Table 2. Boolean functions (BF) of the IBD model for the internal and the output nodes.

INTERNAL NODES

TLR2 = PGN

TLR4 = LPS

NOD2 = MDP

NFkB = TLR2 | NOD2 | TLR4

IL6 = (MACR & PGN) | (DC & (LPS | PGN)) | (Th17 & IL23) | (NFkB &! (IL4 | IL10))

$TNFa=\left(\right(NFkB\&LPS\left)\right|(MACR\&(IL2\left|\right(IFNg\&LPS\left)\right|\mathit{P}\mathit{G}\mathit{N}\left)\right)\left|\right(NK\&\left(MDP\right|PGN\left|LPS\right)\&\left(\right(IL2|$ $IL12)\&(IL2\left|IL15\right)\left)\right|(FIBROBLAST\&IFNg)\left|\right((CD4\_NKG2D|CD8\_NKG2D|NK\_NKG2D)\&(IEC\_MICA\_B|$ $IEC\_ULPB1\_6\left)\right))\&!({\bigcap }_{i=1}^{downre{g}_{cyt}=4}{IL10}^{t-i}\&({\bigcap }_{i=1}^{downre{g}_{cyt}=4}{TLR2}^{t-i}|{\bigcap }_{i=1}^{downre{g}_{cyt}=4}{TLR4}^{t-i})\&TNFa)$

TGFb = (Treg | MACR)

$Th0={\bigcap }_{i=1}^{THR\_Th0=3}{LPS}^{t-i}|{\bigcap }_{i=1}^{THR\_Th0=3}{MDP}^{t-i}|{\bigcap }_{i=1}^{THR\_Th0=3}{PGN}^{t-i}$

Th0_M = (Th0 & (IL23 | IL12)) | Th0_M

IL18 = ((MACR | DC) & LPS) & NFkB

$IL1b=\left(\right(MACR\left|DC\right)\&LPS\&NFkB)\&!(IL1b\&{\bigcup }_{i=1}^{downreg\_cyt=4}{IL10}^{t-i})$

$IFNg=\left(\left(NK\&\left(PGN\right|LPS\right|MDP\right|\&\left(IL23\right|\left(IL12\&\left(IL2\right|IL15\right|IL18\left)\right)\left)\right)\left|\right(Th0\_M\&\left(LPS\right|MDP\left|PGN\right)$ $\&\left(IL12\right|IL23\left)\right)\left|Th1\right|\left(\right(CD8\_NKG2D|NK\_NKG2D)\&(IEC\_MICA\_B|IEC\_ULPB1\_6\left)\right)\left|\right(Th17\&\left(PGN\right|LPS|$ $MDP\left)\right)\left|\right(\left(MACR\right|Th0)\&IL18\&IL12))\&!((IFNg\&({\bigcap }_{i=1}^{downreg\_cyt=4}{TGFb}^{t-i}\left|{\bigcap }_{i=1}^{downre{g}_{cyt}=4}{IL10}^{t-i}\right|Th2)$

IL23 = (MACR & IL1b) | DC

$IL22=Th17\left|\right(NK\&\left(\right(IL18\&IL12\left)\right|IL23\left)\right)|CD4\_NKG2D|\left(\right((IL22\&Th0\&IL21)\&!({\bigcap }_{i=1}^{upreg\_cyt=3}{IL22}^{t-i}\&$ ${\bigcap }_{i=1}^{upreg\_cyt=3}{Th0}^{t-i}\&{\bigcap }_{i=1}^{upreg\_cyt=3}{IL21}^{t-i}\left)\right)\&!TGFb)$

IL21 = Th17 | ((Th0 & IL6) &! (IL4 | IFNg | TGFb))

$IL17=\left(Th17\right|(Th17\_M\&(LPS\left|MDP\right|PGN\left)\right)\left|\right(CD4\_NKG2D\&(IEC\_MICA\_B|IEC\_ULPB1\_6\left)\right))\&!$ $\left(\right({\bigcap }_{i=1}^{downreg\_cyt=4}{TGFb}^{t-i}\left|{\bigcap }_{i=1}^{downreg\_cyt=4}{IL13}^{t-i}\right)\&IL17)$

IL10 = Treg|(Th2 &! IL23)|((TLR2 & NFkB) &! (MACR & IFNg)) | ((MACR & LPS) &! IL4) | (DC & LPS)

$Th17=\left(\right(\mathrm{T}\mathrm{h}0\&\left(\mathrm{I}\mathrm{L}1\mathrm{b}\right|\mathrm{I}\mathrm{L}23\left|\mathrm{I}\mathrm{L}6\right)\left)\right|\left(\right(\mathrm{T}\mathrm{h}17\&\mathrm{I}\mathrm{L}23)\&!({\bigcap }_{\mathrm{i}=1}^{\mathrm{u}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{g}\_cell=2}{\mathrm{T}\mathrm{h}17}^{\mathrm{t}-\mathrm{i}}\&{\bigcap }_{\mathrm{i}=1}^{\mathrm{u}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{g}\_cell=2}{\mathrm{I}\mathrm{l}23}^{\mathrm{t}-\mathrm{i}}\left)\right))\&!$ $\left(\right({\bigcup }_{i=1}^{downreg\_cell=2}{TGFb}^{t-i}\left|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{L}\mathbf{12}}^{\mathit{t}-\mathit{i}}|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{L}\mathbf{4}}^{\mathit{t}-\mathit{i}}\right|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{F}\mathit{N}\mathit{g}}^{\mathit{t}-\mathit{i}}|$ ${\bigcup }_{i=1}^{downreg\_cell=2}{Treg}^{t-i})\&\mathrm{T}\mathrm{h}17)$

