SUPPLEMENTARY INFORMATION doi: 10.1038/nnano.2011.10
2
1. Details on the experimental testing protocol
We prepared E. coli (Migula) Castellani & Chalmers (ATCC#25254, Manassas, VA) strain at 37 oC overnight, using LB broth. Then, the cultures were centrifuged at 3220 g for 10 min and resuspended in sterilized physiological saline. Bacteria density was adjusted to 0.5 × 109 – 1.66 × 109 bacteria/mL as determined by colony forming unit (CFU) counting on LB Petri dishes.
We determined the cytotoxicity of the metal oxide nanoparticles in terms of EC50 (the
concentration of the metal oxide nanoparticles effects the reduction of bacteria viability of 50%) based on the curve fitting least squares procedure.
We also used bacterial heterotrophic mineralization of glucose to determine the metabolic rate of
selected samples and it was measured as follows. After washing 3 times with physiological saline, 100 μL of E. coli suspensions were added to 10-20 mL of distilled water (control) or 10-20 mL of nanoparticle/distilled water solution at nominal concentrations of 200 mg/L, 400 mg/L and 600 mg/L, respectively. To assure dispersal the stock solutions were prepared at the concentration of 1.2 g/L with a sonication treatment (FS30 ultrasonic system; Fisher Scientific) at 25 oC for 20 min. They were sonicated again for 10 min right before the exposure experiments started. The control and experimental groups were then agitated for 2 h at a speed of 150 rpm. A mineralization count of 14CO2 released during metabolic respiration of radio-labeled UL-14C D-glucose dissolved in ethanol (S.A. 2.48 mCi/mmol Sigma Inc.) was conducted after the 2 h incubation period. At time zero, the Pyrex milk dilution bottle was sealed with a silicone stopper and a center well containing a folded filter paper (Whatman #1) soaked with 0.7 mL of β-phenylethylamine for CO2 trapping. They were allowed to trap over night (8-12 h) after injection with 2 N H2SO4 at the end of 2 h incubation. Then, the filter papers were removed and placed in 20 mL scintillation vials containing 8 mL of Ultima Gold scintillation fluid (Packard; Meriden, CT, USA) and counted with a liquid scintillation analyzer (Packard Instrument, model TR 1600). Data was calculated from DPM (disintegrations per minute) readings to compute the percent mineralizations.
We took the results for 7 oxides: ZnO, CuO, Al2O3, La2O3, Fe2O3, SnO2, and TiO2 from our previously published paper,1 whereas the cytotoxicity of the remaining 10 oxides was experimentally tested according to the same protocol in two Batchs: Batch I (V2O3, Y2O3, Bi2O3, In2O3, Sb2O3, SiO2, ZrO2) and Batch II (CoO, NiO, Cr2O3). To ensure that there was no systematic error between the particular series of experiments caused by varying laboratory conditions, in the later experiments we repeated toxicity measurements for selected oxides, that were tested in the previous series. Reference 1. Hu, X., Cook, S., Wang, P. & Hwang, H. M. In vitro evaluation of cytotoxicity of engineered metal oxide nanoparticles. Sci. Total Environ. 407, 3070-3072 (2009).
We calculated a pool of 12 variables quantitatively describing variability of the nanoparticles' structure (structural descriptors, Table 1). The calculations have been performed at the semi-empirical level of the theory with use of PM6 method1 in MOPAC 2009 software package2. Semi-empirical methods are usually much faster that quantum-mechanical ab initio and Density Functional Theory (DFT) calculations, enable to perform calculations for larger systems, but their accuracy is often disputable3. It is worth noting, however, that PM6 method, which is a novel parametrization of previously used PM3 Hamiltonian, delivers very accurate results, comparing to those from DFT4.
