Role of extracellular polymeric substances in the acute inhibition of activated sludge by polystyrene nanoparticles

Role of extracellular polymeric substances in the acute inhibition of activated sludge by polystyrene nanoparticles

Environmental Pollution 238 (2018) 859e865 Contents lists available at ScienceDirect Environmental Pollution journal homepage: www.elsevier.com/loca...

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Environmental Pollution 238 (2018) 859e865

Contents lists available at ScienceDirect

Environmental Pollution journal homepage: www.elsevier.com/locate/envpol

Role of extracellular polymeric substances in the acute inhibition of activated sludge by polystyrene nanoparticles* Li-Juan Feng a, Jing-Jing Wang a, Shu-Chang Liu b, Xiao-Dong Sun a, Xian-Zheng Yuan a, *, Shu-Guang Wang a a Shandong Key Laboratory of Water Pollution Control and Resource Reuse, School of Environmental Science and Engineering, Shandong University, Jinan, Shandong Province 250100, PR China b College of Science and Engineering, Yantai Academy of China Agricultural University, Yantai, Shandong Province 264670, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 December 2017 Received in revised form 27 March 2018 Accepted 28 March 2018

Microplastics and nanoplastics in aquatic systems have become a global concern because of their persistence and adverse consequences to ecosystems and potentially human health. Though wastewater treatment plants (WWTPs) are considered a potential source of microplastics in the environment, the role of extracellular polymeric substances (EPS) of activated sludge on the fate of nanoplastics is not clear. In this study, the role of EPS in the influence of polystyrene nanoparticles (PS-NPs) on the endogenous respiration of activated sludge was investigated for the first time. The results showed that the acute inhibition of activated sludge by PS-NPs was enhanced with increasing PS-NPs concentration. X-ray photoelectron spectroscopy (XPS) results indicate that the functional groups involved in the interactions between PS-NPs and EPS were carbonyl and amide groups and the side chains of lipids or amino acids. Furthermore, the Fourier transform infrared (FTIR) spectroscopy results show that the protein secondary structures in EPS were changed by PS-NPs and lead to the bioflocculation of activated sludge, which provides a better understanding on the fate of nanoplastics in WWTPs. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Polystyrene nanoparticles Extracellular polymeric substances Acute inhibition Activated sludge Secondary structures of protein

1. Introduction As the production and utilization of plastic has increased steadily in the last decades, the presence of plastics in marine and freshwater systems is a growing global concern (do Sul and Costa, 2014; Eerkes-Medrano et al., 2015; Hidalgo-Ruz et al., 2012; Jambeck et al., 2015). In this research field, which involves macroplastics (>5 mm) to microplastics (<5 mm), there is special concern regarding nanoplastics. Nanoplastics have large surface area-tovolume ratio and nano-specific properties (Besseling et al., 2014; Rossi et al., 2014; Wang et al., 2008). According to previous research, nanoplastics may come primarily from the products and applications where nanoplastics are used or formed (Dekkers et al., 2011; Lu et al., 2006). Another speculated source is the degradation of microplastics to nanoscale particles via abiotic and biotic factors (Sivan, 2011). Nanoplastics can cause growth inhibition (Cole and

*

This paper has been recommended for acceptance by B. Nowack. * Corresponding author. School of Environmental Science and Engineering, Shandong University 27 Shanda Nanlu, Jinan, Shandong Province, 250100, PR China. E-mail address: [email protected] (X.-Z. Yuan). https://doi.org/10.1016/j.envpol.2018.03.101 0269-7491/© 2018 Elsevier Ltd. All rights reserved.

Galloway, 2015), reproductive dysfunction (Besseling et al., 2014), and reduced viability (Canesi et al., 2015) in marine organisms. Based on waste management, hydrological information, and population density, Lebreton et al. (2017) estimated that 1.15 to 2.41 million tonnes of plastic debris enter the ocean via rivers every year. Though the presence and concentration of nanoplastics in the environment have yet to be confirmed owing to the current separation technology, the toxicity of plastics, especially nanoplastics, in freshwater systems has received increasing attention (Besseling et al., 2014; Mattsson et al., 2015). Wastewater treatment plants (WWTPs), a critical component of urban water systems, are considered as a potential source of microscale and nanoscale plastics in the environment (Mani et al., €ki WWTP in Helsinki sug2015). A case study of the Viikinma gested that the average fiber and particle concentrations in the final effluent were 25 and 3 times higher, respectively, than those in the receiving water body (Talvitie and Heinonen, 2014). By using a high-volume sampling device, Ziajahromi et al. (2017) found an average of 1.54, 0.48, and 0.28 microplastic particles per liter in primary, secondary, and tertiary treated effluent, respectively. That is to say, the present WWTP processes may not remove

