Investigating Possible Enzymatic Degradation on Polymer Shells around Inorganic Nanoparticles

Inorganic iron oxide nanoparticle cores as model systems for inorganic nanoparticles were coated with shells of amphiphilic polymers, to which organic fluorophores were linked with different conjugation chemistries, including 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) chemistry and two types of “click chemistry”. The nanoparticle-dye conjugates were exposed to different enzymes/enzyme mixtures in order to investigate potential enzymatic degradation of the fluorophore-modified polymer shell. The release of the dyes and polymer fragments upon enzymatic digestion was quantified by using fluorescence spectroscopy. The data indicate that enzymatic cleavage of the fluorophore-modified organic surface coating around the inorganic nanoparticles in fact depends on the used conjugation chemistry, together with the types of enzymes to which the nanoparticle-dye conjugates are exposed.

To synthesize Fe3O4 NPs cores with diameter of ~4 nm, a thermal decomposition reaction was performed following the methodology reported by Sun et al [1]. In brief, the synthesis was carried out in an oxygen-and water-free glovebox. Under a blanket of nitrogen, Fe(acac)3 (2 mmol, Sigma Aldrich, #517003), 1, 2-hexadecanediol (10 mmol, Sigma Aldrich, #213748), oleic acid (6 mmol, Sigma Aldrich, #O1008), oleylamine (6 mmol, Sigma Aldrich, #O7805), and phenyl ether (20 mL, Sigma Aldrich, #108014) were mixed and stirred at 200 ℃ for 30 min. After that, the mixture was heated up to 265 ℃ for another 30 min. In this reaction, Fe(acac)3 is used as metal precursor, which upon thermal decomposition is reduced by 1,2-hexadecanediol into Fe3O4 NPs. Finally, the black-brown mixture was cooled down to room temperature and taken out from the glovebox. For the purification of the Fe3O4 NPs, the product was separated into two 50 mL centrifuge tubes and then 25 mL of ethanol was added to each tube. Centrifugation at 6000 rpm for 10 min was applied and supernatants were discarded. The black precipitate was dissolved in 20 mL hexane with oleic acid (0.05 mL) and oleylamine (0.05 mL) in each tube. The centrifugation process was performed again and the Fe3O4 NPs were finally re-dispersed in hexane. Note that no analysis to confirm Fe3O4 structure was carried out, as the precise nature of the iron oxide core is irrelevant for this work. The corresponding transmission electron microscopy (TEM) images of the NPs dried on a TEM grid are presented in Figure S1 and confirm good monodispersity of the NPs with an average core diameter of dc = (4.4 ± 0.7) nm. Figure S1. (A) TEM image of hydrophobic Fe3O4 NPs, and (B) the size distribution diagram N(dc) of the core diameter dc as obtained from Image J analysis. The average diameter, dc of the Fe3O4 NP core was determined to be (4.42 ± 0.73) nm. Amphiphilic polymers have been widely used for the over-coating of NPs with the purpose of transferring hydrophobic NPs from organic solution to aqueous solution [2][3][4]. There are a large variety of amphiphilic polymers that can be used to coat NPs. In this work, dodecylamine modified poly(isobutylene-alt-maleic anhydride) (PMA) was selected based on previous work, which consists of dodecylamine hydrophobic side chains for interfacing the NP surface and a hydrophilic backbone of poly(isobutylenealt-maleic anhydride) [2]. The hydrophobic dodecylamine side chains bearing amino groups were linked to 75% of the anhydride rings of the hydrophilic backbone in a onepot reaction, leaving 25% intact anhydride rings [5]. During the polymer coating procedure, the hydrophobic side chains intercalate the hydrophobic surface capping of the NPs, and the leftover 25% anhydride rings of the hydrophilic backbone open up in basic condition yielding negatively charged carboxyl groups, which make the NPs soluble in aqueous medium. The electrostatic repulsion of the individual NPs due to the negatively charged amphiphilic polymer leads to a stable NP dispersion in water.
For the synthesis of PMA (a scheme is given in Figure S2), 2.70 g (15 mmol) dodecylamine (Sigma-Aldrich, #325163) were dissolved in 100 mL anhydrous tetrahydrofuran (THF, Sigma-Aldrich, #401757) in a 250 mL round bottom flask. Then, 3.084 g poly(isobutylene-alt-maleic anhydride) (average molecular weight of monomer unit Mw ~6,000 g/mol, Sigma-Aldrich, #531278) was added to this flask. After sonication of this mixture for 20 s, it was refluxed at 55-60 ℃ under constant stirring (800 rpm) for 3 h. Then, the solution was concentrated to around 30 mL by evaporation using a rotavapor (Heidolph, Laborota 4003 control) and then refluxed overnight for the reaction of the PMA backbone with dodecylamine. Finally, the solvent was completely evaporated and the product was dissolved in 40 mL anhydrous chloroform to get the final concentration of cp = 0.5 M of polymer monomer units [5]. Figure S2. Reaction scheme of the PMA synthesis. The hydrophilic backbone and hydrophobic dodecylamine side chains are presented in blue and red color, respectively.

