In silico exploration of graphene nanoflakes: From DFT simulations to machine learning-driven toxicity predictions
Abstract
Nuria Aguilar, Patricia de la Fuente, Natalia Fernandez-Pampín, Sonia Martel, Laura Gomez-Cuadrado, Pedro Angel Marcos, Alfredo Bol, Carlos Rumbo, Santiago Aparicio The present theoretical work provides a ground-breaking and comprehensive study of graphene nanoflakes integrating Density Functional Theory (DFT) simulations, toxicity predictions and a machine learning approach. The properties of graphene nanoflakes as a function of size, shape, and symmetry are systematically analysed using DFT calculations. The interaction of these nanoflakes with human proteins and cell membranes, considered as Molecular Initiating Events for diverse Adverse Outcome Pathways, is explored to infer potential toxicity effects. Leveraging the generated data, machine learning models were developed to predict flake properties and biological interactions. A single score representing the biological interaction or impact of graphene nanoflakes on both proteins and plasma membranes is assigned to each evaluated nanoflake to infer its potential toxicity. Our multiscale approach bring valuable insights into the structure-property-toxicity relationships of graphene nanoflakes, paving the way for their safe and efficient design and application
Full text
S1 Supplementary Information In silico exploration of graphene nanoflakes: From DFT simulations to machine learning-driven toxicity predictions Nuria Aguilara, Patricia de la Fuente,b Natalia Fernández,b Sonia Martelb, Laura GómezCuadrado,b Pedro Angel Marcosb,c, Alfredo Bolb,c, Carlos Rumbob, Santiago Aparicio*a,c a Department of Chemistry, University of Burgos, 09001 Burgos, Spain b International Research Center in Critical Raw Materials for Advanced Industrial Technologies (ICCRAM), University of Burgos, 09001 Burgos, Spain c Department of Physics, University of Burgos, 09001 Burgos, Spain *Corresponding author: [email protected] (S. A.)
S2 Table S1. Total number of carbons (nC) and hydrogen (nH) atoms, shape (HEX: hexagonal, RECT: rectangular and TRI: triangular), type of edge (ARM: armchair and ZIG: zigzag) and dimensions, of each of the 98 graphene nanoflakes studied in this work. L, I indicates de largest and smallest dimensions, respectively. Graphene nanoflake nC nH Shape Edge_1 Edge_2 Size / Å L l HEX_ARM_C42H18 42 18 HEX ARM ARM 13.5 11.8 HEX_ARM_C84H24 84 24 HEX ARM ARM 17.8 16.7 HEX_ARM_C222H42 222 42 HEX ARM ARM 30.6 26.5 HEX_ZIG_C24H12 24 12 HEX ZIG ZIG 9.3 9.2 HEX_ZIG_C54H18 54 18 HEX ZIG ZIG 14.2 13.5 HEX_ZIG_C96H24 96 24 HEX ZIG ZIG 19.1 17.8 HEX_ZIG_C150H30 