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microplastics completely. Furthermore, WWTPs showed high retention potentials for microplastics (Murphy et al., 2016). As nanoplastics are smaller than microplastics, they are more difficult to remove from effluent, and WWTPs are more likely to be significant point sources or conduits of nanoplastics than of microplastics to the environment. Though previous results indicated that higher microplastic contents were observed downstream than upstream of WWTPs (Estahbanati and Fahrenfeld, 2016; McCormick et al., 2014), it is unknown how the nanoplastics influence the effluent of the WWTPs during transport through the facilities. Microbial aggregation, including sludge flocs, biofilms, and granular aggregates, promotes the adsorption and degradation of organic pollutants in WWTPs. Extracellular polymeric substances (EPS) have been observed in various microbial aggregations (Sheng et al., 2010). EPS contain proteins, polysaccharides, nucleic acids, humic-like substances, lipids, etc. Because substrates must pass through the EPS layer before interacting with the cells, EPS could impact the mass transfer efficiency of the substrates (Flemming and Wingender, 2010). In addition, organic pollutants could be removed by EPS through adsorption and biotransformation (Liu et al., 2001). Nanoplastics is expected interact with EPS as nanoplastics enter the WWTPs. However, the details regarding the impacts and mechanism of nanoplastics with EPS are lacking. In this study, polystyrene nanoparticles (PS-NPs), one of the most largely used plastics worldwide, were used to evaluate the influence of nanoplastics on the endogenous respiration of activated sludge. Furthermore, the role of EPS in the reaction between nanoplastics and activated sludge was elucidated through X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FTIR) spectroscopy. The results obtained in this study provide a better understanding on the complex interaction of nanoplastics with activated sludge in the biological process of WWTPs.

2. Material and methods 2.1. Preparation of PS-NPs PS-NPs were synthesized in the laboratory through nitrogenprotected emulsion polymerization with styrene as a monomer (Fig S1 and Fig S2). The emulsifier and initiator were sodium dodecyl sulfate (SDS) and ammonium persulfate (APS), respectively (Wang and Fang, 2014; Wang et al., 2016). The solution was transferred to a dialysis bag for removal of redundant styrene monomer, APS, or SDS in the reaction system.

2.3. EPS extraction and binding with PS-NPs EPS extraction was carried out according to previous studies, with minor modification (Frølund et al., 1996; Wei et al., 2011). Specifically, the sludge was centrifuged at 6000 r/min for 15 min at 4  C to remove any EPS from the bulk water. Then, the sludge pellets were resuspended to their original volume in 1% sodium chloride solution containing cation exchange resin (CER) (60 g/g MLSS). The suspension was stirred at 500 r/min for 12 h at 4  C. The extracted EPS were collected by centrifugation of the CER and sludge mixture at 10,000 r/min for 10 min to remove the CER. Finally, the supernatants were filtered through 0.22 mm acetate cellulose membranes and lyophilized to obtain crude EPS. Proteins and carbohydrates were 38.5% and 18.9%, respectively, of the EPS. The EPS and PS-NPs were dissolved with 0.2 M phosphate buffer solution (PBS, pH ¼ 7.4) in 50 mL centrifuge tubes. The final concentrations of EPS and PS-NPs were 100 mg/L and 0.05 mg/mL, respectively. Then, the mixed solution was put into an oscillator to mix and balanced without stirring for 6 h at room temperature (20  C) before spectral analysis. 2.4. Analytical methods 2.4.1. Characteristics of the PS-NPs and EPS The morphology of the PS-NPs was characterized using a scanning electron microscope (SEM, TESCAN MIRA3) and transmission electron microscope (TEM, FEI F20). The average particle size of the PS-NPs was tested via a Malvern laser particle size analyzer (Zetasizer Nano S90, Malvern, UK). The concentration of the synthetic nanoplastics was measured based on the analysis of decomposition gases of polymers by a combining thermogravimetric solid-phase extraction and thermal desorption gas chromatography mass spectrometry (TED-GC-MS) (Duemichen et al., 2014, 2017). Bradford's method using a BioRad protein assay kit was employed to measure the protein content of the EPS (Bradford, 1976). The polysaccharide content of the EPS was determined with the phenol-sulfuric acid spectrophotometric method (DuBois et al., 1956).

