ten times, suggesting a less

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distortion with the PFFCA method (Figure 2a-f). The item “distortion” is commonly

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used in image processing and communication engineering to describe the alteration of

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the original shape, peak, image, or waveform. Since our work was focused on the

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improvement of data processing, this term was thus selected to represent the alteration

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of the EEMs and concentration sequence. The residuals (actual landscape minus

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estimated landscape) at simulated Ex/Em 330/340 nm were significantly positive and

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the left and top sides were significantly negative (Figure 2b), implying that Peak A

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moved slightly to the top left corner. For Peak B (Figure 2d), a new peak was

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generated at simulated Ex/Em 325/330 nm, implying that the actual component was

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unimodal, while the estimated component was multimodal. The distortion of

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landscapes might be confusing when recognizing the assignment of the peaks. The

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result indicates that it is feasible to use a core consistency diagnostic in determining

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the correct component number when handling non-trilinear data, but the

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decomposition results may be distorted because they have to conform to the trilinear

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structure.

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The impacts of the amplitude of Peak C and the SNR are also examined (Figure

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S4). The RSS (residual sum of squares) of the landscape and the RSS of the amplitude

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of the PFFCA method were less than those in PARAFAC. With an increase in the

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amplitude of Peak C, the residuals notably increased in PARAFAC while exhibiting

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no clear increase in PFFCA. The SNR had no significant effect on the residuals for

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Peaks A and B (Figure S4a-d). However, with an increase in SNR, the residuals of

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Peak C exhibited a significant decrease (Figures S4e-f). This result is consistent with

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the fact that the high noise level will increase the residuals during fitting. Therefore,

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the reduction percentage is diluted when the number of factors is increased. The

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increase in the SNR tends to choose fewer factors, as confirmed in Table S4. As a

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result, with more factors involved, PFFCA can provide more precise results and

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overcome the limitation of trilinear structures faced by PARAFAC. The robustness in

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dealing with non-trilinear datasets will provide PFFCA with more extensive

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applications compared to PARAFAC analysis.

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Determination of Component Number in Synthetic Samples. The EEM

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spectra of the HA and BSA mixture were decomposed by the PFFCA method. Fifteen

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factors were determined by the residuals reduction rate and clustered into 3

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components shown in Figure 3a-c. These 3 components corresponded to BSA, HA

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and second-order Rayleigh scattering, respectively. PARAFAC analysis with a core

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consistency diagnostic was also tested as a comparison. The PARAFAC model with

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three factors had a consistency index of 96.41%, which decreased to 69.05% and

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37.94%, respectively, when four and five factors were considered. The residual

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analysis indicated that the 3-factor model was adequate (Figure 3d-f), with the first

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factor corresponding to BSA. However, the second and third factors corresponded to

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only part of HA. The correlation coefficient scores of the second factor and the third

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factor were both 0.930, indicating that these two factors might correspond to the same

256

component in the samples. There are two possible explanations for this result. First,

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the impact of second-order Rayleigh scatterings destroyed the trilinear structure of

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HA. Second, as a complex mixture of many different moieties containing fluorescent

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fractions such as quinonyl, amino and many other aromatic groups, HA has many

260

fluorescent groups that all correspond to its concentration. In other words, these

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fluorescent groups are not independent in HA samples.

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To find out why HA was separated into 2 factors, all of the samples were tested

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with the 290-nm-cutoff long pass filter. The PFFCA determined 2 components

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clustered by 5 factors. These two components corresponded to BSA and HA,

265

respectively. The EEM landscape of these 2 components was similar to the

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corresponding components in the result with second-order Rayleigh scatterings (R2

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values of HA and BSA were 0.993 and 0.952, respectively, in Table 2). This result

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indicate that PFFCA is robust even when the peaks are highly overlapped with

269

second-order Rayleigh scatterings.