150 30 HEX ZIG ZIG 24.1 22.1 HEX_ZIG_C216H36 216 36 HEX ZIG ZIG 29.0 26.3 RECT_zz2ac2_C16H10 16 10 RECT ZIG ARM 8.0 7.1 RECT_zz2ac4_C28H14 28 14 RECT ZIG ARM 11.4 8.0 RECT_zz2ac6_C40H18 40 18 RECT ZIG ARM 15.8 8.0 RECT_zz2ac8_C52H22 52 22 RECT ZIG ARM 20.1 8.0 RECT_zz2ac10_C64H26 64 26 RECT ZIG ARM 24.4 8.0 RECT_zz2ac12_C76H30 76 30 RECT ZIG ARM 28.7 8.0 RECT_zz2ac14_C88H34 88 34 RECT ZIG ARM 33.0 8.0 RECT_zz2ac16_C100H38 100 38 RECT ZIG ARM 37.3 8.0 RECT_zz2ac18_C112H42 112 42 RECT ZIG ARM 41.6 8.0 RECT_zz2ac20_C124H46 124 46 RECT ZIG ARM 45.9 8.0 RECT_zz2ac22_C136H50 136 50 RECT ZIG ARM 50.2 8.0 RECT_zz2ac24_C148H54 148 54 RECT ZIG ARM 54.5 8.0 RECT_zz2ac26_C160H58 160 58 RECT ZIG ARM 58.8 8.0 RECT_zz2ac28_C172H62 172 62 RECT ZIG ARM 63.2 8.0 RECT_zz2ac30_C184H66 184 66 RECT ZIG ARM 67.5 8.0 RECT_zz2ac32_C196H70 196 70 RECT ZIG ARM 71.8 8.0 RECT_zz4ac2_C28H14 28 14 RECT ZIG ARM 12.9 7.2 RECT_zz4ac4_C48H18 48 18 RECT ZIG ARM 12.9 11.5 RECT_zz4ac6_C68H22 68 22 RECT ZIG ARM 15.8 12.9 RECT_zz4ac8_C88H26 88 26 RECT ZIG ARM 20.1 12.9 RECT_zz4ac10_C108H30 108 30 RECT ZIG ARM 24.4 12.9 RECT_zz4ac12_C128H34 128 34 RECT ZIG ARM 28.7 12.9 RECT_zz4ac14_C148H38 148 38 RECT ZIG ARM 32.9 13.0 RECT_zz4ac16_C168H42 168 42 RECT ZIG ARM 37.2 13.0 RECT_zz4ac18_C188H46 188 46 RECT ZIG ARM 41.5 13.0 RECT_zz4ac20_C208H50 208 50 RECT ZIG ARM 45.7 13.0 RECT_zz4ac26_C268H62 268 62 RECT ZIG ARM 58.6 13.0 RECT_zz4ac28_C288H66 288 66 RECT ZIG ARM 62.9 13.0 RECT_zz6ac2_C40H18 40 18 RECT ZIG ARM 17.8 7.2 RECT_zz6ac4_C68H22 68 22 RECT ZIG ARM 17.8 11.5 RECT_zz6ac6_C96H26 96 26 RECT ZIG ARM 17.9 15.8 RECT_zz6ac10_C152H34 152 34 RECT ZIG ARM 24.3 17.9 RECT_zz6ac12_C180H38 180 38 RECT ZIG ARM 28.6 17.9 RECT_zz6ac14_C208H42 208 42 RECT ZIG ARM 32.9 17.9 RECT_zz6ac16_C236H46 236 46 RECT ZIG ARM 37.2 17.9 RECT_zz6ac18_C264H50 264 50 RECT ZIG ARM 41.5 17.9 RECT_zz8ac2_C52H22 52 22 RECT ZIG ARM 22.7 7.2 RECT_zz8ac4_C88H26 88 26 RECT ZIG ARM 22.8 11.5 RECT_zz8ac6_C124H30 124 30 RECT ZIG ARM 22.8 15.8 RECT_zz8ac8_C160H34 160 34 RECT ZIG ARM 22.8 20.1 RECT_zz8ac10_C196H38 196 38 RECT ZIG ARM 24.3 22.8 RECT_zz8ac12_C232H42 232 42 RECT ZIG ARM 28.6 22.8 RECT_zz8ac14_C268H46 268 46 RECT ZIG ARM 32.8 22.8 RECT_zz10ac2_C64H26 64 26 RECT ZIG ARM 27.6 7.2 RECT_zz10ac4_C108H30 108 30 RECT ZIG ARM 27.7 11.5 RECT_zz10ac6_C152H34 152 34 RECT ZIG ARM 27.7 15.8
