## Cell lines and media

RPE1 cells were grown in DMEM/F12 containing 10% v/v FBS, penicillin-streptomycin, and L-glutamate (2 mM). RPE1 cells were stably transfected by mXFPe-IL-27Rα (= 'RPE1 IL-27Rα'), mutants and the chimeric construct by PEI method according to standard protocols. Using G418 selection (0.6 mg/ml) individual clones were selected, proliferated and characterized. RPE1 cells previously knocked out for endogenous GP130 (*Martinez-Fabregas et al., 2019*) were stably transfected as above with mXFPm-GP130 (= 'RPE1 10x[GP130]'%).

## Flow cytometry staining and antibodies

For measuring dose-response curves of STAT1/3 phosphorylation (either Th-1 cells or RPE1 clones), 96-well plated were prepared with 50 µl of cell suspensions at 2 × 10⁶ cells/ml/well for Th-1 and 2 × 10⁵ cells/ml/well for RPE1. The latter were detached using Accutase (Sigma). Cells were stimulated with a set of different concentrations to obtain dose-response curves. To this end, cells were stimulated for 15 min at 37°C with the respective cytokines followed by PFA fixation (2%) for 15 min at RT.

For kinetic experiments, cell suspensions were stimulated with a defined, saturating concentration of cytokines (10 nM IL-27, 20 nM HypIL-6, 100 nM wt-IL-6) in a reverse order so that all cell suspensions were PFA-fixed (2%) simultaneously. For pSTAT1/3 kinetic experiments at JAK inhibition, Tofacitinib (2 µM, Stratech, #S2789-SEL) was added after 15 min of stimulation and cells were PFA-fixed in correct order.

After fixation (15 min at RT), cells were spun down at 300 g for 6 min at 4°C. Cell pellets were resuspended and permeabilized in ice-cold methanol and kept for 30 min on ice. After permeabilization cells were fluorescently barcoded according to Krutzik and Nolan, 2006. In brief: using two NHS-dyes (PacificBlue, #10163, DyLight800, #46421, Thermo Scientific), individual wells were stained with a combination of different concentrations of these dyes. After barcoding, cells are pooled and stained with anti-pSTAT1<sup>Alexa647</sup> (Cell Signaling Technologies, #8009) and anti-pSTAT3<sup>Alexa488</sup> (Biolegend, #651006) at a 1:100 dilution in PBS + 0.5% BSA for 1 hr at RT. T-cells were also stained with anti-CD8<sup>AlexaFlour700</sup> (1:120, Biolegend, #300920), anti-CD4<sup>PE</sup> (1:120, Biolegend, #357404), anti-CD3<sup>BrilliantViolet510</sup> (1:100, Biolegend, #300448). Cells were analyzed at the flow cytometer (Beckman Coulter, Cytoflex S) and individual cell populations were identified by their barcoding pattern (supp. Fig 1b). Mean fluorescence intensity (MFI) of pSTAT1<sup>647</sup> and pSTAT3<sup>488</sup> was measured for all individual cell populations.

For measuring total STAT levels, methanol-permeabilized cells were stained with anti-STAT1<sup>Alexa647</sup> (1:70, Biolegend, #558560) or anti-STAT3<sup>APC</sup> (1:50, Biolegend, #560392). Total IRF1 levels methanol-permeabilized cells were stained with anti-IRF1<sup>Alexa647</sup> (1:50, Biolegend, #14105). For measuring cell surface levels of GP130, cells were detached with Accutase (Sigma) and stained with anti-GP130<sup>APC</sup> (1:100, Biolegend, #362006) for 1 hr on ice. For measuring cell surface levels of mXFPe-IL-27Rα variants, cells were detached with Accutase (Sigma) and stained with αGFP-enNB<sup>Dy647</sup> (10 nM) for 30 min on ice.

## RNA transcriptome sequencing

Human Th-1 cells from three donors each (StemCell Technologies) were cultivated and stimulated as described in above. Cells were washed in Hank's balanced salt solution (HBSS, Gibco) and snap frozen for storage. RNA was isolated using the RNeasy Kit (Qiagen) according to manufacturer's protocol. All RNA 260/280 ratios were above 1.9. Of each sample, 1 µg of RNA was used. Transcriptomic analysis was done by Novogene as follows. Sequencing libraries were generated using NEBNext UltraTM RNA Library Prep Kit for Illumina (NEB, USA) following manufacturer's recommendations and index codes were added to attribute sequences to each sample. Briefly, mRNA was purified from total RNA using poly-T oligo-attached magnetic beads. Fragmentation was carried out using divalent cations under elevated temperature in NEBNext First Strand Synthesis Reaction Buffer (5X). First strand cDNA was synthesized using random hexamer primer and M-MuLV Reverse Transcriptase (RNase H-). Second strand cDNA synthesis was subsequently performed using DNA Polymerase I and RNase H. Remaining overhangs were converted into blunt ends via exonuclease/ polymerase activities. After adenylation of 3' ends of DNA fragments, NEBNext Adaptor with hairpin loop structure were ligated to prepare for hybridization. In order to select cDNA fragments of preferentially 150 ~ 200 bp in length, the library fragments were purified with AMPure XP system
## Cell lines and media

RPE1 cells were grown in DMEM/F12 containing 10% v/v FBS, penicillin-streptomycin, and L-glutamate (2 mM). RPE1 cells were stably transfected by mXFPe-IL-27Rα (= 'RPE1 IL-27Rα'), mutants and the chimeric construct by PEI method according to standard protocols. Using G418 selection (0.6 mg/ml) individual clones were selected, proliferated and characterized. RPE1 cells previously knocked out for endogenous GP130 (Martinez-Fabregas et al., 2019) were stably transfected as above with mXFPm-GP130 (= 'RPE1 10x[GP130]').

## Flow cytometry staining and antibodies

For measuring dose-response curves of STAT1/3 phosphorylation (either Th-1 cells or RPE1 clones), 96-well plated were prepared with 50 µl of cell suspensions at 2 × 10⁶ cells/ml/well for Th-1 and 2 × 10⁵ cells/ml/well for RPE1. The latter were detached using Accutase (Sigma). Cells were stimulated with a set of different concentrations to obtain dose-response curves. To this end, cells were stimulated for 15 min at 37°C with the respective cytokines followed by PFA fixation (2%) for 15 min at RT.

For kinetic experiments, cell suspensions were stimulated with a defined, saturating concentration of cytokines (10 nM IL-27, 20 nM HypIL-6, 100 nM wt-IL-6) in a reverse order so that all cell suspensions were PFA-fixed (2%) simultaneously. For pSTAT1/3 kinetic experiments at JAK inhibition, Tofacitinib (2 µM, Stratech, #S2789-SEL) was added after 15 min of stimulation and cells were PFA-fixed in correct order.

After fixation (15 min at RT), cells were spun down at 300 g for 6 min at 4°C. Cell pellets were resuspended and permeabilized in ice-cold methanol and kept for 30 min on ice. After permeabilization cells were fluorescently barcoded according to Krutzik and Nolan, 2006. In brief: using two NHS-dyes (PacificBlue, #10163, DyLight800, #46421, Thermo Scientific), individual wells were stained with a combination of different concentrations of these dyes. After barcoding, cells are pooled and stained with anti-pSTAT1<sup>Alexa647</sup> (Cell Signaling Technologies, #8009) and anti-pSTAT3<sup>Alexa488</sup> (Biolegend, #651006) at a 1:100 dilution in PBS + 0.5% BSA for 1 hr at RT. T-cells were also stained with anti-CD8<sup>AlexaFlour700</sup> (1:120, Biolegend, #300920), anti-CD4<sup>PE</sup> (1:120, Biolegend, #357404), anti-CD3<sup>BrilliantViolet510</sup> (1:100, Biolegend, #300448). Cells were analyzed at the flow cytometer (Beckman Coulter, Cytoflex S) and individual cell populations were identified by their barcoding pattern (supp. Fig 1b). Mean fluorescence intensity (MFI) of pSTAT1<sup>647</sup> and pSTAT3<sup>488</sup> was measured for all individual cell populations.

For measuring total STAT levels, methanol-permeabilized cells were stained with anti-STAT1<sup>Alexa647</sup> (1:70, Biolegend, #558560) or anti-STAT3<sup>APC</sup> (1:50, Biolegend, #560392). Total IRF1 levels methanol-permeabilized cells were stained with anti-IRF1<sup>Alexa647</sup> (1:50, Biolegend, #14105). For measuring cell surface levels of GP130, cells were detached with Accutase (Sigma) and stained with anti-GP130<sup>APC</sup> (1:100, Biolegend, #362006) for 1 hr on ice. For measuring cell surface levels of mXFPe-IL-27Rα variants, cells were detached with Accutase (Sigma) and stained with αGFP-enNB<sup>Dy647</sup> (10 nM) for 30 min on ice.

## RNA transcriptome sequencing

Human Th-1 cells from three donors each (StemCell Technologies) were cultivated and stimulated as described in above. Cells were washed in Hank's balanced salt solution (HBSS, Gibco) and snap frozen for storage. RNA was isolated using the RNeasy Kit (Qiagen) according to manufacturer's protocol. All RNA 260/280 ratios were above 1.9. Of each sample, 1 µg of RNA was used. Transcriptomic analysis was done by Novogene as follows. Sequencing libraries were generated using NEBNext UltraTM RNALibrary Prep Kit for Illumina (NEB, USA) following manufacturer's recommendations and index codes were added to attribute sequences to each sample. Briefly, mRNA was purified from total RNA using poly-T oligo-attached magnetic beads. Fragmentation was carried out using divalent cations under elevated temperature in NEBNext First StrandSynthesis Reaction Buffer (5X). First strand cDNA was synthesized using random hexamer primer and M-MuLV Reverse Transcriptase (RNase H-). Second strand cDNA synthesis was subsequently performed using DNA Polymerase I and RNase H. Remaining overhangs were converted into blunt ends via exonuclease/ polymerase activities. After adenylation of 3' ends of DNA fragments, NEBNext Adaptor with hairpin loop structure were ligated to prepare for hybridization. In order to select cDNA fragments of preferentially 150 ~ 200 bp in length, the library fragments were purified with AMPure XP system
(Beckman Coulter, Beverly, USA). Then 3 µl USER Enzyme (NEB, USA) was used with size-selected, adaptor-ligated cDNA at 37°C for 15 min followed by 5 min at 95°C before PCR. Then PCR was performed with Phusion High-Fidelity DNA polymerase, Universal PCR primers and Index (X) Primer. At last, PCR products were purified (AMPure XP system) and library quality was assessed on the Agilent Bioanalyzer 2100 system.

## RNA sequencing data analysis

Primary data analysis for quality control, mapping to reference genome and quantification was conducted by Novogene as outlined below.

**Quality control:** Raw data (raw reads) of FASTQ format were firstly processed through in-house scripts. In this step, clean data (clean reads) were obtained by removing reads containing adapter and poly-N sequences and reads with low quality from raw data. At the same time, Q20, Q30 and GC content of the clean data were calculated. All the downstream analyses were based on the clean data with high quality.

**Mapping to reference genome:** Reference genome and gene model annotation files were downloaded from genome website browser (NCBI/UCSC/Ensembl) directly. Paired-end clean reads were mapped to the reference genome using HISAT2 software. HISAT2 uses a large set of small GFM indexes that collectively cover the whole genome. These small indexes (called local indexes), combined with several alignment strategies, enable rapid and accurate alignment of sequencing reads.

**Quantification:** HTSeq was used to count the read numbers mapped of each gene, including known and novel genes. And then RPKM of each gene was calculated based on the length of the gene and reads count mapped to this gene. RPKM, (Reads Per Kilobase of exon model per Million mapped reads), considers the effect of sequencing depth and gene length for the reads count at the same time and is currently the most commonly used method for estimating gene expression levels.

For each identified gene, the fold change was calculated by the ratio of cytokine stimulated/unstimulated expression levels within each donor and an unpaired, two-tailed t test was applied to calculate p values. Genes were considered to be significantly altered if: p value ≤ 0.05, and log₂ fold change ≥+1 or ≤-1. Genes with an RPKM of less than one in two or more donors were excluded from analysis so as to remove genes with abundance near detection limit. Genes without annotated function were also removed. Functional annotation of genes (KEGG pathways, GO terms) was done using DAVID Bioinformatics Resource functional annotation tool (Huang et al., 2009a; Huang et al., 2009b). Clustered heatmap was generated using R Studio PHeatmap package.

## siRNA-mediated knockdown of IRF1 in RPE1 cells

A set of four IRF1-siRNAs were purchased from Dharmacon and tested individually to determine levels of knockdown achieved. The siRNA providing the highest level of IRF1. knockdown (Horizon, LQ-011704-00-0005, siRNA #2: UGAACUCCCUGCCAGAUAU) were subsequently used in all the experiments. RPE1 IL-27Rα cells were plated in six-well dishes (0.4 × 10⁶ cells per well) and transfected the next day with IRF1-siRNA or control-GAPDH siRNA (Horizon, D-001830-10-05) (Dharmacon) using DharmaFect one transfection reagent (Dharmacon) following the manufacturer's instructions for 24 hr. At different timepoints of IL-27 (2 nM) or HypIL-6 (10 nM) stimulation, samples were collected from each one six-well. Cells were trypsinized and each sample was spun down and pellets snap-frozen in liquid nitrogen for subsequent RNA isolation (90%) or PFA-fixed for total IRF1 staining (10%) by flow cytometry.

## Real-time quantitative PCR

Cells were subject to RNA isolation using the Qiagen RNeasy kit. RNA (100 ng) was reverse transcribed to complementary DNA (cDNA) using an iScript cDNA synthesis kit (BioRad, #1708890), which was used as template for quantitative PCR. PowerTrack SYBR Green Master Mix (Takara, #A46109) was used for the reaction with the following primers:

<table><thead><tr><td>Target</td><td>For</td><td>Rev</td><td>Size</td></tr></thead><tbody><tr><td>β-actin</td><td>CATGTACGTTGCTATCCAGGC</td><td>CTCCTTAATGTCACGCACGAT</td><td>250 bp</td></tr></tbody></table>

*Continued on next page*
(Beckman Coulter, Beverly, USA). Then 3 µl USER Enzyme (NEB, USA) was used with size-selected, adaptor-ligated cDNA at 37°C for 15 min followed by 5 min at 95°C before PCR. Then PCR was performed with Phusion High-Fidelity DNA polymerase, Universal PCR primers and Index (X) Primer. At last, PCR products were purified (AMPure XP system) and library quality was assessed on the Agilent Bioanalyzer 2100 system.

## RNA sequencing data analysis

Primary data analysis for quality control, mapping to reference genome and quantification was conducted by Novogene as outlined below.

**Quality control:** Raw data (raw reads) of FASTQ format were firstly processed through in-house scripts. In this step, clean data (clean reads) were obtained by removing reads containing adapter and poly-N sequences and reads with low quality from raw data. At the same time, Q20, Q30 and GC content of the clean data were calculated. All the downstream analyses were based on the clean data with high quality.

**Mapping to reference genome:** Reference genome and gene model annotation files were downloaded from genome website browser (NCBI/UCSC/Ensembl) directly. Paired-end clean reads were mapped to the reference genome using HISAT2 software. HISAT2 uses a large set of small GFM indexes that collectively cover the whole genome. These small indexes (called local indexes), combined with several alignment strategies, enable rapid and accurate alignment of sequencing reads.

**Quantification:** HTSeq was used to count the read numbers mapped of each gene, including known and novel genes. And then RPKM of each gene was calculated based on the length of the gene and reads count mapped to this gene. RPKM, (Reads Per Kilobase of exon model per Million mapped reads), considers the effect of sequencing depth and gene length for the reads count at the same time and is currently the most commonly used method for estimating gene expression levels.

For each identified gene, the fold change was calculated by the ratio of cytokine stimulated/unstimmulated expression levels within each donor and an unpaired, two-tailed t test was applied to calculate p values. Genes were considered to be significantly altered if: p value ≤ 0.05, and log₂ fold change ≥+1 or ≤-1. Genes with an RPKM of less than one in two or more donors were excluded from analysis so as to remove genes with abundance near detection limit. Genes without annotated function were also removed. Functional annotation of genes (KEGG pathways, GO terms) was done using DAVID Bioinformatics Resource functional annotation tool (Huang et al., 2009a; Huang et al., 2009b). Clustered heatmap was generated using R Studio PHeatmap package.

## siRNA-mediated knockdown of IRF1 in RPE1 cells

A set of four IRF1-siRNAs were purchased from Dharmacon and tested individually to determine levels of knockdown achieved. The siRNA providing the highest level of IRF1. knockdown (Horizon, LQ-011704-00-0005, siRNA #2: UGAACUCCCUGCCAGAUAU) were subsequently used in all the experiments. RPE1 IL-27Rα cells were plated in six-well dishes (0.4 × 10⁶ cells per well) and transfected the next day with IRF1-siRNA or control-GAPDH siRNA (Horizon, D-001830-10-05) (Dharmacon) using DharmaFect one transfection reagent (Dharmacon) following the manufacturer's instructions for 24 hr. At different timepoints of IL-27 (2 nM) or HypIL-6 (10 nM) stimulation, samples were collected from each one six-well. Cells were trypsinized and each sample was spun down and pellets snap-frozen in liquid nitrogen for subsequent RNA isolation (90%) or PFA-fixed for total IRF1 staining (10%) by flow cytometry.

## Real-time quantitative PCR

Cells were subject to RNA isolation using the Qiagen RNeasy kit. RNA (100 ng) was reverse transcribed to complementary DNA (cDNA) using an iScript cDNA synthesis kit (BioRad, #1708890), which was used as template for quantitative PCR. PowerTrack SYBR Green Master Mix (Takara, #A46109) was used for the reaction with the following primers:

<table><thead><tr><td>Target</td><td>For</td><td>Rev</td><td>Size</td></tr></thead><tbody><tr><td>β-actin</td><td>CATGTACGTTGCTATCCAGGC</td><td>CTCCTTAATGTCACGCACGAT</td><td>250 bp</td></tr></tbody></table>

*Continued on next page*
Continued

<table><thead><tr><td>Target</td><td>For</td><td>Rev</td><td>Size</td></tr></thead><tbody><tr><td>STAT1</td><td>CTAGTGGAGTGGAAGCGGAG</td><td>CACCACAAACGAGCTCTGAA</td><td>252 bp</td></tr><tr><td>GBP5</td><td>TCCTCGGATTATTGCTCGGC</td><td>CCTTTGCGCTTCAGCCTTTT</td><td>309 bp</td></tr><tr><td>OAS1</td><td>GAAGGCAGCTCACGAAACC</td><td>AGGCCTCAGCCTCTTGTG</td><td>114 bp</td></tr><tr><td>SOCS3</td><td>GTCCCCCAGAAGAGCCTATTA</td><td>TTGACGGTCTTCCGACAGAGAT</td><td>118</td></tr></tbody></table>

β-actin was used as housekeeping gene for normalization. Each siRNA knockdown experiment was performed in four replicates with each sample for qPCR being done in two technical replicates.

## Mathematical models

We developed two new mathematical models, making use of ordinary differential equations (ODEs), for the initial steps of cytokine-receptor binding, dimer formation and signal activation by HypIL-6 and IL-27, respectively; namely, a set of ODEs for the HypIL-6 system and a separate one for the IL-27 system (see Supplementary material 1 for the set of ODEs describing each model). These ODEs describe the rate of change of the concentration for each molecular species considered in the receptor-ligand systems (HypIL-6 and IL-27) over time. By solving these ODEs, a time-course for the concentration of total (free and bound) phosphorylated STAT1 and STAT3 can be obtained and compared to the experimental data (Supp. Fig. 5c and 5d). The HypIL-6 and IL-27 mathematical models differ due to the reactions involved in the formation of the signaling dimer for each cytokine. Under stimulation with HypIL-6, two HypIL-6 bound GP130 monomers are required to form the homodimer (Supp. Fig. 4b), Figure 2—figure supplement 1. Schematic model of involved reactions and parameters for IL-27 and HypIL-6 receptor activation. whereas under IL-27 stimulation, we assume that IL-27 binds to the IL-27Rα chain and not to GP130 (Supp. Fig. 4c) and hence the heterodimer is comprised of an IL-27 molecule bound to an IL-27Rα monomer and one GP130 chain. In the mathematical models, we assume that upon formation of the dimers (homo- or heterodimer), these receptor chains become immediately phosphorylated. The models do not consider JAK molecules explicitly. We are assuming that these molecules are constitutively bound to their corresponding receptor chains and that they phosphorylate immediately upon receptor phosphorylation (dimer formation). After the formation of the dimer, which we denote by $D_6$ or $D_{27}$, formed by HypIL-6 or IL-27 respectively, the biochemical reactions included in each mathematical model are similar, and are summarized as follows. Table 2 provides a description of the rates for each reaction considered in each (and both) mathematical model(s). In what follows we assume mass action kinetics for all the reactions. A free cytoplasmic unphosphorylated STAT1 or STAT3 molecule can bind to either receptor chain in the dimer, provided that the intracellular tyrosine residue of the receptor in the dimer is free (Supp. Fig. 4d and 4e). The STAT1 or STAT3 molecule can subsequently dissociate from the receptor chain in the dimer or can become phosphorylated (with rate $q$) whilst bound to the dimer. We have assumed that the rate of STAT1 or STAT3 phosphorylation when bound does not depend on the STAT type (1 or 3) or on the receptor chain (Supp. Fig. 4d and 4e). Phosphorylated STAT1 (pSTAT1) and STAT3 (pSTAT3) molecules can dissociate from the dimer. Once free in the cytoplasm, they can then dephosphorylate (Supp. Fig. 4h). We have assumed that this rate of STAT dephosphorylation only depends on the concentration of the respective pSTAT type. We note that no allostery has been considered in the models and hence, phosphorylated and unphosphorylated STAT molecules dissociate from the receptor with the same rate (Supp. Fig. 4d and 4e). Finally, any molecular species containing receptor molecules can be lost from the system, due to internalization or degradation processes, via one of two hypothesized mechanisms (Supp. Fig. 4f and 4g):

* hypothesis 1 ($H_1$): receptors (free or bound, phosphorylated or unphosphorylated) are internalized/degraded with a rate proportional to the concentration of the species in which they are contained, or

* hypothesis 2 ($H_2$): receptors (free or bound, phosphorylated or unphosphorylated) are internalized/degraded with a rate proportional to the product of the concentration of the species in which they are contained and the sum of the concentrations of free cytoplasmic phosphorylated STAT1 and STAT3.
Continued

<table><thead><tr><td>Target</td><td>For</td><td>Rev</td><td>Size</td></tr></thead><tbody><tr><td>STAT1</td><td>CTAGTGGAGTGGAAGCGGAG</td><td>CACCACAAACGAGCTCTGAA</td><td>252 bp</td></tr><tr><td>GBP5</td><td>TCCTCGGATTATTGCTCGGC</td><td>CCTTTGCGCTTCAGCCTTTT</td><td>309 bp</td></tr><tr><td>OAS1</td><td>GAAGGCAGCTCACGAAACC</td><td>AGGCCTCAGCCTCTTGTG</td><td>114 bp</td></tr><tr><td>SOCS3</td><td>GTCCCCCAGAAGAGCCTATTA</td><td>TTGACGGTCTTCCGACAGAGAT</td><td>118</td></tr></tbody></table>

β-actin was used as housekeeping gene for normalization. Each siRNA knockdown experiment was performed in four replicates with each sample for qPCR being done in two technical replicates.