I.3 Modification of PMA with furfurylamine and propargylamine
Similar to the linkage of dodecylamine to the hydrophilic backbone of PMA, molecules with an amino group can be linked via amide bonds to the maleic anhydride rings [6,7]. This method was used to add further molecular anchors, here furfurylamine and propargylamine, to the polymer, which later-on were used to attach different fluorophores. After the synthesis of PMA, 25% intact anhydride rings of the amphiphilic polymer can still be utilized to link furfurylamine or propargylamine. Here, to link these molecules to PMA, 2% of the total anhydride rings of the amphiphilic polymer were firstly modified by the reaction of the maleic anhydride rings with the amino groups of furfurylamine or propargylamine molecules, which is described schematically in Figure S3. In details, 10 mL of cp = 0.5 M amphiphilic polymer (concentration referring to the monomer units) in chloroform was mixed with a solution of 0.1 mmol furfurylamine (Sigma-Aldrich, F20009) or 0.1 mmol propargylamine (Sigma-Aldrich, P50900) in a round flask and the reaction mixture was refluxed at 55-60 ℃ overnight. Afterwards, the solvent mixture was evaporated with a rotavapor and the modified polymer was redissolved in 20 mL anhydrous chloroform to obtain a final polymer monomer concentration of cp = 0.25 M. As it has been mentioned, 75% of the anhydride rings were reacted with dodecylamine as described, and thus after linkage of 2% of the anhydride rings with furfurylamine or propargylamine, i.e. in total 23% of the anhydride rings remained unreacted. The amphiphilic polymer linked with furfurylamine and propargylamine is in the following termed as PMA-Furf and PMA-Prop, respectively. Note that 100% reaction efficiency was assumed, though actual reaction efficiencies may be less [8].

I.4 Polymer coating and purification of Fe3O4 NPs
The polymer coating was carried out as reported before [2,3]. The amount of polymer solution VP added to the NPs was determined as: Here cNP (cf. Chapter I.5) and VNP are the concentration and the volume of the NP solution, respectively. In this order, cp and Vp are the monomer concentration and the volume of the amphiphilic polymer solution. deff is the effective diameter of NPs including the diameter of inorganic core and twice the thickness hydrophobic surfactant shell: deff = dc + 2lligand. Here dc = 4.4 nm as determined by TEM and lligand = 1 nm were used. RP/Area is the ratio of polymer units per nm 2 of effective NP surface. For the Fe3O4 NPs in the present study, the value RP/Area = 100 nm -2 was chosen [5].
Polymer coating with the three different polymers (PMA, PMA-Furf, and PMA-Prop) was carried out in chloroform [5]. First, the hydrophobic Fe3O4 NPs in chloroform were mixed with PMA, PMA-Furf, and PMA-Prop separately in three different flasks. Each solution was stirred manually for 5 min and then the solvent was completely evaporated in a rotary evaporator under heating to 40 C in order to force the polymer to wrap around the NPs. To obtain a homogeneous coating, a few mL of anhydrous chloroform was added to the flask to reconstitute the solid film and again the solvent was removed under reduced pressure. After that, alkaline sodium borate buffer (SBB 12, 50 mM, pH 12 adjusted with NaOH) was added and the mixture was vigorously stirred until the solution turned clear. In this way, all the NPs were transferred into SBB 12 solution [5].
After the polymer coating, there was free PMA in the NP solution [9]. Thus, a cleaning process was carried out to warrant for the purity of Fe3O4 NPs. Firstly, the NP samples in SBB 12 were cleaned by using centrifugal filters (15 mL, Amicon Ultra, 100 kDa) at 4000 rpm for 15 min [5]. After concentrating the samples, loading buffer (20% of the sample by volume) for gel electrophoresis was added to the samples. The loading buffer was prepared by mixing 35 mL 0.5× tris-borate-EDTA buffer (TBE, Sigma-Aldrich, #T3913), 25 mL glycerol (Sigma-Aldrich, # G8773) and 130 mg Orange G (Sigma-Aldrich, # 861286). The mixture then was loaded on a 2% agarose gel in a Tris-Borate-EDTA buffer (TBE 0.5x, Sigma-Aldrich, # T3913) for running of gel electrophoresis at 110 V for 1 h [5]. Figure S4 represents the corresponding gel pictures of Fe3O4 PMA NPs, Fe3O4 PMA-Prop NPs, and Fe3O4 PMA-Furf NPs. Due to the negative charge of the PMA, the NPs showed good electrophoretic mobility. The narrow band corresponding to the NPs on the gel confirmed the good monodispersity of the NPs. Some free polymers can still remain in the solution after gel electrophoresis [5]. Thus, ultracentrifugation was also carried out for three times to make sure of the removal of unbound polymers (54000 revolutions per minute (rpm), 1 h). After the application of voltage, the negatively charged NPs run through the pre-made 2% agarose gel towards the positive pole.

