Table S1. Genetic mutation rates of core CDH based on targeted exon sequencing in melanoma samples from Taiwanese patients Extracellular domain Substitution eventsa Intracellular domain Substitution eventsa Total mutation rate and transmembrane mutation rate (%) (%) (cases/ total mutation rate (%) samples) CDH6 9.09% exon9:c.A1400G:p.K467R 18.18% exon12:c.G2170A:p.D724N 22.73% exon12:c.G2236A:p.V746M (5/22) CDH10 18.18% exon3:c.C346G:p.R116G 9.09% exon12:c.G2044A:p.E682K 22.73% exon3:c.C377T:p.T126I (5/22) exon5:c.G607A:p.E203K exon7:c.C1163T:p.S388F

CDH18 13.63% exon4:c.G310A:p.D104N 13.63% exon16:c.G2345A:p.G782E 22.73% exon8:c.G1124A:p.G375E (5/22) exon9:c.G455A:p.G152E CDH12 18.18% exon6:c.C28T:p.L10F 0% None detected 18.18% exon6:c.C65T:p.P22L (4/22) exon12:c.T1301C:p.I434T exon15:c.G1802A:p.C601Y exon16:c.C2186T:p.T729I CDH9 9.09% exon2:c.C62T:p.T21I 0% None Detected 13.63% exon4:c.G541A:p.V181I (3/22) CDH24 9.09% exon3:c.C395T:p.P132L 4.54% exon13:c.G2036A:p.R679Q 13.63% exon3:c.C470T:p.A157V (3/22) exon8:c.G1279A:p.E427K CDH1 9.09% exon8:c.C1082T:p.A361V 4.54 exon14:c.G2287A:p.E763K 9.09% exon10:c.G1483A:p.V495M (2/22) CDH2 4.54% exon9:c.G1276A:p.D426N 9.09% exon15:c.G2476A:p.A826T 9.09% exon11:c.C1725A:p.F575L exon16:c.T2593G:p.S865A (2/22) CDH4 9.09% exon1:c.C44T:p.P15L 0% None detected 9.09% exon14:c.A2338C:p.I780L (2/22) CDH5 9.09% exon4:c.C556T:p.H186Y 0% None detected 9.09% exon11:c.G1798A:p.A600T (2/22) CDH7 9.09% exon3:c.G433A:p.D145N 4.54% exon12:c.C2264T:p.S755F 9.09% exon11:c.G1789A:p.E597K (2/22) exon11:c.G1864A:p.V622M CDH8 9.09% exon3:c.G340A:p.V114I 0% None detected 9.09% exon3:c.C445G:p.P149A (2/22) exon10:c.A1589C:p.Y530S CDH11 9.09% exon3:c.C65T:p.A22V 0% None detected 9.09% exon5:c.G607A:p.E203K (2/22) CDH13 4.54% exon5:c.C557T:p.S186F 9.09% exon14:c.C2143T:p.P715S 9.09% exon6:c.G760A:p.V254I exon14:c.G2170A:p.V724I (2/22) CDH15 4.54% exon9:c.G1306A:p.V436M 0% Not detected 4.54% (1/22) ac- chromosomal base substitution; p- amino acid substitution Table S2. Calculation of catenin-binding free energy differences between WT and known mutations in core CDH genes in melanoma Binding ∆∆𝑮𝑴𝒖𝒕𝒂𝒕𝒊𝒐𝒏 Mutation Domain 𝑩𝒊𝒏𝒅𝒊𝒏𝒈 protein (kJ/mol) D661N CDH6, CDH9, CDH10 JMD p120-catenin 4.60 ± 0.69 E662K CDH6, CDH9 JMD p120-catenin 7.50 ± 2.11 G663E CDH18 JMD p120-catenin 42.29 ± 7.57 G665R CDH10 JMD p120-catenin -15.34 ± 13.85 E666K CDH9 JMD p120-catenin 21.95 ± 4.39 E667K CDH18 JMD p120-catenin 1.56 ± 2.88 R689Q CDH6 CBD -catenin 8.17 ± 4.91 D691N CDH6 CBD -catenin 5.96 ± 0.96 E722K CDH6 CBD -catenin -0.07 ± 5.04 D726N CDH6 CBD -catenin 5.98 ± 1.77 D733N CDH9 CBD -catenin 15.62 ± 1.83 E741K CDH9 CBD -catenin 16.38 ± 2.35 G742E CDH10 CBD -catenin -19.63 ± 6.25 L767F CDH10 CBD -catenin -1.60 ± 5.56 R773Q CDH6, CDH9 CBD -catenin 8.70 ± 5.05