2.2. Acute inhibition of activated sludge by PS-NPs

2.4.2. XPS analysis X-ray photoelectron spectroscopy (ESCALAB 250, Thermo, USA) with an Al Ka X-ray source (1486.7 eV) was used to measure the elemental composition and determine the local functionality of the samples. A broad survey scan (20.0 eV) was performed for major element component analysis, and a high-resolution scan (70.0 eV pass energy) was employed for component speciation. Binding energies were calibrated using the containment carbon (C 1s ¼ 284.6 eV) to compensate for surface charging effects. The XPS spectra peaks were fitted using XPS Peak 4.1 software.

The acute inhibition of activated sludge by PS-NPs was carried out in a series of fully aerated batch reactors. The activated sludge was gathered from the end of the aeration tank of a WWTP in Jinan, Shandong province, China. Endogenous respiration rate (OURen) was used to indicate the acute inhibition of the activated sludge by PS-NPs. All the experiments were initiated with the activated sludge alone to maintain the initial oxygen utilization rate (OUR) level (Surmacz-Gorska et al., 1996). After aeration for two days, the PS-NPs were injected at a time and the final concentration of PSNPs in the reactors were 0.1, 0.5, 1, 5 mg/mL, respectively. Meanwhile, the OURen data were monitored. The OURen was determined as dissolved oxygen declined during the mixing without aeration. Control experiments, i.e., without PS-NPs, were conducted in the reactors. All the experiments were carried out in triplicate, and the results were expressed as means.

2.4.3. FTIR analysis The infrared spectra of EPS with or without PS-NPs were measured in potassium bromide pellets using an FTIR spectrometer (Aratar, Thermo NicoLet, USA) at wavenumbers from 4000 to 400 cm1. Each spectrum was collected with a resolution of 2 cm1, and the ordinate was expressed as absorbance. To obtain detailed information regarding protein secondary structures, the amide I region (1700e1600 cm1) of the FTIR spectrum was further analyzed. The amide I region was deconvoluted to divided overlapping peaks by increasing the spectral resolution. Then, the spectrum was further broken up into component peaks as protein secondary structures through nine-point SavitzkyeGolay derivative function analysis and smoothing (Yin et al., 2015). A Lorentzian line shape was quantitated for the amide I region prior to curve fitting the original spectra using Peakfit 4.12 software.

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3. Results and discussion 3.1. Acute inhibition of the activated sludge by PS-NPs As shown in Fig. 1 (a) and (b), the morphology of the PS-NPs is almost spherical. From the dynamic light scattering results (Fig. 1 (c)), the particle sizes in water range from 28.2 nm to 91.3 nm with a z-potential of 12.6 mV. The average diameters of the PSNPs in water and PBS (pH ¼ 7.4) were 49.1 nm and 49.8 nm, respectively, which implies that the synthesized PS-NPs did not aggregate in PBS. This is probably due to the lower salinity of PBS in respect to seawater. In real environment, lots of environmental parameters would affect the behavior and fate of PS nanoparticles, such as pH and salinity (Chen et al., 2018; Velzeboer et al., 2014). Della Torre et al. found that the higher salt concentration can screen the particle surface charges leading to the observed aggregation (Della Torre et al., 2014), which maybe affect the mechanism of PSNPs on EPS. The acute inhibition of the activated sludge by PS-NPs in the form of endogenous respiration is shown in Fig. 1 (d). When the activated sludge was in endogenous respiration, the OURen was obtained from the slope of the dissolved oxygen profiles. And the statistical significance of OURen was estimated by the two-tailed ttest. When 0.1 mg/mL of PS-NPs was injected into the vessel, the average OURen decreased from 0.236 mg O2/(L$min) to 0.205 mg O2/(L$min) (P < 0.05). The average OURen decreased with increasing PS-NPs concentration. And when the PS-NPs concentration was 5 mg/mL, the value of the average OURen obviously decreased (P < 0.001). The OURen is a significant indicator of the activity of activated sludge, which is directly related to the efficiency and effectiveness of sewage treatment. It is worthy to study the mechanism of PS-NPs on the endogenous respiration of activated sludge. However, the presence and concentration of nanoplastics in the environment have not yet to be confirmed owing to the current separation technology. These emerging contaminants need a starting point in assessing their toxicity, even when natural concentrations and behavior (speciation, complexation, and