I.5 Conjugation of Fe3O4 NPs with different dyes
To conjugate the dyes to the Fe3O4 NPs, different chemistry including "click chemistry" was carried out and analyzed. Click chemistry has been used to synthesize multiple biomaterials [10]. It takes place usually in room atmosphere and is insensitive to water and oxygen [11]. In our experiments the Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) reactionand the Diels-Alder reaction were performed for the linkage of Fe3O4 PMA-Prop NPs with Coumarin and Fe3O4 PMA-Furf NPs with Cy5.5, respectively [12,13]. The original "click chemistry", referred to broadly as CuAAC, was first introduced to by Sharpless in 2001 [11]. The CuAAC reaction has broad applications in medicinal chemistry for the linkage of peptides, nucleotides, small molecules, supramolecular structures, polymers, etc [14]. The Diels-Alder reaction is also one of the most common "click chemistry" strategies, discovered by Otto Diels and Kurt Alder between a conjugated diene and a substituted alkene [15]. Beside these strategies, the Fe3O4 PMA NPs were furthermore conjugated with amine-modified Dy-605 via 1-Ethyl-3-(3dimethylaminopropyl)carbodiimide (EDC) chemistry, in which EDC is used as a carboxyl activating agent to couple amines [16,17].
Before the reaction, the concentration cNP of the Fe3O4 PMA NPs was calculated by Beer-Lambert's law using

