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Nanomaterials and nanoparticles (NPs) possess unique physicochemical properties (size, shape, chemical composition, physiochemical stability, crystal structure, surface area, surface energy, and surface roughness), which give them beneficial characteristics. Quantitative structureactivity relationship, or QSAR, is an area of molecular modeling that studies relationships between structure and activity using mathematical statistics and machine learning methods. QSAR is efficiently used to predict toxicity of chemical substances.
Source 
Dataset 
Endpoint of Cytotoxicity Measurement 
n 
R^{2 1} 
Software ^{2} 
Statistical Method 
Descriptors 

Escherichia coli 

^{[24]} 
^{[24]} 
LD_{50} 
7 
0.979 
 
Multiple linear regression (MLR) 
Metal cation charge 
^{[20]} 
^{[20]} 
LD_{50} 
17 
0.862 
MATLAB 
MLR 
Enthalpy of formation of a gaseous cation 
^{[25]} 
^{[20]} 
LD_{50} 
17 
0.741–0.838 
CORAL 
Monte Carlo 
SMILESbased optimal descriptor 
^{[26]} 
^{[20]} 
LD_{50} 
17 
0.933 
Minitab 16 
MLR 
Energy gap, hardness, softness, electronegativity, and electrophilicity index 
^{[27]} 
^{[20]} 
LD_{50} 
17 
0.81–0.90 
 
MLR 
Electronegativity, charge of the metal cation corresponding to a given oxide 
^{[28]} 
^{[20]} 
LD_{50} 
17 
0.93 
RandomForest package 
Random forest (RF) 
S_{1}—unbonded twoatomic fragments [Me] … [Me], which were encoded based on Simplex representation of molecular structures (SiRMS)derived descriptors ^{[33]}^{[34]}, describing distance where potential reaches minimum at van der Waals interactions; rw—Wigner–Seitz radius; ρ—mass density; (CPP)—cation polarizing power; S_{2}—SiRMSderived electronegativity aligned descriptor of oxides molecules—in a sense of the acidbase property of oxides (this parameter increases with a number of oxygens in molecule); S_{3}—triatomic fragments [Me][O][Me], which were encoded by SiRMSderived descriptors, encoding electronegativity; and (SV)—proportion of surface molecules to molecules in volume 
^{[29]} 
^{[20]} 
LD_{50} 
17 
0.955 
Ensemble learning 
Oxygen percent, molar refractivity, and polar surface area 

^{[30]} 
^{[20]} 
LD_{50} 
17 
 
MATLAB 
Readacross 
Ionization enthalpy of the detached metal atoms 
^{[18]} 
^{[20]} 
LD_{50} 
17 
0.889–0.982 
CORAL 
MLR 
SMILESbased optimal descriptor 
^{[35]} 
^{[20]} 
LD_{50} 
16 
0.91 
 
MLR 
Enthalpy of formation of a gaseous cation (ΔH_{Me+}), charge of the metal cation (χ_{ox}), and pEC_{50} of HaCaT 
^{[32]} 
^{[20]} 
LD_{50} 
16 
0.879 
SYBYL X1.1 and SPSS statistics v.17 
MLR 
Enthalpy of formation of a gaseous cation (ΔH_{me+}) and polarization force (Z/r) 
^{[36]} 
^{[20]} 
LD_{50} 
16 
0.79 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[37]} 
^{[20]} 
LD_{50} 
17 
0.92 
 
Counter propagation artificial neural network 
Metal electronegativity by Pauling scale, number of metal atoms in oxide, number of oxygen atoms in oxide, and charge of metal cation 
^{[38]} 
^{[20]} 
LD_{50} 
17 
0.968 
 
RF 
Oxygen in weight percentage and enthalpy of formation of a gaseous cation 
^{[39]} 
^{[20]} 
LD_{50} 
17 
0.877 and 0.903 
 