## Mathematical models

We developed two new mathematical models, making use of ordinary differential equations (ODEs), for the initial steps of cytokine-receptor binding, dimer formation and signal activation by HypIL-6 and IL-27, respectively; namely, a set of ODEs for the HypIL-6 system and a separate one for the IL-27 system (see Supplementary material 1 for the set of ODEs describing each model). These ODEs describe the rate of change of the concentration for each molecular species considered in the receptor-ligand systems (HypIL-6 and IL-27) over time. By solving these ODEs, a time-course for the concentration of total (free and bound) phosphorylated STAT1 and STAT3 can be obtained and compared to the experimental data (Supp. Fig. 5c and 5d). The HypIL-6 and IL-27 mathematical models differ due to the reactions involved in the formation of the signaling dimer for each cytokine. Under stimulation with HypIL-6, two HypIL-6 bound GP130 monomers are required to form the homodimer (Supp. Fig. 4b), Figure 2—figure supplement 1. Schematic model of involved reactions and parameters for IL-27 and HypIL-6 receptor activation. whereas under IL-27 stimulation, we assume that IL-27 binds to the IL-27Rα chain and not to GP130 (Supp. Fig. 4c) and hence the heterodimer is comprised of an IL-27 molecule bound to an IL-27Rα monomer and one GP130 chain. In the mathematical models, we assume that upon formation of the dimers (homo- or heterodimer), these receptor chains become immediately phosphorylated. The models do not consider JAK molecules explicitly. We are assuming that these molecules are constitutively bound to their corresponding receptor chains and that they phosphorylate immediately upon receptor phosphorylation (dimer formation). After the formation of the dimer, which we denote by $D_6$ or $D_{27}$, formed by HypIL-6 or IL-27 respectively, the biochemical reactions included in each mathematical model are similar, and are summarized as follows. Table 2 provides a description of the rates for each reaction considered in each (and both) mathematical model(s). In what follows we assume mass action kinetics for all the reactions. A free cytoplasmic unphosphorylated STAT1 or STAT3 molecule can bind to either receptor chain in the dimer, provided that the intracellular tyrosine residue of the receptor in the dimer is free (Supp. Fig. 4d and 4e). The STAT1 or STAT3 molecule can subsequently dissociate from the receptor chain in the dimer or can become phosphorylated (with rate $q$) whilst bound to the dimer. We have assumed that the rate of STAT1 or STAT3 phosphorylation when bound does not depend on the STAT type (1 or 3) or on the receptor chain (Supp. Fig. 4d and 4e). Phosphorylated STAT1 (pSTAT1) and STAT3 (pSTAT3) molecules can dissociate from the dimer. Once free in the cytoplasm, they can then dephosphorylate (Supp. Fig. 4h). We have assumed that this rate of STAT dephosphorylation only depends on the concentration of the respective pSTAT type. We note that no allostery has been considered in the models and hence, phosphorylated and unphosphorylated STAT molecules dissociate from the receptor with the same rate (Supp. Fig. 4d and 4e). Finally, any molecular species containing receptor molecules can be lost from the system, due to internalization or degradation processes, via one of two hypothesized mechanisms (Supp. Fig. 4f and 4g):

* hypothesis 1 ($H_1$): receptors (free or bound, phosphorylated or unphosphorylated) are internalized/degraded with a rate proportional to the concentration of the species in which they are contained, or

* hypothesis 2 ($H_2$): receptors (free or bound, phosphorylated or unphosphorylated) are internalized/degraded with a rate proportional to the product of the concentration of the species in which they are contained and the sum of the concentrations of free cytoplasmic phosphorylated STAT1 and STAT3.
<table><caption>**Table 2.** Parameter mathematical notation, description, and units, where $i \in \{1, 3\}$ so that STAT $i$ corresponds to STAT1 or STAT3.</caption><thead><tr><th>Parameter</th><th>Description</th><th>Unit</th></tr></thead><tbody><tr><td>r<sub>1,6</sub><sup>+</sup>, r<sub>1,27</sub><sup>+</sup></td><td>Rate of receptor-ligand binding</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>r<sub>1,6</sub><sup>-</sup>, r<sub>1,27</sub><sup>-</sup></td><td>Rate of receptor-ligand dissociation</td><td>s<sup>-1</sup></td></tr><tr><td>r<sub>2,6</sub><sup>+</sup>, r<sub>2,27</sub><sup>+</sup></td><td>Rate of monomer-monomer binding (or dimer formation)</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>r<sub>2,6</sub><sup>-</sup>, r<sub>2,27</sub><sup>-</sup></td><td>Rate of dimer dissociation</td><td>s<sup>-1</sup></td></tr><tr><td>k<sub>ia</sub><sup>+</sup></td><td>Rate of STATi binding to GP130</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>k<sub>ib</sub><sup>+</sup></td><td>Rate of STATi binding to IL-27Rα</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>k<sub>ia</sub><sup>-</sup></td><td>Rate of STATi dissociating GP130</td><td>s<sup>-1</sup></td></tr><tr><td>k<sub>ib</sub><sup>-</sup></td><td>Rate of STATi dissociating IL-27Rα</td><td>s<sup>-1</sup></td></tr><tr><td>q</td><td>Rate of STATi phosphorylation on a dimer</td><td>s<sup>-1</sup></td></tr><tr><td>d<sub>i</sub></td><td>Rate of pSTATi dephosphorylation</td><td>s<sup>-1</sup></td></tr><tr><td>β<sub>6</sub>, β<sub>27</sub></td><td>Rate of receptor internalization/degradation under hypothesis 1</td><td>s<sup>-1</sup></td></tr><tr><td>γ<sub>6</sub>, γ<sub>27</sub></td><td>Rate of receptor internalization/degradation under hypothesis 2</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>[R<sub>1</sub>(0)]</td><td>Initial concentration of GP130</td><td>nM</td></tr><tr><td>[R<sub>2</sub>(0)]</td><td>Initial concentration of IL-27Rα</td><td>nM</td></tr><tr><td>[S<sub>i</sub>(0)]</td><td>Initial concentration of STATi</td><td>nM</td></tr></tbody></table>

We note that hypothesis 1 assumes that receptor molecules (free or bound, phosphorylated or unphosphorylated) are being internalized/degraded as part of the natural cellular trafficking cycle. Hypothesis 2 is consistent with a potential feedback mechanism, whereby the free cytoplasmic pSTAT molecules would migrate to the nucleus and increase the translation of negative feedback proteins, such as SOCS3, which down-regulate cytokine signaling. Thus, the internalization/degradation rate of receptor molecules (free or bound, phosphorylated or unphosphorylated) under hypothesis 2 increases with the total amount of free cytoplasmic phosphorylated STAT1 and STAT3, to account for this negative feedback on surface receptor expression. A depiction of the reactions in both the HypIL-6 and IL-27 mathematical models and under each hypothesis is given in Supp. Fig. 4 where (b), (d), (f) and (h) describe the HypIL-6 model and (c), (e), (g) and (h) describe the IL-27 model. In this figure, $i \in \{1, 3\}$ so that the reactions shown can involve STAT1 or STAT3. Each reaction arrow has been shown with its rate (above or below the arrow). We note that we assume mass action kinetics for each reaction. The notation for the rate constants and initial molecular concentrations in the models, along with their descriptions and units, are given in **Table 2**.

The HypIL-6 mathematical model was formulated based on biochemical reactions involving the following species:

* $L_6$ = HypIL-6,

* $R_1$ = GP130,

* $C_1$ = GP130 - HypIL-6 monomer,

* $D_6$ = phosphorylated GP130 - HypIL-6 - HypIL-6 - GP130 homodimer,

* $S_1$ = unbound cytoplasmic unphosphorylated STAT1,

* $S_3$ = unbound cytoplasmic unphosphorylated STAT3,

* $D_6 \cdot S_1$ = dimer bound to STAT1,

* $D_6 \cdot S_3$ = dimer bound to STAT3,

* $D_6 \cdot pS_1$ = dimer bound to pSTAT1,

* $D_6 \cdot pS_3$ = dimer bound to pSTAT3,

* $S_1 \cdot D_6 \cdot S_1$ = dimer bound to two molecules of STAT1,

* $pS_1 \cdot D_6 \cdot S_1$ = dimer bound to two molecules of STAT1, one of which is phosphorylated,

* $pS_1 \cdot D_6 \cdot pS_1$ = dimer bound to two molecules of pSTAT1,

* $S_3 \cdot D_6 \cdot S_3$ = dimer bound to two molecules of STAT3,

* $pS_3 \cdot D_6 \cdot S_3$ = dimer bound to two molecules of STAT3, one of which is phosphorylated,

* $pS_3 \cdot D_6 \cdot pS_3$ = dimer bound to two molecules of pSTAT3,
<table><caption>**Table 2.** Parameter mathematical notation, description, and units, where $i \in \{1, 3\}$ so that STAT $i$ corresponds to STAT1 or STAT3.</caption><thead><tr><th>Parameter</th><th>Description</th><th>Unit</th></tr></thead><tbody><tr><td>r<sub>1,6</sub><sup>+</sup>, r<sub>1,27</sub><sup>+</sup></td><td>Rate of receptor-ligand binding</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>r<sub>1,6</sub><sup>-</sup>, r<sub>1,27</sub><sup>-</sup></td><td>Rate of receptor-ligand dissociation</td><td>s<sup>-1</sup></td></tr><tr><td>r<sub>2,6</sub><sup>+</sup>, r<sub>2,27</sub><sup>+</sup></td><td>Rate of monomer-monomer binding (or dimer formation)</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>r<sub>2,6</sub><sup>-</sup>, r<sub>2,27</sub><sup>-</sup></td><td>Rate of dimer dissociation</td><td>s<sup>-1</sup></td></tr><tr><td>k<sub>ia</sub><sup>+</sup></td><td>Rate of STATi binding to GP130</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>k<sub>ib</sub><sup>+</sup></td><td>Rate of STATi binding to IL-27Rα</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>k<sub>ia</sub><sup>-</sup></td><td>Rate of STATi dissociating GP130</td><td>s<sup>-1</sup></td></tr><tr><td>k<sub>ib</sub><sup>-</sup></td><td>Rate of STATi dissociating IL-27Rα</td><td>s<sup>-1</sup></td></tr><tr><td>q</td><td>Rate of STATi phosphorylation on a dimer</td><td>s<sup>-1</sup></td></tr><tr><td>d<sub>i</sub></td><td>Rate of pSTATi dephosphorylation</td><td>s<sup>-1</sup></td></tr><tr><td>β<sub>6</sub>, β<sub>27</sub></td><td>Rate of receptor internalization/degradation under hypothesis 1</td><td>s<sup>-1</sup></td></tr><tr><td>γ<sub>6</sub>, γ<sub>27</sub></td><td>Rate of receptor internalization/degradation under hypothesis 2</td><td>nM<sup>-1</sup>s<sup>-1</sup></td></tr><tr><td>[R<sub>1</sub>(0)]</td><td>Initial concentration of GP130</td><td>nM</td></tr><tr><td>[R<sub>2</sub>(0)]</td><td>Initial concentration of IL-27Rα</td><td>nM</td></tr><tr><td>[S<sub>i</sub>(0)]</td><td>Initial concentration of STATi</td><td>nM</td></tr></tbody></table>

We note that hypothesis 1 assumes that receptor molecules (free or bound, phosphorylated or unphosphorylated) are being internalized/degraded as part of the natural cellular trafficking cycle. Hypothesis 2 is consistent with a potential feedback mechanism, whereby the free cytoplasmic pSTAT molecules would migrate to the nucleus and increase the translation of negative feedback proteins, such as SOCS3, which down-regulate cytokine signaling. Thus, the internalization/degradation rate of receptor molecules (free or bound, phosphorylated or unphosphorylated) under hypothesis 2 increases with the total amount of free cytoplasmic phosphorylated STAT1 and STAT3, to account for this negative feedback on surface receptor expression. A depiction of the reactions in both the HypIL-6 and IL-27 mathematical models and under each hypothesis is given in Supp. Fig. 4 where (b), (d), (f) and (h) describe the HypIL-6 model and (c), (e), (g) and (h) describe the IL-27 model. In this figure, $i \in \{1, 3\}$ so that the reactions shown can involve STAT1 or STAT3. Each reaction arrow has been shown with its rate (above or below the arrow). We note that we assume mass action kinetics for each reaction. The notation for the rate constants and initial molecular concentrations in the models, along with their descriptions and units, are given in **Table 2**.

The HypIL-6 mathematical model was formulated based on biochemical reactions involving the following species:

* $L_6$ = HypIL-6,

* $R_1$ = GP130,

* $C_1$ = GP130 - HypIL-6 monomer,

* $D_6$ = phosphorylated GP130 - HypIL-6 - HypIL-6 - GP130 homodimer,

* $S_1$ = unbound cytoplasmic unphosphorylated STAT1,

* $S_3$ = unbound cytoplasmic unphosphorylated STAT3,

* $D_6 \cdot S_1$ = dimer bound to STAT1,

* $D_6 \cdot S_3$ = dimer bound to STAT3,

* $D_6 \cdot pS_1$ = dimer bound to pSTAT1,

* $D_6 \cdot pS_3$ = dimer bound to pSTAT3,

* $S_1 \cdot D_6 \cdot S_1$ = dimer bound to two molecules of STAT1,

* $pS_1 \cdot D_6 \cdot S_1$ = dimer bound to two molecules of STAT1, one of which is phosphorylated,

* $pS_1 \cdot D_6 \cdot pS_1$ = dimer bound to two molecules of pSTAT1,

* $S_3 \cdot D_6 \cdot S_3$ = dimer bound to two molecules of STAT3,

* $pS_3 \cdot D_6 \cdot S_3$ = dimer bound to two molecules of STAT3, one of which is phosphorylated,

* $pS_3 \cdot D_6 \cdot pS_3$ = dimer bound to two molecules of pSTAT3,
* $S_1 \cdot D_6 \cdot S_3$ = dimer bound to one molecule of STAT1 and one of STAT3,

* $pS_1 \cdot D_6 \cdot S_3$ = dimer bound to one molecule of pSTAT1 and one of STAT3,

* $S_1 \cdot D_6 \cdot pS_3$ = dimer bound to one molecule of STAT1 and one of pSTAT3,

* $pS_1 \cdot D_6 \cdot pS_3$ = dimer bound to one molecule of pSTAT1 and one of pSTAT3,

* $pS_1$ = unbound cytoplasmic phosphorylated STAT1,

* $pS_3$ = unbound cytoplasmic phosphorylated STAT3.

The initial reactions in the HypIL-6 signaling pathway can then be described by the ODEs (1) – (22) in the supplementary text, under the law of mass action, where the terms involving the parameter $\beta_6$ apply only to the model under hypothesis 1 and the terms involving the parameter $\gamma_6$ apply only to the model under hypothesis 2. Square brackets around a species denote the concentration of this species with unit nM, and "." implies a reaction bond between two molecules/species. The ODEs are valid for any time $t$, with $t \ge 0$, but time has been omitted in the species concentration for ease of notation. We note here that, for example $[R_1] = [R_1](t)$ for all $t \ge 0$.

Similarly, and with some species in common with the HypIL-6 model, the IL-27 model has been formulated based on biochemical reactions involving the following species:

* $L_{27}$ = IL-27,

* $R_1$ = GP130,

* $R_2$ = IL-27R$\alpha$,

* $C_2$ = IL-27R$\alpha$ - IL-27 monomer,

* $D_{27}$ = phosphorylated IL-27R$\alpha$ - IL-27 - GP130 heterodimer,

* $S_1$ = unbound cytoplasmic unphosphorylated STAT1,

* $S_3$ = unbound cytoplasmic unphosphorylated STAT3,

* $S_1 \cdot D_{27}$ = dimer bound to STAT1 via $R_1$,

* $S_3 \cdot D_{27}$ = dimer bound to STAT3 via $R_1$,

* $pS_1 \cdot D_{27}$ = dimer bound to pSTAT1 via $R_1$,

* $pS_3 \cdot D_{27}$ = dimer bound to pSTAT3 via $R_1$,

* $D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$,

* $D_{27} \cdot S_3$ = dimer bound to STAT3 via $R_2$,

* $D_{27} \cdot pS_1$ = dimer bound to pSTAT1 via $R_2$,

* $D_{27} \cdot pS_3$ = dimer bound to pSTAT3 via $R_2$,

* $S_1 \cdot D_{27} \cdot S_1$ = dimer bound to two molecules of STAT1,

* $pS_1 \cdot D_{27} \cdot S_1$ = dimer bound to two molecules of STAT1, phosphorylated on $R_1$,

* $S_1 \cdot D_{27} \cdot pS_1$ = dimer bound to two molecules of STAT1, phosphorylated on $R_2$,

* $pS_1 \cdot D_{27} \cdot pS_1$ = dimer bound to two molecules of pSTAT1,

* $S_3 \cdot D_{27} \cdot S_3$ = dimer bound to two molecules of STAT3,

* $pS_3 \cdot D_{27} \cdot S_3$ = dimer bound to two molecules of STAT3, phosphorylated on $R_1$,

* $S_3 \cdot D_{27} \cdot pS_3$ = dimer bound to two molecules of STAT3, phosphorylated on $R_2$,

* $pS_3 \cdot D_{27} \cdot pS_3$ = dimer bound to two molecules of pSTAT3,

* $S_1 \cdot D_{27} \cdot S_3$ = dimer bound to STAT1 via $R_1$ and STAT3 via $R_2$,

* $S_3 \cdot D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$ and STAT3 via $R_1$,

* $pS_1 \cdot D_{27} \cdot S_3$ = dimer bound to pSTAT1 via $R_1$ and STAT3 via $R_2$,

* $S_3 \cdot D_{27} \cdot pS_1$ = dimer bound to pSTAT1 via $R_2$ and STAT3 via $R_1$,

* $S_1 \cdot D_{27} \cdot pS_3$ = dimer bound to STAT1 via $R_1$ and pSTAT3 via $R_2$,

* $pS_3 \cdot D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$ and pSTAT3 via $R_1$,

* $pS_1 \cdot D_{27} \cdot pS_3$ = dimer bound to pSTAT1 via $R_1$ and pSTAT3 via $R_2$,

* $pS_3 \cdot D_{27} \cdot pS_1$ = dimer bound to pSTAT3 via $R_1$ and pSTAT1 via $R_1$,

* $pS_1$ = unbound cytoplasmic phosphorylated STAT1,

* $pS_3$ = unbound cytoplasmic phosphorylated STAT3.

Again, under the law of mass action, the initial reactions in the IL-27 signaling pathway can be described by the ODEs (23) – (55) in the supplementary text. Similarly, to the HypIL-6 model, the terms in the supplementary Equations (23) – (55) involving the parameter $\beta_{27}$ apply only to the model under hypothesis 1 and the terms involving the parameter $\gamma_{27}$ apply only to the model under hypothesis 2.

We now describe how we have made use of the experimental data (Supp. Fig. 5c and 5d) to parameterize the mathematical models described above. Since the experimental outputs are levels of pSTAT1 and pSTAT3 as a function of time under HypIL-6 and IL-27 stimulation (Supp. Fig. 5c & 5d), we consider two model outputs of interest for the HypIL-6 and IL-27 mathematical models,
* $S_1 \cdot D_6 \cdot S_3$ = dimer bound to one molecule of STAT1 and one of STAT3,

* $pS_1 \cdot D_6 \cdot S_3$ = dimer bound to one molecule of pSTAT1 and one of STAT3,

* $S_1 \cdot D_6 \cdot pS_3$ = dimer bound to one molecule of STAT1 and one of pSTAT3,

* $pS_1 \cdot D_6 \cdot pS_3$ = dimer bound to one molecule of pSTAT1 and one of pSTAT3,

* $pS_1$ = unbound cytoplasmic phosphorylated STAT1,

* $pS_3$ = unbound cytoplasmic phosphorylated STAT3.

The initial reactions in the HypIL-6 signaling pathway can then be described by the ODEs (1) – (22) in the supplementary text, under the law of mass action, where the terms involving the parameter $\beta_6$ apply only to the model under hypothesis 1 and the terms involving the parameter $\gamma_6$ apply only to the model under hypothesis 2. Square brackets around a species denote the concentration of this species with unit nM, and "." implies a reaction bond between two molecules/species. The ODEs are valid for any time $t$, with $t \ge 0$, but time has been omitted in the species concentration for ease of notation. We note here that, for example $[R_1] = [R_1](t)$ for all $t \ge 0$.

Similarly, and with some species in common with the HypIL-6 model, the IL-27 model has been formulated based on biochemical reactions involving the following species:

* $L_{27}$ = IL-27,

* $R_1$ = GP130,

* $R_2$ = IL-27R$\alpha$,

* $C_2$ = IL-27R$\alpha$ - IL-27 monomer,

* $D_{27}$ = phosphorylated IL-27R$\alpha$ - IL-27 - GP130 heterodimer,

* $S_1$ = unbound cytoplasmic unphosphorylated STAT1,

* $S_3$ = unbound cytoplasmic unphosphorylated STAT3,

* $S_1 \cdot D_{27}$ = dimer bound to STAT1 via $R_1$,

* $S_3 \cdot D_{27}$ = dimer bound to STAT3 via $R_1$,

* $pS_1 \cdot D_{27}$ = dimer bound to pSTAT1 via $R_1$,

* $pS_3 \cdot D_{27}$ = dimer bound to pSTAT3 via $R_1$,

* $D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$,

* $D_{27} \cdot S_3$ = dimer bound to STAT3 via $R_2$,

* $D_{27} \cdot pS_1$ = dimer bound to pSTAT1 via $R_2$,

* $D_{27} \cdot pS_3$ = dimer bound to pSTAT3 via $R_2$,

* $S_1 \cdot D_{27} \cdot S_1$ = dimer bound to two molecules of STAT1,

* $pS_1 \cdot D_{27} \cdot S_1$ = dimer bound to two molecules of STAT1, phosphorylated on $R_1$,

* $S_1 \cdot D_{27} \cdot pS_1$ = dimer bound to two molecules of STAT1, phosphorylated on $R_2$,

* $pS_1 \cdot D_{27} \cdot pS_1$ = dimer bound to two molecules of pSTAT1,

* $S_3 \cdot D_{27} \cdot S_3$ = dimer bound to two molecules of STAT3,

* $pS_3 \cdot D_{27} \cdot S_3$ = dimer bound to two molecules of STAT3, phosphorylated on $R_1$,

* $S_3 \cdot D_{27} \cdot pS_3$ = dimer bound to two molecules of STAT3, phosphorylated on $R_2$,

* $pS_3 \cdot D_{27} \cdot pS_3$ = dimer bound to two molecules of pSTAT3,

* $S_1 \cdot D_{27} \cdot S_3$ = dimer bound to STAT1 via $R_1$ and STAT3 via $R_2$,

* $S_3 \cdot D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$ and STAT3 via $R_1$,

* $pS_1 \cdot D_{27} \cdot S_3$ = dimer bound to pSTAT1 via $R_1$ and STAT3 via $R_2$,

* $S_3 \cdot D_{27} \cdot pS_1$ = dimer bound to pSTAT1 via $R_2$ and STAT3 via $R_1$,

* $S_1 \cdot D_{27} \cdot pS_3$ = dimer bound to STAT1 via $R_1$ and pSTAT3 via $R_2$,

* $pS_3 \cdot D_{27} \cdot S_1$ = dimer bound to STAT1 via $R_2$ and pSTAT3 via $R_1$,

* $pS_1 \cdot D_{27} \cdot pS_3$ = dimer bound to pSTAT1 via $R_1$ and pSTAT3 via $R_2$,

* $pS_3 \cdot D_{27} \cdot pS_1$ = dimer bound to pSTAT3 via $R_1$ and pSTAT1 via $R_1$,

* $pS_1$ = unbound cytoplasmic phosphorylated STAT1,

* $pS_3$ = unbound cytoplasmic phosphorylated STAT3.