c = ×
Here A is the absorbance of NPs at 450 nm and ε is the extinction coefficient of the NPs at 450 nm, l is the path length of the cuvette, which is 1 cm in our experiments [3].
The calculation of the molar extinction coefficient been published previously [7,18]. In the following the numbers for one measurement are given as example. The mass concentration of Fe in one sample was measured by inductive coupled plasma mass spectrometry (ICP-MS) as CFe = 0.0889 mg/mL. From the chemical formula of Fe3O4, the atom ratio of iron to oxygen is 3/4. Therefore, the content of the oxygen is CO = 4/3×CFe×(MO×MFe) = 0.03378 mg/mL, using the molar mass of oxygen, MO = 15.9 g/mol, and of iron, MFe = 55.8 g/mol. The total mass concentration of the investigated sample thus was CNP = CFe + CO = 0.1227 mg/mL.
To calculate the molar extinction coefficient, the molecular weight MNP of the NPs has also to be estimated. By the assuming that Fe3O4 NPs are spheres of 4.4 nm core diameter (dc = 4.4 nm), the volume of one NP core is VFe3O4 = (4/3) ×π× (dcore/2) 3 = 4.46×10 -20 cm 3 . The density of Fe3O4 is ρFe3O4 = 5.18 g/cm 3 . Then, the mass of each Fe3O4 NP core is mNP = ρFe3O4 × VFe3O4 = 2.31×10 -19 g. From the mass of one NP, the molecular weight MNP can be determined as MNP = mNP × NA= 1.  After the concentration determination of Fe3O4 NPs the dye conjugation was performed. The reactions are individually presented in Figure S6: CuAAC reaction ( Figure S6 A), Diels-Alder reaction (Figure S6 B), and EDC chemistry (Figure S6 C). The CuAAC reaction is a 1,3-dipolar cycloaddition for generating 1,4-disubtituted 1,2,3-triazoles between terminal alkynes and azides using Cu(I) salts as a catalyst [19]. In our experiment, the Fe3O4 PMA-Prop NPs containing terminal alkyne groups were reacted with azide-modified Coumarin. Ascorbic acid was added to the copper sulfate to reduce Cu(II) to Cu(Ι), as Cu(I) is the reaction catalyst. The Diels-Alder reaction involved a cycloaddition between Fe3O4 PMA-Furf NPs with an electron-rich diene and Cy5.5 with an electron-poor dienophile, and the final product they formed is a cyclohexene derivative. In the third reaction, Fe3O4 PMA NPs containing carboxyl groups were firstly activated by EDC, which is a water-soluble carbodiimide. Then the activated carboxyl group was conjugated with the amine group in Dy605 to yield an amide group. The reaction details are explained in the following. After all the reactions, the unreacted dye molecules were washed out. This is a critical step as non-covalently bond dyes would falsify the degradation results. Firstly, each sample was cleaned by membrane dialysis (10 kDa, Spectrum, #G235055) in 10 mM NaOH solution for 4 h, where unbound dye could diffuse out of the dialysis bath, whereas the NPs were retained [5]. Then, the dialysis bath was changed and the dialysis step was repeated 2 times. Next, the sample was collected and washed with centrifuge filters (5 mL, 100 kDa molecular weight cut-off (MWCO)) at 4000 rpm for 10 min [5]. This step was repeated until there was basically no longer free dye in the eluent.

II.1 Characterization of dye-conjugated Fe3O4 NPs
All NPs were characterized using different spectroscopic and microscopic techniques. Nuclear magnetic resonance (NMR) and infrared (IR) characterizations were attempted. However, no meaningful information was obtained for the here described dye conjugated NPs, since each polymer has multiple functional groups, which makes quantification of dye-conjugation complexes complicated. Instead, emphasis was given to fluorescence and gel electrophoresis data for the confirmation of the polymer coating and the dye conjugation. This gave clear results, as the Fe3O4 NPs without attached dye are not fluorescent.
Dye conjugation of Fe3O4 NPs was confirmed from their absorbance, fluorescence, dynamic light scattering (DLS), zeta potential, and gel electrophoresis analysis data. In each case, the absorbance spectra of conjugated NPs showed the presence of the characteristic dye features (cf. Figure 1 of the main manuscript). Since NPs without dyes are not fluorescent, fluorescence spectroscopy is a good way to confirm the dye conjugation. Similar to absorption spectra, the spectral fluorescence features of the dyes were seen in each of the spectra recorded of dye conjugated NPs ( Figure S7). For the case of Cy5.5 conjugation, a substantial shift of the fluorescence peak (~20 nm) was seen, which might be due to some structural re-arrangement of the dye upon conjugation [20]. The decrease of luminescent intensity from free dyes to NP-dye conjugates can be result of re-absorbance of the NPs. The fluorescence spectral features of dyes were seen in each dye conjugated NPs. The quenching effect of dyes attached on NPs was reported by Jang et al [21]. After the removal of free dye, the hydrodynamic diameter distribution and the zeta potential of the Fe3O4 NPs before and after dye conjugation were determined via DLS by a Zetasizer Nano ZS Malvern Instruments in Figures S8 and S9. All the values are calculated as average of at least three measurements with corresponding standard deviation. The hydrodynamic diameter dh of Fe3O4 coated with PMA-Prop, PMA, PMA-Furf was found to be 9-12 nm. After conjugation with coumarin, Dy605 and Cy5.5, there were increases in their size at different level, with the final dh value between 13 to 21 nm. The increase of the size is mainly caused by the dye attachment, but also will involve some slight agglomeration effects. After dye conjugation, also in the zeta potential measured an obvious change was observed, which varied from approximately -60 mV to -35 mV. The decrease of zeta potential may not only be result of the dye attachment but may be due to reduction in the density of the polymer coating during the intensive cleaning process which was carried out in order to remove free dye.  After the purification of unbound excess dye, gel electrophoresis was carried out to further confirm the conjugation of the NPs with dye. Dyes used in this work are nearly neutral and therefore significant migration was not seen, whereas conjugated NPs moved towards the positive pole due to their negative net charge originating from the polymer shell, see Figure S10.