Th17_M = ((Th0_M & (PGN | MDP | LPS)) & ((IL1b & IL6) | IL23 | IL2)) | Th17_M

$Th1=\left(Th0\&\left((IL12\right|IFNg\right|IL18\left)\right|(DC\&IL12\&IL23\&LPS)\left)\right)\&!\left(\right(({\bigcup }_{i=1}^{downreg\_cell=2}{IL17}^{t-i}\&$ ${\bigcup }_{i=1}^{downreg\_cell=2}{IL12}^{t-i}\left)\right|\left({\bigcup }_{i=1}^{downreg\_cell=2}{Treg}^{t-i}\right|{\bigcup }_{i=1}^{downreg\_cell=2}{Th2}^{t-i}\left|{\bigcup }_{i=1}^{downreg\_cell=2}{TGFb}^{t-i}\right|$ ${\bigcup }_{i=1}^{downreg\_cell=2}{IL10}^{t-i}\left|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{L}\mathbf{4}}^{\mathit{t}-\mathit{i}}\right))\&\mathit{T}\mathit{h}\mathbf{1})$

$Th2=(\mathit{T}\mathit{h}\mathbf{0}\&(\mathit{I}\mathit{L}\mathbf{10}\left|\right(\left(\mathit{I}\mathit{L}\mathbf{18}\&\mathit{I}\mathit{L}\mathbf{4}\right)\&!\mathit{I}\mathit{L}\mathbf{12}\left)\right)\left|\right(\left(\mathit{T}\mathit{h}\mathbf{2}\&\mathit{I}\mathit{L}\mathbf{4}\right)\&!({\bigcap }_{\mathit{i}=\mathbf{1}}^{\mathit{u}\mathit{p}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{T}\mathit{h}\mathbf{2}}^{\mathit{t}-\mathit{i}}\&{\bigcap }_{\mathit{i}=\mathbf{1}}^{\mathit{u}\mathit{p}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{L}\mathbf{4}}^{\mathit{t}-\mathit{i}})\left)\right)\&!$ $\left(\right({\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{T}\mathit{r}\mathit{e}\mathit{g}}^{\mathit{t}-\mathit{i}}\left|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{I}\mathit{F}\mathit{N}\mathit{g}}^{\mathit{t}-\mathit{i}}\right|{\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}\mathit{g}\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}=\mathbf{2}}{\mathit{T}\mathit{G}\mathit{F}\mathit{b}}^{\mathit{t}-\mathit{i}})\&\mathit{T}\mathit{h}\mathbf{2})$

IL4 = Th2

IL15 = (FIBROBLAST & (MDP | LPS | PGN)) | (MACR & (LPS | IFNg))

$IL12=\left(\right(\left(\right(MACR\left|DC\right)\&\left(LPS\right|PGN)\&IFNg)\&!(IL12\&{\bigcup }_{i=1}^{downreg\_cyt=4}{TNFa}^{t-i})\left)\right|(DC\&IL1b)|$ $(IL12\&(IL13\left|IL4\right)\left)\right)\&!\left(\right({\bigcup }_{i=1}^{downreg\_cyt=4}{TGFb}^{t-i}\left|{\bigcup }_{i=1}^{downreg\_cyt=4}{IL10}^{t-i}\right)\&IL12)$

IL13 = Th2

$Treg=({\bigcap }_{i=1}^{{THR\_Th0\_Treg}_{=3}}{Th0}^{t-i}\&(TGFb\left|\mathit{T}\mathit{L}\mathit{R}\mathbf{2}\right))\&!(\left({\bigcup }_{i=1}^{downreg\_cell=2}{IL6}^{t-i}\right|{\bigcup }_{i=1}^{downreg\_cell=2}{IL21}^{t-i}|$ ${\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}{\mathit{g}}_{\_\mathit{c}\mathit{e}\mathit{l}\mathit{l}}=\mathbf{2}}{\mathit{I}\mathit{L}\mathbf{23}}^{\mathit{t}-\mathit{i}}\left|{\bigcup }_{i=1}^{downreg\_cell=2}{Th17}^{t-i}|{\bigcup }_{i=1}^{downreg\_cell=2}{IL22}^{t-i}\right|{\bigcup }_{i=1}^{downreg\_cell=2}{TNFa}^{t-i})\&Treg)$