MLR and support vector machines (SVM) 
HOMO energy, αLUMO and βLUMO energy, the average of αLUMO and βLUMO, the energy gap between the frontier molecular orbitals ∆E, and molar heat capacity 
^{[8]} 
^{[20]} 
LD_{50} 
17 
0.93 
 
Partial least squares (PLS) 
Charge of metal ion, metal ion chargebased SiRMS, number of oxygen atoms in brutto formula weighted by ionic potential, covalent index weighted by charge of metal ion, molecular weight of metal oxide weighed by size of nanoparticle, squared thickness of interfacial layer, van der Waals repulsion weighted by size of nanoparticle, and WignerSeitz radius weighted by size of nanoparticle 
^{[31]} 
^{[31]} 
LD_{50} 
17 
0.87 
Selfwritten program 
MLR 
Electronegativity of metal and electronegativity of metal oxide 
^{[40]} 
^{[40]} 
IC_{50} 
24 
 
R 
SVM 
Conduction band energy and hydration enthalpy (ΔH_{hyd}) 
Human keratinocyte cell line (HaCaT) 

^{[28]} 
^{[41]} 
LD_{50} 
18 
0.96 
RandomForest package 
RF 
S_{1}, rw, ρ, (CI)—covalent index of the metal ion, S_{2}, and (AP)—aggregation parameter 
^{[30]} 
^{[41]} 
LD_{50} 
18 
 
MATLAB 
Readacross 
Mulliken’s electronegativity 
^{[41]} 
^{[41]} 
LD_{50} 
18 
0.93 
 
MLR 
Enthalpy of formation of metal oxide, Mulliken’s electronegativity 
^{[18]} 
^{[41]} 
LD_{50} 
18 
0.961–0.999 
CORAL 
MLR 
SMILESbased optimal descriptor 
^{[35]} 
^{[41]} 
LD_{50} 
16 
0.88 
 
MLR 
Enthalpy of formation of metal oxide (ΔH_{f}) nanocluster, electronic chemical potential of the cluster, and pEC_{50} of E. coli 
^{[36]} 
^{[41]} 
LD_{50} 
16 
0.79 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[38]} 
^{[41]} 
LD_{50} 
18 
0.918 
 
RF 
10based logarithm of solubility measured in mol/L (LogS), topological polar surface area (TPSA), Mulliken’s electronegativity 
^{[8]} 
^{[41]} 
LD_{50} 
18 
0.83 
 
PLS 
Atom chargebased SiRMS descriptor, charge of the atom weighted by the bond ionicity, charge of metal ion weighted by ionicity of bond, squared ionic potential, ion changebased SiRMS descriptor, number of oxygen atoms in brutto formula per interfacial layer, mass density weighted by ionicity of bond, WignerSeitz radius weighted by ionicity of bond, and ionicity of bond based SiRMS 
^{[42]} 
^{[41]}^{[43]}^{[44]} 
Cell viability (%) 
21 
 
CORAL 
Hierarchical cluster analysis (HCA) and min–max normalization 
QuasiSMILES 
Transformed bronchial epithelial cells (BEAS2B) 

^{[45]} 
^{[45]} 
% of membranedamaged cells 
9 
 
Weka 
RF 
Atomization energy of the metal oxide, period of the nanoparticle metal, nanoparticle primary size, and nanoparticle volume fraction 
^{[6]} 
^{[6]} 
Cell viability (%) 
24 
 
 
Regression tree 
Metal solubility and energy of conduction 
^{[46]} 
^{[6]} 
Cell viability (%) 
24 
 
RandomForest package 
RF 
Mass density, covalent index, cation polarizing power, Wigner–Seitz radius, surface areatovolume ratio, aggregation parameter, and triatomic descriptor of atomic charges 
^{[47]} 
^{[47]} 
LD_{50} 
24 
 