II.2 Quantification of dye conjugation
In each case, the ratio of dye per NP was calculated using Beer-Lambert's law and the corresponding UV-vis absorption mentioned in §I.5. Absorbance was recorded at wavelengths with minimized overlap of NP and dye absorption. Absorbance at 450 nm A450 was used for determining the concentration of Fe3O4 PMA-Dy605 NPs and Fe3O4 PMA-Furf-Cy5.5 NPs, since the corresponding free dyes do not have significant absorbance at this wavelength (Table S1). For Fe3O4 PMA-Prop-coumarin NPs, absorbance A500 for determining the NP concentration was collected at 500 nm instead of 450 nm, as coumarin has its absorbance peak near 437 nm and has hardly any absorbance at 500 nm. The concentration ratios of dyes and NPs which correspond to the number of dye molecules per NP NDye/NP = cDye/cNP were found to be 5.48, 5.61, and 7.66 for the Fe3O4 PMA-Dy605, Fe3O4 PMA-Furf-Cy5.5, and Fe3O4 PMA-Prop-Coumarin NPs, respectively, see Table S1. This confirms that a similar number of dyes per NP was attached for all cases. Errors in the absolute numbers may in particular arise from uncertainties in the determination of NP.   As already mentioned, the absorbance at 450 nm A450 was used for Fe3O4 NPs conjugated with Dy605 and Cy5.5 since corresponding free dyes do not have any absorbance at this wavelength. For Fe3O4-coumarin NPs, absorbance at 500 nm A500 was collected instead of 450 nm, as coumarin has ignorable absorbance at 500 nm. Besides, to calculate the concentration of coumarin, the absorbance at 437 nm was collected. As Fe3O4 NPs also has absorbance peak at 437 nm, after subtracting the contribution from NPs, the concentration of coumarin was calculated. The absorbance at 500 nm and 437 nm (A500 = 0.195, A437 = 0.54) was from the absorbance spectra in Figure S11 A. The molar extinction coefficients of Fe3O4 at 437 nm and 500 nm was determined based on the absorption spectrum and the molar extinction at at 450 nm (Figure S11 C and S11 D, εNP(500) = 6. nM (εDye(437) = 39000 M -1 cm -1 ). The ratio of conjugated Cy5.5 per NP was cDye/cNP = 7.66, and the fluorescence intensity at the peak at 720 nm was 2.16×10 6 . Figure S11. (A, B) UV-vis absorption spectra A(λ) and fluorescence spectra I(λ) of Fe3O4 NPs conjugated with coumarin as recorded in MilliQ water. (C, D) Absorption at 437 and 500 nm of this sample in a cuvette of path length l= 1 cm, plotted versus the NP concentration, cNP, which was used to determine the extinction coefficients at two different wavelengths.

A
In Fe3O4 PMA-Dy605 samples, the absorbance at 450 nm (A450 = 0.485, λ = 450 nm is the wavelength used to determine the NPs concentration) and the absorbance at 600 nm (A600 = 0.36, λ = 600 is the wavelength of maximum dye absorbance) were recorded and are shown in Figure S12 A. Based on the molar extinction coefficient of Fe3O4 NPs at 450 nm as described before (εNP (450) = 1.17×10 6 M -1 cm -1 ), and the molar extinction coefficient value of Dy605 provided by the supplier at the absorbance peak at 600 nm (εDy605(600) = 110000 M -1 cm -1 ), applying the Beer-Lambert's law, concentrations of NPs, Dy605, and the ratio of dyes per NP were calculated (cNP = 414.5 nM, cDye = 2272.7 nM, cDye/cNP = 5.48). Apart from the absorbance spectra and calculated values above, fluorescence spectra and intensity at the emission maximum at 625 nm (I625 = 5.6x10 6 [a.u.]) are all illustrated in Figure 12 B. To determine the dye conjugation of Fe3O4 PMA-Furf-Cy5.5 quantitatively, a similar calculation process was performed. The corresponding spectra are shown in Figure S13.  III. Enzyme-induced degradation of the polymer shell of dye conjugated Fe3O4 NPs

