\documentclass[11pt]{article} \usepackage{geometry} % See geometry.pdf to learn the layout options. There are lots. \geometry{a4paper} % ... or a4paper or a5paper or ... %\geometry{landscape} % Activate for for rotated page geometry %\usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent \usepackage{graphicx} \usepackage{amssymb} \usepackage{epstopdf} \usepackage{url} \usepackage{graphicx} \usepackage{color} \usepackage{mathtools} \usepackage{booktabs} \usepackage{multirow} \usepackage{amssymb} \usepackage{graphicx} \usepackage{booktabs} \usepackage{multirow} \usepackage{bm} \usepackage{array} \DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png} \title{A Hierarchical Representations for Predicting Protein-Protein Interaction Sites \\ \ \\Supplementary Material } \author{Michela Quadrini \and Sebastian Daberdaku \and Carlo Ferrari} \date{} % Activate to display a given date %or no date \begin{document} \maketitle \section{Data} In this section of the Supplementary Material, we report the tables of the datasets used in this study. Each molecule is given by its PDB code and its chain ID (the PDB code in parentheses identifies the corresponding bound complex in the DB5 database). Table \ref{dataset} shows the molecules of the Protein-Protein Docking Benchmark 5.0 divided in accord to their biological function, while Table \ref{2-lay} reports the ligands of the Protein-Protein Docking Benchmark 5.0 characterized by 2-layer Sandwich architecture. Such ligands are randomly split into training, validation, and test. \begin{table*}[h!] \caption{Protein classes from the Protein--Protein Docking Benchmark 5.0 organized according to their biological functions. \\} \label{dataset} \centering \resizebox{0.85 \textwidth}{!}{\scriptsize \begin{tabular}{|c|m{0.4\linewidth}|m{0.3\linewidth}|m{0.4\linewidth}|}\hline \textbf{Dataset} & \textbf{Training set} & \textbf{Validation set} &\textbf{Test set} \\ \hline \textbf{A$_r$} & 2I24.N (2I25), 3EO0.AB (3EO1), 3G6A.LH (3G6D), 3HMW.LH (3HMX), 3L7E.LH (3L5W), 3MXV.LH (3MXW), 3V6F.AB (3V6Z), & 1AY1.HL (1BGX), 1BVL.BA (1BVK), 2FAT.HL (2FD6), 4GXV.HL (4GXU) & 1FGN.LH (1AHW), 1DQQ.CD (1DQJ), 1QBL.HL (1WEJ), 1GIG.LH (2VIS), 2VXU.HL (2VXT), 3RVT.CD (3RVW), 4G5Z.HL (4G6J) \\\hline \textbf{A$_l$} & 1IK0.A (3G6D), 1F45.AB (3HMX), 3M1N.A (3MXW), 3KXS.F (3V6Z), 1DOL.A (4DN4), 4I1B.A (4G6J), 1RUZ.HIJKLM (4GXU) & 1TAQ.A (1BGX), 3LZT (1BVK), 1A43 (1E6J), 1YWH.A (2FD6), 3F5V.A (3RVW) & 1TFH.A (1AHW), 1HRC (1WEJ), 2VIU.ACE (2VIS), 1J0S.A (2VXT), 1QM1.A (2W9E), 1TGJ.AB (3EO1), 3F74.A (3EOA), 2FK0.ABCDEF (4FQI) \\\hline \textbf{AB$_r$} & 1K4C.AB (1K4C), 1KXQ.H (1KXQ), 2JEL.HL (2JEL), 1QFW.HL (9QFW) & 1BJ1.HL (1BJ1), 1I9R.HL (1I9R), 1FSK.BC (1FSK) & 1IQD.AB (1IQD), 1NCA.HL (1NCA), 1NSN.HL (1NSN), 1QFW.IM (1QFW), 2HMI.CD (2HMI) \\\hline \textbf{AB$_l$} & 7NN9 (1NCA), 1HRP.AB (1QFW), 1S6P.AB (2HMI), 1POH (2JEL) & 2VPF.GH (1BJ1), 1BV1 (1FSK), 1D7P.M (1IQD) & 1ALY.ABC (1I9R), 1JVM.ABCD (1K4C), 1PPI (1KXQ), 1KDC (1NSN) \\\hline \textbf{EI$_r$} & 3GMU.B (1JTG), 1QLP.A (1OPH), 1SCD.A (1OYV), 2DCY.A (2B42), 966C.A (2J0T), 1ZM8.A (2O3B), 1SUP (2SIC), 1A3S.A (3A4S), 2QA9.E (3SGQ), 3VLA.A (3VLB), 1UNK.D (7CEI) & 1QQU.A (1AVX), 1PIG (1BVN), 2CGA.B (1CGI), 1JAE.A (1CLV), 1EAX.A (1EAW), 1TRM.A (1EZU), 4PEP (1F34), 1K2I.1(1GL1), 2PKA.XY (1HIA), 1AKL.A (1JIW), 1X9Y.A (1PXV), 4HWX.AB (4HX3) & 2CGA.B (1ACB), 1RGH.B (1AY7), 1HCL (1BUH), 2TGT (1D6R), 9RSA.B (1DFJ), 9EST.A (1FLE), 1CK7.A (1GXD), 3QI0.A (1JTD), 1J06.B (1MAH), 1UDH. (1UDI), 2GHU.A (1YVB), 1KWM.A (1ZLI), 8CPA.A (4CPA), 1ERK.A (4IZ7) \\\hline \textbf{EI$_l$} & 1ZG4.A (1JTG), 1UTQ.A (1OPH), 1PJU.A (1OYV), 1LU0.A (1PPE), 1B1U.A (1TMQ), 1CEW.I (1YVB), 2JTO.A (1ZLI), 1ZFI.A (2ABZ), 1T6E.X (2B42), 1D2B.A (2J0T), 2NNR.A (2OUL), 2CI2.I (2SNI), 2UUX.A (2UUY), 3A4R.A (3A4S), 3VL8.A (3VLB), & 1EGL (1ACB), 1BA7.B (1AVX), 1HOE (1BVN), 1HPT (1CGI), 1QFD.A (1CLV), 2BNH (1DFJ), 1F32.A (1F34), 1PMC.A (1GL1), 1BX8 (1HIA), 1BTL.A (1JTD), 1NYC.A (1PXV), 1C7K.A (4HX3) & 1A19.B (1AY7), 1DKS.A (1BUH), 1K9B.A (1D6R), 2BNH (1DFJ), 9PTI (1EAW), 1ECZ.AB (1EZU), 2REL.A (1FLE), 1BR9.A (1GXD), 2RN4.A (1JIW), 1FSC (1MAH), 2GKR.I (1R0R), 2UGI.B (1UDI), 1J57.A (2O3B), 3SSI (2SIC), 1H20.A (4CPA), 2LS7.A (4IZ7), 1M08.B (7CEI) \\\hline \textbf{ER$_r$} & 1B3K.A (1OC0), 1R6C.X (1R6Q), 2FXS.A (1US7), 2AYN.A (2AYO), 3OWG.A (2GAF), 1L7E.AB (2OOR), 1YZU.A (2OT3), 2YVF.A (2YVJ), 2D1I.A (2Z0E), 2EDI.A (3FN1), & 1IXM.AB (1F51), 1BU6.O (1GLA), 1AUQ (1M10), 1JXQ.A (1NW9), 1BPB.A (3K75), 1UPL.A (4FZA) & 1AUQ (1IJK), 1JMJ.A (1JMO), 3EED.AB (1JWH), 1JZO.AB (1JZD), 1V8Z.AB (1WDW), 1MH1 (2NZ8), 4JJ7.AB (3H11), 3LVM.AB (3LVK), 3PC6.A (3PC8), 1XVB.ABCDEF (4GAM) \\\hline \end{tabular}} \end{table*} \begin{table*}[h!] \caption{Protein classes from the Protein--Protein Docking Benchmark 5.0 organized according to their biological functions (continued).