Supplementary information for: Community detection for networks with. unipartite and bipartite structure. Chang Chang 1, 2, Chao Tang 2

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1 Supplementary information for: Community detection for networks with unipartite and bipartite structure Chang Chang 1, 2, Chao Tang 2 1 School of Life Sciences, Peking University, Beiing , China 2 Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, Peking University, Beiing , China chang.connected@pku.edu.cn and tangc@pku.edu.cn 1

2 CONTENTS I. RESULTS OF TWO CASE STUDIES OF THE GENE ONTOLOGY ENRICHMENT ANALYSIS MENTIONED IN THE MAIN TEXT... 3 II. MODEL SPECIFIC FOR A MIXTURE, UNDIRECTED NETWORK

3 I. RESULTS OF TWO CASE STUDIES OF THE GENE ONTOLOGY ENRICHMENT ANALYSIS MENTIONED IN THE MAIN TEXT Supplementary figure 1. The cell cycle and the metabolic -related module. 3

4 Supplementary table 1. The enriched gene ontology terms for downstream target genes in the cell cycle and the metabolic -related module. GOID TERM FALSE DISCOVERY RATE NUM_ANNOTATION S GO: DNA packaging 0 21 (of 59) GO: nucleosome assembly 0 19 (of 50) GO: protein-dna complex assembly 0 19 (of 51) GO: DNA conformation change 0 24 (of 75) GO: chromatin assembly 0 19 (of 52) regulation of GO: nucleobase-containing compound metabolic (of 767) GO: chromatin assembly or disassembly 0 20 (of 58) GO: nucleosome organization 0 20 (of 58) GO: protein-dna complex subunit organization 0 20 (of 58) GO: regulation of nitrogen compound metabolic (of 790) 4

5 GO: DNA metabolic 0 53 (of 249) GO: organic cyclic compound metabolic (of 1198) GO: heterocycle metabolic (of 1169) GO: cellular nitrogen compound metabolic (of 1194) nucleobase-containing GO: compound metabolic (of 1139) GO: chromatin organization (of 154) GO: regulation of transcription, DNA-dependent (of 659) GO: regulation of RNA metabolic (of 683) GO: regulation of RNA biosynthetic (of 663) GO: nucleic acid metabolic (of 1028) GO: cellular aromatic compound metabolic (of 1166) 5

6 regulation of GO: macromolecule metabolic (of 934) GO: chromosome organization (of 200) GO: nitrogen compound metabolic (of 1250) regulation of cellular GO: macromolecule biosynthetic (of 723) GO: regulation of gene expression (of 765) GO: regulation of cellular biosynthetic (of 742) regulation of GO: macromolecule biosynthetic (of 729) GO: interphase (of 101) GO: regulation of biosynthetic (of 746) GO: organelle organization (of 542) GO: cell cycle (of 326) GO: regulation of primary (of 959) 6

7 metabolic GO: regulation of cellular metabolic (of 975) GO: interphase of mitotic cell cycle (of 99) GO: transcription, DNA-dependent (of 568) GO: G2/M transition of mitotic cell cycle (of 39) GO: regulation of metabolic (of 1041) GO: regulation of cellular (of 1507) 7

8 Supplementary figure 2. The immune system-related module. 8

9 Supplementary table 2. The enriched gene ontology terms for downstream target genes in the immune system-related module. GOID TERM FALSE DISCOVE RY RATE NUM_ANNOT ATIONS GO: innate immune response 0 37 (of 86) GO: defense response 0 43 (of 131) GO: defense response to virus 0 29 (of 47) GO: immune response 0 40 (of 123) GO: immune effector 0 31 (of 68) GO: response to virus 0 30 (of 63) GO: response to biotic stimulus 0 35 (of 107) GO: response to type I interferon 0 21 (of 27) GO: type I interferon-mediated signaling pathway 0 21 (of 27) GO: cellular response to type I interferon 0 21 (of 27) GO: response to other organism 0 34 (of 100) GO: response to cytokine stimulus 0 32 (of 99) GO: immune system 0 49 (of 287) GO: cellular response to cytokine stimulus 0 29 (of 81) GO: cytokine-mediated signaling pathway 0 26 (of 70) GO: response to interferon-gamma 0 15 (of 20) GO: multi-organism 0 43 (of 329) 9