Table 1. List of the structural descriptors No. Symbol Description Type
1. HOF Standard heat of formation of the oxide cluster I 2. TE Total energy of the oxide cluster I 3. EE Electronic energy of the oxide cluster I 4. Core Core-core repulsion energy of the oxide cluster I 5. CA Area of the oxide cluster calculated based on COSMO I 6. CV Volume of the oxide cluster calculated based on COSMO I 7. HOMO Energy of the highest occupier molecular orbital of the oxide cluster II 8. LUMO Energy of the lowest unoccupied molecular orbital of the oxide cluster II 9. GAP Energy difference between HOMO and LUMO energies II
10. ΔHClust Enthalpy of detachment of metal cations Men+ from the cluster surface III 11. ΔHMe+ Enthalpy of formation of a gaseous cation III 12. ΔHL Lattice energy of the oxide III
Because the size of the metal oxides nanoparticles we tested (15 - 90 nm) was too large even to perform calculations at the semi-empirical level it was necessary to simplify the molecular models used for calculations of the descriptors. We assumed that the simplified molecular models could be applied to calculate the descriptors because of the following reasons: First, our preliminary investigations on clusters of different sizes5 revealed that some potentially important molecular descriptors (e.g., heat of formation, solvent accessible surface area) change linearly with the cluster size. This trend is also very intuitive. We named this type of descriptors as Type I. However both, our previous studies on the clusters5 and recent contributions based on the experiment6 show that large, size-dependent change of some electronic properties (i.e., ionization potential and electron affinity) for metal oxides particles occur below about 5 nm. The property value variation with the increasing size of the nanomaterial does not occur until it reaches so-called the saturation point - starting from which the property value does change. Therefore, the property changes between 15 and 90 nm are negligible, and we named such type of descriptors Type II. In our study we assumed that (i) the clusters must be of the same size, thus the descriptors of Type I are dependent on other features than the size and (ii) the clusters must be bigger than the size representing saturation points for all the studied oxides. In this way, the molecular
SUPPLEMENTARY INFORMATION doi: 10.1038/nnano.2011.10
4
descriptors that we used are size-independent and reliably reflect various properties of the metal oxides nanoparticles. We calculated the descriptors of Type I and Type II based on the clusters prepared in the following way. At first, the initial unit cell coordinates were taken from publically available crystallographic data (Table 2). Then, we subsequently increased the lattice parameters in respect to all three dimensions. In the first step we increased twice one of the dimensions of the initial unit cell. In the second step, we have used as the initial cluster the structure obtained in the previous step and additionally doubled the second dimension. Then, we doubled the last - the third of the unit cell dimensions, increasing the cluster size more than twice from the initial size. We repeated this procedure until we obtain cubic cluster having size of 12 Å.
Table 2. Crystallographic data utilized to construct the metal oxides clusters
Metal oxide Reference
ZnO Karzel, H. et al. X-ray diffractometer for high pressure and low temperatures. Mater. Sci. Forum 79, 419-426 (1991).
CuO Stergiou, A., Kerasiotis, I. & Stergiou, C. Crystallographic study of NdxBa1-xCuOy (x=0.2, 0.4, 0.6, 0.8) compounds prepared by heating of component mixtures. J. Optoelectron. Adv. Mater. 9, 1772-1778 (2007).
V2O3 Rozier, P., Ratuszna, A. & Galy, J. Comparative Structural and Electrical Studies of V2O3 and V2-xNixO3 (0 < x < 0.75) Solid Solution. Z. Anorg. Allg. Chem. 628, 1236-1242 (2002).
Y2O3 Zachariasen, W.H. Untersuchungen über die Kristallstruktur von Sesquioxyden und Verbindungen ABO3. Skr. Norske Vid. Akad. 4, 1-165 (1928).
Bi2O3 Jovalekic, C., Zdujic, M., Poleti, D., Karanovic, L. & Mitric, M. Structural and electrical properties of the 2Bi2O3. 3ZrO2 system. J. Solid State Chem. 181, 1321-1329 (2008).
In2O3 Nadaud, N., Lequeux, N., Nanot, M., Jove, J. & Roisnel, T. Structural Studies of Tin-Doped Indium Oxide (ITO) and In4Sn3O12. J. Solid State Chem. 135, 140-148 (1998).
Sb2O3 Whitten, A.E., Dittrich, B., Spackman, M.A., Turner, P. & Brown, T.C. Charge density analysis of two polymorphs of antimony(III) oxide. Dalton Trans. 1, 23-29 (2004).
Fe2O3 Baron, V., Gutzmer, J., Rundloef, H. & Tellgren, R. Neutron Powder Diffraction Study of Mn-Bearing Hematite, alpha-Fe2-xMnxO3, in the Range 0<x<0.176. Solid State Sci. 7, 753-759 (2005).