Again, under the law of mass action, the initial reactions in the IL-27 signaling pathway can be described by the ODEs (23) – (55) in the supplementary text. Similarly, to the HypIL-6 model, the terms in the supplementary Equations (23) – (55) involving the parameter $\beta_{27}$ apply only to the model under hypothesis 1 and the terms involving the parameter $\gamma_{27}$ apply only to the model under hypothesis 2.

We now describe how we have made use of the experimental data (Supp. Fig. 5c and 5d) to parameterize the mathematical models described above. Since the experimental outputs are levels of pSTAT1 and pSTAT3 as a function of time under HypIL-6 and IL-27 stimulation (Supp. Fig. 5c & 5d), we consider two model outputs of interest for the HypIL-6 and IL-27 mathematical models,
which are proportional to the experimental data in Supp. Fig. 5c & 5d; namely, the sum of all molecular species (variables) containing phosphorylated STAT1 (free or bound) ($[pS_1]^{T,j}$, for $j \in \{6, 27\}$) and the sum of all species (variables) containing phosphorylated STAT3 (free or bound) ($[pS_3]^{T,j}$, for $j \in \{6, 27\}$). The total concentrations of the two model outputs of interest at any time $t$ are defined by the following equations, where $T$ denotes the total concentration of the given molecular species:

$$[pS_1]^{T,6}(t) = [D_6 \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot S_1](t) + 2[pS_1 \cdot D_6 \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot S_3](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_1](t) \quad (1)$$

$$[pS_3]^{T,6}(t) = [D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot S_3](t) + 2[pS_3 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot S_1](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_3](t) \quad (2)$$

for the HypIL-6 model, and by

$$[pS_1]^{T,27}(t) = [pS_1 \cdot D_{27}](t) + [D_{27} \cdot pS_1](t) + [pS_1 \cdot D_{27} \cdot pS_1](t) + [S_1 \cdot D_{27} \cdot pS_1](t) + 2[pS_1 \cdot D_{27} \cdot pS_1](t) + [pS_1 \cdot D_{27} \cdot S_3](t) + [S_3 \cdot D_{27} \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_1](t), \quad (3)$$

$$[pS_3]^{T,27}(t) = [pS_3 \cdot D_{27}](t) + [D_{27} \cdot pS_3](t) + [pS_3 \cdot D_{27} \cdot pS_3](t) + [S_3 \cdot D_{27} \cdot pS_3](t) + 2[pS_3 \cdot D_{27} \cdot pS_3](t) + [pS_3 \cdot D_{27} \cdot S_1](t) + [S_1 \cdot D_{27} \cdot pS_3](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_3](t), \quad (4)$$

for the IL-27 model.

## Bayesian inference

Having developed two mathematical models to describe the experimental system of HypIL-6 and IL-27 stimulation, it was then our objective to parameterize the rates of these models, making use of approximate Bayesian Computation sequential Monte Carlo (ABC-SMC) and Bayesian model selection (selecting between hypothesis 1 and 2, as described in the previous section). In this way, we can learn about which reactions and parameters in the models are regulating the differential signaling by pSTAT1 observed when stimulating with HypIL-6 and IL-27.

Model (hypothesis) selection and parameter estimation are carried out together in the Bayesian sequential Monte Carlo framework used. In the traditional ABC rejection algorithm (Sunnåker et al., 2013), the parameters of a mathematical model are sampled from determined prior distributions and the mathematical model is simulated with the sampled (from those prior distributions) parameter values. If the model output is 'close' to the experimental data, as defined by a quantitative measure of distance $d$, that is, if the distance between mathematical model output and experimental data points is smaller than a fiducial threshold $\delta$, that is, $d<\delta$, then the parameters sampled for this instance are accepted into a posterior distribution, otherwise they are rejected. This process is repeated until a posterior of size $N$ is obtained. For ODE models with a small number of parameters and variables, this approach can work well. However, for larger, more complex models, such as the models considered here, this approach can be very time consuming, since one must simulate the model a large number of times in order to obtain a posterior sample of size $N$. This is due to the high dimensionality of the parameter space. For example, in the case of the HypIL-6 model, there are 16 parameters, and thus, a 16-dimensional parameter space. There is, therefore, likely to be large areas of parameter space for which, when the parameters are sampled, the distance measure, $d$, between the model and data is always greater than $\delta$, and hence this procedure is not an efficient sampling strategy.

To this end, we chose to use a more accurate, iterative method, ABC-SMC. At the first iteration, the algorithm works in the same way as the rejection algorithm (described above), where "particles" (parameter sets) are accepted if they result in a distance $d<\delta_1$, where $\delta_1$ is reasonably large; for instance, if approximately 50% of all parameter sets sampled lead to a distance $d<\delta_1$. At each successive iteration, the parameters are sampled not from the prior distributions, but from the posterior distributions which have been obtained from the previous iteration, with weights that depend on
which are proportional to the experimental data in Supp. Fig. 5c & 5d; namely, the sum of all molecular species (variables) containing phosphorylated STAT1 (free or bound) ($[pS_1]^{T,j}$, for $j \in \{6, 27\}$) and the sum of all species (variables) containing phosphorylated STAT3 (free or bound) ($[pS_3]^{T,j}$, for $j \in \{6, 27\}$). The total concentrations of the two model outputs of interest at any time $t$ are defined by the following equations, where $T$ denotes the total concentration of the given molecular species:

$$[pS_1]^{T,6}(t) = [D_6 \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot S_1](t) + 2[pS_1 \cdot D_6 \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot S_3](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_1](t) \quad (1)$$

$$[pS_3]^{T,6}(t) = [D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot S_3](t) + 2[pS_3 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot S_1](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_3](t) \quad (2)$$

for the HypIL-6 model, and by

$$[pS_1]^{T,27}(t) = [pS_1 \cdot D_{27}](t) + [D_{27} \cdot pS_1](t) + [pS_1 \cdot D_{27} \cdot pS_1](t) + [S_1 \cdot D_{27} \cdot pS_1](t) + 2[pS_1 \cdot D_{27} \cdot pS_1](t) + [pS_1 \cdot D_{27} \cdot S_3](t) + [S_3 \cdot D_{27} \cdot pS_1](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_1](t), \quad (3)$$

$$[pS_3]^{T,27}(t) = [pS_3 \cdot D_{27}](t) + [D_{27} \cdot pS_3](t) + [pS_3 \cdot D_{27} \cdot pS_3](t) + [S_3 \cdot D_{27} \cdot pS_3](t) + 2[pS_3 \cdot D_{27} \cdot pS_3](t) + [pS_3 \cdot D_{27} \cdot S_1](t) + [S_1 \cdot D_{27} \cdot pS_3](t) + [pS_1 \cdot D_6 \cdot pS_3](t) + [pS_3 \cdot D_6 \cdot pS_1](t) + [pS_3](t), \quad (4)$$

for the IL-27 model.

## Bayesian inference

Having developed two mathematical models to describe the experimental system of HypIL-6 and IL-27 stimulation, it was then our objective to parameterize the rates of these models, making use of approximate Bayesian Computation sequential Monte Carlo (ABC-SMC) and Bayesian model selection (selecting between hypothesis 1 and 2, as described in the previous section). In this way, we can learn about which reactions and parameters in the models are regulating the differential signaling by pSTAT1 observed when stimulating with HypIL-6 and IL-27.

Model (hypothesis) selection and parameter estimation are carried out together in the Bayesian sequential Monte Carlo framework used. In the traditional ABC rejection algorithm (Sunnåker et al., 2013), the parameters of a mathematical model are sampled from determined prior distributions and the mathematical model is simulated with the sampled (from those prior distributions) parameter values. If the model output is 'close' to the experimental data, as defined by a quantitative measure of distance $d$, that is, if the distance between mathematical model output and experimental data points is smaller than a fiducial threshold $\delta$, that is, $d<\delta$, then the parameters sampled for this instance are accepted into a posterior distribution, otherwise they are rejected. This process is repeated until a posterior of size $N$ is obtained. For ODE models with a small number of parameters and variables, this approach can work well. However, for larger, more complex models, such as the models considered here, this approach can be very time consuming, since one must simulate the model a large number of times in order to obtain a posterior sample of size $N$. This is due to the high dimensionality of the parameter space. For example, in the case of the HypIL-6 model, there are 16 parameters, and thus, a 16-dimensional parameter space. There is, therefore, likely to be large areas of parameter space for which, when the parameters are sampled, the distance measure, $d$, between the model and data is always greater than $\delta$, and hence this procedure is not an efficient sampling strategy.

To this end, we chose to use a more accurate, iterative method, ABC-SMC. At the first iteration, the algorithm works in the same way as the rejection algorithm (described above), where "particles" (parameter sets) are accepted if they result in a distance $d<\delta_1$, where $\delta_1$ is reasonably large; for instance, if approximately 50% of all parameter sets sampled lead to a distance $d<\delta_1$. At each successive iteration, the parameters are sampled not from the prior distributions, but from the posterior distributions which have been obtained from the previous iteration, with weights that depend on
both the prior and the previous iteration distributions. The parameters are then perturbed slightly using a perturbation kernel (for more details see Toni et al., 2009) and the model is simulated as above. A particle at iteration *i* is accepted if it results in a distance measure *d*<*δ*<sub>*i*</sub>, where the delta values form a decreasing sequence, *δ*<sub>1</sub>>*δ*<sub>2</sub>>*δ*<sub>3</sub>>...>*δ*<sub>*M*</sub>, for *M* iterations. In this way, at each iteration the parameters are sampled from a reduced parameter space region, and hence this approach leads to a faster, more efficient, convergence to the posterior distributions.

A model (hypothesis) selection can be performed making use of the iterative method described above (see Toni et al., 2009). We consider a given model (hypothesis) and its parameters are sampled from either the prior (iteration 1) or the previous iterations posterior distributions (iteration *i* such that 1<i<*M*>, in which case the parameters are also perturbed), and again the particle is accepted if the distance between mathematical model output and experimental data points is such that *d*<*δ*<sub>*i*</sub> for iteration *i*. This procedure continues until we obtain a posterior distribution of size *N* for each mathematical model (hypothesis) considered. The mathematical models are initially given equal weight; that is, they are considered to be equally likely. However, as the iterations of the inference algorithm proceed, if one mathematical model (hypothesis) results in parameter values that better explain the experimental data, this model (hypothesis) will have a greater number of parameter sets accepted per iteration, in the limit *i* → *M*. Thus, model selection between two mathematical models (hypotheses) can be determined by the computation of the relative probability for each model (hypothesis) *k* at iteration *i*, denoted by *P*<sub>*i*</sub><sup>*k*</sup>, and defined as follows:

$$P_i^k = \frac{\text{number of accepted particles at iteration } i \text{ from model (hypothesis) } k}{N},$$

for *k* ∈ {1, 2}. The limit *lim*<sub>*i*→*M*</sub>*P*<sub>*i*</sub><sup>*k*</sup> gives the probability *P*<sup>*k*</sup> which yields the relative probability of mathematical model *k* in light of the experimental data.

The data sets we used to compare with the mathematical model outputs were the mean relative fluorescence intensity of total phosphorylated STAT1 and total phosphorylated STAT3 for the cytokine stimulation experiments with both RPE1 and Th-1 cells (Supp. Figure 5b and 5c). Given that the data points have units of mean fluorescence intensity and the model output has dimensions of concentration (in nM units), we normalized the data sets to obtain dimensionless values, which in turn can be compared with the normalized mathematical model outputs. To this end, and firstly, we constructed a linear model for the fluorescence intensity (background fluorescence) of antibodies of phosphorylated STAT1 and STAT3 in unstimulated cells. We then subtracted the value of this linear model at each time point from the corresponding fluorescence intensity in HypIL-6 and IL-27-stimulated cells, for each repeat of the experiment and cell type. Let us denote by *f* the experimental fluorescence intensity, *f*(*r*, *i*, *tp*, *j*, *d*) corresponds to the fluorescence intensity for the *r* th repeat, *r* ∈ *R* = {1, 2, 3, 4} with antibody for STAT1, *i* ∈ *I* = {1, 3} at time point *tp*,

$$tp \in TP = \{0\text{min}, 5\text{min}, 15\text{min}, 30\text{min}, 60\text{min}, 90\text{min}, 120\text{min}, 180\text{min}\}$$

under stimulation by cytokine IL-j (HypIL-j when *j* = 6), with *j* ∈ *J* = {6, 27} and in cell type *d* ∈ *D* = {RPE1, Th-1}. Each data point *data*(*r*, *i*, *tp*, *j*, *d*), to be used in the Bayesian inference and Bayesian model selection was then obtained from *f*(*r*, *i*, *tp*, *j*, *d*) with the following normalization,

$$\text{data}(r, i, tp, j, d) = \frac{f(r, i, tp, j, d)}{f(r, i, tp = 30\text{min}, j = 27, d)}. \qquad (5)$$

That is, our normalization has been chosen to be the time point 30 minutes with IL-27 stimulation. To compare the mathematical model output, denoted by *sim*(*i*, *tp*, *j*, *d*), with the normalized experimental data, the mathematical output was normalized in the same way as the data, that is,

$$\text{sim}(i, tp, j, d) = \frac{[pS_i]^{Tp}(tp, d)}{[pS_i]^{T,27}(30\text{min}, d)}, \qquad (6)$$

where [*pS*<sub>*i*</sub>]<sup>*T,j*</sup>(*tp*, *d*) denotes the total, *T*, concentration of phosphorylated STAT1 at time *tp* (see Equations 1–4) when considering cell type *d* and cytokine stimulation *j* ∈ *J* = {6, 27}. The data points for IL-27 stimulation at time 30 mins were chosen as normalization in Equation (5), since they correspond to the maximal experimental value, and thus the data, when normalized in this way, was
both the prior and the previous iteration distributions. The parameters are then perturbed slightly using a perturbation kernel (for more details see Toni et al., 2009) and the model is simulated as above. A particle at iteration *i* is accepted if it results in a distance measure *d*<*δ*<sub>*i*</sub>, where the delta values form a decreasing sequence, *δ*<sub>1</sub>>*δ*<sub>2</sub>>*δ*<sub>3</sub>>...>*δ*<sub>*M*</sub>, for *M* iterations. In this way, at each iteration the parameters are sampled from a reduced parameter space region, and hence this approach leads to a faster, more efficient, convergence to the posterior distributions.

A model (hypothesis) selection can be performed making use of the iterative method described above (see Toni et al., 2009). We consider a given model (hypothesis) and its parameters are sampled from either the prior (iteration 1) or the previous iterations posterior distributions (iteration *i* such that 1<i<*M*>, in which case the parameters are also perturbed), and again the particle is accepted if the distance between mathematical model output and experimental data points is such that *d*<*δ*<sub>*i*</sub> for iteration *i*. This procedure continues until we obtain a posterior distribution of size *N* for each mathematical model (hypothesis) considered. The mathematical models are initially given equal weight; that is, they are considered to be equally likely. However, as the iterations of the inference algorithm proceed, if one mathematical model (hypothesis) results in parameter values that better explain the experimental data, this model (hypothesis) will have a greater number of parameter sets accepted per iteration, in the limit *i* → *M*. Thus, model selection between two mathematical models (hypotheses) can be determined by the computation of the relative probability for each model (hypothesis) *k* at iteration *i*, denoted by *P*<sup>*k*</sup><sub>*i*</sub>, and defined as follows:

$$P_i^k = \frac{\text{number of accepted particles at iteration } i \text{ from model (hypothesis) } k}{N},$$

for *k* ∈ {1, 2}. The limit *lim*<sub>*i*→*M*</sub>*P*<sup>*k*</sup><sub>*i*</sub> gives the probability *P*<sup>*k*</sup> which yields the relative probability of mathematical model *k* in light of the experimental data.

The data sets we used to compare with the mathematical model outputs were the mean relative fluorescence intensity of total phosphorylated STAT1 and total phosphorylated STAT3 for the cytokine stimulation experiments with both RPE1 and Th-1 cells (Supp. Figure 5b and 5c). Given that the data points have units of mean fluorescence intensity and the model output has dimensions of concentration (in nM units), we normalized the data sets to obtain dimensionless values, which in turn can be compared with the normalized mathematical model outputs. To this end, and firstly, we constructed a linear model for the fluorescence intensity (background fluorescence) of antibodies of phosphorylated STAT1 and STAT3 in unstimulated cells. We then subtracted the value of this linear model at each time point from the corresponding fluorescence intensity in HypIL-6 and IL-27-stimulated cells, for each repeat of the experiment and cell type. Let us denote by *f* the experimental fluorescence intensity, *f*(*r*, *i*, *tp*, *j*, *d*) corresponds to the fluorescence intensity for the *r* th repeat, *r* ∈ *R* = {1, 2, 3, 4} with antibody for STAT1, *i* ∈ *I* = {1, 3} at time point *tp*,

$$tp \in TP = \{0\text{min}, 5\text{min}, 15\text{min}, 30\text{min}, 60\text{min}, 90\text{min}, 120\text{min}, 180\text{min}\}$$

under stimulation by cytokine IL-j (HypIL-j when *j* = 6), with *j* ∈ *J* = {6, 27} and in cell type *d* ∈ *D* = {RPE1, Th-1}. Each data point *data*(*r*, *i*, *tp*, *j*, *d*), to be used in the Bayesian inference and Bayesian model selection was then obtained from *f*(*r*, *i*, *tp*, *j*, *d*) with the following normalization,

$$data(r, i, tp, j, d) = \frac{f(r, i, tp, j, d)}{f(r, i, tp = 30\text{min}, j = 27, d)}. \qquad (5)$$

That is, our normalization has been chosen to be the time point 30 minutes with IL-27 stimulation. To compare the mathematical model output, denoted by *sim*(*i*, *tp*, *j*, *d*), with the normalized experimental data, the mathematical output was normalized in the same way as the data, that is,

$$sim(i, tp, j, d) = \frac{[pS_i]^{Tp}(tp, d)}{[pS_i]^{T,27}(30\text{min}, d)}, \qquad (6)$$

where [*pS*<sub>*i*</sub>]<sup>*T,j*</sup>(*tp*, *d*) denotes the total, *T*, concentration of phosphorylated STAT1 at time *tp* (see Equations 1–4) when considering cell type *d* and cytokine stimulation *j* ∈ *J* = {6, 27}. The data points for IL-27 stimulation at time 30 mins were chosen as normalization in Equation (5), since they correspond to the maximal experimental value, and thus the data, when normalized in this way, was
transformed to a scale in the interval [0, 1]. Mathematical model outputs were normalized in the same way, and therefore model outputs for IL-27 will naturally go through the value 1 at time 30 mins. This choice of normalization has not influenced the results of our study. To this end, we have repeated our analysis with a different normalization time point of $f(r, i, tp = 15min, j = 27, d)$ (results not shown here). In particular, we found that the posterior distributions and the result of the model (hypothesis) selection were rather similar for each choice of normalization.

Once data sets and mathematical outputs have been normalized and can be compared, there is a need to quantify how close (or not) they are. To this end, we make use of a quantitative measure, called a distance and denoted by $\delta(\text{sim}, \text{data})$. In our case, we have chosen a generalization of the Euclidean distance, where

$$[\delta^d(\text{sim}, \text{data})]^2 = \sum_{i \in I} \sum_{tp \in TP} \sum_{j \in J} [\text{sim}(i, tp, j, d) - \mu_{\text{data}}(i, tp, j, d)]^2, \quad (7)$$

$d \in D = \{\text{RPE1}, \text{Th} - 1\}$, with $\mu_{\text{data}}(i, tp, j, d)$ defined as the mean of the four experimental repeats. The mean is given by

$$\mu_{\text{data}}(i, tp, j, d) = \frac{1}{4} \sum_{r=1}^{4} \text{data}(r, i, tp, j, d). \quad (8)$$

With a choice of measure, we can now carry out both Bayesian (mathematical) model selection and parameter inference. Before we do so, our prior beliefs of the parameters need to be considered and defined. Each of the parameters (reaction rates in the mathematical models) and initial concentrations for the molecules in the model were sampled from a prior distribution, where the distribution was informed by independent experiments or published values, when possible. The choice of prior distributions is given in **Table 3**.

We now provide additional details of the model selection and parameter estimation carried out with the normalized experimental data and mathematical models. We have experimental data for two different cell types (RPE1 and Th-1). There are a number of parameters in the HypIL-6 and IL-27 mathematical models which we have assumed to be independent of the cell type. The only parameters which we would expect to differ between cell types are the initial concentrations of the molecules $([R_1(0)], [R_2(0)], [S_1(0)], [S_3(0)])$, the rate of STAT phosphorylation ($q$), the rates of pSTAT dephosphorylation ($d_1, d_3$) and the rates of internalization/degradation of the receptor molecules ($\beta_6, \beta_{27}, \gamma_6, \gamma_{27}$). Therefore, the aforementioned parameters have been estimated for each cell type, separately, and the rest of the parameters have been estimated with one cell type. We have chosen to make use of the RPE1 data to estimate these shared parameters. In particular, we ran the analysis in two stages (all our numerical codes were written in Python), in order to reduce the number of parameters to be estimated in a given ABC-SMC analysis. We first made use of the RPE1 data and secondly, the Th-1 data. We ran the model (hypothesis) selection algorithm with the RPE1 data, for a sample of size $N = 10^4$ and $M = 15$ iterations, with the following sequence of delta values $\{100, 10, 5, 3, 2.5, 2.25, 2, 1.75, 1.5, 1.25, 1.1, 1, 0.9, 0.8, 0.7\}$.