10 GO: negative regulation of viral genome replication 0 11 (of 13) GO: negative regulation of viral reproduction 0 11 (of 13) GO: response to stress 0 54 (of 550) GO: response to interferon-beta 0 9 (of 9) GO: cellular response to organic substance 0 34 (of 237) GO: regulation of viral genome replication 0 12 (of 19) GO: response to organic substance 0 41 (of 351) GO: negative regulation of multi-organism 0 11 (of 16) GO: interferon-gamma-mediated signaling pathway 0 10 (of 13) GO: negative regulation of reproductive 0 12 (of 22) GO: cellular response to interferon-gamma 0 10 (of 14) GO: regulation of multi-organism 0 17 (of 57) GO: regulation of immune system 0 24 (of 131) GO: regulation of immune response 0 18 (of 68) GO: cellular response to chemical stimulus 0 34 (of 287) GO: regulation of defense response 0 18 (of 75) GO: response to chemical stimulus 0 43 (of 461) GO: response to stimulus 0 70 (of 1071) GO: regulation of viral reproduction 0 13 (of 39) 10

11 GO: regulation of type I interferon production 0 10 (of 21) GO: response to interferon-alpha 0 7 (of 8) GO: regulation of immune effector 0 12 (of 35) GO: virus-host interaction 0 18 (of 100) GO: regulation of response to stress 0 20 (of 133) GO: regulation of innate immune response 0 12 (of 44) GO: regulation of reproductive 0 13 (of 54) GO: interaction with host 0 18 (of 111) GO: symbiosis, encompassing mutualism through parasitism 0 18 (of 114) GO: interspecies interaction between organisms 0 18 (of 114) GO: cell surface receptor signaling pathway 0 29 (of 296) GO: viral reproductive 0 20 (of 151) GO: positive regulation of type I interferon production 0 6 (of 9) GO: multi-organism reproductive 0 21 (of 171) GO: regulation of cytokine production 0 12 (of 54) GO: negative regulation of biological 0 42 (of 590) GO: cellular response to stimulus 0 51 (of 817) GO: positive regulation of interferon-beta production 0 5 (of 7) GO: signal transduction 0 41 (of 588) 11

12 GO: cellular response to interferon-beta 0 4 (of 4) GO: regulation of response to stimulus 0 30 (of 368) GO: negative regulation of type I interferon production 0 6 (of 13) GO: response to dsrna 0 6 (of 14) GO: viral reproduction 0 21 (of 211) GO: regulation of interferon-beta production 0 5 (of 9) GO: signaling 0 42 (of 656) GO: single organism signaling 0 42 (of 656) GO: regulation of symbiosis, encompassing mutualism through parasitism 0 4 (of 5) GO: positive regulation of cytokine production 0 7 (of 23) GO: regulation of multicellular organismal 0 22 (of 244) GO: negative regulation of cytokine production 0 7 (of 26) GO: cell communication 0 42 (of 683) GO: regulation of defense response to virus 0 6 (of 18) GO: regulation of response to biotic stimulus 0 6 (of 20) GO: regulation of biological 0 74 (of 1562) GO: extracellular transport (of 3) GO: intracellular transport of viral proteins in host cell (of 3) 12

13 GO: symbiont intracellular protein transport in host (of 3) GO: regulation of interferon-alpha production (of 3) GO: positive regulation of interferon-alpha production (of 3) regulation of viral-induced cytoplasmic GO: pattern recognition receptor signaling (of 3) pathway GO: regulation of RIG-I signaling pathway (of 3) GO: regulation of viral entry into host cell (of 3) GO: negative regulation of viral entry into host cell (of 3) GO: regulation of viral protein levels in host cell (of 3) GO: intracellular protein transport in other organism involved in symbiotic interaction (of 3) GO: positive regulation of RIG-I signaling pathway (of 3) GO: response to exogenous dsrna (of 7) GO: regulation of adaptive immune response (of 13) GO: biological regulation (of 1642) GO: positive regulation of immune system (of 67) GO: regulation of response to cytokine stimulus (of 22) 13