S3 RECT_zz10ac8_C196H38 196 38 RECT ZIG ARM 27.7 20.1 RECT_zz10ac10_C240H42 240 42 RECT ZIG ARM 27.7 24.3 RECT_zz10ac12_C284H46 284 46 RECT ZIG ARM 28.6 27.7 RECT_zz12ac2_C76H30 76 30 RECT ZIG ARM 32.5 7.2 RECT_zz12ac4_C128H34 128 34 RECT ZIG ARM 32.6 11.5 RECT_zz12ac6_C180H38 180 38 RECT ZIG ARM 32.6 15.8 RECT_zz12ac8_C232H42 232 42 RECT ZIG ARM 32.6 20.1 RECT_zz12ac10_C284H46 284 46 RECT ZIG ARM 32.6 24.3 RECT_zz14ac2_C88H34 88 34 RECT ZIG ARM 37.4 7.2 RECT_zz14ac4_C148H38 148 38 RECT ZIG ARM 37.5 11.5 RECT_zz14ac6_C208H42 208 42 RECT ZIG ARM 37.5 15.8 RECT_zz14ac8_C268H46 268 46 RECT ZIG ARM 37.5 20.1 RECT_zz16ac2_C100H38 100 38 RECT ZIG ARM 42.3 7.2 RECT_zz16ac4_C168H42 168 42 RECT ZIG ARM 42.4 11.5 RECT_zz16ac6_C236H46 236 46 RECT ZIG ARM 42.4 15.8 RECT_zz18ac2_C112H42 112 42 RECT ZIG ARM 47.2 7.2 RECT_zz18ac4_C188H46 188 46 RECT ZIG ARM 47.3 11.5 RECT_zz18ac6_C264H50 264 50 RECT ZIG ARM 47.4 15.8 RECT_zz20ac2_C124H46 124 46 RECT ZIG ARM 52.1 7.2 RECT_zz20ac4_C208H50 208 50 RECT ZIG ARM 52.2 11.5 RECT_zz20ac6_C292H54 292 54 RECT ZIG ARM 52.3 15.8 RECT_zz22ac2_C136H50 136 50 RECT ZIG ARM 57.0 7.2 RECT_zz22ac4_C228H54 228 54 RECT ZIG ARM 57.2 11.5 RECT_zz24ac2_C148H54 148 54 RECT ZIG ARM 61.9 7.2 RECT_zz24ac4_C248H58 248 58 RECT ZIG ARM 62.0 11.5 RECT_zz26ac2_C160H58 160 58 RECT ZIG ARM 66.8 7.2 RECT_zz26ac4_C268H62 268 62 RECT ZIG ARM 67.0 11.5 RECT_zz28ac2_C172H62 172 62 RECT ZIG ARM 71.7 7.2 RECT_zz28ac4_C288H66 288 66 RECT ZIG ARM 71.9 11.5 RECT_zz30ac2_C184H66 184 66 RECT ZIG ARM 76.6 7.2 RECT_zz32ac2_C196H70 196 70 RECT ZIG ARM 81.6 7.2 TRI_ARM_C36H18 36 18 TRI ARM ARM 13.6 11.8 TRI_ARM_C60H24 60 24 TRI ARM ARM 17.9 15.5 TRI_ARM_C90H30 90 30 TRI ARM ARM 22.1 19.2 TRI_ARM_C126H36 126 36 TRI ARM ARM 26.4 22.9 TRI_ARM_C168H42 168 42 TRI ARM ARM 30.7 26.6 TRI_ARM_C216H48 216 48 TRI ARM ARM 35.0 30.3 TRI_ZIG_C22H12 22 12 TRI ZIG ZIG 9.3 9.2 TRI_ZIG_C46H18 46 18 TRI ZIG ZIG 14.2 13.5 TRI_ZIG_C78H24 78 24 TRI ZIG ZIG 19.1 17.8 TRI_ZIG_C118H30 118 30 TRI ZIG ZIG 24.0 22.0 TRI_ZIG_C166H36 166 36 TRI ZIG ZIG 28.9 26.3 TRI_ZIG_C222H42 222 42 TRI ZIG ZIG 33.8 30.6 TRI_ZIG_C286H48 286 48 TRI ZIG ZIG 38.8 34.8
S4 Table S2. BIOVIA Materials Studio descriptors chosen for the 98 GNFs. Atom Volumes and Surfaces VAMP Electrostatics Connolly surface area Total energy Connolly surface occupied volume Electronic energy Solvent surface area Heat of formation Solvent surface occupied volume HOMO eigenvalue Atomistic Descriptors LUMO eigenvalue Total molecular mass Molecular surface area Atom count Molecular point group Element count Total dipole DMol3 Molecular Dipole x Total energy Dipole y Binding energy Dipole z HOMO energy Quadrupole xx LUMO energy Quadrupole xy LUMO-HOMO energy Quadrupole yy Total dipole Quadrupole xz Dipole x Quadrupole yz Dipole y Quadrupole zz Dipole z Octupole xxx Dielectric energy Octupole xxy Solvation energy Octupole xxz Surface area Octupole xyy Cavity volume Octupole xyz Forcite Energetics Octupole