A uniform perturbation kernel (Filippi et al., 2013) was used to perturb the parameters sampled at each iteration $1<i \le M$. The result of the model selection clearly indicated that hypothesis 1 could explain the experimental data best.

When carrying out model (hypothesis) selection, and during the latter iterations, there were still some parameter sets accepted for hypothesis 2. Therefore, we ran the ABC-SMC parameter estimation algorithm for the RPE1 data only for hypothesis 1, in order to generate a complete posterior distribution of size $N = 10^4$. In the second stage of the inference, we then considered the Th-1 data and ran the ABC-SMC parameter estimation algorithm to infer Th-1 specific parameters (only for hypothesis 1). Those parameters that were assumed to be independent of cell type were sampled from the posterior distributions obtained during the previous RPE1 ABC-SMC inference. The same sample size, number of iterations, vector of delta values and perturbation kernel were used in the Th-1 and RPE1 analysis. We finally note that, although we used the experimental data sets in the order RPE1 followed by Th-1 here, the ordering of the cell type does not have a significant effect on the results (not shown here). Namely, our model selection results and those of the parameter inference and posterior distributions are similar to those presented here, when we reverse the order.
transformed to a scale in the interval [0, 1]. Mathematical model outputs were normalized in the same way, and therefore model outputs for IL-27 will naturally go through the value 1 at time 30 mins. This choice of normalization has not influenced the results of our study. To this end, we have repeated our analysis with a different normalization time point of $f(r, i, tp = 15min, j = 27, d)$ (results not shown here). In particular, we found that the posterior distributions and the result of the model (hypothesis) selection were rather similar for each choice of normalization.

Once data sets and mathematical outputs have been normalized and can be compared, there is a need to quantify how close (or not) they are. To this end, we make use of a quantitative measure, called a distance and denoted by $\delta(\text{sim}, \text{data})$. In our case, we have chosen a generalization of the Euclidean distance, where

$$[\delta^d(\text{sim}, \text{data})]^2 = \sum_{i \in I} \sum_{tp \in TP} \sum_{j \in J} [\text{sim}(i, tp, j, d) - \mu_{\text{data}}(i, tp, j, d)]^2, \quad (7)$$

$d \in D = \{\text{RPE1}, \text{Th} - 1\}$, with $\mu_{\text{data}}(i, tp, j, d)$ defined as the mean of the four experimental repeats. The mean is given by

$$\mu_{\text{data}}(i, tp, j, d) = \frac{1}{4} \sum_{r=1}^{4} \text{data}(r, i, tp, j, d). \quad (8)$$

With a choice of measure, we can now carry out both Bayesian (mathematical) model selection and parameter inference. Before we do so, our prior beliefs of the parameters need to be considered and defined. Each of the parameters (reaction rates in the mathematical models) and initial concentrations for the molecules in the model were sampled from a prior distribution, where the distribution was informed by independent experiments or published values, when possible. The choice of prior distributions is given in **Table 3**.

We now provide additional details of the model selection and parameter estimation carried out with the normalized experimental data and mathematical models. We have experimental data for two different cell types (RPE1 and Th-1). There are a number of parameters in the HypIL-6 and IL-27 mathematical models which we have assumed to be independent of the cell type. The only parameters which we would expect to differ between cell types are the initial concentrations of the molecules $([R_1(0)], [R_2(0)], [S_1(0)], [S_3(0)])$, the rate of STAT phosphorylation ($q$), the rates of pSTAT dephosphorylation ($d_1, d_3$) and the rates of internalization/degradation of the receptor molecules ($\beta_6, \beta_{27}, \gamma_6, \gamma_{27}$). Therefore, the aforementioned parameters have been estimated for each cell type, separately, and the rest of the parameters have been estimated with one cell type. We have chosen to make use of the RPE1 data to estimate these shared parameters. In particular, we ran the analysis in two stages (all our numerical codes were written in Python), in order to reduce the number of parameters to be estimated in a given ABC-SMC analysis. We first made use of the RPE1 data and secondly, the Th-1 data. We ran the model (hypothesis) selection algorithm with the RPE1 data, for a sample of size $N = 10^4$ and $M = 15$ iterations, with the following sequence of delta values $\{100, 10, 5, 3, 2.5, 2.25, 2, 1.75, 1.5, 1.25, 1.1, 1, 0.9, 0.8, 0.7\}$.

A uniform perturbation kernel (Filippi et al., 2013) was used to perturb the parameters sampled at each iteration $1<i \le M$. The result of the model selection clearly indicated that hypothesis 1 could explain the experimental data best.

When carrying out model (hypothesis) selection, and during the latter iterations, there were still some parameter sets accepted for hypothesis 2. Therefore, we ran the ABC-SMC parameter estimation algorithm for the RPE1 data only for hypothesis 1, in order to generate a complete posterior distribution of size $N = 10^4$. In the second stage of the inference, we then considered the Th-1 data and ran the ABC-SMC parameter estimation algorithm to infer Th-1 specific parameters (only for hypothesis 1). Those parameters that were assumed to be independent of cell type were sampled from the posterior distributions obtained during the previous RPE1 ABC-SMC inference. The same sample size, number of iterations, vector of delta values and perturbation kernel were used in the Th-1 and RPE1 analysis. We finally note that, although we used the experimental data sets in the order RPE1 followed by Th-1 here, the ordering of the cell type does not have a significant effect on the results (not shown here). Namely, our model selection results and those of the parameter inference and posterior distributions are similar to those presented here, when we reverse the order.
<caption>**Table 3.** Prior distribution assigned to each parameter and initial molecular concentration.</caption>

*These distributions are centered around measurements obtained from cell surface receptor quantification experiments. **These distributions were derived based on $K_d$ values obtained from the literature (Wiederkehr-Adam et al., 2003). ***These distributions are based on values derived from experimental data in which the cells were treated with Tofacitinib. † These distributions were based on values derived from experimental data in which the cells were treated with cycloheximide. ‡ These distributions were based on computations involving approximate cell sizes and average numbers of molecules per cell.

<table><thead><tr><th>Parameter</th><th>Prior distribution</th><th>Reference</th></tr></thead><tbody><tr><td>r<sub>1.6</sub><sup>+</sup></td><td>10<sup>r</sup> for r ~ N(-3, 1.5)</td><td>*</td></tr><tr><td>r<sub>1.6</sub><sup>-</sup></td><td>10<sup>r</sup> for r ~ N(-3.9, 1.96)</td><td>*</td></tr><tr><td>r<sub>1.27</sub><sup>+</sup></td><td>10<sup>r</sup> for r ~ N(-2.34, 1.17)</td><td>*</td></tr><tr><td>r<sub>1.27</sub><sup>-</sup></td><td>10<sup>r</sup> for r ~ N(-2.82, 1.41)</td><td>*</td></tr><tr><td>r<sub>2,j</sub><sup>+</sup> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-2, 3)</td><td>Kozer et al., 2013</td></tr><tr><td>r<sub>2,j</sub><sup>-</sup> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-3, 1)</td><td>Kozer et al., 2013</td></tr><tr><td>k<sub>ia</sub><sup>+</sup>, k<sub>ib</sub><sup>+</sup> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-7, 1)</td><td>**</td></tr><tr><td>k<sub>ia</sub><sup>-</sup>, k<sub>ib</sub><sup>-</sup> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-2, 1)</td><td>**</td></tr><tr><td>q</td><td>10<sup>r</sup> for r ~ Unif(-3, 2)</td><td>Assumed</td></tr><tr><td>d<sub>i</sub> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-5, -2)</td><td>***</td></tr><tr><td>β<sub>j</sub> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-5, -1)</td><td>†</td></tr><tr><td>γ<sub>j</sub> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-5, -1)</td><td>†</td></tr><tr><td>[R<sub>1</sub>(0)]</td><td>N(12.7, 6.35)</td><td>‡</td></tr><tr><td>[R<sub>2</sub>(0)]</td><td>N(33.8, 16.9)</td><td>‡</td></tr><tr><td>[S<sub>1</sub>(0)]</td><td>N(300, 100)</td><td>Itzhak et al., 2016</td></tr><tr><td>[S<sub>2</sub>(0)]</td><td>N(400, 100)</td><td>Itzhak et al., 2016</td></tr></tbody></table>

## Mathematical model validation

Once we have carried out model selection and parameter inference as described in the previous section, we want to explore the potential of the mathematical models of cytokine early signaling to reproduce other independent experiments. We note that we make use of the posterior parameter distributions obtained from the RPE1 data ABC-SMC. Our first interest was to reproduce the dose response curve seen in Supp. Fig. 2a. To this end, we run both models using the 10⁴ accepted parameters sets from the ABC-SMC for 18 different values of cytokine concentration, within the range [10⁻⁴-10²] log nM. The results of this analysis are seen in Supp. Fig. 13b. Our second interest was to describe the IL-27Rα-GP130 chimera experiments (Figure 3c). This required us to modify the mathematical model as follows: we considered the ODEs of the IL-27 mathematical model involved in the formation of the dimer, Equations (23) – (26) (Supplementary information 1), and the ODEs of the HypIL-6 mathematical model post-dimer formation, Equations (5) – (22) (Supplementary information 1), in which $D_6$ was replaced by $D_{27}$. The ODE of the IL-27 induced dimer in the chimera model was modified as follows,

$$ \frac{d[D_{27}]}{dt} = r_{2,27}^{+}[C_2][R_1] - r_{2,27}^{-}[D_{27}] - 2k_{1a}^{+}[D_{27}][S_1] + k_{1a}^{-}([S_1'D_{27}] + [pS_1'D_{27}]) \\ -2k_{3a}^{+}[D_{27}][S_3] + k_{3a}^{-}([S_3'D_{27}] + [pS_3'D_{27}]) - \beta_{27}[D_{27}]. \quad (9) $$

We simulated both the original mathematical model of IL-27 and the chimera model using the accepted parameter sets from the ABC-SMC. The results can be seen in Supp. Fig. 3a.

Finally, the mathematical model was used to describe one of the mutant varieties of the IL-27Rα chain, Y613F. We sought to reproduce the results of Figure 3b making use of the mathematical model of IL-27 signaling. Since the Y613F mutation decreases the affinity of STAT1 to IL-27Rα, we fixed the association and dissociation rates of STAT1 to the IL 27Rα chain, $k_{1b}^{+}$ and $k_{1b}^{-}$, respectively,
<caption>**Table 3.** Prior distribution assigned to each parameter and initial molecular concentration.</caption>

*These distributions are centered around measurements obtained from cell surface receptor quantification experiments. **These distributions were derived based on $K_d$ values obtained from the literature (Wiederkehr-Adam et al., 2003). ***These distributions are based on values derived from experimental data in which the cells were treated with Tofacitinib. † These distributions were based on values derived from experimental data in which the cells were treated with cycloheximide. ‡ These distributions were based on computations involving approximate cell sizes and average numbers of molecules per cell.

<table><thead><tr><th>Parameter</th><th>Prior distribution</th><th>Reference</th></tr></thead><tbody><tr><td>r<sub>1.6</sub><sup>+</sup></td><td>10<sup>r</sup> for r ~ N(-3, 1.5)</td><td>*</td></tr><tr><td>r<sub>1.6</sub><sup>-</sup></td><td>10<sup>r</sup> for r ~ N(-3.9, 1.96)</td><td>*</td></tr><tr><td>r<sub>1.27</sub><sup>+</sup></td><td>10<sup>r</sup> for r ~ N(-2.34, 1.17)</td><td>*</td></tr><tr><td>r<sub>1.27</sub><sup>-</sup></td><td>10<sup>r</sup> for r ~ N(-2.82, 1.41)</td><td>*</td></tr><tr><td>r<sub>2,j</sub><sup>+</sup> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-2, 3)</td><td>Kozer et al., 2013</td></tr><tr><td>r<sub>2,j</sub><sup>-</sup> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-3, 1)</td><td>Kozer et al., 2013</td></tr><tr><td>k<sub>ia</sub><sup>+</sup>, k<sub>ib</sub><sup>+</sup> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-7, 1)</td><td>**</td></tr><tr><td>k<sub>ia</sub><sup>-</sup>, k<sub>ib</sub><sup>-</sup> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-2, 1)</td><td>**</td></tr><tr><td>q</td><td>10<sup>r</sup> for r ~ Unif(-3, 2)</td><td>Assumed</td></tr><tr><td>d<sub>i</sub> for i∈{1,3}</td><td>10<sup>r</sup> for r ~ Unif(-5, -2)</td><td>***</td></tr><tr><td>β<sub>j</sub> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-5, -1)</td><td>†</td></tr><tr><td>γ<sub>j</sub> for j∈{6,27}</td><td>10<sup>r</sup> for r ~ Unif(-5, -1)</td><td>†</td></tr><tr><td>[R<sub>1</sub>(0)]</td><td>N(12.7, 6.35)</td><td>‡</td></tr><tr><td>[R<sub>2</sub>(0)]</td><td>N(33.8, 16.9)</td><td>‡</td></tr><tr><td>[S<sub>1</sub>(0)]</td><td>N(300, 100)</td><td>Itzhak et al., 2016</td></tr><tr><td>[S<sub>2</sub>(0)]</td><td>N(400, 100)</td><td>Itzhak et al., 2016</td></tr></tbody></table>

## Mathematical model validation

Once we have carried out model selection and parameter inference as described in the previous section, we want to explore the potential of the mathematical models of cytokine early signaling to reproduce other independent experiments. We note that we make use of the posterior parameter distributions obtained from the RPE1 data ABC-SMC. Our first interest was to reproduce the dose response curve seen in Supp. Fig. 2a. To this end, we run both models using the 10⁴ accepted parameters sets from the ABC-SMC for 18 different values of cytokine concentration, within the range [10⁻⁴-10²] log nM. The results of this analysis are seen in Supp. Fig. 13b. Our second interest was to describe the IL-27Rα-GP130 chimera experiments (Figure 3c). This required us to modify the mathematical model as follows: we considered the ODEs of the IL-27 mathematical model involved in the formation of the dimer, Equations (23) – (26) (Supplementary information 1), and the ODEs of the HypIL-6 mathematical model post-dimer formation, Equations (5) – (22) (Supplementary information 1), in which $D_6$ was replaced by $D_{27}$. The ODE of the IL-27 induced dimer in the chimera model was modified as follows,

$$ \frac{d[D_{27}]}{dt} = r_{2,27}^{+}[C_2][R_1] - r_{2,27}^{-}[D_{27}] - 2k_{1a}^{+}[D_{27}][S_1] + k_{1a}^{-}([S_1'D_{27}] + [pS_1'D_{27}]) \\ -2k_{3a}^{+}[D_{27}][S_3] + k_{3a}^{-}([S_3'D_{27}] + [pS_3'D_{27}]) - \beta_{27}[D_{27}]. \quad (9) $$

We simulated both the original mathematical model of IL-27 and the chimera model using the accepted parameter sets from the ABC-SMC. The results can be seen in Supp. Fig. 3a.

Finally, the mathematical model was used to describe one of the mutant varieties of the IL-27Rα chain, Y613F. We sought to reproduce the results of Figure 3b making use of the mathematical model of IL-27 signaling. Since the Y613F mutation decreases the affinity of STAT1 to IL-27Rα, we fixed the association and dissociation rates of STAT1 to the IL 27Rα chain, $k_{1b}^{+}$ and $k_{1b}^{-}$, respectively,
at values which lead to a high affinity (of the order of µM values). The specific values chosen were $k_{1b}^{+} = 10^{-5}$ nM$^{-1}$s$^{-1}$ and $k_{1b}^{-} = 10^{1}$ s$^{-1}$, which yield an affinity of $10^2$µM. The rate $k_{1b}^{-}$ was chosen as approximately the median of the ABC-SMC posterior distribution for this parameter, and the rate $k_{1b}^{+}$ was then significantly decreased in order to increase the affinity. We simulated the mathematical model of IL-27 signaling using the $10^4$ accepted ABC-SMC parameter sets, but where the rates $k_{1b}^{+}$ and $k_{1b}^{-}$, were fixed as described above. The pointwise medians and 95% credible intervals of these simulations are plotted in Supp. Fig. 13c, as well as the simulations for the WT IL-27Rα chain, without altering any of the parameter values from the posterior distributions. Altering the binding affinity of STAT1 to IL-27Rα in this way in the mathematical model allows us to generate results which qualitatively and quantitatively reproduce the experimental observations for the Y613F mutant from Figure 3b.

## Live-cell dual-color single-molecule imaging studies

Single-molecule imaging experiments were carried out by total internal reflection fluorescence (TIRF) microscopy with an inverted microscope (Olympus IX71) equipped with a triple-line total internal reflection (TIR) illumination condenser (Olympus) and a back-illuminated electron multiplied (EM) CCD camera (iXon DU897D, 512 × 512 pixel, Andor Technology) as recently described (Wilmes et al., 2015; Wilmes et al., 2020; Moraga et al., 2015b). A ×150 magnification objective with a numerical aperture of 1.45 (UAPO 150 3/1.45 TIRFM, Olympus) was used for TIR illumination. All experiments were carried out at room temperature in medium without phenol red supplemented with an oxygen scavenger and a redox-active photoprotectant to minimize photobleaching (Vogelsang et al., 2008). For Heterodimerization experiments of IL-27Rα and GP130 cell surface labeling of RPE1 GP130 KO, co-transfected with mXFPe-IL-27Rα and mXFPm-GP130, was achieved by adding αGFP-enNB<sup>RHO11</sup> and αGFP-miNB<sup>DY647</sup> to the medium at equal concentrations (5 nM) and incubated for at least 5 min prior to stimulation with IL-27 (20 nM) or HypIL-6 (20 nM). For homodimerization experiments with mXFPm-GP130, αGFP-miNB<sup>DY647</sup> and αGFP-miNB<sup>RHO11</sup> (Kirchhofer et al., 2010) were used for cell surface receptor labeling as described above. The nano-bodies were kept in the bulk solution during the whole experiment in order to ensure high equilibrium binding to mXFP-GP130. For simultaneous dual-color acquisition, αGFP-NB<sup>RHO11</sup> was excited by a 561 nm diode-pumped solid-state laser at 0.95 mW (~32 W/cm²) and αGFP-NB<sup>DY647</sup> by a 642 nm laser diode at 0.65 mW (~22 W/cm²). Fluorescence was detected using a spectral image splitter (DualView, Optical Insight) with a 640 DCXR dichroic beam splitter (Chroma) in combination with the bandpass filter 585/40 (Semrock) for detection of RHO11 and 690/70 (Chroma) for detection of DY647 dividing each emission channel into 512 × 256 pixel. Image stacks of 150 frames were recorded at 32 ms/frame.

Single-molecule localization and single-molecule tracking were carried out using the multiple-target tracing (MTT) algorithm (Sergé et al., 2008) as described previously (You et al., 2016). Step-length histograms were obtained from single-molecule trajectories and fitted by two fraction mixture model of Brownian diffusion. Average diffusion constants were determined from the slope (2–10 steps) of the mean square displacement versus time lapse diagrams. Immobile molecules were identified by the density-based spatial clustering of applications with noise (DBSCAN) algorithm as described recently (Röder et al., 2014). For comparing diffusion properties and for co-tracking analysis, immobile particles were excluded from the data set. Prior to co-localization analysis, imaging channels were aligned with sub-pixel precision by using a spatial transformation. To this end, a transformation matrix was calculated based on a calibration measurement with multicolor fluorescent beads (TetraSpeck microspheres 0.1 mm, Invitrogen) visible in both spectral channels (cp2tform of type 'affine', The MathWorks MATLAB 2009a).

Individual molecules detected in the both spectral channels were regarded as co-localized, if a particle was detected in both channels of a single frame within a distance threshold of 100 nm radius. For single-molecule co-tracking analysis, the MTT algorithm was applied to this dataset of co-localized molecules to reconstruct co-locomotion trajectories (co-trajectories) from the identified population of co-localizations. For the co-tracking analysis, only trajectories with a minimum of 10 steps (~320 ms) were considered in order to robustly remove random receptor co-localizations (Wilmes et al., 2020). For heterodimerization experiments of mXFPe-IL-27Rα and mXFPm-GP130, the relative fraction of dimerized receptors was calculated from the number of co-trajectories
at values which lead to a high affinity (of the order of µM values). The specific values chosen were $k_{1b}^{+} = 10^{-5}$ nM$^{-1}$s$^{-1}$ and $k_{1b}^{-} = 10^{1}$ s$^{-1}$, which yield an affinity of $10^2$µM. The rate $k_{1b}^{-}$ was chosen as approximately the median of the ABC-SMC posterior distribution for this parameter, and the rate $k_{1b}^{+}$ was then significantly decreased in order to increase the affinity. We simulated the mathematical model of IL-27 signaling using the $10^4$ accepted ABC-SMC parameter sets, but where the rates $k_{1b}^{+}$ and $k_{1b}^{-}$, were fixed as described above. The pointwise medians and 95% credible intervals of these simulations are plotted in Supp. Fig. 13c, as well as the simulations for the WT IL-27Rα chain, without altering any of the parameter values from the posterior distributions. Altering the binding affinity of STAT1 to IL-27Rα in this way in the mathematical model allows us to generate results which qualitatively and quantitatively reproduce the experimental observations for the Y613F mutant from Figure 3b.

## Live-cell dual-color single-molecule imaging studies

Single-molecule imaging experiments were carried out by total internal reflection fluorescence (TIRF) microscopy with an inverted microscope (Olympus IX71) equipped with a triple-line total internal reflection (TIR) illumination condenser (Olympus) and a back-illuminated electron multiplied (EM) CCD camera (iXon DU897D, 512 × 512 pixel, Andor Technology) as recently described (Wilmes et al., 2015; Wilmes et al., 2020; Moraga et al., 2015b). A ×150 magnification objective with a numerical aperture of 1.45 (UAPO 150 3/1.45 TIRFM, Olympus) was used for TIR illumination. All experiments were carried out at room temperature in medium without phenol red supplemented with an oxygen scavenger and a redox-active photoprotectant to minimize photobleaching (Vogelsang et al., 2008). For Heterodimerization experiments of IL-27Rα and GP130 cell surface labeling of RPE1 GP130 KO, co-transfected with mXFPe-IL-27Rα and mXFPm-GP130, was achieved by adding αGFP-enNB<sup>RHO11</sup> and αGFP-miNB<sup>DY647</sup> to the medium at equal concentrations (5 nM) and incubated for at least 5 min prior to stimulation with IL-27 (20 nM) or HypIL-6 (20 nM). For homodimerization experiments with mXFPm-GP130, αGFP-miNB<sup>DY647</sup> and αGFP-miNB<sup>RHO11</sup> (Kirchhofer et al., 2010) were used for cell surface receptor labeling as described above. The nano-bodies were kept in the bulk solution during the whole experiment in order to ensure high equilibrium binding to mXFP-GP130. For simultaneous dual-color acquisition, αGFP-NB<sup>RHO11</sup> was excited by a 561 nm diode-pumped solid-state laser at 0.95 mW (~32 W/cm²) and αGFP-NB<sup>DY647</sup> by a 642 nm laser diode at 0.65 mW (~22 W/cm²). Fluorescence was detected using a spectral image splitter (DualView, Optical Insight) with a 640 DCXR dichroic beam splitter (Chroma) in combination with the bandpass filter 585/40 (Semrock) for detection of RHO11 and 690/70 (Chroma) for detection of DY647 dividing each emission channel into 512 × 256 pixel. Image stacks of 150 frames were recorded at 32 ms/frame.