\\} %\label{dataset} \centering \resizebox{0.85 \textwidth}{!}{\scriptsize \begin{tabular}{|c|m{0.4\linewidth}|m{0.3\linewidth}|m{0.4\linewidth}|}\hline \textbf{Dataset} & \textbf{Training set} & \textbf{Validation set} &\textbf{Test set} \\ \hline \textbf{ER$_l$} & 2W0G.A (1US7), 1GEQ.A (1WDW), 1VPT.A (2GAF), 1NTY.A (2NZ8), 1E3T.A (2OOR), 1TXU.A (2OT3), 2E4P.A (2YVJ), 1V49.A (2Z0E), 1DCJ.A (3LVK), 2LQ7.A (3FN1) & 1SRR.C (1F51), 1FVU.AB (1IJK), 2OPY.A (1NW9), 3PC7.A (3PC8), 3GGF.A (4FZA), 1CKV.A (4GAM) & 1F3Z.A (1GLA), 2CN0.HL (1JMO), 3C13.A (1JWH), 1JPE.A (1JZD), 1M0Z.B (1M10), 2JQ8.A (1OC0), 2W9R.A (1R6Q), 2FCN.A (2AYO), 3H13.A (3H11), 3K77.A (3K75) \\\hline \textbf{ES$_r$} & 1GJR.A (1EWY), 1B39.A (1FQ1), 1N0V.C (1ZM4), 3UIU.A (2A1A), 2BBK.JM (2MTA), 1SUR.A (2O8V), 2OOA.A (2OOB), & 1E1N.A (1E6E), 1GIQ.A (4H03), 4LW2.AB (4LW4) & 1CL0.A (1F6M), 1QUP.A (1JK9), 1JB1.ABC (1KKL), 1L6P (1Z5Y), 1U90.A (2A9K), 1J54.A (2IDO), 1CCP (2PCC) \\\hline \textbf{ES$_l$} & 1CJE.D (1E6E), 1CZP.A (1EWY), 1FPZ.F (1FQ1), 2JCW.A (1JK9), 2HPR (1KKL), 1Q46.A (2A1A), 2C8B.X (2A9K), 1SE7.A (2IDO), 2RAC.A (2MTA), 1NI7.A (4LW4), 1GIQ.A (4H03) & 1E1N.A (1E6E), 4LW2.AB (4LW4) & 2TIR.A (1F6M), 2B1K.A (1Z5Y), 1XK9.A (1ZM4), 1YJ1.A (2OOB), 1YCC (2PCC), 1IJJ.A (4H03) \\\hline \textbf{OG$_r$} & 1MH1 (1I4D), 5P21.A (1LFD), 6Q21.D (1WQ1), 2ZKM.X (2FJU), 1GFI.A (2GTP), 1MH1 (2H7V), 3CPI.G (3CPH) & 1QG4.A (1A2K), 1AB8.AB (1AZS), 1CTQ.A (1BKD), 1MH1 (1E96), & 1TND.C (1FQJ), 1A4R.A (1GRN), 1MH1 (1HE1), 821P (1HE8), 1RRP.AB (1K5D), 1HUR.A (1R8S), 2BME.A (1Z0K), 1FKM.A (2G77) \\\hline \textbf{OG$_l$} & 1HE9.A (1HE1), 1OXZ.A (1J2J), 1LXD.A (1LFD), 1R8M.E (1R8S), 1WER (1WQ1), 1YZM.A (1Z0K), 1Z06.A (2G77) & 1OUN.AB (1A2K), 1AZT.A (1AZS), 1HH8.A (1E96), 1RGP (1GRN), & 1FQI.A (1FQJ), 1TBG.DH (1GP2), 1A12.A (1I2M), 1F59.A (1IBR), 1YRG.B (1K5D), 2BV1.A (2GTP), 1G16.A (3CPH) \\\hline \textbf{OR$_r$} &1QFK.HL (1FAK), 1B98.AM (1HCF), 1NOB.F (1KAC), 1FZV.AB (1RV6), 1BEC (1SBB), 1ACC.A (1T6B), 1JX6.A (1ZHH), 1YWH.A (2I9B), 3L88.ABC (3L89) & 1BUY.A (1EER), 1MKF.AB (1ML0), 1U5Y.ABD (1XU1), 1H0C.AB (3R9A), 1N6U.A (3S9D) & 3AVE.AB (1E4K), 1C3D (1GHQ), 1G0Y.R (1IRA), 1MZN.AB (1K74), 1TGK (1KTZ), 1BQU.A (1PVH), 1R42.A (2AJF), 2BBA.A (2HLE), 1S62.A (2X9A) \\\hline \textbf{OR$_l$} & 1LY2.A (1GHQ), 1WWB.X (1HCF), 1SHU.X (1T6B), 2GHV.E (2AJF), 1IKO.P (2HLE), 2I9A.A (2I9B), 2X9B.A (2X9A), 1CKL.A (3L89), 2C0M.A (3R9A), & 1EMR.A (1PVH), 1QSZ.A (1RV6), 2HJE.A (1ZHH), 1ITF.A (3S9D), 1M1U.A (4M76) & 1FNL.A (1E4K), 1ERN.AB (1EER), 1TFH.B (1FAK), 1ILR.1 (1IRA), 1ZGY.AB (1K74), 1F5W.B (1KAC), 1M9Z.A (1KTZ), 1DOL (1ML0), 1SE4 (1SBB), 1XUT.A (1XU1) \\\hline \textbf{OX$_r$}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hline \textbf{OX$_l$} & 4J93.A (1AK4), 3DNI (1ATN), 1CX8.AB (1DE4), 1G83.A (1EFN), 1FC1.AB (1FC2), 2IGG.A (1FCC), 1FWP.A (1FFW), 1GCP.B (1GCQ), 1D0N.B (1H1V), 1STE (1KLU), 1MQ9.A (1MQ8), 2VAW.A (1OFU), 1CCZ.A (1QA9), 3MYI.A (1RKE), 1L2Z.A (1SYX), 1Z1A.A (1ZHI) & 1Z9E.A (2B4J), 2BJN.A (2CFH), 1OAP.A (2HQS), 2IYL.D (2J7P), 3FYK.X (2OZA), 1MYO.A (3AAA), 1TEY.A (3AAD), 2R1D.A (3BIW), 2GOM.A (3D5S), 2HD7.A (3DAW), 1WI6.A (3H2V), 3IO2.A (3P57), 2H3K.A (3SZK), 1W3S.A (4JCV) & 1CD8.AB (1AKJ), 1IAS.A (1B6C), 1QDV.ABCD (1EXB), 1K9V.F (1GPW), 1ILF.A (1H9D), 1KUY.A (1IB1), 1KW2.B (1KXP), 2NIP.AB (1N2C), 1HBP (1RLB), 1YJ1.A (1S1Q), 1S3X.A (1XQS), 1UX5.A (1Y64), 2A5S.A (2A5T), 1PNE (2BTF), 1C44.A (2C0L), 2HQT.A (2HRK), 2J5Y.A (2VDB), 3BP3.A (3BP8), 3OSK.A (3BX7), 1X0O.A (3F1P) \\\hline \end{tabular}} \end{table*} \begin{table*}[h!] \caption{Ligands from the Protein--Protein Docking Benchmark 5.0 characterized by 2-layer Sandwich architecture. \\ } \label{2-lay} \centering \resizebox{0.85 \textwidth}{!}{\scriptsize \begin{tabular}{|m{0.4\linewidth}|m{0.3\linewidth}|m{0.4\linewidth}|}\hline \textbf{Training set} & \textbf{Validation set} &\textbf{Test set} \\ \hline 1FWP.A (1FFW), 1BV1 (1FSK), 2HPR (1KKL), 1PJU.A (1OYV), 2GKR.I (1R0R), 2W9R.A (1R6Q), 1L2Z.A (1SYX), 1ZFI.A (2ABZ), 2GHV.E (2AJF), 1PNE (2BTF), 1C44.A (2C0L), 2BJN.A (2CFH), 1OAP.A (2HQS), 1POH (2JEL), 3SSI (2SIC), 2CI2.I (2SNI), 3BP3.A (3BP8) & 1A19.B (1AY7), 1DKS.A (1BUH), 1HPT (1CGI), 1F32.A (1F34) & 1EGL (1ACB), 1QDV.ABCD (1EXB), 1X0O.A (3F1P), 1WI6.A (3H2V), 1DCJ.A (3LVK) \\\hline \end{tabular}} \end{table*} \newpage \begin{table}[h!] \caption{Rates of architectures that characterize each class of Receptors in Table \ref{dataset}. \\ } \vspace{0.4cm} \resizebox{0.80 \textwidth}{!