SiO2 Goresy, A. et al. Seifertite, a dense orthorhombic polymorph of silica from the Martian meteorites Shergotty and Zagami. Eur. J. Mineral. 20, 523-528 (2008).
ZrO2 Bondars, B. et al. Powder diffraction investigations of plasma sprayed zirconia. J. Mater. Sci. 30, 1621-1625 (2002).
SnO2 Maekawa, T., Minagoshi, C., Nakamura, S., Nomura, K. & Kageyama, H. Crystal structure analysis of the catalysts based on tin oxide using a neutron diffraction method. Chemical sensors 24, 19-21 (2008).
TiO2 Rubio-Ponce, A., Conde-Gallardo, A. & Olguin, D. First-principles study of anatase and rutile TiO2 doped with Eu ions: A comparison of GGA and LDA+U calculations. Phys. Rev. B: Condens. Matter 78, 035107_035101-035107_035109 (2008).
CoO Redman, M.J. & Steward, E.G. Cobaltous Oxide with the Zinc Blende/Wurtzite-type Crystal Structure. Nature 193, 867-867 (1962).
NiO Shimomura, Y., Kojima, M. & Saito, S. Crystal structure of ferromagnetic nickel oxide. J. Phys. Soc. Jpn. 11, 1136-1146 (1956).
Cr2O3 Saalfeld, H. Strukturuntersuchungen im system Al2O3-Cr2O3. Z. Kristallogr. 120, 342-348 (1964).
La2O3 Aldebert, P. & Traverse, J.P. Etude par diffraction neutronique des structures de haute temperature de La2O3 et Nd2O3. Mater. Res. Bull. 14, 303-323 (1979).
We then used the clusters as the molecular models of the studied nanoparticles for quantum-mechanical calculations at the semi-empirical PM6 level. We performed the calculations in MOPAC 2009 software package. The calculations involved two steps: (i) optimization of the molecular geometry with the increased criteria of precision, (ii) calculation of the descriptors based on the optimized geometry. We also calculated three descriptors of the Type III (nos. 10, 11 and 12). First two descriptors were the enthalpies of two hypothetical reactions:
• The reaction of detachment of metal cations Men+ from the cluster surface:
Clust − Me + n ⋅ H + → Men+ + Clust − H( )n ΔHClust
• Enthalpy of formation of a gaseous cation:
Me (s) → Men+ (g) + n ⋅ e ΔHMe+
The third descriptor was the lattice energy, calculated according to the Born-Haber thermodynamic cycle.
During the model developing, we tested various descriptors, which were in some cases more interpretative than ΔHMe+, but the correlation was not satisfactory. For example, the correlation coefficient for the ΔHL lattice energy (describing dissolution of nanoparticles without oxidation or reduction of the cation) with the toxicity was of 0.64. This means ΔHL can explain differences in the toxicity between the oxides for only about 40% (R2=0.41). Similarly, when correlating only electronic properties of the oxides describing their redox properties (e.g., energies of the highest occupied (HOMO) and the lowest unoccupied molecular orbitals (LUMO), and the HOMO-LUMO energy band gap) with the toxic endpoint, the corresponding models were also poor (R2<0.60).
Surprisingly, we were not able to optimize geometry of the La2O3 cluster and, in consequence, to calculate the descriptors nos. 1-10 for this structure. There are two possible explanations of this problem: the crystal structure applied was inappropriate (wrongly determined); or (more probable) there is an artifact of the PM6 method. Because we managed to calculate the value of descriptor no. 11 for La2O3 and this descriptor has been finally selected as the most significant to the final model, we were able to use lanthanum oxide as a validation compound. Thus, arbitrary assign it to the validation set (V2).
2.2. Splitting data for a training and validation set
To perform appropriate validation of the model we split the studied oxides into the training and
SUPPLEMENTARY INFORMATION doi: 10.1038/nnano.2011.10
6
the external validation set. The splitting algorithm was as follows:
1. 13 metal oxides for which toxicity data had been either taken from the previous paper, or they had been tested in Batch I were sorted based on decreasing toxicity.