Table S3. Gene set enrichment analyses of reactomes/pathways concurrently up-regulated with mutations in top-four core CDH genes in melanomaa NOM Reactome /Pathwayb ES NES p-value 1. Liver_Cancer_Subclass_G3_Up 0.6493 1.7587 0.0159 2. Doxorubicin_Resistance_Up 0.7836 1.6533 0.0175 3. Antigen_Response 0.6726 1.7603 0.0236 4. Thyroid_Carcinoma_Anaplastic_Up 0.5938 1.7737 0.0276 5. T_Lymphocyte_Up 0.7554 1.6582 0.0320 6. Epithelial_Mesenchymal_Transition_Up 0.6731 1.7110 0.0333 7. M_G1_Transition 0.6640 1.6491 0.0345 8. Core_Serum_Response_Up 0.6037 1.6801 0.0352 9. Cell_Cycle_Mitotic 0.6362 1.6307 0.0369 10. Synthesis_Of_DNA 0.6648 1.6498 0.0381 11. Mitotic_G1/G1_S_Phases 0.5985 1.6321 0.0386 12. CDC20_Mediated_Degradation_Of_Mitotic_Proteins 0.6666 1.6343 0.0423 13. DNA_Replication 0.6606 1.6724 0.0437 14. Mitotic_M/M_G1_Phases 0.6589 1.6693 0.0437 15. Cervical_Cancer_Proliferation_Cluster 0.6992 1.6660 0.0483 aAbbreviations: ES, enrichment score; NES, normalized enrichment score; NOM p-value, nominalized p-value. bReactomes or pathways with NOM p-values < 0.05 were considered as significantly relevant with mutations in top-four core CDH genes.

Figure S1. Double-system/single-box setup. (A) Two branches of a thermodynamic cycle are placed in one simulation box. The different boxes in the scheme are indicated by the solid (𝜆 0) and broken (𝜆1) lines. (B) An example of a simulation setup for the catenin binding free energy calculation. The free energy difference corresponds to a double free energy difference: ΔΔG = ΔG1 – ΔG2.

Figure S2. Mutations in and nectin-like genes in skin cutaneous melanoma. (A) Mutation frequencies and (B) mutational profiles of nectin and nectin-like genes in skin cutaneous melanoma were analyzed by using NGS data from the TCGA cohort (TCGA, PanCancer Atlas; n = 448).

Figure S3. Validation of mutation frequencies in key adherens junction (AJ) genes in non- TCGA cohort. Mutation frequencies of key AJ genes, including (A) top-five highly-mutated genes identified in TCGA cohort, (B) nectin and (C) nectin-like genes, were analyzed by using NGS data from non-TCGA cohort (n = 396). The non-TCGA cohort include patients from Broad/Dana Farber (n = 26, Nature 2012), MSKCC (n = 64, NEJM 2014), Broad (n = 121, Cell 2012), Yale (n = 147, Nat Genet 2012), and UCLA (n = 38, Cell 2016).

Figure S4. Dual-color immunofluorescence staining of CDH6 and -catenin on melanoma tissues from Taiwanese patients. Tissue sections were prepared from Taiwanese patients with melanoma. Dual-color immunofluorescence staining, red for CDH6 and green for -catenin, was performed on melanocyte from normal skin counterpart (upper), melanoma with wild type CDHs (middle), and melanoma with D724N mutation (lower). Cell nuclei were counterstained with DAPI.