14 GO: positive regulation of multicellular organismal (of 55) GO: regulation of defense response to virus by host (of 8) GO: protein trimerization (of 8) GO: intracellular receptor mediated signaling pathway (of 33) GO: negative regulation of multicellular organismal (of 47) GO: negative regulation of immune system (of 25) GO: regulation of response to interferon-gamma (of 9) GO: cellular response to dsrna (of 9) GO: positive regulation of biological (of 624) GO: regulation of leukocyte mediated cytotoxicity (of 4) GO: positive regulation of T cell mediated immunity (of 4) positive regulation of adaptive immune GO: response based on somatic recombination of immune receptors built from (of 4) immunoglobulin superfamily domains GO: JAK-STAT cascade (of 10) 14

15 GO: regulation of type I interferon-mediated signaling pathway (of 10) GO: positive regulation of response to stimulus (of 145) GO: regulation of cellular (of 1507) GO: leukocyte activation (of 53) GO: reproductive (of 305) GO: regulation of leukocyte mediated immunity (of 11) GO: reproduction (of 306) GO: positive regulation of leukocyte mediated immunity (of 5) GO: positive regulation of lymphocyte mediated immunity (of 5) GO: regulation of T cell mediated immunity (of 5) GO: regulation of cell killing (of 5) GO: retinoic acid receptor signaling pathway (of 5) GO: regulation of cytokine-mediated signaling pathway (of 20) GO: negative regulation of immune effector (of 12) GO: response to tumor necrosis factor (of 12) GO: regulation of locomotion (of 58) GO: negative regulation of locomotion (of 22) 15

16 GO: response to organic cyclic compound (of 90) GO: positive regulation of adaptive immune response (of 6) GO: positive regulation of immune response (of 34) GO: regulation of signal transduction (of 304) GO: response to lipid (of 79) GO: single-organism (of 1169) GO: regulation of T cell mediated cytotoxicity (of 2) GO: positive regulation of T cell mediated cytotoxicity (of 2) GO: regulation of macrophage derived foam cell differentiation (of 2) GO: ISG15-protein conugation (of 2) GO: regulation of MyD88-dependent toll-like receptor signaling pathway (of 2) GO: cellular response to interferon-alpha (of 2) GO: cytoplasmic pattern recognition receptor signaling pathway in response to virus (of 2) GO: regulation of MDA-5 signaling pathway (of 2) GO: regulation of MHC class I biosynthetic (of 2) GO: cytosol to ER transport (of 2) 16

17 GO: cellular response to exogenous dsrna (of 2) GO: positive regulation of MDA-5 signaling pathway (of 2) GO: regulation of lymphocyte mediated immunity (of 7) GO: regulation of toll-like receptor signaling pathway (of 7) GO: cell activation (of 81) GO: regulation of signaling (of 339) GO: cellular response to lipid (of 26) GO: cellular response to organic cyclic compound (of 26) GO: regulation of cell communication (of 342) regulation of adaptive immune response GO: based on somatic recombination of immune receptors built from immunoglobulin (of 8) superfamily domains GO: regulation of interferon-gamma-mediated signaling pathway (of 8) GO: negative regulation of defense response (of 18) GO: response to growth hormone stimulus (of 9) GO: protein import into nucleus (of 30) GO: protein targeting to nucleus (of 30) GO: regulation of cellular component movement (of 59) 17

18 GO: nuclear import (of 31) GO: positive regulation of leukocyte mediated cytotoxicity (of 3) GO: antigen ing and presentation of endogenous peptide antigen (of 3) GO: mrna modification (of 3) GO: antigen ing and presentation of endogenous antigen (of 3) GO: antigen ing and presentation of endogenous peptide antigen via MHC class I (of 3) GO: regulation of ribonuclease activity (of 3) GO: cellular response to tumor necrosis factor (of 10) GO: negative regulation of transport (of 47) GO: negative regulation of cellular component movement (of 21) GO: cellular response to biotic stimulus (of 21) GO: negative regulation of gene expression (of 197) GO: regulation of localization (of 197) GO: positive regulation of immune effector (of 11) GO: regulation of cell migration (of 49) 18