2. In a next step they were split into two sets: the training set (T) and the validation set (V1) in a way ensured that the points from V1 were evenly distributed within the range of the toxicity of the training set compounds (T). We utilized the following pattern of splitting: T-T-V1-T-T-T-V1-T-T-T-V1-T-T.
3. Finally, three additional compounds tested in Batch II and La2O3 were additionally included in the validation set (those compounds are indicated with V2).
We split the data in an above discussed way because of three reasons:
(i) to ensure that the compounds V1 are evenly distributed within the range of toxicity log (1/EC50),
(ii) to have both experimental batches represented in the validation set, whereas only compounds from the Batch I were used for training,
(iii) to include to the validation set some additional compounds (V2) having toxicity not necessarily within the range of the training set (this would be impossible, if we have merged compounds from Batch I and II together and then labeled every third compound as a member of the validation set). Indeed, observed toxicity of CoO was higher than toxicity of the most toxic compound in the training set (ZnO).
2.3. Data preprocessing
The descriptors have been auto-scaled, which means that the average value was subtracted from the descriptors and the resultant values divided by the standard deviation to ensure the same scale and range of all variables.
2.4. Developing the model
We employed the multiple linear regression combined with a genetic algorithm (GA-MLR) as the method of modeling. MLR is a standard regression technique in which the response y (here toxicity: log 1/EC50) is expressed as a linear combination of independent variables xi (here: descriptors) (1). y = b0 + b1x1 + b2x2 + ... + bnxn (1)
The coefficients vector b is calculated, assuming minimization of the squared residuals, according to the formula (2): b = (XT X)−1XT y (2) where X is the descriptor matrix containing an additional (first) column with ones, which is necessary to calculate the intercept (b0).
In order to select the optimal combination of the molecular descriptors we used the Holland’s
genetic algorithm (GA)7. The algorithm is a mathematical procedure based on the analogy to the Darwinian theory – the evolution of DNA, driven by the “survival of the fittest” approach. The selection procedure is as follows. Initially, the genetic algorithm creates a “population” of randomly chosen solutions – “specimens” (i.e., combinations of descriptors). Thereafter, the specimens are evaluated based on the lowest residual values, described as the “fitness function”. The variable subsets that give the lowest residuals are “recombined” to form a new population (a second “generation” of solutions). The algorithm stops after many steps (many generations), when the average fitness of specimens in a population reaches the satisfactory level8. The algorithm is controlled by a set of steering parameters. In our studies we used the following ones: the size of a population: 112, the percentage of the initial terms: 50%, the maximum number of generations: 100, the percentage of convergence: 50%, the mutation rate: 0.005, cross-over: double, the number of repetitions: 10.
We obtained a statistically significant QSAR model (F = 45.4, p = 1x10-4) capable to successfully predict the cytotoxicity of the metal oxide nanoparticles. The model utilized only one descriptor (3).
log 1 / EC50( )= 2.59 − 0.50 ⋅ ΔH Me+ (3)
Both the intercept and coefficient were significantly different from zero, based on the Student's t-
test (Table 3). The ratio between the number of descriptors and training compounds (1:10) was two times higher than the minimum Toppliss and Costello9 criterion (should be at least 1:5).
Table 3. Statistics for the model's coefficients bi std. error t-value p-value b0 (intercept) 2.59 ±0.07 37.05 3 x 10-10 b1 (coefficient) -0.50 ±0.07 -6.74 1 x 10-4
2.5. Internal validation, statistical measures of goodness-of-fit and robustness
We used the determination coefficient R2 (4) and the Root Mean Square Error of Calibration RMSEC (5) as the two measures of the goodness-of-fit.
( )
( )
2
2 1
2
1
1
nobs predi i
in
obs obsi
i
y yR
y y
=
=
−= −
−
∑
∑ %
(4)
( )2
1
nobs predi i
ny y
RMSECn
=
−=∑
(5)
where: yiobs – experimental (observed) value of the property for the ith compound; yi
pred – predicted value for the ith compound; n – the number of compounds in the training set.