Figure S5. Dual-color immunofluorescence staining of CDH9 and -catenin on melanoma tissues from Taiwanese patients. Tissue sections were prepared from Taiwanese patients with melanoma. Dual-color immunofluorescence staining, red for CDH9 and green for -catenin, was performed on melanocyte from normal skin epithelium counterpart (upper), melanoma with wild type CDHs (middle). Cell nuclei were counterstained with DAPI.

Figure S6. Dual-color immunofluorescence staining of CDH10 and -catenin on melanoma tissues from Taiwanese patients. Tissue sections were prepared from Taiwanese patients with melanoma. Dual-color immunofluorescence staining, red for CDH10 and green for -catenin, was performed on melanocyte from normal skin epithelium counterpart (upper), melanoma with wild type CDHs (middle), and melanoma with E682K mutation (lower). Cell nuclei were counterstained with DAPI.

Figure S7. Dual-color immunofluorescence staining of CDH18 and -catenin on melanoma tissues from Taiwanese patients. Tissue sections were prepared from Taiwanese patients with melanoma. Dual-color immunofluorescence staining, red for CDH18 and green for -catenin, was performed on melanocyte from normal skin epithelium counterpart (upper), melanoma with wild type CDHs (middle), and melanoma with G782E mutation (lower). Cell nuclei were counterstained with DAPI.

Figure S8. The predicted CDH6/p120-catenin (-catenin) complex structures and their binding free energy differences (ΔΔG) between WT and MT CDH6. (A) The predicted structure of JMD (residues 660-677, in blue) in complex with p120-catenin (-catenin, in green) was generated by using the MODELLER program. The known mutated sites, D661 and D662, on the JMD (in orange) were found to interact with K444 and K574 on the p120-catenin, respectively. (B) A double-system/single-box setup was used to estimate the binding free energy differences (ΔΔG) caused by mutations.

Figure S9. The predicted CDH6/-catenin complex structures and their binding free energy differences (ΔΔG) between WT and MT CDH6. (A) The predicted structure of CBD (residues 687-784, in blue) in complex with -catenin (green) was generated by using MODELLER program. The known mutated sites were highlighted in orange spheres. A double- system/single-box setup was used to estimate the binding free energy differences (ΔΔG) caused by (B) R689Q, (C) D691N, (D) E722K, (F) E726N, and (G) R773Q substitutions. Cartoon representations indicated the binding interfaces between mutated residues on CBD (yellow) and the interacting residues on -catenin.

Figure S10. Reactomes/pathways associated with mutations in top-four highly mutated cadherin (core CDHs) genes in skin cutaneous melanoma. Gene set enrichment analysis (GSEA) was performed using mRNA expression data from the TCGA group (TCGA, PanCancer Atlas; n = 448). Patients without mutations in any cadherin genes were utilized as the controls. Concurrent up-regulated reactomes with p-values less than 0.05 were shown here. Two pathways, Antigen Response and T-Lymphocyte Up, were also shown in Fig. 7C. A CDH9 CDH9 wild type score p = 0.0148* WTmutant type score 120120 MT

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00 1 2 3 4 5 6 7 8 9 0 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3 3 32 33 34 35 36 37 38 39 40 41 G86E I201K G54D L446F S749L S143L S734L S450L P452L L533P V474F E120K E140K E741K E156K E662K E666K E708K P269S E375K E498K E643K H111Y Y659H D748E R133K D744N R773C R127C D151N D661N D733N G310E G327E N464D D515N D574N D592N R267Q G742W amino acid substitutions in CDH9 B CDH10 CDH10 wild type score p = 0.0030** mutantWT type score 120120 MT