xzz Total energy Octupole yyy Non bond energy Octupole yyz van der Waals energy Octupole yzz Spatial Descriptors Octupole zzz Molecular area Total ZDO dipole Molecular volume ZDO Dipole x Molecular density ZDO Dipole y Principal moments of inertia ZDO Dipole z Principal moment of inertia X Mean polarizability Principal moment of inertia Y Principal moment of inertia Z Radius of gyration Ellipsoidal volume Shadow area: XY plane Shadow area: YZ plane Shadow area: ZX plane Shadow area fraction: XY plane Shadow area fraction: YZ plane Shadow area fraction: ZX plane Shadow length: LX Shadow length: LY Shadow length: LZ Shadow ratio
S5 Table S3. Human proteins (100) considered in this work. Family PID Family PID ANTITUMOR 2rmn METAL BINDING 2kax APOPTOSIS 1o9k MONOOXYGENASE 5pah 2o2m OXIDOREDUCTASE 1r9o 2ac0 4gqs 1e31 4xrz CARRIER 1ao6 2hi4 CELL ADHESION 4oeo 3gph 1p53 3gzo CHROMOSOMAL 1ubq 1dgf COMPLEMENT 1gkg 1d7w CYTOKINE 1m8a 3b96 1i1b 1u3u 5m2m 6dqg 1il8 5l01 1msg 4fr8 ELECTRON TRANSPORT 5z62 2z5y HORMONE 1fzv 1ba9 6gnq 5te8 HYDROLASE 1gqs OXYGEN STORAGE/TRANSPORT 2h35 1p0p SIGNALING 1ro5 1owe 4fl5 4gwc 2mgs 4c6i 4g5q 3lii 6pxw 2c2m STUCTURAL 6v5v 2pm8 TRANSCRIPTION 1svc 4zcg 4dm4 2glq TRANSFERASE 3w8q 1m6d 2e9n 1yk8 2nzt 1r6h 4fsm 3kme 3i5z 4gqq 2wzb 1l6j 4g1n IMMUNE SYSTEM 4glr 5ikp 4tqe 1oth 5d14 4ijq 3oxs 3ie3 4mhe 2avd ISOMERASE 4fm9 4ic8 1ek5 4x90 4zvj 4ez3 LIPID BINDING 1g5w 2xir LYASE 2b3x 2zb2 5d6b TRANSPORT 2jk4 4fpt 6pzt LIGASE (CARBOXYLATE) 2hgs 5eqg MEMBRANE 6agf 6c0v 7e1z 4act 6irg 4act 2znt
S6 Table S4. 33 GNFs (Column I) used for pre-processing, model optimization, and training of Random Forest predictive models; 7 GNFs (Column II) used for testing the performance of the models. I. Graphene flake (training set) II. Graphene flake (testing set) HEX_ARM_C42H18 HEX_ZIG_C54H18 HEX_ARM_C84H24 HEX_ZIG_C96H24 HEX_ZIG_C24H12 RECT_zz2ac4_C28H14 HEX_ZIG_C150H30 RECT_zz6ac12_C180H38 RECT_zz2ac2_C16H10 RECT_zz8ac4_C88H26 RECT-zz4ac2-C28H14 TRI_ARM_C60H24 RECT-zz4ac4-C48H18 TRI_ARM_C90H30 RECT-zz4ac10-C108H30 RECT-zz4ac18-C188H46 RECT-zz6ac2-C40H18 RECT_zz6ac6_C96H26 RECT_zz6ac16_C236H46 RECT-zz8ac2-C52H22 RECT-zz8ac8-C160H34 RECT-zz10ac2-C64H26 RECT-zz10ac6-C152H34 RECT-zz12ac2-C76H30 RECT-zz12ac4-C128H34 RECT-zz14ac2-C88H34 RECT-zz14ac6-C208H42 RECT-zz16ac2-C100H38 RECT-zz18ac2-C112H42 RECT-zz20ac2-C124H46 RECT-zz22ac2-C136H50 RECT-zz24ac2-C148H54 RECT-zz26ac2-C160H58 RECT-zz28ac2-C172H62 RECT-zz30ac2-C184H66 RECT-zz32ac2-C196H70 TRI_ARM_C36H18 TRI_ARM_C216H48 TRI_ZIG_C22H12 TRI_ZIG_C46H18