SUPPLEMENTARY INFORMATION doi: 10.1038/nnano.2011.10
8
For both optimization and calibration steps we additionally applied the internal validation (cross-validation leave-one-out technique, CV LOO) to reduce probability of the model’s overfitting to the training data, and to measure robustness of the model on the presence/absence of particular metal oxides in the training set. According to the CV LOO algorithm each oxide from the training set was removed, one at a time. Thus, 10 reduced models were calculated; each of these models was developed with the remaining 9 oxides and used to predict the cytotoxicity of the oxide temporarily removed. The cross-validated correlation coefficient Q2
CV (6) and cross-validated root mean square error of prediction RMSECV (7) were calculated from the sum of squared differences between the observed and estimated cytotoxicity. We used the lowest possible number of descriptors and the value of RMSECV as the criteria of selecting the most optimal model’s complexity10.
( )
( )
2
2 1
2
1
1
nobs predcvi i
iCV n
obs obsi
i
y yQ
y y
=
=
−= −
−
∑
∑ %
(6)
( )2
1
nobs predcvi i
ny y
RMSECVn
=
−=∑
(7)
where: yi
obs – experimental (observed) value of the property for the ith compound; yipredcv – predicted
value for the temporary included (cross-validated) ith compound; ỹobs – the mean experimental value of the property in the training set; n – number of compounds in the training set.
The cross-validated correlation coefficient of the finally selected model was Q2
CV = 0.77. The root mean square error of calibration (the measure of the goodness-of-fit) and the root mean square error of cross-validation (the measure of the robustness) were RMSEC = 0.20 and RMSECV = 0.24, respectively.
To avoid the correlation by chance and to confirm significance of the QSAR model, we
additionally performed the Y-scrambling numerical experiment. We built 100 random ‘models’ utilizing the same descriptor (ΔHMe+) but correlated it with the cytotoxicity data randomly shuffled every time. Those random ‘models’, of course, do not have any physical meaning. However, based on the calculations of the RMSEC and RMSECV values for these models we were able to determine the level of noise – the minimal error that can be calculated without presence of any model10. Since the values of both RMSEC and RMSECV for our ‘true’ QSAR model were about two times lower then these for the randomly obtained models (FigureSI1), we have confirmed the significance of the QSAR. This clearly confirms that the model has not been obtained by a chance correlation.
2.6. External validation and measures of predictive ability
To confirm the models’ ability to predict the cytotoxicity of new metal oxides (not previously used to develop the model) we carried out the external validation by applying of the model to the validation set. The measures of predictive ability based on external validation (the externally validated determination coefficient Q2
Ext and the root mean square error of prediction RMSEP) are defined by the equations (8) and (9):
( )
( )
2
12
2
1
1ˆ
kobs predj j
jExt k
obs obsj
j
y yQ
y y
=
=
−= −
−
∑
∑ (8)
( )2
1
kobs predj j
jy y
RMSEPk
=
−=∑
(9)
where: yj
obs – experimental (observed) value of the property for the jth compound; yjpred – predicted value
for jth compound; ŷobs – the mean experimental value of the property in the validation set; k – the number of compounds in the validation set11,12.
The values of the externally validated correlation coefficient Q2
Ext = 0.83 and the root mean square error of prediction, based on the external validation RMSEP = 0.19 confirmed predictive ability of the model. Since any of the compounds from V1 and V2 were not involved in the training step, both
SUPPLEMENTARY INFORMATION doi: 10.1038/nnano.2011.10
10
subgroups of the validation set could be utilized together to calculate the RMSEP value. However, taking into account the splitting method, the compounds from V1 could never have the toxicity values outside the range of the training compounds values. Thus, in order to develop a fully validated model, we compared the RMSEP values, calculated based on V1, V2 and both (V1+V2) validation subsets (Table 4). Since the values of RMSEPV1, RMSEPV2 and RMSEP were not significantly different from RMSEC and RMSECV we concluded that model is capable to make the predictions even for the compounds slightly exceeding the toxicity range covered by the training compounds. Toxicity of any validation compounds (either from V1 or from V2) has been predicted with a residual value not exceeding distance of ±2.5 standard deviations from the mean residual in the training set.