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00 1 2 3 4 5 6 7 8 9 3 5 7 10 11 12 1 14 15 16 17 18 19 20 21 22 23 24 2 26 27 28 29 30 31 32 33 34 35 36 3 38 39 40 41 42 43 44 45 46 47 N59K H50R R51C D81N G69R I132N I690N L765F L279F L480V P487L S387F S421F S597F E121K P170S E214K P357S A462V P606S E648K P698S F391C H112Y D712Y Y306N D539Y H394Y R230K N466K G740E D152N G243S G363E R424H G520S G580S D649N D659N E683G R307Q G553R R638Q G663R R699W amino acid substitutions in CDH10 C CDH18 CDH18 wild type score p = 0.0070** mutantWT type score 120120 MT

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0 Antigen-tolerance score score Antigen-tolerance 0 score Antigen-tolerance Antig 1 2 3 4 5 6 7 8 9 0 1 6 7 3 0 3 9 0 4 6 1 1 12 13 14 15 1 1 18 19 20 21 22 2 24 25 26 27 28 29 3 31 32 3 34 35 36 37 38 3 4 41 42 43 4 45 4 47 K52E H78P D82E R50C M303I P535L P679L P730L T559A E144K E230K E379K E394K E543K E653K E666K E694K E714K V402A E426K P452S E498K D711Y K114N R226K R325K R555K D105N D109N G175S G204E G314E K340Q D376N D562N N545D G662E D754N D763N G768E D467H G192R R598Q G520R R652W amino acid substitutions in CDH18

Figure S11. Neo-antigen potentials of mutations in core CDH genes in skin cutaneous melanoma. Antigen-tolerance scores of known mutations in the extracellular domain of (A) CDH9; (B) CDH10; and (C) CDH18 were analyzed by using NetMHCpan algorithm and compared with the scores with wild type sequence. Substitutions with lower scores indicate higher neo-antigen potentials. Two-way ANOVA was utilized to compare the differences between wild type and mutant type. Statistical significance: *, p < 0.05; **, p < 0.01.

A CDH6 p = 0.0013** p = 0.0096** p = 0.0953 p = 0.0076** 250 400 300 400

200 300 300 200 150 200 200 100 100 100 100 50 0

Macrophages M1 0 NK cells activated 0 T cells gamma delta 0 -100 -100 -100 -50 WT CDHs MT core WT CDHs MT core WT CDHs MT coreT cells CD4 memory activated WT CDHs MT core

1500 p = 0.0188* 400 p = 0.0498* 300 p = 0.1031 300 p = 0.0011**

300 200 1000 200 200 100 500 100 0

T cells CD8 0 Monocytes 100 0 Cytolytic Score -100 -100 T cells follicular helper -500 -200 -200 0 WT CDHs MT core WT CDHs MT core WT CDHs MT core WT CDHs MT core

B core CDHs p = 0.0145* p = 0.0414* p = 0.1942 p = 0.0285* 250 400 300 400

200 300 300 200

150 200 200 100 100 100 100 50 0 0 0 Macrophages M1 NK cells activated T cells gamma delta 0 -100 -100 -100

-50 T cells CD4 memory activated WT CDHs MT core WT CDHs MT core WT CDHs MT core WT CDHs MT core

p = 0.0749 p = 0.1003 p = 0.0490* p = 0.0258* 1500 400 400 300

300 300 1000 200 200 200 500 100 100

0 0 T cells CD8 Monocytes 100 0 Cytolytic Score -100 -100 T cells follicular helper -500 -200 -200 0 WT CDHs MT core WT CDHs MT core WT CDHs MT core WT CDHs MT core

Figure S12. Changes of tumor microenvironments in skin cutaneous melanoma by mutations in core CDH genes. Microenvironment immune types were analyzed in tumors with mutations in (A) CDH6 or (B) core CDH genes, and compared with the data in tumors with wild type CDHs. The immune scores include T cells, M1 macrophages, activated NK cells, activated CD4+ memory T cells, CD8+ T cells, monocytes, follicular helper T cells and cytolytic score.