S7 Table S5. Intensities, in km/mol, and its infrared frequencies, in cm-1, predicted for the most relevant vibrational modes, calculated with wB97x/def2-TZVP for three GNFs – HEX_ZIG_C54H18, RECT_zz2ac4_C28H14 and TRI_ARM_C60H24 –, sampling the types three shapes (HEX, RECT and TRI), the two types of edges (ARM, ZIG) and different sizes (42, 72 and 82 atoms). The scaling factor applied is 1.0. The final Gibbs free energy, in Eh, calculated as G = H - T*S, for these three GFNs is also reported. GFN Mode Frequency / cm-1 Intensity / km.mol-1 Gibbs / Eh HEX_ZIG_C54H18 56 80 102 129 130 145 146 195 196 623.05 834.20 973.42 1199.60 1200.12 1328.47 1329.62 1696.40 1696.53 39.79 92.57 172.55 16.41 17.15 24.90 25.76 15.83 15.03 -2068.54 RECT_zz2ac4_C28H14 38 45 48 54 56 97 106 678.93 792.42 831.30 901.41 913.08 1486.21 1655.87 16.48 22.07 27.73 105.68 45.78 32.46 18.60 -1075.30 TRI_ARM_C60H24 48 93 98 104 168 169 183 193 194 198 199 201 202 478.98 814.93 848.75 871.40 1314.55 1316.02 1395.81 1481.33 1482.29 1503.57 1503.88 1533.03 1534.21 14.66 152.79 88.77 112.73 22.07 21.78 15.04 17.57 16.98 21.23 21.77 34.14 33.95 -2300.70
S8 Table S6. Docking mean (100 considered proteins) binding affinity and standard deviation of the protein – graphene flakes interaction per carbon atom in flake. Graphene flake nC Binding affinity / kcal.mol-1 Standard deviation / kcal.mol-1 HEX_ARM_C42 42 -0.3 0.0 HEX_ARM_C84 84 -0.2 0.0 HEX_ARM_C222 222 -0.1 0.0 HEX_ZIG_C24 24 -0.4 0.1 HEX_ZIG_C54 54 -0.2 0.0 HEX_ZIG_C96 96 -0.2 0.0 HEX_ZIG_C150 150 -0.1 0.0 RECT_zz2ac2_C16 16 -0.5 0.1 RECT_zz2ac4_C28 28 -0.4 0.0 RECT_zz4ac2_C28 28 -0.4 0.1 RECT_zz4ac4_C48 48 -0.3 0.0 RECT_zz4ac10_C108 108 -0.2 0.0 RECT_zz4ac18_C188 188 -0.1 0.0 RECT_zz6ac2_C40 40 -0.3 0.0 RECT_zz6ac6_C96 96 -0.2 0.0 RECT_zz6ac12_C180 180 -0.1 0.0 RECT_zz6ac16_C236 236 -0.1 0.0 RECT_zz8ac2_C52 52 -0.3 0.0 RECT_zz8ac4_C88 88 -0.2 0.0 RECT_zz8ac8_C160 160 -0.1 0.0 RECT_zz10ac2_C64 64 -0.2 0.0 RECT_zz10ac6_c152 152 -0.1 0.0 RECT_zz12ac2_C76 76 -0.2 0.0 RECT_zz12ac4_C128 128 -0.2 0.0 RECT_zz14ac2_C88 88 -0.2 0.0 RECT_zz14ac6_C208 208 -0.1 0.0 RECT_zz16ac2_C100 100 -0.2 0.0 RECT_zz18ac2_C112 112 -0.1 0.0 RECT_zz20ac2_C124 124 -0.1 0.0 RECT_zz22ac2_C136 136 -0.1 0.0 RECT_zz24ac2_C148 148 -0.1 0.0 RECT_zz26ac2_C160 160 -0.1 0.0 RECT_zz28ac2_C172 172 -0.1 0.0 RECT_zz30ac2_C184 184 -0.1 0.0 RECT_zz32ac2_C196 196 -0.1 0.0 TRI_ARM_C36 36 -0.3 0.0 TRI_ARM_C60 60 -0.2 0.0 TRI_ARM_C90 90 -0.2 0.0 TRI_ARM_C216 216 -0.1 0.0 TRI_ZIG_C22 22 -0.4 0.1 TRI_ZIG_C46 46 -0.3 0.0 TRI_ZIG_C118 118 -0.2 0.0