Fig. 1. Characteristics of the PS-NPs via SEM image (a), TEM image (b), dynamic light scattering (c), and the average endogenous respiration rate (OUR) of the activated sludge with different concentration of PS-NPs (d. The statistical significance of OUR was estimated by the two-tailed t-test and differences were considered significance at p < 0.05 and are referred to as *p < 0.05, **p < 0.001).

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aggregation) are unknown. The use of high concentrations in ecotoxicological studies can be viewed as a proof-of-concept, producing ground-breaking data for assessing the potential risk of a new class of contaminants, such as nanoplastics, and helping to define biomarkers and phenotypic impairment. According to previous studies, the PS-NPs might be firstly absorbed by the EPS as a protective barrier against pollutants before they interact with the lez et al., 2010). cell wall (Flemming and Wingender, 2010; Gonza Hence, it is important to explore the interaction between PS-NPs and EPS. 3.2. XPS analysis As shown in Fig. 2 (a) and Table 1, the elemental compositions of EPS (I of Fig. 2 a) and PS-NPs-bound EPS (II of Fig. 2 a) were measured by XPS over the energy range of 0e1200 eV. In the EPS, the O/C was 1.475. After reaction with the PS-NPs, the O/C increased greatly to 2.369. This indicates that the oxygen-containing compounds in the EPS increased from the binding with the PS-NPs. To quantify the variation in the functional groups of the EPS with or without PS-NPs, the C 1s, O 1s, and N 1s were determined via high-resolution XPS spectra. The molar ratios of the functional groups to total carbon (C 1s) are also shown in Table 1. From Fig. 2 (b) and (c), the peak at 283.65 eV was associated with C-(C, H) from the side chains of lipids or amino acids. After reaction with the PS-NPs, this functional group decreased from 21.2% to 8.7%. Amino acids and lipids are the major building blocks of bacterial membranes. Rossi et al., 2014 found that PS-NPs can permeate easily into membranes and change membrane structure. The shift of C-(C, H) may be related to the acute inhibition of endogenous respiration rate of activated sludge by PS-NPs. The second peak at 284.95 eV was the dominant group in the carbon element of the EPS and PS-NPs-bound EPS, with values of 0.587 and 0.812, respectively. This shift indicates that the electron distribution in the EPS was disturbed, as the electronic density around the C in C(O, N) decreased. In addition, the functional group C-(O, N) has a positive relationship with the bioflocculation of microbial aggregates (Badireddy et al., 2010). Hence, the ability of activated sludge aggregation was promoted by the interaction between EPS and PS-NPs. The third peak, at 287 eV, accounted for 13.6% and 10.1% of the EPS and PS-NPs-bound EPS, respectively. These functional groups could hamper the bioflocculation (Badireddy et al., 2010). The last peak at 288.5 eV indicates the presence of RO-C¼O or HO-C¼O in the EPS, which only accounted for 6.5%. After reaction with the PS-NPs, this peak disappeared. As shown in Fig. 2 (d) and (e), the O 1s peak was resolved as two component peaks, one peak at 530.39 eV and the other peak at approximately 531.49 eV. The variations in the two functional groups were less than 15%. From Fig. 2 (f) and (g), only a non-protonated nitrogen peak from amines and amides, at 398.89 eV, was detected in the EPS samples. This manifests that amides (peptides) were dominant in the EPS samples, which was similar to the results of B. subtilis (Omoike and Chorover, 2004). After the interaction with the PS-NPs, the non-protonated nitrogen peak decreased to 0.291. Furthermore, a new peak at 399.5 eV was found with a value of 0.709. This peak is protonated nitrogen in amino acids and amino sugars (Song et al., 2014). The protonation process may be revealed as the electronic density toward nitrogen atoms was increased via electron cloud transfer from carbon atoms. This process is related to the variations in C-(O, N). Through XPS analysis, it was found that the PS-NPs mainly reacted with carbonyl and amide groups and the side chains of lipids or amino acids in the EPS. 3.3. FTIR spectroscopy analysis The FTIR spectra in the range of 400e4000 cm1 were used to identify the possible variation in the functional groups involved in

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Fig. 2. XPS wide survey scans (a) and high-resolution 1s XPS spectra of carbon (b, c), oxygen (d, e), and nitrogen (f, g) from EPS (b, d, f) and PS-NPs-bound EPS (c, e, g).