}{\scriptsize \begin{tabular}{|l|llll|}\hline & {\bf Training} & {\bf Validation} & {\bf Test} & \\ \hline $A_r$ & Sandwich ($100\%$) & Sandwich ($100\%$) & Sandwich ($100\%$) & \\ & & & & \\ \hline $AB_r$ &Sandwich ($100\%$) & Sandwich ($100\%$) & Sandwich ($100\%$) & \\ & & & & \\ \hline $EI_r$ & Sandwich ($9\%$) & Sandwich ($0 \%$) & Sandwich ($0 \%$) & \\ & 2-Layer Sandwich ($9\%$) & 2-Layer Sandwich ($8\%$) & 2-Layer Sandwich ($0\%$) & \\ & 3-Layer Sandwich ($36\%$) & 3-Layer Sandwich ($0.0\%$) & 3-Layer Sandwich ($25\%$) & \\ & Roll ($9\%$) & Roll ($0\%$) & Roll ($17\%$) & \\ & Beta Barrel ($9\%$) & Beta Barrel ($58\%$) & Beta Barrel ($25\%$) & \\ & Orthogonal Bundle ($9\%$) & Orthogonal Bundle ($8.0\%$) & Orthogonal Bundle ($0\%$) & \\ & Propeller ($0\%$) & Propeller ($0\%$) & Propeller ($8\%$) & \\ & Alpha-Beta Complex ($0\%$) & Alpha-Beta Complex ($0\%$) &Alpha-Beta Complex ($8\%$) & \\ & 2 or more arch. ($9\%$) & 2 or more arch. ($33\%$) & 2 or more arch. ($33\%$) & \\ & & & & \\ \hline $ER_r$ & Orthogonal Bundle ($10\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & \\ & 2-Layer Sandwich ($10\%$) & 2-Layer Sandwich ($17\%$) & 2-Layer Sandwich ($0\%$) & \\ & 3-Layer Sandwich ($20\%$) & 3-Layer Sandwich ($33\%$) & 3-Layer Sandwich ($40\%$) & \\ & Alpha-Beta Complex ($10\%$) & Alpha-Beta Complex ($0\%$) &Alpha-Beta Complex ($0\%$) & \\ & Roll ($10\%$) & Roll ($0\%$) & Roll ($0\%$) & \\ & 2 or more arch. ($40\%$) & 2 or more arch. ($50\%$) & 2 or more arch. ($60\%$) & \\ & & & & \\ \hline $ES_r$ & Orthogonal Bundle ($15\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & \\ & 3-Layer Sandwich ($14\%$) & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($43\%$) & \\ & Alpha-Beta Complex ($0\%$) & Alpha-Beta Complex ($33\%$) &Alpha-Beta Complex ($8\%$) & \\ & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($14\%$) & \\ & Sandwich ($0\%$) & Sandwich ($0 \%$) & Sandwich ($14 \%$) & \\ & 2 or more arch. ($71\%$) & 2 or more arch. ($67\%$) & 2 or more arch. ($14\%$) & \\ & & & & \\ \hline $OG_r$ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($12\%$) & \\ & 3-Layer Sandwich ($57\%$) & 3-Layer Sandwich ($50\%$) & 3-Layer Sandwich ($50\%$) & \\ & 2 or more arch. ($43\%$) & 2 or more arch. ($50\%$) & 2 or more arch. ($12\%$) & \\ & & & & \\ \hline $OR_r$ & Ribbon ($11\%$) &Ribbon ($0\%$) & Ribbon ($12\%$) & \\ & Up-down Bundle ($0\%$) & Up-down Bundle ($2\%$) & Up-down Bundle ($0\%$) & \\ & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($12\%$) & \\ & 3-Layer Sandwich ($11\%$) & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($0\%$) & \\ & Sandwich ($33\%$) & Sandwich ($20 \%$) & Sandwich ($25 \%$) & \\ & Alpha/alpha barrel ($0\%$) & Alpha/alpha barrel ($0\%$) & Alpha/alpha barrel ($13\%$) & \\ & 2 or more arch. ($45\%$) & 2 or more arch. ($60\%$) & 2 or more arch. ($38\%$) & \\ & & & & \\ \hline $OX_r$ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($9\%$) & Orthogonal Bundle ($0\%$) & \\ & 2-Layer Sandwich ($6\%$) & 2-Layer Sandwich ($28\%$) & 2-Layer Sandwich ($0\%$) & \\ & Alpha-Beta Barrel ($6\%$) & Alpha-Beta Barrel ($9\%$) & Alpha-Beta Barrel ($0\%$) & \\ & Sandwich ($12\%$) & Sandwich ($0 \%$) & Sandwich ($6 \%$) & \\ & 3-Layer Sandwich ($12\%$) & 3-Layer Sandwich ($9\%$) & 3-Layer Sandwich ($11\%$) & \\ & Up-down Bundle ($11\%$) & Up-down Bundle ($9\%$) & Up-down Bundle ($6\%$) & \\ & Roll ($6\%$) & Roll ($0\%$) & Roll ($12\%$) & \\ & Beta Barrel ($6\%$) & Beta Barrel ($0\%$) & Beta Barrel ($6\%$) & \\ & Alpha Horseshoe ($6\%$) & Alpha Horseshoe ($9\%$) & Alpha Horseshoe ($0\%$) & \\ & 2 or more arch. ($35\%$) & 2 or more arch. ($27\%$) & 2 or more arch. ($58\%$) & \\ & & & & \\ \hline \end{tabular} } \end{table} \begin{table}[h!] \caption{Rates of architectures that characterize each class of ligands in Table \ref{dataset}. } \vspace{0.4cm} \resizebox{0.80 \textwidth}{!}{\scriptsize \begin{tabular}{|l|llll|}\hline & {\bf Training} & {\bf Validation} & {\bf Test} & \\ \hline $A_l$ &Sandwich ($0\%$) & Sandwich ($0\%$) & Sandwich ($12\%$) & \\ & Trefoil ($14\%$) & Trefoil ($20\%$) & Trefoil ($12\%$) & \\ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($20\%$) & Orthogonal Bundle ($26\%$) & \\ & Ribbon ($0\%$) &Ribbon ($20\%$) & Ribbon ($12\%$) & \\ & Up-down Bundle ($14\%$) & Up-down Bundle ($0\%$) & Up-down Bundle ($0\%$) & \\ & Beta Barrel ($14\%$) & Beta Barrel ($0\%$) & Beta Barrel ($0\%$) & \\ & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($12\%$) & \\ & 2 or more arch. ($58\%$) & 2 or more arch. ($20\%$) & 2 or more arch. ($26\%$) & \\ & & & & \\ \hline $AB_l$ &Sandwich ($0\%$) & Sandwich ($33\%$) & Sandwich ($0\%$) & \\ & 2 or more arch. ($50\%$) & 2 or more arch. ($34\%$) & 2 or more arch. ($75\%$) & \\ & Propeller ($25\%$) & Propeller ($0\%$) & Propeller ($0\%$) & \\ & 2-Layer Sandwich ($25\%$) & 2-Layer Sandwich ($33\%$) & 2-Layer Sandwich ($0\%$) & \\ & Orthogonal Bundle ($9\%$) & Orthogonal Bundle ($8.0\%$) & Orthogonal Bundle ($0\%$) & \\ & & & & \\ \hline $EI_l$ & Sandwich ($14\%$) & Sandwich ($8 \%$) & Sandwich ($6 \%$) & \\ & 2-Layer Sandwich ($20\%$) & 2-Layer Sandwich ($26\%$) & 2-Layer Sandwich ($24\%$) & \\ & 3-Layer Sandwich ($6\%$) & 3-Layer Sandwich ($17\%$) & 3-Layer Sandwich ($6\%$) & \\ & Roll ($14\%$) & Roll ($0\%$) & Roll ($6\%$) & \\ & Beta Barrel ($20\%$) & Beta Barrel ($8\%$) & Beta Barrel ($6\%$) & \\ & Irregular ($6\%$) & Irregular ($0\%$) & Irregular ($11\%$) \\ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($6\%$) & \\ & Ribbon ($0\%$) &Ribbon ($8\%$) & Ribbon ($12\%$) & \\ & Trefoil ($0\%$) & Trefoil ($8\%$) & Trefoil ($0\%$) & \\ & Alpha-Beta Horseshoe ($0\%$) & Alpha-Beta Horseshoe ($8\%$) & Alpha-Beta Horseshoe ($12\%$) & \\ & 2 or more arch. ($20\%$) & 2 or more arch. ($17\%$) & 2 or more arch. ($11\%$) & \\ & & & & \\ \hline $ER_l$ & Up-down Bundle ($10\%$) & Up-down Bundle ($0\%$) & Up-down Bundle ($0\%$) & \\ & Alpha-Beta Barrel ($10\%$) & Alpha-Beta Barrel ($0\%$) & Alpha-Beta Barrel ($0\%$) & \\ & 3-Layer Sandwich ($30\%$) & 3-Layer Sandwich ($33\%$) & 3-Layer Sandwich ($9\%$) & \\ & 2-Layer Sandwich ($20\%$) & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($9\%$) & \\ & Roll ($10\%$) & Roll ($0\%$) & Roll ($9\%$) & \\ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($17\%$) & Orthogonal Bundle ($0\%$) & \\ & Alpha-Beta Complex ($0\%$) & Alpha-Beta Complex ($17\%$) &Alpha-Beta Complex ($0\%$) & \\ & Irregular ($0\%$) & Irregular ($0\%$) & Irregular ($9\%$) \\ & Beta Barrel ($0\%$) & Beta Barrel ($0\%$) & Beta Barrel ($9\%$) & \\ & Sandwich ($0\%$) & Sandwich ($0 \%$) & Sandwich ($18 \%$) & \\ & Alpha-Beta Horseshoe ($0\%$) & Alpha-Beta Horseshoe ($0\%$) & Alpha-Beta Horseshoe ($9\%$) & \\ & 2 or more arch. ($20\%$) & 2 or more arch. ($33\%$) & 2 or more arch. ($28\%$) & \\ & & & & \\ \hline $ES_l$ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($17\%$) & \\ & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($32\%$) & \\ & Up-down Bundle ($9\%$) & Up-down Bundle ($0\%$) & Up-down Bundle ($0\%$) & \\ & 2-Layer Sandwich ($9\%$) & 2-Layer Sandwich ($0\%$) & 2-Layer Sandwich ($0\%$) & \\ & Sandwich ($18\%$) & Sandwich ($0 \%$) & Sandwich ($0 \%$) & \\ & Alpha-Beta Complex ($37\%$) & Alpha-Beta Complex ($0\%$) &Alpha-Beta Complex ($17\%$) & \\ & Roll ($18\%$) & Roll ($0\%$) & Roll ($17\%$) & \\ & 2 or more arch. ($9\%$) & 2 or more arch. ($100\%$) & 2 