270

With regard to PARAFAC, the 2-factor model had a consistency index of 99.99%

271

and fell to 76.28 and 30.75%, respectively, when three and four factors were

272

considered. Compared with the dataset without the filter, the absence of the

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second-order Rayleigh scatterings reduced the core consistency index. This

274

observation confirmed that the non-trilinear structure may affect the correctness of

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factor number estimation. The two factors in the 2-factor model represented BSA and

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HA, respectively. The R2 values of the model landscapes with the EEM landscapes of

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pure HA and BSA were 0.814 and 0.932, respectively (Table 2). The 3-factor model

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had one factor corresponding to BSA and two factors corresponding to part of HA,

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similar to the result without the filter. This 3-factor model was also validated by the

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split-half analysis. The correlation coefficient of the score between the second factor

281

and the third factor was 0.970, higher than that without the filter. This difference

282

resulted from the impact of second-order Rayleigh scattering. Referring to the score of

283

the second and the third factors as weights, the weighted sum of their model

284

landscapes was calculated. The R2 values of these landscapes with the EEM

285

landscapes of pure HA and BSA were 0.911 and 0.935, respectively, which were

286

higher than those in the 2-factor model. This result indicates that HA may not conform

287

to trilinear structure. Taking the complexity of HA into account, the non-independence

288

of the fluorescent groups in HA might be a possible explanation of this observation.

289

Therefore, the factors whose scores are highly correlated should not be

290

considered as independent components, but only as part of one component, which is

291

the basic principle behind the PFFCA method. To reduce the potential risk of the

292

impact of the non-trilinear structure in the dataset, the first step decomposes the

293

dataset into many factors to reduce the RSS in an attempt to interpret the dataset more

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correctly. Nevertheless, it increases the risk of overestimating the number of

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components if each factor is treated as an independent component. In the second step,

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the risk of mis-estimation can be eliminated because the factors that are highly

297

correlated will be clustered during the process. As a result, a better interpretation of

298

the dataset without overestimation of the components number can be achieved, and

299

the non-trilinear dataset can also be well handled using the PFFCA approach.

300

Unique Decomposition Results in Natural Water Samples. Three datasets of

301

the Lake samples were analyzed first. Although the factor numbers in Datasets E, W,

302

and EW were 11, 8, and 18, respectively, all of the datasets were decomposed into 2

303

components with PFFCA analysis. One of the components represented an HA-like

304

substance, and the other represented a protein-like substance.28 PARAFAC analysis

305

was also evaluated as a comparison, and two components were determined in all

306

datasets using a core consistency diagnostic and validated by the split-half analysis.

307

However, the difference between the components decomposed by the two methods

308

was remarkable (Figure S5).

309

In natural water samples, the EEM landscapes and concentrations of the HA-like

310

and protein-like substances were unknown, and therefore we cannot decide which

311

decomposition approach is superior by comparing the RSS of the concentrations or

312

the EEM landscapes between estimated values and real samples. Meanwhile, because

313

the concentrations and components are fixed in one sample, the decomposition result

314

should be the same, whether it is decomposed with other samples or not. Thus, the

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decomposition results of East Lake samples from Dataset E should be equal to those

316

decomposed from Dataset EW. However, the decomposition results of the three

317

datasets were slightly different (Figures S5e-f and S6). The average residuals of

318

corresponding components of Dataset E and Dataset EW (or Dataset W and Dataset

319

EW) in each sample are shown in Figure 4. The residuals of PARAFAC (Figure 4e-h)

320

show some notable positive and negative peaks in the EEM landscape, implying that

321

the landscape of the peak was shifted as the dataset changed. Conversely, the residuals

322

of PFFCA (Figure 4a-d) were far less than those of PARAFAC, suggesting that

323

PFFCA outperformed PARAFAC analysis. These results demonstrated that samples in

324

PFFCA analysis did not affect each other during decomposition.