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Table 1 The atomic ratios and functional groups with respect to C from the high-resolution XPS spectra of EPS and PS-NPs-bound EPS. Sample

Chemical functions (molar ratio with respect to total carbon) Elemental composition (molar ratio with respect to total carbon) N/C

O/C

C-(C,H) C-(O,N) 284.95 eV C¼O, O-C-O 287 eV COOR 288.5 eV C¼O 530.39 eV C-O-C 531.49 eV Nnonpr 398.89 eV Npr 399.5 eV 283.65 eV EPS 0.107 1.475 0.212 0.587 0.136 0.065 0.679 0.321 1.000 0.000 PS-NPs bound EPS 0.112 2.369 0.087 0.812 0.101 0.000 0.546 0.454 0.291 0.709

the interaction between EPS and PS-NPs. As shown in Fig. 3 (a) and Table 2, the strong absorbance at around 3367 cm1 in EPS converged into one, at 3357 cm1, and the band intensity decreased. This transformation indicates that the bands of N-H or O-H in the EPS were affected by the PS-NPs. When electron donating groups of PS-NPs bond with hydrogen 6tatoms of N-H or O-H in EPS, the electron donating groups increased electron density of oxygen or nitrogen, amplifying the dipole and lessen the vibrational energies of N-H or O-H in EPS. Owing to the overlapping signals of amine and hydroxyl groups, it was not possible to confirm which group caused the variations (Song et al., 2014). Another band, at approximately 2924 cm1, decreased with the addition of PS-NPs. The FTIR spectra also revealed significant shifts in the major functional groups of proteins: amide I band (1700e1600 cm1), denoting C¼O stretching vibration; amide II band (1600e1500 cm1), depicting a combination of N-H bending and CN stretching (Meesungnoen et al., 2012; Sun et al., 2009). After PSNP binding to EPS, a sharp decrease occurred in the band intensity of C¼O (amide I), indicating the complexation of PS-NPs with the functional groups (C¼O) of protein. The result was similar with the shift in C¼O or O-C-O observed in the XPS analysis. Meanwhile, three-dimensional EEM fluorescence spectroscopy was employed to evaluate the effect of PS-NPs on the component of EPS, which found tryptophan protein-like substance in EPS was broken by PSNPs (Fig. S3). The disappearance of the amide II may be attributed to the change in the amino groups for the binding with the PS-NPs. Therefore, C¼O stretching vibration, a combination of N-H bending and C-N stretching, and C¼O symmetric stretching of -COO- groups of proteins were the major chemical processes involved in the interaction. This indicates that proteins in the EPS were the major

compounds responsible for the interaction of PS-NPs. Many previous studies have also suggested that pollutants mainly reacted with the proteins of EPS in microbial aggregation. The bacteria could secreted more proteins to neutralize the contaminants to prevent toxic chemicals from binding to or entering the cell (Henriques and Love, 2007; Leriche et al., 2003). The secondary structures of proteins were obtained from the derivative spectra in the amide I region (1700e1600 cm1) (Fig. 3 (b) and (c)). According to spectral data, the protein secondary structures in the EPS and PS-NPs-bound EPS were categorized as: aggregated strands (1625e1610 cm1), b-sheets (1640e1630 cm1), Random coils (1645e1640 cm1), a-helices (1657e1648 cm1), 3-turn helical structures (1666e1659 cm1), and antiparallel b-sheets (1695e1680 cm1) (Badireddy et al., 2010; Yin et al., 2015). The secondary structures of proteins in the EPS in the absence and presence of the PS-NPs are shown in Table 3. In the amide I band, the relative abundances of the helical content (sum of a- and 3-turn) in the EPS without or with the PS-NPs were both dominant (47.69% or 50.30%) than other secondary structures, which is in agreement with previous reports on the EPS compositions of activated sludge in stationary phase (Badireddy et al., 2010). As the PS-NPs reacted with the EPS, the antiparallel b-sheets and random coils decreased from 28.04% to 24.61%. These two secondary structures in proteins have a negative effect on bioflocculation (Badireddy et al., 2010). In addition, the total relative abundances of aggregated strands, b-sheets, and a-helices for the EPS and PS-NPs-bound EPS were 49.14% and 62.06%, respectively. Aggregated strands, b-sheets, and a-helices can promote bioflocculation formation (Badireddy et al., 2010). The 3turn helix, without obvious corresponding relationship with flocculability, decreased from 15.03% to 9.74% for the bound PS-NPs.