RapidMiner 
SVM 
Conduction band energy and ionic index of metal cation 
^{[48]} 
^{[49]} 
% of membranedamaged cells 
24 
0.68 
CORAL 
Monte Carlo 
SMILESbased optimal descriptor, dose, and exposure time 
^{[42]} 
^{[6]}^{[50]}^{[51]} 
Cell viability (%) 
21 
0.713–0.733 
CORAL 
HCA and minmax normalization 
QuasiSMILES 
Murine myeloid cells (RAW 264.7) 

^{[6]} 
^{[6]} 
Cell viability (%) 
24 
 
 
Regression tree 
Metal solubility and energy of conduction 
^{[46]} 
^{[6]} 
Cell viability (%) 
24 
 
RandomForest package 
RF 
Mass density, molecular weight, aligned electronegativity, covalent index, surface area, surface areatovolume ratio, twoatomic descriptor of van der Waals interactions, tetraatomic descriptor of atomic charges, and size in DMEM 
^{[47]} 
^{[47]} 
LD_{50} 
24 
 
RapidMiner 
SVM 
Conduction band energy and ionic index of metal cation 
^{[52]} 
^{[52]} 
Lactate dehydrogenase (LDH) release 
25 
 
R 
PLS 
Metal cation charge, hydration rate, radius of the metallic cation, and Pauling electronegativity 
Rat L2 lung epithelial cells and rat lung alveolar macrophages 

^{[53]} 
^{[53]} 
Membrane damage (units L^{−1}) 
42 
 
 
Multivariate linear regression and linear discriminant analysis (LDA) 
Size, concentration, size in phosphate buffered saline, size in water, and zeta potential 
^{[54]} 
^{[53]} 
Membrane damage (units L^{−1}) 
42 
 
 
MLR and simple classification 
Size, concentration, size in phosphate buffered saline, and size in water 
^{1} Missing R^{2} value means that an SAR model was built instead of QSAR. ^{2} If software record is missing, then it was not mentioned in the original paper.
Source 
Dataset 
Cell Type 
Endpoint of Cytotoxicity Measurement 
n 
R^{2} 
Software 
Statistical Method 
Descriptors 

^{[55]} 
^{[56]} 
Monocytes, hepatocytes, endothelial, and smooth muscle cells 
Cellular viability 
51 
0.72 
WinSVM, ISIDA 
SVM classification and k Nearest Neighbors (kNN) regression 
Size, zeta potential, R1 and R2 relaxivities 
^{[55]} 
^{[57]} 
PaCa2 human pancreatic cancer cells, U937 macrophage cell lines, primary human macrophages, HUVEC human umbilical vein endothelial cells 
Cellular uptake 
109 
0.65–0.80 
WinSVM, ISIDA 
SVM classification and k Nearest Neighbors (kNN) regression 
Lipophilicity, number of double bonds 
^{[58]} 
^{[56]} 
Smooth muscle cells 
Cell apoptosis 
31 
0.81 
 
MLR and Bayesian regularized artificial neural network 
I_{Fe2O3}, I_{dextran}, and I_{surf.chg} 
^{[59]} 
^{[56]} 
Monocytes, hepatocytes, endothelial, and smooth muscle cells 
Cellular viability 
44 
 
 
Naive Bayesian classifier 
Primary size, spinlattice and spinspin relaxivities, zeta potential 
^{[60]} 
^{[60]} 
Zebrafish embryo 
24 h postfertilization mortality 
82 
 
ABMiner 
Numerical prediction 
Concentration, shell composition, surface functional groups, purity, core structure, and surface charge 
^{[61]} 
^{[61]} 
Mammalian cell lines 
TC_{50} 
1681 
 
STATISTICA v.6 
LDA 
Molar volume, polarizability, and size of the particles 
^{[62]} 
^{[62]} 
Algae, bacteria, cell lines, crustaceans, plants, fish, and others 
CC_{50}, EC_{50}, IC_{50}, TC_{50}, LC_{50} 
36488 
 
STATISTICA 
LDA 
Molar volume, polarizability, size of NPs, electronegativity, hydrophobicity, and polar surface area of surface coating 
^{[63]} 
^{[63]} 
Bacteria, algae, crustaceans, fish, and others 
EC_{50}, IC_{50}, TC_{50}, LC_{50} 
5520 
 