325

For the River samples, a 2-factor model was determined by a core consistency

326

diagnostic and validated using the split-half analysis when performing PARAFAC

327

analysis. One component represented a HA-like substance, and the other represented a

328

protein-like substance.4, 29 As shown in Figure S7e-h, the residuals of each sub-dataset

329

and corresponding samples in the total dataset showed a pair of evident positive and

330

negative peaks, indicating the shift of the peaks. For the protein-like substance, the

331

emission wavelength of the odd sub-dataset had a blue shift (Figure S7e), while a red

332

shift (Figure S7g) was observed for the even sub-dataset. For the HA-like substance, a

333

red shift was noticed for the odd dataset, and a blue shift in the even dataset was

334

clearly observed. Unlike in PARAFAC analysis, no notable peaks were found in the

335

residuals of the sub-dataset and corresponding samples in the total dataset (Figure

17



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336

S7a-d), suggesting that the samples in PFFCA analysis did not affect each other

337

during decomposition.

338

One possible reason for this observation is that when the dataset was combined

339

with some new samples with slight differences in composition, the landscape of the

340

factors will shift to reduce the RSS (the reason for the peaks shift for PARAFAC when

341

decomposing with new samples is provide in SI). As a consequence, the estimates of

342

the original dataset will be inevitably changed, which may mislead our understanding

343

of the samples. However, by using adequate factors determined by the RSS reduction

344

rate, the PFFCA method can acquire better performance in reducing the RSS. When

345

combining with new samples, the original dataset will not be affected because it can

346

always be well decomposed. Although the landscape and even the numbers of the

347

factors are different, the subsequent clustering analysis will integrate them into one

348

single component, which avoids generating too many components that cannot be

349

interpreted.

350

Advantages of PFFCA over PARAFAC. The main differences between

351

PARAFAC and PFFCA are listed in Table S5. PARAFAC analysis extracts

352

components under the assumption that fluorescent substances are linearly independent.

353

In other words, it couples the data decomposition process and components

354

determination by simply making the number of components equal to the number of

355

linear independent factors. It is reasonable in simple situations, but in more

356

complicated environmental cases, the assumption is no longer valid because of the

18


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357

complexity of fluorescent substance such as HA. In contrast, the PFFCA method

358

extracts the components by following a different assumption—that the fluorescent

359

groups whose intensities are highly correlated come from the same substance or are

360

affected by the same impact. It is unreasonable to separate them as independent

361

components before more information is known. Therefore, these factors should be

362

clustered together as a single component. Taking advantage of this novel strategy,

363

more factors can be involved to provide a better fitting and accordingly a unique

364

decomposition result.

365

Before performing conventional PARAFAC analysis, it is essential to remove

366

Rayleigh and Raman scatterings.30-32 For PFFCA analysis, it is not necessary to

367

remove scatterings before decomposition because the strategy can robustly treat

368

non-trilinear structures. The PFFCA method can effectively recognize and separate

369

them automatically after decomposition even when they are highly overlapped.

370

Significance of This Work. In the present study, a new method, PFFCA, is

371

proposed with a focus on non-trilinear EEM dataset decomposition. By using this

372

novel data-handling strategy, a robust, unique and interpretable decomposition result

373

can be approached even when the data are not linearly independent and overlap highly

374

with scatterings. Because components of natural water, such as DOM and HA, are

375

complex and may contain several fluorophores, PFFCA may be a better performing

376

alternative method for accurately revealing their internal components. Our work

377

yields new insights into the decomposition process and decouples the data

19



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378

decomposition and components determination to treat synthetic and environmental

379

samples. In addition, as a framework, the two steps can be replaced by other suitable

380

methods. For example, PARAFAC can be replaced by other decomposition methods

381

such as alternating trilinear decomposition or self-weighted alternating trilinear

382

decomposition. Clustering analysis can be replaced by support vector machine,

383

artificial neural network or other machine learning algorithms. The replaceability of

384

this framework may help us to achieve a faster and more precise decomposition

385

method in DOM-related issues. Moreover, this robust method may find potential

386

applications in engineering fields. For example, chromophoric substances in soluble

387

microbial products and extracellular polymeric substances from biological wastewater

388

treatment plants could be better separated and interpreted by using PFFCA.