Table 4. Comparison of the RMSEP values for V1 and V2
n RMSEP
V1 3 0.28 V2 4 0.07 V1+V2 7 0.19
2.7. Evaluation of the optimum prediction space (applicability domain) of the model
In addition to the predictive ability validation, we also verified the response and nanoparticle structure space, in which the model makes predictions with the most optimal reliability. Defining borders of the space, so-called ‘the optimum prediction space’ or ‘applicability domain’ is important especially for the compounds with unavailable experimental data to verify the quality of the predictions13. When a compound is located outside the optimum, the predicted results are extrapolated. Thus, they should be treated with greater care as less reliable. In our study we employed the leverage approach and Williams plot to visualize the results14. The leverage value hi for each ith compound is calculated from the descriptor matrix (X) according to the formula:
hi = xi
T (XTX)-1 xi
where xi is a row vector of molecular descriptors for a particular (ith) compound. The value of hi greater than the warning h* value indicates that the structure of a compound substantially differs from those used for the calibration. Therefore, the compound is located outside the optimum prediction space. The h* value is calculated as follows:
h* =3(p + 1)
n
where p is the number of variables used in the model, n is the number of training compounds.11 Neither any training nor validation compound from our study did exceed the critical h* = 0.6 value (Figure SI2). When analyzing the cross validated residuals for the training set and from the predictions for the validation set, we did not identify any significantly outlying results (the residuals differing by more than 2.5 standard deviations from 0, Figure SI2). Thus, the model can be applied for predicting toxicity of any other metal oxides, if their structures are not substantially different from the training set (their calculated leverage values are not higher than the critical value of h*=0.6).
La2O3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 1017.22 -2969.336 N/A - Descriptor value is not available. For a detailed explanation please refer to text above.
References 1 Stewart, J.J.P. Optimization of parameters for semiempirical methods V: modification of NDDO
approximations and application to 70 elements. J. Mol. Model. 13, 1173-1213 (2007). 2 Stewart, J.J.P. MOPAC2009 (Stewart Computational Chemistry, 2009). 3 Jensen, F. Introduction to computational chemistry. (John Wiley & Sons, Chichester, 1999). 4 Puzyn, T., Suzuki, N., Haranczyk, M. & Rak, J. Calculation of Quantum-Mechanical Descriptors
for QSPR at the DFT Level: Is It Necessary? J. Chem. Inf. Model. 48, 1174-1180 (2008). 5 Gajewicz, A., Puzyn, T., Leszczynska, D. & Leszczynski, J. Size-dependent quantum-
mechanical descriptors of the nanometers - sized metal oxides for nano - QSAR. in preparation (2010).
6 Kukreja, L.M., Barik, S. & Misra, P. Variable band gap ZnO nanostructures grown by pulsed laser deposition. J. Cryst. Growth 268, 531-535 (2004); Zhai, H.J. and Wang, L.S., Probing the Electronic Structure and Band Gap Evolution of Titanium Oxide Clusters (TiO2)n- (n = 1−10) Using Photoelectron Spectroscopy. J. Am. Chem. Soc. 129, 3022-3026 (2007).
7 Holland, J. Adaptation in Natural and Artificial Systems. (MIT Press, Michigan, 1992). 8 Rogers, D. & Hopfinger, A.J. Application of Genetic Function Approximation to Quantitative
Structure-Activity Relationships and Quantitative Structure-Property Relationships. J. Chem. Inf. Comput. Sci. 34, 854-866 (1994).
9 Topliss, J.G. & Costello, R.J. Chance correlations in structure-activity studies using multiple regression analysis. J. Med. Chem. 15, 1066-1068 (1972).
10 OECD, 2007. 11 Gramatica, P. Principles of QSAR models validation: internal and external. QSAR Comb. Sci.
26, 694-701 (2007). 12 Tropsha, A.,Annual Reports in Computational Chemistry, Vol. 2. edited by D.C. Spellmeyer
(Elsevier, Amsterdam, 2006). 13 Dearden, J.C., Cronin, M.T. & Kaiser, K.L. How not to develop a quantitative structure-activity
or structure-property relationship (QSAR/QSPR). SAR QSAR Environ. Res. 20, 241-266 (2009). 14 Jaworska, J., Nikolova-Jeliazkova, N. & Aldenberg, T. QSAR Applicability Domain Estimation
by Projection of the Training Set in Descriptor Space: A Review. ATLA 33, 445-459 (2005); Tropsha, A., Gramatica, P. & Gombar, V.K. The importance of being earnest: Validation is the absolute essential for successful application and interpretation of QSPR models. QSAR Comb. Sci. 22, 69-77 (2003).