Single-molecule localization and single-molecule tracking were carried out using the multiple-target tracing (MTT) algorithm (Sergé et al., 2008) as described previously (You et al., 2016). Step-length histograms were obtained from single-molecule trajectories and fitted by two fraction mixture model of Brownian diffusion. Average diffusion constants were determined from the slope (2–10 steps) of the mean square displacement versus time lapse diagrams. Immobile molecules were identified by the density-based spatial clustering of applications with noise (DBSCAN) algorithm as described recently (Röder et al., 2014). For comparing diffusion properties and for co-tracking analysis, immobile particles were excluded from the data set. Prior to co-localization analysis, imaging channels were aligned with sub-pixel precision by using a spatial transformation. To this end, a transformation matrix was calculated based on a calibration measurement with multicolor fluorescent beads (TetraSpeck microspheres 0.1 mm, Invitrogen) visible in both spectral channels (cp2tform of type ‘affine’, The MathWorks MATLAB 2009a).

Individual molecules detected in the both spectral channels were regarded as co-localized, if a particle was detected in both channels of a single frame within a distance threshold of 100 nm radius. For single-molecule co-tracking analysis, the MTT algorithm was applied to this dataset of co-localized molecules to reconstruct co-locomotion trajectories (co-trajectories) from the identified population of co-localizations. For the co-tracking analysis, only trajectories with a minimum of 10 steps (~320 ms) were considered in order to robustly remove random receptor co-localizations (Wilmes et al., 2020). For heterodimerization experiments of mXFPe-IL-27Rα and mXFPm-GP130, the relative fraction of dimerized receptors was calculated from the number of co-trajectories
relative to the number of IL-27Rα trajectories. GP130 was expressed in moderate excess (~1.5–2 fold), so that maximal receptor assembly was not limited by abundance of the low-affinity subunit GP130.

For homodimerization experiments with GP130, the relative fraction of co-tracked molecules was determined with respect to the absolute number of trajectories and corrected for GP130 stochastically double-labeled with the same fluorophore species as follows:

$$AB^* = \frac{AB}{2 \times \left[ \left( \frac{A}{A+B} \right) \times \left( \frac{B}{A+B} \right) \right]}, rel.co - locomotion = \frac{2 \times AB^*}{(A+B)}$$

where A, B, AB, and AB* are the numbers of trajectories observed for Rho11, DY647, co-trajectories and corrected co-trajectories, respectively.

The two-dimensional equilibrium dissociation constants ($K_D^{2D}$) were calculated according to the law of mass action for a monomer-dimer equilibrium:

Heterodimerization (IL-27Rα + GP130):

$$K_D^{2D} = \frac{([GP130] - (\alpha \times [IL27Ra])) \times ([IL27Ra] - (\alpha \times [IL27Ra]))}{(\alpha \times [IL27Ra])}$$

or

$$K_D^{2D} = [GP130] \times \left( \frac{1}{\alpha} - 1 \right) + [IL27Ra] \times (\alpha - 1)$$

with:

$$\alpha = \text{fraction of IL27 bound IL27 Rain complex with GP130}$$

Homodimerization (GP130 + GP130):

$$K_D^{2D} = \frac{[M]^2}{[D]} = \frac{([M]_0 - 2[D])^2}{[D]}$$

$$K_D^{2D} = \frac{([GP130] - 2 \times (\alpha \times [GP130]))^2}{2 \times (\alpha \times [GP130])}$$

with:

$$\alpha = \text{fraction of GP130 homodimers relative to [GP130]/2}$$

where [M] and [D] are the concentrations of the monomer and the dimer, respectively, and [M]₀ is the total receptor concentration.

## Acknowledgements

We thank members of the Moraga, Molina-París, Piehler and Mitra laboratories for helpful advice and discussion. We thank G Hikade and H Kenneweg for technical support, C P Richter for providing software for single-molecule image analysis, R Kurre (Integrated Bioimaging Facility Osnabrück) for support with fluorescence microscopy and the FingerPrints Proteomics facility (Dundee) for support with the mass spectrometry data. Graphic material was provided by smart servier medical art. This work was supported by the Wellcome-Trust-202323/Z/16/Z (IM EP), ERC-206-STG grant (IM JMF EP PKF), EMBO (SW 454–2017), DFG (SFB 944, P8/Z, JP), National Heart, Lung and Blood Institute (K22HL125593, MK) and Contrat de Plan Etat Région Hauts de France and Institut pour la Recherche sur le Cancer de Lille (SM SG). CMP and GL were supported by H2020 (ITN QuanTII, grant agreement number 764698). PJ is supported by the EPSRC, AstraZeneca and the Smith Institute (Smith Institute CASE studentship, award reference 1969354). Numerical work was undertaken on ARC3, which is part of the High-Performance Computing facilities at the University of Leeds, UK.
relative to the number of IL-27Rα trajectories. GP130 was expressed in moderate excess (~1.5–2 fold), so that maximal receptor assembly was not limited by abundance of the low-affinity subunit GP130.

For homodimerization experiments with GP130, the relative fraction of co-tracked molecules was determined with respect to the absolute number of trajectories and corrected for GP130 stochastically double-labeled with the same fluorophore species as follows:

$$AB^* = \frac{AB}{2 \times \left[ \left( \frac{A}{A+B} \right) \times \left( \frac{B}{A+B} \right) \right]}, rel.co - locomotion = \frac{2 \times AB^*}{(A+B)}$$

where A, B, AB, and AB* are the numbers of trajectories observed for Rho11, DY647, co-trajectories and corrected co-trajectories, respectively.

The two-dimensional equilibrium dissociation constants ($K_D^{2D}$) were calculated according to the law of mass action for a monomer-dimer equilibrium:

Heterodimerization (IL-27Rα + GP130):

$$K_D^{2D} = \frac{([GP130] - (\alpha \times [IL27Ra])) \times ([IL27Ra] - (\alpha \times [IL27Ra]))}{(\alpha \times [IL27Ra])}$$

or

$$K_D^{2D} = [GP130] \times \left( \frac{1}{\alpha} - 1 \right) + [IL27Ra] \times (\alpha - 1)$$

with:

$$\alpha = \text{fraction of IL27 bound IL27 Rain complex with GP130}$$

Homodimerization (GP130 + GP130):

$$K_D^{2D} = \frac{[M]^2}{[D]} = \frac{([M]_0 - 2[D])^2}{[D]}$$

$$K_D^{2D} = \frac{([GP130] - 2 \times (\alpha \times [GP130]))^2}{2 \times (\alpha \times [GP130])}$$

with:

$$\alpha = \text{fraction of GP130 homodimers relative to [GP130]/2}$$

where [M] and [D] are the concentrations of the monomer and the dimer, respectively, and [M]₀ is the total receptor concentration.

## Acknowledgements

We thank members of the Moraga, Molina-París, Piehler and Mitra laboratories for helpful advice and discussion. We thank G Hikade and H Kenneweg for technical support, C P Richter for providing software for single-molecule image analysis, R Kurre (Integrated Bioimaging Facility Osnabrück) for support with fluorescence microscopy and the FingerPrints Proteomics facility (Dundee) for support with the mass spectrometry data. Graphic material was provided by smart servier medical art. This work was supported by the Wellcome-Trust-202323/Z/16/Z (IM EP), ERC-206-STG grant (IM JMF EP PKF), EMBO (SW 454–2017), DFG (SFB 944, P8/Z, JP), National Heart, Lung and Blood Institute (K22HL125593, MK) and Contrat de Plan Etat Région Hauts de France and Institut pour la Recherche sur le Cancer de Lille (SM SG). CMP and GL were supported by H2020 (ITN QuanTII, grant agreement number 764698). PJ is supported by the EPSRC, AstraZeneca and the Smith Institute (Smith Institute CASE studentship, award reference 1969354). Numerical work was undertaken on ARC3, which is part of the High-Performance Computing facilities at the University of Leeds, UK.
# Additional information

## Funding

<table><thead><tr><td>Funder</td><td>Grant reference number</td><td>Author</td></tr></thead><tbody><tr><td>Horizon 2020 Framework Programme</td><td>714680</td><td>Stephan Wilmes<br>Jonathan Martinez-Fabregas<br>Paul K Fyfe<br>Ignacio Moraga</td></tr><tr><td>Wellcome Trust</td><td>202323/Z/16/Z</td><td>Elizabeth Pohler<br>Ignacio Moraga</td></tr><tr><td>EPSRC</td><td>1969354</td><td>Polly-Anne Jeffrey</td></tr><tr><td>University of Leeds</td><td>764698</td><td>Grant Lythe<br>Carmen Molina-París</td></tr><tr><td>Wellcome Trust</td><td>ERC-206-STG</td><td>Jonathan Martinez-Fabregas<br>Paul K Fyfe<br>Elizabeth Pohler<br>Ignacio Moraga</td></tr><tr><td>EMBO</td><td>454–2017</td><td>Stephan Wilmes</td></tr><tr><td>DFG</td><td>SFB 944, P8/Z</td><td>Jacob Piehler</td></tr><tr><td>National Heart, Lung, and Blood Institute</td><td>K22HL125593</td><td>Jacob Piehler</td></tr></tbody></table>

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

## Author contributions

Stephan Wilmes, Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft; Polly-Anne Jeffrey, Conceptualization, Data curation, Formal analysis, Methodology, Writing - review and editing; Jonathan Martinez-Fabregas, David Launay, Investigation, Methodology, Writing - review and editing; Maximillian Hafer, Paul K Fyfe, Elizabeth Pohler, Silvia Gaggero, Suman Mitra, Conceptualization, Investigation, Methodology, Writing - review and editing; Martín López-García, Formal analysis, Methodology; Grant Lythe, Conceptualization, Writing - review and editing; Charles Taylor, Formal analysis; Thomas Guerrier, Methodology; Jacob Piehler, Conceptualization, Methodology, Writing - review and editing; Carmen Molina-París, Conceptualization, Supervision, Investigation, Methodology, Writing - review and editing; Ignacio Moraga, Conceptualization, Data curation, Supervision, Funding acquisition, Investigation, Writing - original draft, Project administration, Writing - review and editing

## Author ORCIDs

Stephan Wilmes https://orcid.org/0000-0002-4112-710X

Polly-Anne Jeffrey https://orcid.org/0000-0001-6476-0402

Jonathan Martinez-Fabregas https://orcid.org/0000-0001-5809-065X

Maximillian Hafer https://orcid.org/0000-0003-0853-2637

Paul K Fyfe https://orcid.org/0000-0003-3541-2294

Martín López-García https://orcid.org/0000-0003-3833-8595

Grant Lythe https://orcid.org/0000-0001-7966-5571

Jacob Piehler https://orcid.org/0000-0002-2143-2270

Ignacio Moraga https://orcid.org/0000-0001-9909-0701

## Ethics

Human subjects: This study was authorized by the French Competent Authority dealing with Research on Human Biological Samples namely the French Ministry of Research. The Authorization number is ECH 19/04. all patients gave their written informed consent.
# Additional information

## Funding

<table><thead><tr><td>Funder</td><td>Grant reference number</td><td>Author</td></tr></thead><tbody><tr><td>Horizon 2020 Framework Programme</td><td>714680</td><td>Stephan Wilmes<br>Jonathan Martinez-Fabregas<br>Paul K Fyfe<br>Ignacio Moraga</td></tr><tr><td>Wellcome Trust</td><td>202323/Z/16/Z</td><td>Elizabeth Pohler<br>Ignacio Moraga</td></tr><tr><td>EPSRC</td><td>1969354</td><td>Polly-Anne Jeffrey</td></tr><tr><td>University of Leeds</td><td>764698</td><td>Grant Lythe<br>Carmen Molina-París</td></tr><tr><td>Wellcome Trust</td><td>ERC-206-STG</td><td>Jonathan Martinez-Fabregas<br>Paul K Fyfe<br>Elizabeth Pohler<br>Ignacio Moraga</td></tr><tr><td>EMBO</td><td>454–2017</td><td>Stephan Wilmes</td></tr><tr><td>DFG</td><td>SFB 944, P8/Z</td><td>Jacob Piehler</td></tr><tr><td>National Heart, Lung, and Blood Institute</td><td>K22HL125593</td><td>Jacob Piehler</td></tr></tbody></table>

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

## Author contributions

Stephan Wilmes, Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft; Polly-Anne Jeffrey, Conceptualization, Data curation, Formal analysis, Methodology, Writing - review and editing; Jonathan Martinez-Fabregas, David Launay, Investigation, Methodology, Writing - review and editing; Maximillian Hafer, Paul K Fyfe, Elizabeth Pohler, Silvia Gaggero, Suman Mitra, Conceptualization, Investigation, Methodology, Writing - review and editing; Martín López-García, Formal analysis, Methodology; Grant Lythe, Conceptualization, Writing - review and editing; Charles Taylor, Formal analysis; Thomas Guerrier, Methodology; Jacob Piehler, Conceptualization, Methodology, Writing - review and editing; Carmen Molina-París, Conceptualization, Supervision, Investigation, Methodology, Writing - review and editing; Ignacio Moraga, Conceptualization, Data curation, Supervision, Funding acquisition, Investigation, Writing - original draft, Project administration, Writing - review and editing

## Author ORCIDs

Stephan Wilmes https://orcid.org/0000-0002-4112-710X

Polly-Anne Jeffrey https://orcid.org/0000-0001-6476-0402

Jonathan Martinez-Fabregas https://orcid.org/0000-0001-5809-065X

Maximillian Hafer https://orcid.org/0000-0003-0853-2637

Paul K Fyfe https://orcid.org/0000-0003-3541-2294

Martín López-García https://orcid.org/0000-0003-3833-8595

Grant Lythe https://orcid.org/0000-0001-7966-5571

Jacob Piehler https://orcid.org/0000-0002-2143-2270

Ignacio Moraga https://orcid.org/0000-0001-9909-0701

## Ethics

Human subjects: This study was authorized by the French Competent Authority dealing with Research on Human Biological Samples namely the French Ministry of Research. The Authorization number is ECH 19/04. all patients gave their written informed consent.
## Decision letter and Author response

Decision letter https://doi.org/10.7554/eLife.66014.sa1

Author response https://doi.org/10.7554/eLife.66014.sa2

## Additional files

### Supplementary files

* Supplementary file 1. Ordinary differential equations for mathematical modeling of IL-27 and HypIL-6 signaling.

* Transparent reporting form

### Data availability

Python (version 3.7) codes for the ABC-SMC model selection and parameter inference can be found in the public repository 'https://github.com/PollyJeffrey/Cytokine_modelling' (copy archived at https://archive.softwareheritage.org/swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d), along with the results of the analysis. Phospho-proteomic and proteomic datasets were uploaded to the Proteome Exchange platform with accession numbers PXD024657 and PXD024188 respectively. RNA-seq dataset was uploaded in the GSE database with accession number GSE164479.

The following datasets were generated:

<table><thead><tr><td>Author(s)</td><td>Year</td><td>Dataset title</td><td>Dataset URL</td><td>Database and Identifier</td></tr></thead><tbody><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE164479</td><td>NCBI Gene Expression Omnibus, GSE164479</td></tr><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ebi.ac.uk/pride/archive/projects/PXD024188</td><td>PRIDE, PXD024188</td></tr><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ebi.ac.uk/pride/archive/projects/PXD024657</td><td>PRIDE, PXD024657</td></tr></tbody></table>

## References

* Awasthi A, Carrier Y, Peron JP, Bettelli E, Kamanaka M, Flavell RA, Kuchroo VK, Oukka M, Weiner HL. 2007. A dominant function for interleukin 27 in generating interleukin 10-producing anti-inflammatory T cells. *Nature Immunology* **8**:1380–1389. DOI: https://doi.org/10.1038/ni1541, PMID: 17994022

* Bancerek J, Poss ZC, Steinparzer I, Sedlyarov V, Pfaffenwimmer T, Mikulic I, Dölken L, Strobl B, Müller M, Taatjes DJ, Kovarik P. 2013. CDK8 kinase phosphorylates transcription factor STAT1 to selectively regulate the interferon response. *Immunity* **38**:250–262. DOI: https://doi.org/10.1016/j.immuni.2012.10.017, PMID: 23352233
## Decision letter and Author response

Decision letter https://doi.org/10.7554/eLife.66014.sa1

Author response https://doi.org/10.7554/eLife.66014.sa2

## Additional files

### Supplementary files

* Supplementary file 1. Ordinary differential equations for mathematical modeling of IL-27 and HypIL-6 signaling.

* Transparent reporting form

### Data availability

Python (version 3.7) codes for the ABC-SMC model selection and parameter inference can be found in the public repository 'https://github.com/PollyJeffrey/Cytokine_modelling' (copy archived at https://archive.softwareheritage.org/swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d), along with the results of the analysis. Phospho-proteomic and proteomic datasets were uploaded to the Proteome Exchange platform with accession numbers PXD024657 and PXD024188 respectively. RNA-seq dataset was uploaded in the GSE database with accession number GSE164479.

The following datasets were generated:

<table><thead><tr><th>Author(s)</th><th>Year</th><th>Dataset title</th><th>Dataset URL</th><th>Database and Identifier</th></tr></thead><tbody><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE164479</td><td>NCBI Gene Expression Omnibus, GSE164479</td></tr><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ebi.ac.uk/pride/archive/projects/PXD024188</td><td>PRIDE, PXD024188</td></tr><tr><td>Wilmes S, Jeffrey P, Martinez-Fabregas J, Hafer M, Fyfe P, Pohler E, Gaggero S, López-García M, Lythe G, Guerrier T, Launay D, Suman M, Piehler J, Molina-París C, Moraga I</td><td>2021</td><td>Competitive binding of STATs to receptor phospho-Tyr motifs accounts for altered cytokine responses in autoimmune disorders</td><td>https://www.ebi.ac.uk/pride/archive/projects/PXD024657</td><td>PRIDE, PXD024657</td></tr></tbody></table>

## References

* Awasthi A, Carrier Y, Peron JP, Bettelli E, Kamanaka M, Flavell RA, Kuchroo VK, Oukka M, Weiner HL. 2007. A dominant function for interleukin 27 in generating interleukin 10-producing anti-inflammatory T cells. *Nature Immunology* **8**:1380–1389. DOI: https://doi.org/10.1038/ni1541, PMID: 17994022

* Bancerek J, Poss ZC, Steinparzer I, Sedlyarov V, Pfaffenwimmer T, Mikulic I, Dölken L, Strobl B, Müller M, Taatjes DJ, Kovarik P. 2013. CDK8 kinase phosphorylates transcription factor STAT1 to selectively regulate the interferon response. *Immunity* **38**:250–262. DOI: https://doi.org/10.1016/j.immuni.2012.10.017, PMID: 23352233
Bender H, Wiesinger MY, Nordhoff C, Schoenherr C, Haan C, Ludwig S, Weiskirchen R, Kato N, Heinrich PC, Haan S. 2009. Interleukin-27 displays interferon-gamma-like functions in human hepatoma cells and hepatocytes. *Hepatology* **50**:585-591. DOI: https://doi.org/10.1002/hep.22988, PMID: 19582813

Betz UA, Müller W. 1998. Regulated expression of gp130 and IL-6 receptor alpha chain in T cell maturation and activation. *International Immunology* **10**:1175-1184. DOI: https://doi.org/10.1093/intimm/10.8.1175, PMID: 9723704

Boulanger MJ, Chow DC, Brevnova EE, Garcia KC. 2003. Hexameric structure and assembly of the interleukin-6/IL-6 alpha-receptor/gp130 complex. *Science* **300**:2101-2104. DOI: https://doi.org/10.1126/science.1083901, PMID: 12829785

Brender C, Tannahill GM, Jenkins BJ, Fletcher J, Columbus R, Saris CJ, Ernst M, Nicola NA, Hilton DJ, Alexander WS, Starr R. 2007. Suppressor of cytokine signaling 3 regulates CD8 T-cell proliferation by inhibition of interleukins 6 and 27. *Blood* **110**:2528-2536. DOI: https://doi.org/10.1182/blood-2006-08-041541, PMID: 17609432

Brown JB, Cheresh P, Zhang Z, Ryu H, Managlia E, Barrett TA. 2012. P-selectin glycoprotein ligand-1 is needed for sequential recruitment of T-helper 1 (Th1) and local generation of Th17 T cells in dextran sodium sulfate (DSS) colitis. *Inflammatory Bowel Diseases* **18**:323-332. DOI: https://doi.org/10.1002/ibd.21779, PMID: 22009715

Camporeale A. 2012. IL-6, IL-17 and STAT3: a holy trinity in auto-immunity? *Frontiers in Bioscience* **17**:2306-2326. DOI: https://doi.org/10.2741/4054

Castro M, de Boer RJ. 2020. Testing structural identifiability by a simple scaling method. *PLOS Computational Biology* **16**:e1008248. DOI: https://doi.org/10.1371/journal.pcbi.1008248, PMID: 33141821

Charlot-Rabiega P, Bardel E, Dietrich C, Kastelein R, Devergne O. 2011. Signaling events involved in interleukin 27 (IL-27)-induced proliferation of human naive CD4+ T cells and B cells. *Journal of Biological Chemistry* **286**:27350-27362. DOI: https://doi.org/10.1074/jbc.M111.221010, PMID: 21669870

Costa-Pereira AP, Tininini S, Strobl B, Alonzi T, Schlaak JF, Is'harc H, Gesualdo I, Newman SJ, Kerr IM, Poli V. 2002. Mutational switch of an IL-6 response to an interferon-β-like response. *PNAS* **99**:8043-8047. DOI: https://doi.org/10.1073/pnas.122236099

Cox J, Neuhauser N, Michalski A, Scheltema RA, Olsen JV, Mann M. 2011. Andromeda: a peptide search engine integrated into the MaxQuant environment. *Journal of Proteome Research* **10**:1794-1805. DOI: https://doi.org/10.1021/pr101065j, PMID: 21254760

Cox J, Mann M. 2008. MaxQuant enables high peptide identification rates, individualized p.p.b.-range mass accuracies and proteome-wide protein quantification. *Nature Biotechnology* **26**:1367-1372. DOI: https://doi.org/10.1038/nbt.1511, PMID: 19029910