S9 Table S7. Free energy of penetration, per carbon atom in flake, through the four types of membranes considered in this work – DMPC, DOPC, POPC and SOPC – calculated at the center of the membrane for graphene flakes. Structure nC DMPC DOPC POPC SOPC ΔG / kcal mol-1 ΔG / kcal mol-1 ΔG / kcal mol-1 ΔG / kcal HEX_ARM_C42H18 42 -0.26 -0.26 -0.26 -0.27 HEX_ARM_C84H24 84 -0.25 -0.25 -0.24 -0.24 HEX_ZIG_C24H12 24 -0.30 -0.29 -0.30 -0.30 HEX_ZIG_C54H18 54 -0.26 -0.26 -0.26 -0.26 HEX_ZIG_C96H24 96 -0.25 -0.25 -0.24 -0.24 HEX_ZIG_C150H30 150 -0.23 -0.24 -0.22 -0.22 RECT_zz2ac2_C16H10 16 -0.32 -0.32 -0.32 -0.32 RECT_zz2ac4_C28H14 28 -0.29 -0.29 -0.29 -0.29 RECT_zz4ac2_C28H14 28 -0.30 -0.30 -0.30 -0.30 RECT_zz4ac4_C48H18 48 -0.27 -0.27 -0.27 -0.27 RECT_zz4ac10_C108H30 108 -0.23 -0.24 -0.22 -0.22 RECT_zz4ac18_C188H46 188 -0.18 -0.19 -0.18 -0.17 RECT_zz6ac2_C40H18 40 -0.29 -0.29 -0.29 -0.29 RECT_zz6ac6_C96H26 96 -0.24 -0.25 -0.24 -0.24 RECT_zz6ac12_C180H38 180 -0.19 -0.22 -0.19 -0.19 RECT_zz6ac16_C236H46 236 -0.18 -0.20 -0.18 -0.17 RECT_zz8ac2_C52H22 52 -0.28 -0.29 -0.28 -0.27 RECT_zz8ac4_C88H26 88 -0.25 -0.26 -0.24 -0.24 RECT_zz8ac8_C160H34 160 -0.17 -0.18 -0.17 -0.16 RECT_zz10ac2_C64H26 64 -0.27 -0.29 -0.27 -0.26 RECT_zz10ac6_C152H34 152 -0.20 -0.22 -0.19 -0.19 RECT_zz12ac2_C76H30 76 -0.26 -0.28 -0.26 -0.25 RECT_zz12ac4_C128H34 128 -0.21 -0.23 -0.21 -0.21 RECT_zz14ac2_C88H34 88 -0.25 -0.27 -0.25 -0.25 RECT_zz14ac6_C208H42 208 -0.07 -0.10 -0.06 -0.06 RECT_zz16ac2_C100H38 100 -0.24 -0.26 -0.24 -0.24 RECT_zz18ac2_C112H42 112 -0.23 -0.26 -0.23 -0.23 RECT_zz20ac2_C124H46 124 -0.22 -0.25 -0.22 -0.22 RECT_zz22ac2_C136H50 136 -0.22 -0.24 -0.22 -0.21 RECT_zz24ac2_C148H54 148 -0.21 -0.23 -0.21 -0.21 RECT_zz26ac2_C160H58 160 -0.21 -0.23 -0.21 -0.21 RECT_zz28ac2_C172H62 172 -0.19 -0.21 -0.19 -0.19 RECT_zz30ac2_C184H66 184 -0.19 -0.21 -0.19 -0.19 RECT_zz32ac2_C196H70 196 -0.19 -0.21 -0.19 -0.19 TRI_ARM_C36H18 36 -0.29 -0.29 -0.29 -0.29 TRI_ARM_C60H24 60 -0.27 -0.27 -0.27 -0.27 TRI_ARM_C90H30 90 -0.25 -0.26 -0.25 -0.25 TRI_ARM_C216H48 216 -0.21 -0.22 -0.21 -0.20 TRI_ZIG_C22H12 22 -0.14 -0.14 -0.13 -0.13 TRI_ZIG_C46H18 46 -0.06 -0.06 -0.05 -0.05
S16 Figure S2. Docking results for (1) 1i1b and (2) 2hi4 proteins with three graphene flakes as ligands: HEX_ZIG_C24 (magenta), RECT_zz2ac2_C16 (orange) and TRI_ZIG_C22 (cyan). Panel (a) representing protein-ligand contacts for 1i1b protein with HEX_ZIG_C24 graphene flake, (b) with RECT_zz2ac2_C16 graphene flake and (c) with TRI_ZIG_C22 graphene flake. Panel (e) representing protein-ligand contacts for 2hi4 protein with HEX_ZIG_C24 graphene flake, (f) with RECT_zz2ac2_C16 graphene flake and (g) with TRI_ZIG_C22 graphene flake.