19 II. MODEL SPECIFIC FOR A MIXTURE, UNDIRECTED NETWORK A. Model Here we propose a model specific for a mixture, undirected network to see if there is any difference for performance between this specific model and the model mentioned in the main text. For the latter model, an undirected edge is viewed as two directed edges in opposite directions. Thus, the probability between any common vertices is considered twice even for the undirected networks. In the specific model, we will only consider such probability once. Thus, the likelihood can be written as A ( U) ( V) i ( ) (V) iz U z z ( U) ( V) iz z A! (U) ( V ) i z l i l iou, OV P G, exp (U) ( V ) l i l iou, OV 1 2 iou, SV i z ( U) ( V) iz z Ai /2 ( U) ( V) iz z z 1 exp ( A /2)! 2 A i! Ai exp z ( U) ( V) iz z A ( U) ( V) i iz z z ( U) ( V) iz z is,! U A i z exp. z ( U) ( V) iz z (S1) subect to constraints that ( U ) (V) (U) ( V ) 0,,, i, iz z i z l l (S2) ust as the model in the main text. The log likelihood is 19

20 ln P G, A ln ( U) (V) ( U) (V) ( U) (V) i iz z iz z l (U) l ( V ) z iz i iou, OV l (U) = ( V ) i iou, OV 1 1 A ln 2 2 A ln ( U) (V) ( U) (V) i iz z iz z z iz ( U) (V) ( U) ( V) i iz z iz z iou, OV z iz A ln ( U) (V) ( U) (V) i iz z iz z isu, z iz ( U ) (V) 1 iz z ( U ) (V) 1 (U) ( V) (U) ( V) A q (z)ln. l ', i, i i iz z 2 i l l l ' iz i' ' q i (z) (S3) Now considering the constraints in Eq. (12), the target function is ( U ) (V) 1 iz z ( U) (V) ( U) (V) L1 (U) ( V) (U) ( V) q (z)ln (U) ( V ), li', l li, l Ai i iz z ciz ' li, l iz z iz 2 i' ' q i (z) (S4) where c iz is the Lagrange multiplier. Differentiating Eq. (S4) with respect to ( U ) iz leads to L 1 Ai q(z) i (V) 1 ( U) (U) ( V ) (U) ( V) ( ) (U) ( V) 2 li', l li, l U z ciz ' li, l iz i' ' iz (S5) When i is a specific vertex, (U) ( V ) ' li, l ' 0, it leads to Eq. (10). When i '' and '' are common vertices that (U) ( V ) ( U ) i'' z li'', l'' 1, let Eq. (S5) equals to 0, we have (V) z A i'' q i'' c (z) i'' z (U) ( V ) li '', l i' (U) ( V ) li ', l. (S6) Similarily, we have 20

21 ( U ) '' z i ( U ) iz i A i i '' q (z) i i '' c i '' z (U) ( V ) li, l '' ' (U) ( V ) li, l '. (S7) Inserting Eqs. (S6) and (S7) back to the constraints (Eq. (10)), c iz is given by c i'' '' z ( U ) 1 (V) 1 '' q '' (z) 1 (U) ( V ) '' q ''(z) 1 (U) ( V ) i iz A i i l ',, 2 i l z A i i i l ' ' 2 i l i ' 1 1 Ai'' q i'' (z) 1 (U) ( V ) A'' q '' (z) 1 (U) ( V ) i l, i i ' ', 2 i l l ' 2 i l i' (S8) z. Inserting Eq. (S8) back to Eqs. (S6) and (S7), we can get ( U ) i'' z 1 1 q (z) 1 A q (z) ( U ) 1 (V) 1 iz 1 (U) ( V ) 1 (U) ( V) i li, l z ' ', 2 l ' 2 i l i' A '' '' (U) ( V ) '' '' (U) ( V ) i i i li, l i i ' li', l ' i' i A q (z) A q (z), i '' i '' S i'' i'' V ( U ) (V) iz i S z V (S9) and A q (z) A q (z) (V) i i '' i '' S i'' i'' V '' z ( U ) (V) i iz S z V (S10) B. Results 21

22 Supplementary figure 3. Heat maps for normalized mutual information of the specific model on random networks generated by symmetric sampling (left panels), asymmetric sampling with c 0.2 (middle panels), and asymmetric sampling with c 0.8 (right panels) using the GN benchmark and the LFR benchmark (undirected networks). For the GN benchmark, both r and s are set to be 10, and 50 random initializations are used for the module detection of each network. For the LFR benchmark, r is set to be 10 and s are set to be 5, and 10 random initializations are used for the module detection of each network. Comparing Supplementary figure 3 here and figure 4 (upper panels) and figure 5 (upper panels) in the main text, we could not see any significant difference between the specific model and the model mentioned in the main text based on GN and LFR benchmarks. 22

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