Croker BA, Krebs DL, Zhang JG, Wormald S, Willson TA, Stanley EG, Robb L, Greenhalgh CJ, Förster I, Clausen BE, Nicola NA, Metcalf D, Hilton DJ, Roberts AW, Alexander WS. 2003. SOCS3 negatively regulates IL-6 signaling in vivo. *Nature Immunology* **4**:540-545. DOI: https://doi.org/10.1038/ni931, PMID: 12754505

Diegelmann J, Olszak T, Göke B, Blumberg RS, Brand S. 2012. A novel role for interleukin-27 (IL-27) as mediator of intestinal epithelial barrier protection mediated via differential signal transducer and activator of transcription (STAT) protein signaling and induction of antibacterial and anti-inflammatory proteins. *Journal of Biological Chemistry* **287**:286-298. DOI: https://doi.org/10.1074/jbc.M111.294355, PMID: 22069308

Diveu C, McGeachy MJ, Boniface K, Stumhofer JS, Sathe M, Joyce-Shaikh B, Chen Y, Tato CM, McClanahan TK, de Waal Malefyt R, Hunter CA, Cua DJ, Kastelein RA. 2009. IL-27 blocks RORc expression to inhibit lineage commitment of Th17 cells. *The Journal of Immunology* **182**:5748-5756. DOI: https://doi.org/10.4049/jimmunol.0801162

Fakruddin JM, Lempicki RA, Gorelick RJ, Yang J, Adelsberger JW, Garcia-Pineres AJ, Pinto LA, Lane HC, Imamichi T. 2007. Noninfectious papilloma virus-like particles inhibit HIV-1 replication: implications for immune control of HIV-1 infection by IL-27. *Blood* **109**:1841-1849. DOI: https://doi.org/10.1182/blood-2006-02-001578, PMID: 17068156

Filippi S, Barnes CP, Cornebise J, Stumpf MP. 2013. On optimality of kernels for approximate bayesian computation using sequential monte carlo. *Statistical Applications in Genetics and Molecular Biology* **12**:87-107. DOI: https://doi.org/10.1515/sagmb-2012-0069, PMID: 23502346

Fischer M, Goldschmitt J, Peschel C, Brakenhoff JP, Kallen KJ, Wollmer A, Grötzinger J, Rose-John S. 1997. I. A bioactive designer cytokine for human hematopoietic progenitor cell expansion. *Nature Biotechnology* **15**:142-145. DOI: https://doi.org/10.1038/nbt0297-142, PMID: 9035138

Fitzgerald DC, Zhang GX, El-Behi M, Fonseca-Kelly Z, Li H, Yu S, Saris CJ, Gran B, Ciric B, Rostami A. 2007. Suppression of autoimmune inflammation of the central nervous system by interleukin 10 secreted by interleukin 27-stimulated T cells. *Nature Immunology* **8**:1372-1379. DOI: https://doi.org/10.1038/ni1540, PMID: 17994023

Francois-Newton V, Livingstone M, Payelle-Brogard B, Uzé G, Pellegrini S. 2012. USP18 establishes the transcriptional and anti-proliferative interferon α/β differential. *Biochemical Journal* **446**:509-516. DOI: https://doi.org/10.1042/BJ20120541, PMID: 22731491

Frank AC, Zhang X, Katsounas A, Bharucha JP, Kottilil S, Imamichi T. 2010. Interleukin-27, an anti-HIV-1 cytokine, inhibits replication of hepatitis C virus. *Journal of Interferon & Cytokine Research* **30**:427-431. DOI: https://doi.org/10.1089/jir.2009.0093, PMID: 20235668

Garbers C, Hermanns HM, Schaper F, Müller-Newen G, Grötzinger J, Rose-John S, Scheller J. 2012. Plasticity and cross-talk of interleukin 6-type cytokines. *Cytokine & Growth Factor Reviews* **23**:85-97. DOI: https://doi.org/10.1016/j.cytogfr.2012.04.001, PMID: 22595692
Bender H, Wiesinger MY, Nordhoff C, Schoenherr C, Haan C, Ludwig S, Weiskirchen R, Kato N, Heinrich PC, Haan S. 2009. Interleukin-27 displays interferon-gamma-like functions in human hepatoma cells and hepatocytes. *Hepatology* **50**:585-591. DOI: https://doi.org/10.1002/hep.22988, PMID: 19582813

Betz UA, Müller W. 1998. Regulated expression of gp130 and IL-6 receptor alpha chain in T cell maturation and activation. *International Immunology* **10**:1175-1184. DOI: https://doi.org/10.1093/intimm/10.8.1175, PMID: 9723704

Boulanger MJ, Chow DC, Brevnova EE, Garcia KC. 2003. Hexameric structure and assembly of the interleukin-6/IL-6 alpha-receptor/gp130 complex. *Science* **300**:2101-2104. DOI: https://doi.org/10.1126/science.1083901, PMID: 12829785

Brender C, Tannahill GM, Jenkins BJ, Fletcher J, Columbus R, Saris CJ, Ernst M, Nicola NA, Hilton DJ, Alexander WS, Starr R. 2007. Suppressor of cytokine signaling 3 regulates CD8 T-cell proliferation by inhibition of interleukins 6 and 27. *Blood* **110**:2528-2536. DOI: https://doi.org/10.1182/blood-2006-08-041541, PMID: 17609432

Brown JB, Cheresh P, Zhang Z, Ryu H, Managlia E, Barrett TA. 2012. P-selectin glycoprotein ligand-1 is needed for sequential recruitment of T-helper 1 (Th1) and local generation of Th17 T cells in dextran sodium sulfate (DSS) colitis. *Inflammatory Bowel Diseases* **18**:323-332. DOI: https://doi.org/10.1002/ibd.21779, PMID: 22009715

Camporeale A. 2012. IL-6, IL-17 and STAT3: a holy trinity in auto-immunity? *Frontiers in Bioscience* **17**:2306-2326. DOI: https://doi.org/10.2741/4054

Castro M, de Boer RJ. 2020. Testing structural identifiability by a simple scaling method. *PLOS Computational Biology* **16**:e1008248. DOI: https://doi.org/10.1371/journal.pcbi.1008248, PMID: 33141821

Charlot-Rabiega P, Bardel E, Dietrich C, Kastelein R, Devergne O. 2011. Signaling events involved in interleukin 27 (IL-27)-induced proliferation of human naive CD4+ T cells and B cells. *Journal of Biological Chemistry* **286**:27350-27362. DOI: https://doi.org/10.1074/jbc.M111.221010, PMID: 21669870

Costa-Pereira AP, Tininini S, Strobl B, Alonzi T, Schlaak JF, Is'harc H, Gesualdo I, Newman SJ, Kerr IM, Poli V. 2002. Mutational switch of an IL-6 response to an interferon-β-like response. *PNAS* **99**:8043-8047. DOI: https://doi.org/10.1073/pnas.122236099

Cox J, Neuhauser N, Michalski A, Scheltema RA, Olsen JV, Mann M. 2011. Andromeda: a peptide search engine integrated into the MaxQuant environment. *Journal of Proteome Research* **10**:1794-1805. DOI: https://doi.org/10.1021/pr101065j, PMID: 21254760

Cox J, Mann M. 2008. MaxQuant enables high peptide identification rates, individualized p.p.b.-range mass accuracies and proteome-wide protein quantification. *Nature Biotechnology* **26**:1367-1372. DOI: https://doi.org/10.1038/nbt.1511, PMID: 19029910

Croker BA, Krebs DL, Zhang JG, Wormald S, Willson TA, Stanley EG, Robb L, Greenhalgh CJ, Förster I, Clausen BE, Nicola NA, Metcalf D, Hilton DJ, Roberts AW, Alexander WS. 2003. SOCS3 negatively regulates IL-6 signaling in vivo. *Nature Immunology* **4**:540-545. DOI: https://doi.org/10.1038/ni931, PMID: 12754505

Diegelmann J, Olszak T, Göke B, Blumberg RS, Brand S. 2012. A novel role for interleukin-27 (IL-27) as mediator of intestinal epithelial barrier protection mediated via differential signal transducer and activator of transcription (STAT) protein signaling and induction of antibacterial and anti-inflammatory proteins. *Journal of Biological Chemistry* **287**:286-298. DOI: https://doi.org/10.1074/jbc.M111.294355, PMID: 22069308

Diveu C, McGeachy MJ, Boniface K, Stumhofer JS, Sathe M, Joyce-Shaikh B, Chen Y, Tato CM, McClanahan TK, de Waal Malefyt R, Hunter CA, Cua DJ, Kastelein RA. 2009. IL-27 blocks RORc expression to inhibit lineage commitment of Th17 cells. *The Journal of Immunology* **182**:5748-5756. DOI: https://doi.org/10.4049/jimmunol.0801162

Fakruddin JM, Lempicki RA, Gorelick RJ, Yang J, Adelsberger JW, Garcia-Pineres AJ, Pinto LA, Lane HC, Imamichi T. 2007. Noninfectious papilloma virus-like particles inhibit HIV-1 replication: implications for immune control of HIV-1 infection by IL-27. *Blood* **109**:1841-1849. DOI: https://doi.org/10.1182/blood-2006-02-001578, PMID: 17068156

Filippi S, Barnes CP, Cornebise J, Stumpf MP. 2013. On optimality of kernels for approximate bayesian computation using sequential monte carlo. *Statistical Applications in Genetics and Molecular Biology* **12**:87-107. DOI: https://doi.org/10.1515/sagmb-2012-0069, PMID: 23502346

Fischer M, Goldschmitt J, Peschel C, Brakenhoff JP, Kallen KJ, Wollmer A, Grötzinger J, Rose-John S. 1997. I. A bioactive designer cytokine for human hematopoietic progenitor cell expansion. *Nature Biotechnology* **15**:142-145. DOI: https://doi.org/10.1038/nbt0297-142, PMID: 9035138

Fitzgerald DC, Zhang GX, El-Behi M, Fonseca-Kelly Z, Li H, Yu S, Saris CJ, Gran B, Ciric B, Rostami A. 2007. Suppression of autoimmune inflammation of the central nervous system by interleukin 10 secreted by interleukin 27-stimulated T cells. *Nature Immunology* **8**:1372-1379. DOI: https://doi.org/10.1038/ni1540, PMID: 17994023

Francois-Newton V, Livingstone M, Payelle-Brogard B, Uzé G, Pellegrini S. 2012. USP18 establishes the transcriptional and anti-proliferative interferon α/β differential. *Biochemical Journal* **446**:509-516. DOI: https://doi.org/10.1042/BJ20120541, PMID: 22731491

Frank AC, Zhang X, Katsounas A, Bharucha JP, Kottilil S, Imamichi T. 2010. Interleukin-27, an anti-HIV-1 cytokine, inhibits replication of hepatitis C virus. *Journal of Interferon & Cytokine Research* **30**:427-431. DOI: https://doi.org/10.1089/jir.2009.0093, PMID: 20235668

Garbers C, Hermanns HM, Schaper F, Müller-Newen G, Grötzinger J, Rose-John S, Scheller J. 2012. Plasticity and cross-talk of interleukin 6-type cytokines. *Cytokine & Growth Factor Reviews* **23**:85-97. DOI: https://doi.org/10.1016/j.cytogfr.2012.04.001, PMID: 22595692
Gorby C, Sotolongo Bellón J, Wilmes S, Warda W, Pohler E, Fyfe PK, Cozzani A, Ferrand C, Walter MR, Mitra S, Piehler J, Moraga I. 2020. Engineered IL-10 variants elicit potent immunomodulatory effects at low ligand doses. *Science Signaling* **13:eabc0653**. DOI: https://doi.org/10.1126/scisignal.abc0653, PMID: 32934073

Heinrich PC, Behrmann I, Haan S, Hermanns HM, Müller-Newen G, Schaper F. 2003. Principles of interleukin (IL)-6-type cytokine signalling and its regulation. *Biochemical Journal* **374**:1–20. DOI: https://doi.org/10.1042/bj20030407, PMID: 12773095

Hirahara K, Ghoreschi K, Yang XP, Takahashi H, Laurence A, Vahedi G, Sciumè G, Hall AO, Dupont CD, Francisco LM, Chen Q, Tanaka M, Kanno Y, Sun HW, Sharpe AH, Hunter CA, O'Shea JJ. 2012. Interleukin-27 priming of T cells controls IL-17 production in trans via induction of the ligand PD-L1. *Immunity* **36**:1017–1030. DOI: https://doi.org/10.1016/j.immuni.2012.03.024, PMID: 22726954

Hirahara K, Onodera A, Villarino AV, Bonelli M, Sciumè G, Laurence A, Sun HW, Brooks SR, Vahedi G, Shih HY, Gutierrez-Cruz G, Iwata S, Suzuki R, Mikami Y, Okamoto Y, Nakayama T, Holland SM, Hunter CA, Kanno Y, O'Shea JJ. 2015. Asymmetric action of STAT transcription factors drives transcriptional outputs and cytokine specificity. *Immunity* **42**:877–889. DOI: https://doi.org/10.1016/j.immuni.2015.04.014, PMID: 25992861

Ho CCM, Chhabra A, Starkl P, Schnorr PJ, Wilmes S, Moraga I, Kwon HS, Gaudenzio N, Sibilano R, Wehrman TS, Gakovic M, Sockolosky JT, Tiffany MR, Ring AM, Piehler J, Weissman IL, Galli SJ, Shizuru JA, Garcia KC. 2017. Decoupling the functional pleiotropy of stem cell factor by tuning c-Kit signaling. *Cell* **168**:1041–1052. DOI: https://doi.org/10.1016/j.cell.2017.02.011, PMID: 28283060

Hochberg MC. 1997. Updating the american college of rheumatology revised criteria for the classification of systemic lupus erythematosus. *Arthritis & Rheumatism* **40**:1725. DOI: https://doi.org/10.1002/art.1780400928, PMID: 9324032

Hu X, Herrero C, Li WP, Antoniv TT, Falck-Pedersen E, Koch AE, Woods JM, Haines GK, Ivashkiv LB. 2002. Sensitization of IFN-gamma Jak-STAT signaling during macrophage activation. *Nature Immunology* **3**:859–866. DOI: https://doi.org/10.1038/ni828, PMID: 12172544

Huang daW, Sherman BT, Lempicki RA. 2009a. Bioinformatics enrichment tools: paths toward the comprehensive functional analysis of large gene lists. *Nucleic Acids Research* **37**:1–13. DOI: https://doi.org/10.1093/nar/gkn923, PMID: 19033363

Huang daW, Sherman BT, Lempicki RA. 2009b. Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources. *Nature Protocols* **4**:44–57. DOI: https://doi.org/10.1038/nprot.2008.211, PMID: 19131956

Hunter CA, Jones SA. 2015. IL-6 as a keystone cytokine in health and disease. *Nature Immunology* **16**:448–457. DOI: https://doi.org/10.1038/ni.3153, PMID: 25898198

Imamichi T, Yang J, Huang daW, Sherman B, Lempicki RA. 2012. Interleukin-27 induces interferon-inducible genes: analysis of gene expression profiles using affymetrix microarray and DAVID. *Methods in Molecular Biology* **820**:25–53. DOI: https://doi.org/10.1007/978-1-61779-439-1_3, PMID: 22131024

Itzhak DN, Tyanova S, Cox J, Borner GH. 2016. Global, quantitative and dynamic mapping of protein subcellular localization. *eLife* **5**:e16950. DOI: https://doi.org/10.7554/eLife.16950, PMID: 27278775

Jones GW, McLoughlin RM, Hammond VJ, Parker CR, Williams JD, Malhotra R, Scheller J, Williams AS, Rose-John S, Topley N, Jones SA. 2010. Loss of CD4+ T cell IL-6R expression during inflammation underlines a role for IL-6 trans signaling in the local maintenance of Th17 cells. *Journal of Immunology* **184**:2130–2139. DOI: https://doi.org/10.4049/jimmunol.0901528, PMID: 20083667

Kamiya S, Owaki T, Morishima N, Fukai F, Mizuguchi J, Yoshimoto T. 2004. An indispensable role for STAT1 in IL-27-induced T-bet expression but not proliferation of naive CD4+ T cells. *The Journal of Immunology* **173**: 3871–3877. DOI: https://doi.org/10.4049/jimmunol.173.6.3871, PMID: 15356135

Kang S, Narazaki M, Metwally H, Kishimoto T. 2020. Historical overview of the interleukin-6 family cytokine. *Journal of Experimental Medicine* **217**:0347. DOI: https://doi.org/10.1084/jem.20190347

Karwacz K, Miraldi ER, Pokrovskii M, Madi A, Yosef N, Wortman I, Chen X, Watters A, Carriero N, Awasthi A, Regev A, Bonneau R, Littman D, Kuchroo VK. 2017. Critical role of IRF1 and BATF in forming chromatin landscape during type 1 regulatory cell differentiation. *Nature Immunology* **18**:412–421. DOI: https://doi.org/10.1038/ni.3683, PMID: 28166218

Kim H, Hawley TS, Hawley RG, Baumann H. 1998. Protein tyrosine phosphatase 2 (SHP-2) moderates signaling by gp130 but is not required for the induction of acute-phase plasma protein genes in hepatic cells. *Molecular and Cellular Biology* **18**:1525–1533. DOI: https://doi.org/10.1128/MCB.18.3.1525, PMID: 9488469

Kimura A, Kishimoto T. 2010. IL-6: regulator of treg/Th17 balance. *European Journal of Immunology* **40**:1830–1835. DOI: https://doi.org/10.1002/eji.201040391, PMID: 20583029

Kirchhofer A, Helma J, Schmidthals K, Frauer C, Cui S, Karcher A, Pellis M, Muyldermans S, Casas-Delucchi CS, Cardoso MC, Leonhardt H, Hopfner KP, Rothbauer U. 2010. Modulation of protein properties in living cells using nanobodies. *Nature Structural & Molecular Biology* **17**:133–138. DOI: https://doi.org/10.1038/nsmb.1727, PMID: 20010839

Korn T, Mitsdoerffer M, Croxford AL, Awasthi A, Dardalhon VA, Galileos G, Vollmar P, Stritesky GL, Kaplan MH, Waisman A, Kuchroo VK, Oukka M. 2008. IL-6 controls Th17 immunity in vivo by inhibiting the conversion of conventional T cells into Foxp3+ regulatory T cells. *PNAS* **105**:18460–18465. DOI: https://doi.org/10.1073/ pnas.0809850105, PMID: 19015529

Kozer N, Barua D, Orchard S, Nice EC, Burgess AW, Hlavacek WS, Clayton AH. 2013. Exploring higher-order EGFR oligomerisation and phosphorylation—a combined experimental and theoretical approach. *Molecular BioSystems* **9**:1849–1863. DOI: https://doi.org/10.1039/c3mb70073a, PMID: 23629589
Gorby C, Sotolongo Bellón J, Wilmes S, Warda W, Pohler E, Fyfe PK, Cozzani A, Ferrand C, Walter MR, Mitra S, Piehler J, Moraga I. 2020. Engineered IL-10 variants elicit potent immunomodulatory effects at low ligand doses. *Science Signaling* **13:eabc0653**. DOI: https://doi.org/10.1126/scisignal.abc0653, PMID: 32934073

Heinrich PC, Behrmann I, Haan S, Hermanns HM, Müller-Newen G, Schaper F. 2003. Principles of interleukin (IL)-6-type cytokine signalling and its regulation. *Biochemical Journal* **374**:1–20. DOI: https://doi.org/10.1042/bj20030407, PMID: 12773095

Hirahara K, Ghoreschi K, Yang XP, Takahashi H, Laurence A, Vahedi G, Sciumè G, Hall AO, Dupont CD, Francisco LM, Chen Q, Tanaka M, Kanno Y, Sun HW, Sharpe AH, Hunter CA, O'Shea JJ. 2012. Interleukin-27 priming of T cells controls IL-17 production in trans via induction of the ligand PD-L1. *Immunity* **36**:1017–1030. DOI: https://doi.org/10.1016/j.immuni.2012.03.024, PMID: 22726954

Hirahara K, Onodera A, Villarino AV, Bonelli M, Sciumè G, Laurence A, Sun HW, Brooks SR, Vahedi G, Shih HY, Gutierrez-Cruz G, Iwata S, Suzuki R, Mikami Y, Okamoto Y, Nakayama T, Holland SM, Hunter CA, Kanno Y, O'Shea JJ. 2015. Asymmetric action of STAT transcription factors drives transcriptional outputs and cytokine specificity. *Immunity* **42**:877–889. DOI: https://doi.org/10.1016/j.immuni.2015.04.014, PMID: 25992861

Ho CCM, Chhabra A, Starkl P, Schnorr PJ, Wilmes S, Moraga I, Kwon HS, Gaudenzio N, Sibilano R, Wehrman TS, Gakovic M, Sockolosky JT, Tiffany MR, Ring AM, Piehler J, Weissman IL, Galli SJ, Shizuru JA, Garcia KC. 2017. Decoupling the functional pleiotropy of stem cell factor by tuning c-Kit signaling. *Cell* **168**:1041–1052. DOI: https://doi.org/10.1016/j.cell.2017.02.011, PMID: 28283060

Hochberg MC. 1997. Updating the american college of rheumatology revised criteria for the classification of systemic lupus erythematosus. *Arthritis & Rheumatism* **40**:1725. DOI: https://doi.org/10.1002/art.1780400928, PMID: 9324032

Hu X, Herrero C, Li WP, Antoniv TT, Falck-Pedersen E, Koch AE, Woods JM, Haines GK, Ivashkiv LB. 2002. Sensitization of IFN-gamma Jak-STAT signaling during macrophage activation. *Nature Immunology* **3**:859–866. DOI: https://doi.org/10.1038/ni828, PMID: 12172544

Huang daW, Sherman BT, Lempicki RA. 2009a. Bioinformatics enrichment tools: paths toward the comprehensive functional analysis of large gene lists. *Nucleic Acids Research* **37**:1–13. DOI: https://doi.org/10.1093/nar/gkn923, PMID: 19033363

Huang daW, Sherman BT, Lempicki RA. 2009b. Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources. *Nature Protocols* **4**:44–57. DOI: https://doi.org/10.1038/nprot.2008.211, PMID: 19131956

Hunter CA, Jones SA. 2015. IL-6 as a keystone cytokine in health and disease. *Nature Immunology* **16**:448–457. DOI: https://doi.org/10.1038/ni.3153, PMID: 25898198

Imamichi T, Yang J, Huang daW, Sherman B, Lempicki RA. 2012. Interleukin-27 induces interferon-inducible genes: analysis of gene expression profiles using affymetrix microarray and DAVID. *Methods in Molecular Biology* **820**:25–53. DOI: https://doi.org/10.1007/978-1-61779-439-1_3, PMID: 22131024

Itzhak DN, Tyanova S, Cox J, Borner GH. 2016. Global, quantitative and dynamic mapping of protein subcellular localization. *eLife* **5**:e16950. DOI: https://doi.org/10.7554/eLife.16950, PMID: 27278775