389 390

Nomenclature BSA

bovine serum albumin

DOM

dissolved organic matter

EEM

excitation-emission matrix

HA

humic acids

IFE

Inner filter effect

PARAFAC

parallel factor

PCA

principal component analysis

PFFCA

parallel factor framework-clustering analysis

RSS

residual sum of squares

SNR

signal to noise ratio

391

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392 393 394

AUTHOR INFORMATION *Corresponding author: Prof. Han-Qing Yu, Fax: +86-551-63601592; E-mail: [email protected]

395 396

ACKNOWLEDGEMENTS

397

We thank the National Natural Science Foundation of China (51538011), the

398

Collaborative Innovation Center of Suzhou Nano Science and Technology of the

399

Ministry of Education of China for the support of this study.

400 401

ASSOCIATED CONTENT

402

Supporting Information Available. Detailed descriptions about data processing

403

procesedures, Coefficients of simulated peaks (Table S1), The levels of SNR and

404

Amplitude (M) in 24 Samples (Table S2), The Concentration of HA and BSA in 36

405

Samples (Table S3), Impact of SNR and amplitude of Peak C to the number of factor

406

(Table S4), Comparison between PARAFAC and PFFCA (Table S5), Sampling points

407

of Chaohu Lake and Nanfeihe River (Figure S1), Decomposition result of the dataset

408

with the amplitude of Peak C at 0.2 and SNR of 15 (Figure S2), RSS of different

409

factors, core consistency of different factors and the estimated amplitude versus actual

410

amplitude of Peaks A and B (Figure S3), RSS of the amplitude and landscape of Peaks

411

A, B and C (Figure S4), the decomposition result of PFFCA and PARAFAC for

412

dataset EW and river samples (Figure S5), the decomposition results of dataset E and

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

413

W using PARAFAC (Figure S6), the average residuals landscape of the protein-like

414

and HA-like substances between the odd sub-dataset and the total dataset decomposed

415

by PARAFAC and PFFCA (Figure S7), Residual of simulated data with one and two

416

factors. Residual of pure HA samples with one and two factors (Figure S8), EEM with

417

the amplitude of HA and one gauss peak, estimated sequence of three factors

418

decomposed by PARAFAC, actual amplitude versus estimated relative amplitude of

419

two factors corresponding to HA and gauss peak (Figure S9), simulated peak with the

420

angle is 45 degree, the RSS of different angles and factors number from one to eight,

421

the relationship between angle and validated factor number (Figure S10), and the

422

average residuals landscape of Peak A and Peak B between sub-dataset and dataset

423

(Figure S11). PFFCA (PFFCA.zip) is available on at http://pubs.acs.org/. This

424

information is available free of charge via the Internet at http://pubs.acs.org/.

425 426

REFERENCES

427 428

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Environ Sci Technol 2003, 37, (24), 5701-5710.

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7. Bro, R., PARAFAC. Tutorial and applications. Chemometr Intell Lab 1997, 38, (2), 149-171. 8. Nebbioso, A.; Piccolo, A., Molecular characterization of dissolved organic matter (DOM): a critical review. Anal Bioanal Chem 2013, 405, (1), 109-124.

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9. Ishii, S. K. L.; Boyer, T. H., Behavior of Reoccurring PARAFAC Components in

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Fluorescent Dissolved Organic Matter in Natural and Engineered Systems: A

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Khan, S. J., Organic Matter Fluorescence in Municipal Water Recycling Schemes:

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Stedmon, C. A., Characterising organic matter in recirculating aquaculture systems

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with fluorescence EEM spectroscopy. Water Res 2015, 83, 112-120.

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Andersen, D. T., Spectrofluorometric characterization of dissolved organic matter

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in a drinking water treatment plant using fluorescence excitation-emission matrices

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River-Dominated Estuary. Environ Sci Technol 2012, 46, (16), 8628-8636.