Fig. 3. FTIR spectra (a) and the curves fitted to the amide I region (1700e1600 cm1) of the EPS and PS-NPs-bound EPS corresponding protein secondary structures (b, c).

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Table 2 Band assignments for FTIR spectral features (cm1) of EPS and PS-NPs bound EPS. Region

EPS

PS-NPs bound EPS

Band assignments

Hydrocarbons

3367 2924 1640 1581 1405

3357 2921 1650 e e 1359

O-H and/or N-H stretching vibrations of hydroxyl and amine groups C-H stretching vibration C¼O stretching vibration (amide I band); NH2 scissors of primary amines a combination of N-H bending and C-N stretching vibration (amide II band) C¼O symmetric stretching of -COO- groups (amide II band) C-O and C-H stretching vibration possibly associated with amino acids

1153, 1074

C-OH and C-O possibly associated with polysaccharide

Proteins

Polysaccharides

e 1087

Table 3 Variation of secondary structures in proteins of EPS for the reaction with PS-NPs. Secondary structures

Wavenumber (cm1)

At % EPS

PS-NPs bound EPS

Aggregated strands b-Sheet Random coil a-Helix 3-Turn helix Antiparallel b-sheet

1625e1610 1640e1630 1645e1640 1657e1648 1666e1659 1695e1680

14.65 7.01 13.01 27.48 22.82 15.03

10.46 17.24 14.87 34.36 13.33 9.74

Sludge stability is considered as the key factor for the solidliquid separation, turbidity increase, and dewatering properties of WWTPs (Neyens et al., 2004). This stability of activated sludge is affected by effective bioflocculation, where EPS play an important role through weak physicochemical interactions (Wilen et al., 2003). EPS are produced to defend against environmental stress, such as toxic substances. In this study, the activated sludge maybe protected itself from the PS-NPs by covering its peripheral surface with a shield of EPS to obstruct the PS-NPs from penetrating the cell lez et al., 2010; Rossi et al., 2014). Furthermore, as surface (Gonza the PS-NPs promoted bioflocculation of the activated sludge, the dispersive PS-NPs in wastewater would be concentrated, maybe resulting in decreasing the amount of PS-NPs in the final effluent of WWTPs. In real environment, some parameters, such as pH and salinity, etc., would affect the behavior and fate of PS-NPs (Chen et al., 2018; Velzeboer et al., 2014). Meanwhile, pollutants in the environment (polycyclic aromatic hydrocarbons and polychlorinated biphenyls) could be adsorbed by PS-NPs (Liu et al., 2015; Velzeboer et al., 2014) and the acute inhibition of activated sludge by PS-NPs may be more complex. Therefore, more attention should be paid to the mechanism of PS-NPs and activated sludge in the future. 4. Conclusion In this study, the role of EPS on the influence of polystyrene nanoparticles (PS-NPs) on the endogenous respiration of activated sludge was investigated for the first time. It was shown that the activity of the activated sludge was acutely inhibited by PS-NPs. Carbonyl and amide groups and the side chains of lipids or amino acids were the main chemical groups involved in the interaction between EPS and PS-NPs. Moreover, the total relative abundances of antiparallel b-sheets and random coils decreased as the total abundances of aggregated strands, b-sheets, and a-helices increased. Thus, the bioflocculation capacity of the activated sludge was promoted by the PS-NPs. This result elucidated that PS-NPs in WWTPs would be concentrated by the EPS of activated sludge. Acknowledgments This work was supported by the National Science Foundation of

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