S17 Figure S3. Representation of the model plasma cell membranes built to run COSMOPerm calculations and the four types of lipids – dmpc, dopc, popc and sopc – considered in this work. Color code: red representing the water molecules placed outside the lipid membrane; blue representing the polar heads and grey representing the non-polar chains of the lipids. Figure S4. Free energy, ΔG, profile through the four membrane types considered in this work – DMPC, DOPC, POPC and SOPC –, measured at the center of the membrane, energy expressed per number of carbon atoms.
S18 Figure S5. Prediction of (1) free energy ΔG, (2) diffusion, (3) entropy and (4) permeability through (a) DMPC, (b) DOPC, (c) POPC and (d) SOPC membranes for a total of 11 graphene flakes, sampling different shapes, edges and sizes.
S19 Figure S6. Prediction of (a) free energy ΔG, (b) diffusion and (c) permeability measured at the center of the membrane (dmpc, dopc, pocp and sopc) for a total of 40 graphene flakes, sampling different shapes, edges and sizes, sorted by shape (HEX, RECT and TRI) and by number of carbon atoms in each shape type. Figure S7. Prediction of (a) free energy ΔG, (b) diffusion and (c) permeability measured at the center of the membrane (DMPC, DOPC, POCP and SOPC) for a total of 16 RECT graphene flakes, all of them having two graphene rings along the armchair edge (ac2) while varying the number of rings along the zigzag edge – from 2 to 32 –, sorted by (largest) size, in Å.
S20 Figure S8. Scree Plot of Principal Components (FAMD): Percentage of Explained Variance. Figure S9. Bar plot of loadings in absolute values, ordered from most to least influential. Each bar represents a variable, and its length corresponds to the magnitude of the loading in the respective Principal Component (PC). The dashed line indicates the threshold value (0.65 for PC1, 0.5 for PC2 and PC3, 0.45 for PC4, and 0.35 for PC5). Grey bars represent variables that exceed the defined threshold.
S21 Figure S10. Correlation matrix. Each element in the matrix represents the strength and direction of the correlation between a pair of variables, based on pairwise Spearman correlations, which range from -1 to 1. The matrix was computed using the 44 selected variables derived from the Factor Analysis of Mixed Data (FAMD). The correlation values are depicted by circles, where the size of each circle corresponds to the magnitude of the correlation (larger circles indicate stronger correlations). A color gradient is used to represent the correlation values, with blue indicating negative correlations, white indicating correlations near zero, and red indicating positive correlations. Only the upper triangle of the matrix is shown, as the lower triangle is redundant due to the symmetry of the correlation values. The diagonal of the matrix is not shown.