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24. Leitao, J. M. M.; Simoes, E. F. C.; da Silva, J. C. G. E., PARAFAC based methods

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25. Andersson, C. A.; Bro, R., The N-way Toolbox for MATLAB. Chemometr Intell

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26. Li, G. L.; Liu, G. J.; Zhou, C. C.; Chou, C. L.; Zheng, L. G.; Wang, J. Z., Spatial

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distribution and multiple sources of heavy metals in the water of Chaohu Lake,

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Anhui, China. Environ Monit Assess 2012, 184, (5), 2763-2773.

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27. Liu, E. F.; Shen, J.; Yang, X. D.; Zhang, E. L., Spatial distribution and human

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Chaohu Lake, a eutrophic shallow lake, China. Environ Monit Assess 2012, 184, (4),

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28. Sheng, G. P.; Yu, H. Q., Characterization of extracellular polymeric substances of

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aerobic and anaerobic sludge using three-dimensional excitation and emission

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matrix fluorescence spectroscopy. Water Res 2006, 40, (6), 1233-1239.

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29. Stedmon, C. A.; Markager, S.; Bro, R., Tracing dissolved organic matter in aquatic

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30. Bahram, M.; Bro, R.; Stedmon, C.; Afkhami, A., Handling of Rayleigh and Raman

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scatter for PARAFAC modeling of fluorescence data using interpolation. J

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Chemometr 2006, 20, (3-4), 99-105.

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31. Eilers, P. H. C.; Kroonenberg, P. M., Modeling and correction of Raman and Rayleigh scatter in fluorescence landscapes. Chemometr Intell Lab 2014, 130, 1-5.

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32. Li, Y.; Wu, H. L.; Yu, Y. J.; Zhang, S. R.; Chen, Y.; Tu, D. Z.; Nie, C. C.; Xu, H.; Yu,

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Page 26 of 33

Table 1. T-test of the Estimates and Actual Amplitudes, and Residuals of PFFCA and PARAFAC P-values of comparing estimate average residuals and actual concentration PFFCA PARAFAC PFFCA PARAFAC P-values of comparing two methods peak A

0.973

0.563

0.004

0.034

1.05E-05

peak B

0.899

0.559

0.003

0.004

0.037

peak C

0.935

0.823

0.006

0.167

9.96E-08

26


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Table 2. R2 Values of Pure HA/BSA and Decomposition Components pure without filter with filter HA/BSA PFFCA PARAFAC,N=3 PFFCA without PFFCA 0.922/0.922 filter PARAFAC,N=3* 0.875/0.922 0.9/0.934 with filter

PFFCA PARAFAC,N=2 PARAFAC,N=3

0.932/0.972 0.814/0.932 0.911/0.935

0.993/0.952 0.874/0.908 0.969/0.927

0.913/0.896 0.867/0.962 0.946/0.964

*: N represents the number of factor.

27


0.94/0.949 0.988/0.962

PARAFAC,N=2

0.952/0.997


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure captions

Figure 1. (a) EEM landscape of the simulated data; and (b) a mixture of 15 mg/LHA and 40 mg/L BSA.

Figure 2. EEM residual landscape of (a) Peak A with PFFCA; (b) Peak A with PARAFAC; (c) Peak B with PFFCA; (d) Peak B with PARAFAC; (e) Peak C with PFFCA; and (f) Peak C with PARAFAC for the simulated dataset.

Figure 3. (a)–(c) 3 components decomposed by PFFCA; (d)–(f) 3 components decomposed by PARAFAC.

Figure 4. The average residuals landscape of the HA-like substance (a, e) and protein-like substance (b, f) between datasets E and WE. The average residuals landscape of HA-like substance (c, g) and protein-like substance (d, h) between datasets W and WE. (a)–(d) were decomposed by PFFCA, and (e)–(h) were decomposed by PARAFAC.

28


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Figure 1

29



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Figure 2

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Figure 3

31



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Figure 4

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Table of Contents (TOC) Art

33


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