or more arch. ($17\%$) & \\ & & & & \\ \hline $OG_l$ & Propeller ($0\%$) & Propeller ($0\%$) & Propeller ($14\%$) & \\ & Alpha-Beta Horseshoe ($0\%$) & Alpha-Beta Horseshoe ($0\%$) & Alpha-Beta Horseshoe ($14\%$) & \\ & Alpha Horseshoe ($0\%$) & Alpha Horseshoe ($25\%$) & Alpha Horseshoe ($14\%$) & \\ & 3-Layer Sandwich ($17\%$) & 3-Layer Sandwich ($0\%$) & 3-Layer Sandwich ($14\%$) & \\ & Irregular ($17\%$) & Irregular ($0\%$) & Irregular ($0\%$) \\ & Orthogonal Bundle ($17\%$) & Orthogonal Bundle ($25\%$) & Orthogonal Bundle ($0\%$) & \\ & Up-down Bundle ($17\%$) & Up-down Bundle ($0\%$) & Up-down Bundle ($0\%$) & \\ & 2 or more arch. ($32\%$) & 2 or more arch. ($50\%$) & 2 or more arch. ($44\%$) & \\ & & & & \\ \hline $OR_l$ & Irregular ($0\%$) & Irregular($0\%$) & Irregular ($10\%$) & \\ & beta barrel ($0\%$) & beta barrel ($0\%$) & beta barrel ($10\%$) & \\ & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($0\%$) & Orthogonal Bundle ($10\%$) & \\ & Trefoil ($0\%$) & Trefoil ($0\%$) & Trefoil ($10\%$) & \\ & Up-down Bundle ($0\%$) & Up-down Bundle ($40\%$) & Up-down Bundle ($0\%$) & \\ & Alpha Horseshoe ($11\%$) & Alpha Horseshoe ($0\%$) & Alpha Horseshoe ($0\%$) & \\ & Roll ($11\%$) & Roll ($0\%$) & Roll ($0\%$) & \\ & 3-Layer Sandwich ($11\%$) & 3-Layer Sandwich ($20\%$) & 3-Layer Sandwich ($0\%$) & \\ & Sandwich ($22\%$) & Sandwich ($20 \%$) & Sandwich ($30 \%$) & \\ & Ribbon ($22\%$) &Ribbon ($0\%$) & Ribbon ($10\%$) & \\ & 2 or more arch. ($22\%$) & 2 or more arch. ($20\%$) & 2 or more arch. ($38\%$) & \\ & & & & \\ \hline $OX_l$ & Beta Barrel ($0\%$) & Beta Barrel ($0\%$) & Beta Barrel ($10\%$) & \\ & Alpha Horseshoe ($0\%$) & Alpha Horseshoe ($8\%$) & Alpha Horseshoe ($0\%$) & \\ & Up-down Bundle ($6\%$) & Up-down Bundle ($15\%$) & Up-down Bundle ($0\%$) & \\ & Sandwich ($6\%$) & Sandwich ($15 \%$) & Sandwich ($10 \%$) & \\ & Roll ($613\%$) & Roll ($0\%$) & Roll ($5\%$) & \\ & Orthogonal Bundle ($66\%$) & Orthogonal Bundle ($8\%$) & Orthogonal Bundle ($5\%$) & \\ & 2-Layer Sandwich ($13\%$) & 2-Layer Sandwich ($15\%$) & 2-Layer Sandwich ($25\%$) & \\ & 3-Layer Sandwich ($18\%$) & 3-Layer Sandwich ($8\%$) & 3-Layer Sandwich ($20\%$) & \\ & 2 or more arch. ($38\%$) & 2 or more arch. ($31\%$) & 2 or more arch. ($25\%$) & \\ & & & & \\ \hline \end{tabular} } \end{table} \bibliographystyle{plain} \bibliography{document} \end{document}