Jones GW, McLoughlin RM, Hammond VJ, Parker CR, Williams JD, Malhotra R, Scheller J, Williams AS, Rose-John S, Topley N, Jones SA. 2010. Loss of CD4+ T cell IL-6R expression during inflammation underlines a role for IL-6 trans signaling in the local maintenance of Th17 cells. *Journal of Immunology* **184**:2130–2139. DOI: https://doi.org/10.4049/jimmunol.0901528, PMID: 20083667

Kamiya S, Owaki T, Morishima N, Fukai F, Mizuguchi J, Yoshimoto T. 2004. An indispensable role for STAT1 in IL-27-induced T-bet expression but not proliferation of naive CD4+ T cells. *The Journal of Immunology* **173**: 3871–3877. DOI: https://doi.org/10.4049/jimmunol.173.6.3871, PMID: 15356135

Kang S, Narazaki M, Metwally H, Kishimoto T. 2020. Historical overview of the interleukin-6 family cytokine. *Journal of Experimental Medicine* **217**:0347. DOI: https://doi.org/10.1084/jem.20190347

Karwacz K, Miraldi ER, Pokrovskii M, Madi A, Yosef N, Wortman I, Chen X, Watters A, Carriero N, Awasthi A, Regev A, Bonneau R, Littman D, Kuchroo VK. 2017. Critical role of IRF1 and BATF in forming chromatin landscape during type 1 regulatory cell differentiation. *Nature Immunology* **18**:412–421. DOI: https://doi.org/10.1038/ni.3683, PMID: 28166218

Kim H, Hawley TS, Hawley RG, Baumann H. 1998. Protein tyrosine phosphatase 2 (SHP-2) moderates signaling by gp130 but is not required for the induction of acute-phase plasma protein genes in hepatic cells. *Molecular and Cellular Biology* **18**:1525–1533. DOI: https://doi.org/10.1128/MCB.18.3.1525, PMID: 9488469

Kimura A, Kishimoto T. 2010. IL-6: regulator of treg/Th17 balance. *European Journal of Immunology* **40**:1830–1835. DOI: https://doi.org/10.1002/eji.201040391, PMID: 20583029

Kirchhofer A, Helma J, Schmidthals K, Frauer C, Cui S, Karcher A, Pellis M, Muyldermans S, Casas-Delucchi CS, Cardoso MC, Leonhardt H, Hopfner KP, Rothbauer U. 2010. Modulation of protein properties in living cells using nanobodies. *Nature Structural & Molecular Biology* **17**:133–138. DOI: https://doi.org/10.1038/nsmb.1727, PMID: 20010839

Korn T, Mitsdoerffer M, Croxford AL, Awasthi A, Dardalhon VA, Galileos G, Vollmar P, Stritesky GL, Kaplan MH, Waisman A, Kuchroo VK, Oukka M. 2008. IL-6 controls Th17 immunity in vivo by inhibiting the conversion of conventional T cells into Foxp3+ regulatory T cells. *PNAS* **105**:18460–18465. DOI: https://doi.org/10.1073/ pnas.0809850105, PMID: 19015529

Kozer N, Barua D, Orchard S, Nice EC, Burgess AW, Hlavacek WS, Clayton AH. 2013. Exploring higher-order EGFR oligomerisation and phosphorylation—a combined experimental and theoretical approach. *Molecular BioSystems* **9**:1849–1863. DOI: https://doi.org/10.1039/c3mb70073a, PMID: 23629589
Krutzik PO, Clutter MR, Trejo A, Nolan GP. 2011. Fluorescent cell barcoding for multiplex flow cytometry. *Current Protocols in Cytometry Chapter 6:Unit 31*. DOI: https://doi.org/10.1002/0471142956.cy0631s55, PMID: 21207359

Krutzik PO, Nolan GP. 2006. Fluorescent cell barcoding in flow cytometry allows high-throughput drug screening and signaling profiling. *Nature Methods* **3**:361–368. DOI: https://doi.org/10.1038/nmeth872, PMID: 16628206

LaPorte SL, Juo ZS, Vaclavikova J, Colf LA, Qi X, Heller NM, Keegan AD, Garcia KC. 2008. Molecular and structural basis of cytokine receptor pleiotropy in the interleukin-4/13 system. *Cell* **132**:259–272. DOI: https://doi.org/10.1016/j.cell.2007.12.030, PMID: 18243101

Levin D, Harari D, Schreiber G. 2011. Stochastic receptor expression determines cell fate upon interferon treatment. *Molecular and Cellular Biology* **31**:3252–3266. DOI: https://doi.org/10.1128/MCB.05251-11, PMID: 21690295

Liao Y, Wang J, Jaehnig EJ, Shi Z, Zhang B. 2019. WebGestalt 2019: gene set analysis toolkit with revamped UIs and APIs. *Nucleic Acids Research* **47**:W199–W205. DOI: https://doi.org/10.1093/nar/gkz401, PMID: 31114916

Lucas S, Ghilardi N, Li J, de Sauvage FJ. 2003. IL-27 regulates IL-12 responsiveness of naive CD4+ T cells through Stat1-dependent and -independent mechanisms. *PNAS* **100**:15047–15052. DOI: https://doi.org/10.1073/pnas.2536517100

Martinez-Fabregas J, Wilmes S, Wang L, Hafer M, Pohler E, Lokau J, Garbers C, Cozzani A, Fyfe PK, Piehler J, Kazemian M, Mitra S, Moraga I. 2019. Kinetics of cytokine receptor trafficking determine signaling and functional selectivity. *eLife* **8**:e49314. DOI: https://doi.org/10.7554/eLife.49314, PMID: 31774398

Matsumoto M, Shigeta A, Furukawa Y, Tanaka T, Miyasaka M, Hirata T. 2007. CD43 collaborates with P-Selectin glycoprotein Ligand-1 to mediate E-Selectin-Dependent T cell migration into inflamed skin. *The Journal of Immunology* **178**:2499–2506. DOI: https://doi.org/10.4049/jimmunol.178.4.2499

Moraga I, Harari D, Schreiber G, Uzé G, Pellegrini S. 2009. Receptor density is key to the alpha2/beta interferon differential activities. *Molecular and Cellular Biology* **29**:4778–4787. DOI: https://doi.org/10.1128/MCB.01808-08, PMID: 19564411

Moraga I, Richter D, Wilmes S, Winkelmann H, Jude K, Thomas C, Suhoski MM, Engleman EG, Piehler J, Garcia KC. 2015a. Instructive roles for cytokine-receptor binding parameters in determining signaling and functional potency. *Science Signaling* **8**:ra114. DOI: https://doi.org/10.1126/scisignal.aab2677, PMID: 26554818

Moraga I, Wernig G, Wilmes S, Gryshkova V, Richter CP, Hong WJ, Sinha R, Guo F, Fabionar H, Wehrman TS, Krutzik P, Demharter S, Plo I, Weissman IL, Minary P, Majeti R, Constantinescu SN, Piehler J, Garcia KC. 2015b. Tuning cytokine receptor signaling by re-orienting dimer geometry with surrogate ligands. *Cell* **160**:1196–1208. DOI: https://doi.org/10.1016/j.cell.2015.02.011, PMID: 25728669

Nadeau OW, Domanski P, Usacheva A, Uddin S, Platanias LC, Pitha P, Raz R, Levy D, Majchrzak B, Fish E, Colamonici OR. 1999. The proximal tyrosines of the cytoplasmic domain of the beta chain of the type I interferon receptor are essential for signal transducer and activator of transcription (Stat) 2 activation evidence that two Stat2 sites are required to reach a threshold of interferon alpha-induced Stat2 tyrosine phosphorylation that allows normal formation of interferon-stimulated gene factor 3. *The Journal of Biological Chemistry* **274**:4045–4052. DOI: https://doi.org/10.1074/jbc.274.7.4045, PMID: 9933596

Neufert C, Becker C, Wirtz S, Fantini MC, Weigmann B, Galle PR, Neurath MF. 2007. IL-27 controls the development of inducible regulatory T cells and Th17 cells via differential effects on STAT1. *European Journal of Immunology* **37**:1809–1816. DOI: https://doi.org/10.1002/eji.200636896, PMID: 17549733

O'Hagan KL, Miller SD, Phee H. 2017. Pak2 is essential for the function of Foxp3+ regulatory T cells through maintaining a suppressive treg phenotype. *Scientific Reports* **7**:17097. DOI: https://doi.org/10.1038/s41598-017-17078-7, PMID: 29213081

O'Shea JJ, Plenge R. 2012. JAK and STAT signaling molecules in Immunoregulation and immune-mediated disease. *Immunity* **36**:542–550. DOI: https://doi.org/10.1016/j.immuni.2012.03.014, PMID: 22520847

Oberg HH, Wesch D, Grüssel S, Rose-John S, Kabelitz D. 2006. Differential expression of CD126 and CD130 mediates different STAT-3 phosphorylation in CD4+CD25- and CD25high regulatory T cells. *International Immunology* **18**:555–563. DOI: https://doi.org/10.1093/intimm/dxh396, PMID: 16540526

Oniki S, Nagai H, Horikawa T, Furukawa J, Belladonna ML, Yoshimoto T, Hara I, Nishigori C. 2006. Interleukin-23 and interleukin-27 exert quite different antitumor and vaccine effects on poorly immunogenic melanoma. *Cancer Research* **66**:6395–6404. DOI: https://doi.org/10.1158/0008-5472.CAN-05-4087, PMID: 16778218

Owaki T, Asakawa M, Morishima N, Mizoguchi I, Fukai F, Takeda K, Mizuguchi J, Yoshimoto T. 2008. STAT3 is indispensable to IL-27-mediated cell proliferation but not to IL-27-induced Th1 differentiation and suppression of proinflammatory cytokine production. *The Journal of Immunology* **180**:2903–2911. DOI: https://doi.org/10.4049/jimmunol.180.5.2903, PMID: 18292512

Petretto A, Carbotti G, Inglese E, Lavarello C, Pistillo MP, Rigo V, Croce M, Longo L, Martini S, Vacca P, Ferrini S, Fabbi M. 2016. Proteomic analysis uncovers common effects of IFN-γ and IL-27 on the HLA class I antigen presentation machinery in human Cancer cells. *Oncotarget* **7**:27258–27263. DOI: https://doi.org/10.18632/oncotarget.12235, PMID: 27683036

Pflanz S, Timans JC, Cheung J, Rosales R, Kanzler H, Gilbert J, Hibbert L, Churakova T, Travis M, Vaisberg E, Blumenschein WM, Mattson JD, Wagner JL, To W, Zurawski S, McClanahan TK, Gorman DM, Bazan JF, de Waal Malefyt R, Rennick D, et al. 2002. IL-27, a heterodimeric cytokine composed of EBI3 and p28 protein, induces proliferation of naive CD4+ T cells. *Immunity* **16**:779–790. DOI: https://doi.org/10.1016/S1074-7613(02)00324-2, PMID: 12121660
Krutzik PO, Clutter MR, Trejo A, Nolan GP. 2011. Fluorescent cell barcoding for multiplex flow cytometry. *Current Protocols in Cytometry Chapter 6:Unit 31*. DOI: https://doi.org/10.1002/0471142956.cy0631s55, PMID: 21207359

Krutzik PO, Nolan GP. 2006. Fluorescent cell barcoding in flow cytometry allows high-throughput drug screening and signaling profiling. *Nature Methods* **3**:361–368. DOI: https://doi.org/10.1038/nmeth872, PMID: 16628206

LaPorte SL, Juo ZS, Vaclavikova J, Colf LA, Qi X, Heller NM, Keegan AD, Garcia KC. 2008. Molecular and structural basis of cytokine receptor pleiotropy in the interleukin-4/13 system. *Cell* **132**:259–272. DOI: https://doi.org/10.1016/j.cell.2007.12.030, PMID: 18243101

Levin D, Harari D, Schreiber G. 2011. Stochastic receptor expression determines cell fate upon interferon treatment. *Molecular and Cellular Biology* **31**:3252–3266. DOI: https://doi.org/10.1128/MCB.05251-11, PMID: 21690295

Liao Y, Wang J, Jaehnig EJ, Shi Z, Zhang B. 2019. WebGestalt 2019: gene set analysis toolkit with revamped UIs and APIs. *Nucleic Acids Research* **47**:W199–W205. DOI: https://doi.org/10.1093/nar/gkz401, PMID: 31114916

Lucas S, Ghilardi N, Li J, de Sauvage FJ. 2003. IL-27 regulates IL-12 responsiveness of naive CD4+ T cells through Stat1-dependent and -independent mechanisms. *PNAS* **100**:15047–15052. DOI: https://doi.org/10.1073/pnas.2536517100

Martinez-Fabregas J, Wilmes S, Wang L, Hafer M, Pohler E, Lokau J, Garbers C, Cozzani A, Fyfe PK, Piehler J, Kazemian M, Mitra S, Moraga I. 2019. Kinetics of cytokine receptor trafficking determine signaling and functional selectivity. *eLife* **8**:e49314. DOI: https://doi.org/10.7554/eLife.49314, PMID: 31774398

Matsumoto M, Shigeta A, Furukawa Y, Tanaka T, Miyasaka M, Hirata T. 2007. CD43 collaborates with P-Selectin glycoprotein Ligand-1 to mediate E-Selectin-Dependent T cell migration into inflamed skin. *The Journal of Immunology* **178**:2499–2506. DOI: https://doi.org/10.4049/jimmunol.178.4.2499

Moraga I, Harari D, Schreiber G, Uzé G, Pellegrini S. 2009. Receptor density is key to the alpha2/beta interferon differential activities. *Molecular and Cellular Biology* **29**:4778–4787. DOI: https://doi.org/10.1128/MCB.01808-08, PMID: 19564411

Moraga I, Richter D, Wilmes S, Winkelmann H, Jude K, Thomas C, Suhoski MM, Engleman EG, Piehler J, Garcia KC. 2015a. Instructive roles for cytokine-receptor binding parameters in determining signaling and functional potency. *Science Signaling* **8**:ra114. DOI: https://doi.org/10.1126/scisignal.aab2677, PMID: 26554818

Moraga I, Wernig G, Wilmes S, Gryshkova V, Richter CP, Hong WJ, Sinha R, Guo F, Fabionar H, Wehrman TS, Krutzik P, Demharter S, Plo I, Weissman IL, Minary P, Majeti R, Constantinescu SN, Piehler J, Garcia KC. 2015b. Tuning cytokine receptor signaling by re-orienting dimer geometry with surrogate ligands. *Cell* **160**:1196–1208. DOI: https://doi.org/10.1016/j.cell.2015.02.011, PMID: 25728669

Nadeau OW, Domanski P, Usacheva A, Uddin S, Platanias LC, Pitha P, Raz R, Levy D, Majchrzak B, Fish E, Colamonici OR. 1999. The proximal tyrosines of the cytoplasmic domain of the beta chain of the type I interferon receptor are essential for signal transducer and activator of transcription (Stat) 2 activation evidence that two Stat2 sites are required to reach a threshold of interferon alpha-induced Stat2 tyrosine phosphorylation that allows normal formation of interferon-stimulated gene factor 3. *The Journal of Biological Chemistry* **274**:4045–4052. DOI: https://doi.org/10.1074/jbc.274.7.4045, PMID: 9933596

Neufert C, Becker C, Wirtz S, Fantini MC, Weigmann B, Galle PR, Neurath MF. 2007. IL-27 controls the development of inducible regulatory T cells and Th17 cells via differential effects on STAT1. *European Journal of Immunology* **37**:1809–1816. DOI: https://doi.org/10.1002/eji.200636896, PMID: 17549733

O'Hagan KL, Miller SD, Phee H. 2017. Pak2 is essential for the function of Foxp3+ regulatory T cells through maintaining a suppressive treg phenotype. *Scientific Reports* **7**:17097. DOI: https://doi.org/10.1038/s41598-017-17078-7, PMID: 29213081

O'Shea JJ, Plenge R. 2012. JAK and STAT signaling molecules in Immunoregulation and immune-mediated disease. *Immunity* **36**:542–550. DOI: https://doi.org/10.1016/j.immuni.2012.03.014, PMID: 22520847

Oberg HH, Wesch D, Grüssel S, Rose-John S, Kabelitz D. 2006. Differential expression of CD126 and CD130 mediates different STAT-3 phosphorylation in CD4+CD25- and CD25high regulatory T cells. *International Immunology* **18**:555–563. DOI: https://doi.org/10.1093/intimm/dxh396, PMID: 16540526

Oniki S, Nagai H, Horikawa T, Furukawa J, Belladonna ML, Yoshimoto T, Hara I, Nishigori C. 2006. Interleukin-23 and interleukin-27 exert quite different antitumor and vaccine effects on poorly immunogenic melanoma. *Cancer Research* **66**:6395–6404. DOI: https://doi.org/10.1158/0008-5472.CAN-05-4087, PMID: 16778218

Owaki T, Asakawa M, Morishima N, Mizoguchi I, Fukai F, Takeda K, Mizuguchi J, Yoshimoto T. 2008. STAT3 is indispensable to IL-27-mediated cell proliferation but not to IL-27-induced Th1 differentiation and suppression of proinflammatory cytokine production. *The Journal of Immunology* **180**:2903–2911. DOI: https://doi.org/10.4049/jimmunol.180.5.2903, PMID: 18292512

Petretto A, Carbotti G, Inglese E, Lavarello C, Pistillo MP, Rigo V, Croce M, Longo L, Martini S, Vacca P, Ferrini S, Fabbi M. 2016. Proteomic analysis uncovers common effects of IFN-γ and IL-27 on the HLA class I antigen presentation machinery in human Cancer cells. *Oncotarget* **7**:27258–27263. DOI: https://doi.org/10.18632/oncotarget.12235, PMID: 27683036

Pflanz S, Timans JC, Cheung J, Rosales R, Kanzler H, Gilbert J, Hibbert L, Churakova T, Travis M, Vaisberg E, Blumenschein WM, Mattson JD, Wagner JL, To W, Zurawski S, McClanahan TK, Gorman DM, Bazan JF, de Waal Malefyt R, Rennick D, et al. 2002. IL-27, a heterodimeric cytokine composed of EBI3 and p28 protein, induces proliferation of naive CD4+ T cells. *Immunity* **16**:779–790. DOI: https://doi.org/10.1016/S1074-7613(02)00324-2, PMID: 12121660
Pflanz S, Hibbert L, Mattson J, Rosales R, Vaisberg E, Bazan JF, Phillips JH, McClanahan TK, de Waal Malefyt R, Kastelein RA. 2004. WSX-1 and glycoprotein 130 constitute a Signal-Transducing receptor for IL-27. *The Journal of Immunology* **172**:2225-2231. DOI: https://doi.org/10.4049/jimmunol.172.4.2225

Pot C, Apetoh L, Awasthi A, Kuchroo VK. 2011. Induction of regulatory Tr1 cells and inhibition of T(H)17 cells by IL-27. *Seminars in Immunology* **23**:438-445. DOI: https://doi.org/10.1016/j.simim.2011.08.003, PMID: 21893418

Pradhan A, Lambert QT, Griner LN, Reuther GW. 2010. Activation of JAK2-V617F by components of heterodimeric cytokine receptors. *Journal of Biological Chemistry* **285**:16651-16663. DOI: https://doi.org/10.1074/jbc.M109.071191, PMID: 20363735

Regis G, Pensa S, Boselli D, Novelli F, Poli V. 2008. Ups and downs: the STAT1:stat3 seesaw of interferon and gp130 receptor signalling. *Seminars in Cell & Developmental Biology* **19**:351-359. DOI: https://doi.org/10.1016/j.semcdb.2008.06.004, PMID: 18620071

Richter D, Moraga I, Winkelmann H, Birkholz O, Wilmes S, Schulte M, Kraich M, Kenneweg H, Beutel O, Selenschik P, Paterok D, Gavutis M, Schmidt T, Garcia KC, Müller TD, Piehler J. 2017. Ligand-induced type II interleukin-4 receptor dimers are sustained by rapid re-association within plasma membrane microcompartments. *Nature Communications* **8**:15976. DOI: https://doi.org/10.1038/ncomms15976, PMID: 28706306

Röder F, Lubk A, Wolf D, Niermann T. 2014. Noise estimation for off-axis electron holography. *Ultramicroscopy* **144**:32-42. DOI: https://doi.org/10.1016/j.ultramic.2014.04.002, PMID: 24821224

Roverling C, Zimmer AD, Kozar I, Hermanns HM, Letellier E, Vallar L, Nazarov PV, Nicot N, Ginolhac A, Haan S, Behrmann I, Haan C. 2017. Crosstalk between different family members: il27 recapitulates ifny responses in HCC cells, but is inhibited by IL6-type cytokines. *Biochimica Et Biophysica Acta (BBA) - Molecular Cell Research* **1864**:516-526. DOI: https://doi.org/10.1016/j.bbamcr.2016.12.006

Rose-John S. 2018. Interleukin-6 family cytokines. *Cold Spring Harbor Perspectives in Biology* **10**:a028415. DOI: https://doi.org/10.1101/cshperspect.a028415, PMID: 28620096

Ruprecht V, Weghuber J, Wieser S, Schütz GJ. 2010. *Advances in Planar Lipid Bilayers and Liposomes*. Amsterdam, Netherlands: Elsevier.