STATISTICA 
LDA 
Molar volume, electronegativity, polarizability, and nanoparticle size 
^{[64]} 
^{[64]} 
Algae, bacteria, fungi, mammal cell lines, crustaceans, plants, fishes, and others 
CC_{50}, EC_{50}, IC_{50}, TC_{50}, LC_{50} 
54371 
 
STATISTICA 
Artificial neural network 
Polar surface area, hydrophobicity, atomic weight, atomic van der Waals radius, electronegativity, and polarizability 
^{[65]} 
^{[66]} 
Danio rerio, Daphnia magna, Pseudokirchneriella subcapitata, and Staphylococcus aureus 
LC_{50}, EC_{50}, MIC (minimum inhibitory concentration) 
400 
 
Weka 
Functional tree, C4.5 decision tree, random tree, and CART 
Molecular polarizability, accessible surface area, and solubility 
^{[67]} 
^{[67]} 
E. coli and Chinese hamster ovary (CHOK1) cells 
EC_{50}, MIC 
17 
0.94 
R 
Nonlinear leastsquaress 
Size and specific surface area (BrunauerEmmettTeller surface) 
Source 
Dataset 
Cell Type 
Endpoint of Cytotoxicity Measurement 
n 
R^{2} 
Software 
Statistical Method 
Descriptors 

^{[69]} 
^{[70]} 
Salmonella typhimurium TA100 
Reverse mutation test TA100 
24 
0.65–0.81 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[71]} 
^{[72]} 
Salmonella typhimurium TA100 
Reverse mutation test TA100 
30 
0.53–0.64 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[73]} 
^{[72]}^{[74]} 
Salmonella typhimurium TA100 
Reverse mutation test TA100 
44 
0.60–0.78 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[75]} 
^{[75]} 
Four types of normal human lung cells (BEAS2B, 16HBE14o, WI38, and HBE) 
Cell viability (%) 
276 
0.60–0.80 
CORAL 
Monte Carlo 
QuasiSMILES 
Source 
Dataset 
Cell Type 
Endpoint of Cytotoxicity Measurement 
n 
R^{2} 
Software 
Statistical Method 
Descriptors 

^{[73]} 
^{[72]}^{[74]} 
Salmonella typhimurium TA100 
Reverse mutation test TA100 
44 
0.60–0.78 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[76]} 
^{[74]} 
S. typhimurium TA100 
Reverse mutation test TA100 
20 
0.76 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[77]} 
^{[74]} 
S. typhimurium TA100 
Reverse mutation test TA100 
20 
0.63–0.76 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[77]} 
^{[74]} 
E. coli WP2 uvrA/pKM101 
Reverse mutation test WP2 uvrA/pKM101 
20 
0.68–0.82 
CORAL 
Monte Carlo 
QuasiSMILES 
Source 
Dataset 
Cell Type 
Endpoint of Cytotoxicity Measurement 
n 
R^{2} 
Software 
Statistical Method 
Descriptors 

^{[78]} 
^{[79]} 
Human embryonic kidney cells HEK293 
Cell viability (%) 
40 
0.80–0.93 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[80]} 
^{[81]} 
Human kidney cells HK2 
Cell viability (%) 
42 
0.83–0.89 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[82]} 
^{[82]} 
16HBE, A549, HaCaT, NRK52E, and THP1 
EC_{25} 
19 
0.83 
CORAL 
Monte Carlo 
QuasiSMILES 
^{[82]} 
^{[82]} 
16HBE, A549, HaCaT, NRK52E, and THP1 
EC_{25} 
19 
0.87 
R 
RF 
Aspect ratio and zeta potential 
^{[83]} 
^{[79]} 
Human embryonic kidney cell line (HEK293) 
Cell viability (%) 
40 
0.80–0.95 
CORAL 
Monte Carlo 
QuasiSMILES 