III.1 NP incubation with enzymes
The enzyme solutions had approximately the same pH as the buffer in which the enzymes were dissolved, i.e. the enzymes did not change the pH, see Figure S14. As next step the samples were filtered with a centrifugal filter (500 μL, Amicon Ultra, 100 kDa MWCO) for 10 minutes at 9000 rpm, whereby the NPs are retained, and dye which got detached due to enzymatic digestion is in the eluate [5]. Filtration was performed to leave as litte volume retained as possible. The eluent from the bottom of the filter was collected and adjusted again with PBS to 500 μL, in order to keep the same volume as the original solution. The fluorescence intensity I1 of the eluent was recorded. Apart from FBS (1%), Trypsin (0.01%), CAT G (10 U/mL), LDH (10 U/mL), ACHE (10 U/mL), AST (5 U/L), and Proteinase K (10 U/mL) were also incubated with the different NPs. Additionally, the impact of enzyme concentration on the degradation efficiency was studied.

III.2 Fluorescence spectra of NPs incubated with enzyme (I0)
In Figure S15, the fluorescence spectra of Fe3O4 PMA-Prop-Coumarin, Fe3O4 PMA-Dy605 and Fe3O4 PMA-Furf-Cy5.5 NPs after incubation with enzymes are presented, together with the spectra of the enzymes themselves. Compared with the fluorescence intensity of dye conjugated NPs, the enzymes themselves shown negligible fluorescence ( Figure S15 A, C, E). In the emission spectra of the dye conjugated NPs (Figure S15 B, D, F), the fluorescence intensity of various samples incubated with enzymes were higher than the ones incubated in PBS without enzymes, which may be caused by the removal of distance quenching caused by underlying Fe3O4 NPs.

III.4 Dependence on enzyme concentration
The impact of enzyme concentration was studied for the degradation, which shows a linearly increasing effect in the I1 values for AST and FBS in all three dye-conjugated NP cases. The intensities are plotted in Figure 3 of the main manuscript and one set of emission spectra for FBS is shown in Figure S17. From these I0 and I1 fluorescence spectra corresponding to the incubation Fe3O4 PMA-Prop-Coumarin NPs (Figure S17 A, D), Fe3O4 PMA-Dy605 (Figure S17 B, E), and Fe3O4 PMA-Furf-Cy5.5 ( Figure S17 C, F) with enzymes, the amount of cleaved dye was increased with the increasing FBS concentration in all cases. In Figures S18-S20, the effects of enzyme concentration (trypsin, CATG, LDH, ACHE and Proteinase K) on I1 are presented. The Trypsin data also show a linear relation, but with a lower slope. For the other cases, the intensity did not change much with the concentration, which may because of the relatively slighter capability of degradation.

III.5 Control experiments
Additional control experiments were carried out to understand the degradation in more detail. The iron content was measured for the lower part (i.e. the eluate) as well as upper part (i.e. the retained NPs) of the centrifuged samples after enzyme incubation (for the case of FBS). This was to check whether the fluorescence intensities of the lower part are due to leaking of intact NPs through the centrifuge filter or not. An Agilent ICP-MS 7500cs inductively coupled plasma-mass spectrometry instrument was used for the analysis. Both the lower and upper part was volume-adjusted to 500 µL. Then, 50 µL of the solution was taken from each part and digested with 150 µL of freshly prepared aqua-regia. The mixture was kept on a shaker for 2 h. The digested samples were then further diluted by 2% of HCl and were then used for the ICP-MS analysis. The corresponding data are presented in Figure S24 A which shows the negligible amounts of iron in the lower part, confirming that the degradation is only from the polymer-shell part, but not from the inorganic Fe3O4 core. For further confirmation, the absorption spectrum of the lower part was collected and compared to the one of free dye and dyeconjugated NPs. The absorption spectrum of the eluate shows the features of the dye, but no absorbance features corresponding to the NPs near 400-450 nm were noticed (Figure S24 B). Control experiments with only dye were also performed in Figure S25. In this case, Dy605 dye was incubated with FBS and then I1 and I0 were collected similarly as mentioned in Chapter III.1 at different concentration of FBS. In this case, the total amount of dyes was not recovered in the eluate (though the free dyes should all cross the filter membrane), which suggests that some of the disconnected dye molecules remain adsorbed to the enzyme surface and remain in the upper part or adsorbed within the filter membranes. Thus, quantitative degradation efficiency analysis is complicated for the case of FBS.