Rusinova I, Forster S, Yu S, Kannan A, Masse M, Cumming H, Chapman R, Hertzog PJ. 2013. Interferome v2.0: an updated database of annotated interferon-regulated genes. *Nucleic Acids Research* **41**:D1040-D1046. DOI: https://doi.org/10.1093/nar/gks1215, PMID: 23203888

Rutz S, Kayagaki N, Phung QT, Eidenschenk C, Noubade R, Wang X, Lesch J, Lu R, Newton K, Huang OW, Cochran AG, Vasser M, Fauber BP, DeVoss J, Webster J, Diehl L, Modrusan Z, Kirkpatrick DS, Lill JR, Ouyang W, et al. 2015. Deubiquitinase DUBA is a post-translational Brake on interleukin-17 production in T cells. *Nature* **518**:417-421. DOI: https://doi.org/10.1038/nature13979, PMID: 25470037

Satoh J, Tabunoki H. 2013. A comprehensive profile of ChIP-Seq-Based STAT1 target genes suggests the complexity of STAT1-Mediated gene regulatory mechanisms. *Gene Regulation and Systems Biology* **7**:GRSB.S11433–.11456. DOI: https://doi.org/10.4137/GRSB.S11433, PMID: 23645984

Schmitz J, Weissenbach M, Haan S, Heinrich PC, Schaper F. 2000. SOCS3 exerts its inhibitory function on interleukin-6 signal transduction through the SHP2 recruitment site of gp130. *Journal of Biological Chemistry* **275**:12848-12856. DOI: https://doi.org/10.1074/jbc.275.17.12848, PMID: 10777583

Sergé A, Bertaux N, Rigneault H, Marguet D. 2008. Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes. *Nature Methods* **5**:687-694. DOI: https://doi.org/10.1038/nmeth.1233, PMID: 18604216

Sharif MN, Tassiulas I, Hu Y, Mecklenbräuker I, Tarakhovsky A, Ivashkiv LB. 2004. IFN-alpha priming results in a gain of proinflammatory function by IL-10: implications for systemic lupus erythematosus pathogenesis. *The Journal of Immunology* **172**:6476-6481. DOI: https://doi.org/10.4049/jimmunol.172.10.6476, PMID: 15128840

Slenter DN, Kutmon M, Hanspers K, Riutta A, Windsor J, Nunes N, Mélius J, Cirillo E, Coort SL, Digles D, Ehrhart F, Giesbertz P, Kalafati M, Martens M, Miller R, Nishida K, Rieswijk L, Waagmeester A, Eijssen LMT, Evelo CT, et al. 2018. WikiPathways: a multifaceted pathway database bridging metabolomics to other omics research. *Nucleic Acids Research* **46**:D661-D667. DOI: https://doi.org/10.1093/nar/gkx1064, PMID: 29136241

Spangler JB, Moraga I, Jude KM, Savvides CS, Garcia KC. 2019. A strategy for the selection of monovalent antibodies that span protein dimer interfaces. *Journal of Biological Chemistry* **294**:13876-13886. DOI: https://doi.org/10.1074/jbc.RA119.009213, PMID: 31387945

Stumhofer JS, Laurence A, Wilson EH, Huang E, Tato CM, Johnson LM, Villarino AV, Huang Q, Yoshimura A, Sehy D, Saris CJ, O'Shea JJ, Hennighausen L, Ernst M, Hunter CA. 2006. Interleukin 27 negatively regulates the development of interleukin 17-producing T helper cells during chronic inflammation of the central nervous system. *Nature Immunology* **7**:937-945. DOI: https://doi.org/10.1038/ni1376, PMID: 16906166

Stumhofer JS, Silver JS, Laurence A, Porrett PM, Harris TH, Turka LA, Ernst M, Saris CJ, O'Shea JJ, Hunter CA. 2007. Interleukins 27 and 6 induce STAT3-mediated T cell production of interleukin 10. *Nature Immunology* **8**:1363-1371. DOI: https://doi.org/10.1038/ni1537, PMID: 17994025

Suh HN, Lee SH, Lee MY, Lee YJ, Lee JH, Han HJ. 2008. Role of interleukin-6 in the control of DNA synthesis of hepatocytes: involvement of PKC, p44/42 MAPKs, and PPARdelta. *Cellular Physiology and Biochemistry* **22**:673-684. DOI: https://doi.org/10.1159/000185551, PMID: 19088449

Sunnåker M, Busetto AG, Numminen E, Corander J, Foll M, Dessimoz C. 2013. Approximate bayesian computation. *PLOS Computational Biology* **9**:e1002803. DOI: https://doi.org/10.1371/journal.pcbi.1002803, PMID: 23341757

Takeda A, Hamano S, Yamanaka A, Hanada T, Ishibashi T, Mak TW, Yoshimura A, Yoshida H. 2003. Cutting edge: role of IL-27/WSX-1 signaling for induction of T-bet through activation of STAT1 during initial Th1
Pflanz S, Hibbert L, Mattson J, Rosales R, Vaisberg E, Bazan JF, Phillips JH, McClanahan TK, de Waal Malefyt R, Kastelein RA. 2004. WSX-1 and glycoprotein 130 constitute a Signal-Transducing receptor for IL-27. *The Journal of Immunology* **172**:2225-2231. DOI: https://doi.org/10.4049/jimmunol.172.4.2225

Pot C, Apetoh L, Awasthi A, Kuchroo VK. 2011. Induction of regulatory Tr1 cells and inhibition of T(H)17 cells by IL-27. *Seminars in Immunology* **23**:438-445. DOI: https://doi.org/10.1016/j.simim.2011.08.003, PMID: 21893418

Pradhan A, Lambert QT, Griner LN, Reuther GW. 2010. Activation of JAK2-V617F by components of heterodimeric cytokine receptors. *Journal of Biological Chemistry* **285**:16651-16663. DOI: https://doi.org/10.1074/jbc.M109.071191, PMID: 20363735

Regis G, Pensa S, Boselli D, Novelli F, Poli V. 2008. Ups and downs: the STAT1:stat3 seesaw of interferon and gp130 receptor signalling. *Seminars in Cell & Developmental Biology* **19**:351-359. DOI: https://doi.org/10.1016/j.semcdb.2008.06.004, PMID: 18620071

Richter D, Moraga I, Winkelmann H, Birkholz O, Wilmes S, Schulte M, Kraich M, Kenneweg H, Beutel O, Selenschik P, Paterok D, Gavutis M, Schmidt T, Garcia KC, Müller TD, Piehler J. 2017. Ligand-induced type II interleukin-4 receptor dimers are sustained by rapid re-association within plasma membrane microcompartments. *Nature Communications* **8**:15976. DOI: https://doi.org/10.1038/ncomms15976, PMID: 28706306

Röder F, Lubk A, Wolf D, Niermann T. 2014. Noise estimation for off-axis electron holography. *Ultramicroscopy* **144**:32-42. DOI: https://doi.org/10.1016/j.ultramic.2014.04.002, PMID: 24821224

Roverling C, Zimmer AD, Kozar I, Hermanns HM, Letellier E, Vallar L, Nazarov PV, Nicot N, Ginolhac A, Haan S, Behrmann I, Haan C. 2017. Crosstalk between different family members: il27 recapitulates ifny responses in HCC cells, but is inhibited by IL6-type cytokines. *Biochimica Et Biophysica Acta (BBA) - Molecular Cell Research* **1864**:516-526. DOI: https://doi.org/10.1016/j.bbamcr.2016.12.006

Rose-John S. 2018. Interleukin-6 family cytokines. *Cold Spring Harbor Perspectives in Biology* **10**:a028415. DOI: https://doi.org/10.1101/cshperspect.a028415, PMID: 28620096

Ruprecht V, Weghuber J, Wieser S, Schütz GJ. 2010. *Advances in Planar Lipid Bilayers and Liposomes*. Amsterdam, Netherlands: Elsevier.

Rusinova I, Forster S, Yu S, Kannan A, Masse M, Cumming H, Chapman R, Hertzog PJ. 2013. Interferome v2.0: an updated database of annotated interferon-regulated genes. *Nucleic Acids Research* **41**:D1040-D1046. DOI: https://doi.org/10.1093/nar/gks1215, PMID: 23203888

Rutz S, Kayagaki N, Phung QT, Eidenschenk C, Noubade R, Wang X, Lesch J, Lu R, Newton K, Huang OW, Cochran AG, Vasser M, Fauber BP, DeVoss J, Webster J, Diehl L, Modrusan Z, Kirkpatrick DS, Lill JR, Ouyang W, et al. 2015. Deubiquitinase DUBA is a post-translational Brake on interleukin-17 production in T cells. *Nature* **518**:417-421. DOI: https://doi.org/10.1038/nature13979, PMID: 25470037

Satoh J, Tabunoki H. 2013. A comprehensive profile of ChIP-Seq-Based STAT1 target genes suggests the complexity of STAT1-Mediated gene regulatory mechanisms. *Gene Regulation and Systems Biology* **7**:GRSB. S11433–.11456. DOI: https://doi.org/10.4137/GRSB.S11433, PMID: 23645984

Schmitz J, Weissenbach M, Haan S, Heinrich PC, Schaper F. 2000. SOCS3 exerts its inhibitory function on interleukin-6 signal transduction through the SHP2 recruitment site of gp130. *Journal of Biological Chemistry* **275**:12848-12856. DOI: https://doi.org/10.1074/jbc.275.17.12848, PMID: 10777583

Sergé A, Bertaux N, Rigneault H, Marguet D. 2008. Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes. *Nature Methods* **5**:687-694. DOI: https://doi.org/10.1038/nmeth.1233, PMID: 18604216

Sharif MN, Tassiulas I, Hu Y, Mecklenbräuker I, Tarakhovsky A, Ivashkiv LB. 2004. IFN-alpha priming results in a gain of proinflammatory function by IL-10: implications for systemic lupus erythematosus pathogenesis. *The Journal of Immunology* **172**:6476-6481. DOI: https://doi.org/10.4049/jimmunol.172.10.6476, PMID: 15128840

Slenter DN, Kutmon M, Hanspers K, Riutta A, Windsor J, Nunes N, Mélius J, Cirillo E, Coort SL, Digles D, Ehrhart F, Giesbertz P, Kalafati M, Martens M, Miller R, Nishida K, Rieswijk L, Waagmeester A, Eijssen LMT, Evelo CT, et al. 2018. WikiPathways: a multifaceted pathway database bridging metabolomics to other omics research. *Nucleic Acids Research* **46**:D661-D667. DOI: https://doi.org/10.1093/nar/gkx1064, PMID: 29136241

Spangler JB, Moraga I, Jude KM, Savvides CS, Garcia KC. 2019. A strategy for the selection of monovalent antibodies that span protein dimer interfaces. *Journal of Biological Chemistry* **294**:13876-13886. DOI: https://doi.org/10.1074/jbc.RA119.009213, PMID: 31387945

Stumhofer JS, Laurence A, Wilson EH, Huang E, Tato CM, Johnson LM, Villarino AV, Huang Q, Yoshimura A, Sehy D, Saris CJ, O'Shea JJ, Hennighausen L, Ernst M, Hunter CA. 2006. Interleukin 27 negatively regulates the development of interleukin 17-producing T helper cells during chronic inflammation of the central nervous system. *Nature Immunology* **7**:937-945. DOI: https://doi.org/10.1038/ni1376, PMID: 16906166

Stumhofer JS, Silver JS, Laurence A, Porrett PM, Harris TH, Turka LA, Ernst M, Saris CJ, O'Shea JJ, Hunter CA. 2007. Interleukins 27 and 6 induce STAT3-mediated T cell production of interleukin 10. *Nature Immunology* **8**: 1363-1371. DOI: https://doi.org/10.1038/ni1537, PMID: 17994025

Suh HN, Lee SH, Lee MY, Lee YJ, Lee JH, Han HJ. 2008. Role of interleukin-6 in the control of DNA synthesis of hepatocytes: involvement of PKC, p44/42 MAPKs, and PPARdelta. *Cellular Physiology and Biochemistry* **22**: 673-684. DOI: https://doi.org/10.1159/000185551, PMID: 19088449

Sunnåker M, Busetto AG, Numminen E, Corander J, Foll M, Dessimoz C. 2013. Approximate bayesian computation. *PLOS Computational Biology* **9**:e1002803. DOI: https://doi.org/10.1371/journal.pcbi.1002803, PMID: 23341757

Takeda A, Hamano S, Yamanaka A, Hanada T, Ishibashi T, Mak TW, Yoshimura A, Yoshida H. 2003. Cutting edge: role of IL-27/WSX-1 signaling for induction of T-bet through activation of STAT1 during initial Th1
commitment. *The Journal of Immunology* **170**:4886-4890. DOI: https://doi.org/10.4049/jimmunol.170.10.4886, PMID: 12734330

Tokuyama M, Kong Y, Song E, Jayewickreme T, Kang I, Iwasaki A. 2018. ERVmap analysis reveals genome-wide transcription of human endogenous retroviruses. *PNAS* **115**:12565-12572. DOI: https://doi.org/10.1073/pnas.1814589115, PMID: 30455304

Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MP. 2009. Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. *Journal of the Royal Society Interface* **6**:187-202. DOI: https://doi.org/10.1098/rsif.2008.0172, PMID: 19205079

Twohig JP, Cardus Figueras A, Andrews R, Wiede F, Cossins BC, Derrac Soria A, Lewis MJ, Townsend MJ, Millrine D, Li J, Hill DG, Uceda Fernandez J, Liu X, Szomolay B, Pepper CJ, Taylor PR, Pitzalis C, Tiganis T, Williams NM, Jones GW, et al. 2019. Activation of naive CD4⁺ T cells re-tunes STAT1 signaling to deliver unique cytokine responses in memory CD4⁺ T cells. *Nature Immunology* **20**:458-470. DOI: https://doi.org/10.1038/s41590-019-0350-0, PMID: 30890796

Umeshita-Suyama R, Sugimoto R, Akaiwa M, Arima K, Yu B, Wada M, Kuwano M, Nakajima K, Hamasaki N, Izuhara K. 2000. Characterization of IL-4 and IL-13 signals dependent on the human IL-13 receptor alpha chain 1: redundancy of requirement of tyrosine residue for STAT3 activation. *International Immunology* **12**:1499-1509. DOI: https://doi.org/10.1093/intimm/12.11.1499, PMID: 11058569

Villarino AV, Stumhofer JS, Saris CJM, Kastelein RA, de Sauvage FJ, Hunter CA. 2006. IL-27 limits IL-2 production during Th1 differentiation. *The Journal of Immunology* **176**:237-247. DOI: https://doi.org/10.4049/jimmunol.176.1.237

Vogelsang J, Kasper R, Steinhauer C, Person B, Heilemann M, Sauer M, Tinnefeld P. 2008. A reducing and oxidizing system minimizes photobleaching and blinking of fluorescent dyes. *Angewandte Chemie International Edition* **47**:5465-5469. DOI: https://doi.org/10.1002/anie.200801518, PMID: 18601270

Wiederkehr-Adam M, Ernst P, Müller K, Bieck E, Gombert FO, Ottl J, Graff P, Grossmüller F, Heim MH. 2003. Characterization of phosphopeptide motifs specific for the src homology 2 domains of signal transducer and activator of transcription 1 (STAT1) and STAT3. *Journal of Biological Chemistry* **278**:16117-16128. DOI: https://doi.org/10.1074/jbc.M300261200, PMID: 12591923

Wilmes S, Beutel O, Li Z, Francois-Newton V, Richter CP, Janning D, Kroll C, Hanhart P, Hötte K, You C, Uzé G, Pellegrini S, Piehler J. 2015. Receptor dimerization dynamics as a regulatory valve for plasticity of type I interferon signaling. *Journal of Cell Biology* **209**:579-593. DOI: https://doi.org/10.1083/jcb.201412049, PMID: 26008745

Wilmes S, Hafer M, Vuorio J, Tucker JA, Winkelmann H, Löchte S, Stanly TA, Pulgar Prieto KD, Poojari C, Sharma V, Richter CP, Kurre R, Hubbard SR, Garcia KC, Moraga I, Vattulainen I, Hitchcock IS, Piehler J. 2020. Mechanism of homodimeric cytokine receptor activation and dysregulation by oncogenic mutations. *Science* **367**:643-652. DOI: https://doi.org/10.1126/science.aaw3242, PMID: 32029621

Wilmes S. 2021. Cytokine_modelling. Software Heritage. swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d. https://archive.softwareheritage.org/swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d

Wong LH, Hatzinisiriou I, Devenish RJ, Ralph SJ. 1998. IFN-gamma priming up-regulates IFN-stimulated gene factor 3 (ISGF3) components, augmenting responsiveness of IFN-resistant melanoma cells to type I IFNs. *Journal of Immunology* **160**:5475-5484. DOI: https://doi.org/10.1165/9605150

Yasukawa H, Ohishi M, Mori H, Murakami M, Chinen T, Aki D, Hanada T, Takeda K, Akira S, Hoshijima M, Hirano T, Chien KR, Yoshimura A. 2003. IL-6 induces an anti-inflammatory response in the absence of SOCS3 in macrophages. *Nature Immunology* **4**:551-556. DOI: https://doi.org/10.1038/ni938, PMID: 12754507

Ye DZ, Field J. 2012. PAK signaling in cancer. *Cellular Logistics* **2**:105-116. DOI: https://doi.org/10.4161/cl.21882, PMID: 23162742

Yoshida H, Hunter CA. 2015. The immunobiology of interleukin-27. *Annual Review of Immunology* **33**:417-443. DOI: https://doi.org/10.1146/annurev-immunol-032414-112134, PMID: 25861977

Yoshimura A, Wakabayashi Y, Mori T. 2010. Cellular and molecular basis for the regulation of inflammation by TGF-beta. *Journal of Biochemistry* **147**:781-792. DOI: https://doi.org/10.1093/jb/mvq043, PMID: 20410014

You C, Marquez-Lago TT, Richter CP, Wilmes S, Moraga I, Garcia KC, Leier A, Piehler J. 2016. Receptor dimer stabilization by hierarchical plasma membrane microcompartments regulates cytokine signaling. *Science Advances* **2**:e1600452. DOI: https://doi.org/10.1126/sciadv.1600452, PMID: 27957535

Zenke K, Muroi M, Tanamoto KI. 2018. IRF1 supports DNA binding of STAT1 by promoting its phosphorylation. *Immunology and Cell Biology* **96**:1095-1103. DOI: https://doi.org/10.1111/imcb.12185, PMID: 29893425
commitment. *The Journal of Immunology* **170**:4886-4890. DOI: https://doi.org/10.4049/jimmunol.170.10.4886, PMID: 12734330

Tokuyama M, Kong Y, Song E, Jayewickreme T, Kang I, Iwasaki A. 2018. ERVmap analysis reveals genome-wide transcription of human endogenous retroviruses. *PNAS* **115**:12565-12572. DOI: https://doi.org/10.1073/pnas.1814589115, PMID: 30455304

Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MP. 2009. Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. *Journal of the Royal Society Interface* **6**:187-202. DOI: https://doi.org/10.1098/rsif.2008.0172, PMID: 19205079

Twohig JP, Cardus Figueras A, Andrews R, Wiede F, Cossins BC, Derrac Soria A, Lewis MJ, Townsend MJ, Millrine D, Li J, Hill DG, Uceda Fernandez J, Liu X, Szomolay B, Pepper CJ, Taylor PR, Pitzalis C, Tiganis T, Williams NM, Jones GW, et al. 2019. Activation of naive CD4⁺ T cells re-tunes STAT1 signaling to deliver unique cytokine responses in memory CD4⁺ T cells. *Nature Immunology* **20**:458-470. DOI: https://doi.org/10.1038/s41590-019-0350-0, PMID: 30890796

Umeshita-Suyama R, Sugimoto R, Akaiwa M, Arima K, Yu B, Wada M, Kuwano M, Nakajima K, Hamasaki N, Izuhara K. 2000. Characterization of IL-4 and IL-13 signals dependent on the human IL-13 receptor alpha chain 1: redundancy of requirement of tyrosine residue for STAT3 activation. *International Immunology* **12**:1499-1509. DOI: https://doi.org/10.1093/intimm/12.11.1499, PMID: 11058569

Villarino AV, Stumhofer JS, Saris CJM, Kastelein RA, de Sauvage FJ, Hunter CA. 2006. IL-27 limits IL-2 production during Th1 differentiation. *The Journal of Immunology* **176**:237-247. DOI: https://doi.org/10.4049/jimmunol.176.1.237

Vogelsang J, Kasper R, Steinhauer C, Person B, Heilemann M, Sauer M, Tinnefeld P. 2008. A reducing and oxidizing system minimizes photobleaching and blinking of fluorescent dyes. *Angewandte Chemie International Edition* **47**:5465-5469. DOI: https://doi.org/10.1002/anie.200801518, PMID: 18601270

Wiederkehr-Adam M, Ernst P, Müller K, Bieck E, Gombert FO, Ottl J, Graff P, Grossmüller F, Heim MH. 2003. Characterization of phosphopeptide motifs specific for the src homology 2 domains of signal transducer and activator of transcription 1 (STAT1) and STAT3. *Journal of Biological Chemistry* **278**:16117-16128. DOI: https://doi.org/10.1074/jbc.M300261200, PMID: 12591923

Wilmes S, Beutel O, Li Z, Francois-Newton V, Richter CP, Janning D, Kroll C, Hanhart P, Hötte K, You C, Uzé G, Pellegrini S, Piehler J. 2015. Receptor dimerization dynamics as a regulatory valve for plasticity of type I interferon signaling. *Journal of Cell Biology* **209**:579-593. DOI: https://doi.org/10.1083/jcb.201412049, PMID: 26008745

Wilmes S, Hafer M, Vuorio J, Tucker JA, Winkelmann H, Löchte S, Stanly TA, Pulgar Prieto KD, Poojari C, Sharma V, Richter CP, Kurre R, Hubbard SR, Garcia KC, Moraga I, Vattulainen I, Hitchcock IS, Piehler J. 2020. Mechanism of homodimeric cytokine receptor activation and dysregulation by oncogenic mutations. *Science* **367**:643-652. DOI: https://doi.org/10.1126/science.aaw3242, PMID: 32029621

Wilmes S. 2021. Cytokine_modelling. Software Heritage. swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d. https://archive.softwareheritage.org/swh:1:rev:9c3e0ddc7a96eac941baad560d1541d660b0515d

Wong LH, Hatzinisiriou I, Devenish RJ, Ralph SJ. 1998. IFN-gamma priming up-regulates IFN-stimulated gene factor 3 (ISGF3) components, augmenting responsiveness of IFN-resistant melanoma cells to type I IFNs. *Journal of Immunology* **160**:5475-5484. DOI: https://doi.org/10.1165/9605150

Yasukawa H, Ohishi M, Mori H, Murakami M, Chinen T, Aki D, Hanada T, Takeda K, Akira S, Hoshijima M, Hirano T, Chien KR, Yoshimura A. 2003. IL-6 induces an anti-inflammatory response in the absence of SOCS3 in macrophages. *Nature Immunology* **4**:551-556. DOI: https://doi.org/10.1038/ni938, PMID: 12754507

Ye DZ, Field J. 2012. PAK signaling in cancer. *Cellular Logistics* **2**:105-116. DOI: https://doi.org/10.4161/cl.21882, PMID: 23162742

Yoshida H, Hunter CA. 2015. The immunobiology of interleukin-27. *Annual Review of Immunology* **33**:417-443. DOI: https://doi.org/10.1146/annurev-immunol-032414-112134, PMID: 25861977

Yoshimura A, Wakabayashi Y, Mori T. 2010. Cellular and molecular basis for the regulation of inflammation by TGF-beta. *Journal of Biochemistry* **147**:781-792. DOI: https://doi.org/10.1093/jb/mvq043, PMID: 20410014

You C, Marquez-Lago TT, Richter CP, Wilmes S, Moraga I, Garcia KC, Leier A, Piehler J. 2016. Receptor dimer stabilization by hierarchical plasma membrane microcompartments regulates cytokine signaling. *Science Advances* **2**:e1600452. DOI: https://doi.org/10.1126/sciadv.1600452, PMID: 27957535

Zenke K, Muroi M, Tanamoto KI. 2018. IRF1 supports DNA binding of STAT1 by promoting its phosphorylation. *Immunology and Cell Biology* **96**:1095-1103. DOI: https://doi.org/10.1111/imcb.12185, PMID: 29893425