$NK=\left(IL15\right|IL2\left|IL12\right|IL23\left|\right(\mathit{I}\mathit{L}\mathbf{18}\&\mathit{I}\mathit{L}\mathbf{10}\left)\right)\&!({\bigcup }_{\mathit{i}=\mathbf{1}}^{\mathit{d}\mathit{o}\mathit{w}\mathit{n}\mathit{r}\mathit{e}{\mathit{g}}_{\mathit{c}\mathit{e}\mathit{l}\mathit{l}}=\mathbf{2}}{\mathit{T}\mathit{r}\mathit{e}\mathit{g}}^{\mathit{t}-\mathit{i}}\&\mathit{N}\mathit{K})$

$DEF=IL22\left|IL17\right|{\bigcap }_{i=1}^{THR\_NOD2\_DEF=3}{NOD2}^{t-i}$

IL2 = Th0 | (Th0_M & (MDP | LPS | PGN)) | DC

$MACR=\left(NFkB\right|\left(\right(MACR\&\left(IFNg\right|IL15\left)\right)\&!({\bigcap }_{i=1}^{upreg\_cell=2}{NFkB}^{t-i}\&({\bigcap }_{i=1}^{upreg\_cell=2}{IFNg}^{t-i}|$ ${\bigcap }_{i=1}^{upreg\_cell=2}{IL15}^{t-i}\left)\right)\left)\right)\&!({\bigcup }_{i=1}^{downreg\_cell=2}{IL10}^{t-i}\&MACR)$

$DC=NFkB\&!({\bigcup }_{i=1}^{downreg\_cell=2}{IL10}^{t-i}\&DC)$

$IEC\_MICA\_B=\left(\right(LPS\left|MDP\right|PGN\left)\right|(IEC\_MICA\_B\&TNFa)\&!({\bigcap }_{i=1}^{upreg\_rec=2}{IEC\_MICA\_B}^{t-i}\&$ ${\bigcap }_{i=1}^{upreg\_rec=2}{TNFa}^{t-i}\left)\right)\&!TGFb$

IEC_ULPB1_6 = CD8_NKG2D & (LPS|MDP|PGN)

$CD8\_NKG2D=\left(LPS\right|PGN\left|MDP\right)\&!\left(\right({\bigcap }_{i=1}^{THR\_LIGANDS\_NKG2D=3}{IEC\_MICA\_B}^{t-i}|{\bigcap }_{i=1}^{THR\_LIGANDS\_NKG2D=3}{IEC\_ULPB\_1\_6}^{t-i}$ $\left|\right({\bigcup }_{i=1}^{downreg\_cell=2}{IL21}^{t-i}\&{\bigcup }_{i=1}^{downreg\_cell=2}{IL2}^{t-i}\left)\right)\&CD8\_NKG2D)$

$NK\_NKG2D=\left(LPS\right|PGN\left|MDP\right)\&!\left({\bigcup }_{i=1}^{downreg\_cell=2}{TGFb}^{t-i}\right|{\bigcap }_{i=1}^{TH{R\_}_{LIGANDS\_NKG2D}=3}{IEC\_MICA\_B}^{t-i}|$ ${\bigcap }_{i=1}^{THR\_LIGANDS\_NKG2D=3}{IEC\_ULPB\_1\_6}^{t-i}\left|\right({\bigcup }_{i=1}^{downreg\_cell=2}{IL21}^{t-i}\&{\bigcup }_{i=1}^{downreg\_cell=2}{IL12}^{t-i}\left)\right)\&NK\_NKG2D)$

$CD4\_NKG2D=\left(LPS\right|PGN\left|MDP\right|(CD4\_NKG2D\&(IL15\left|TNFa\right))\&!({\bigcap }_{i=1}^{upreg\_rec=2}{CD4\_NKG2D}^{t-i}$ $\&\left({\bigcap }_{i=1}^{upreg\_rec=2}{IL15}^{t-i}\right|{\bigcap }_{i=1}^{upreg\_rec=2}{TNFa}^{t-i}\left)\right))\&!(\left({\bigcup }_{i=1}^{downreg\_cell=2}{IL10}^{t-i}\right|$ ${\bigcap }_{i=1}^{TH{R\_}_{LIGANDS\_NKG2D}=3}{IEC\_MICA\_B}^{t-i}\left|{\bigcap }_{i=1}^{THR\_LIGANDS\_NKG2D=3}{IEC\_ULPB\_1\_6}^{t-i}\right)\&CD4\_NKG2D\left)\right)$

$FIBROBLAST=\left(\right(MACR\&\left(IL4\right|IL13\left|TGFb\right)\left)\right|IL2)\&!(\left({\bigcup }_{i=1}^{downreg\_cell=2}{IFNg}^{t-i}\right|{\bigcup }_{i=1}^{downreg\_cell=2}{IL12}^{t-i})$ $\&FIBROBLAST)$

PERFOR = NK | NK_NKG2D

GRANZB = CD8_NKG2D | NK | NK_NKG2D | (DC &! (LPS | PGN))

OUTPUT NODE

MMPs = (MACR & TNFa) | (FIBROBLAST & (IL21 | IL17 | IL1b | TNFa))

Bold text within Boolean equations indicates that the information belongs to animal data