Experimental and Computational Studies of IL-6 Signaling in Endothelial Cells under Hypoxia Serum Starvation Conditions

Abstract

Many diseases associated with angiogenesis involve inflammatory cytokine mediated responses. Targeting angiogenesis as a predominant strategy has shown limited effects in many contexts including peripheral arterial disease (PAD). One potential reason for the unsuccessful outcome is the interdependence between inflammation and angiogenesis. Inflammation-based therapies primarily target inflammatory cytokines such as interleukin-6 (IL-6) in T cells, macrophages, cancer cells, muscle cells. However, the mechanism of how these cytokines act on endothelial cells under PAD-specific hypoxia serum starvation (HSS) conditions are not well understood. Thus, we focus on one of the major inflammatory cytokines, IL-6, mediated intracellular signaling in endothelial cells under HSS conditions by conducting relevant in vitro experiments on human umbilical vein endothelial cells (HUVECs) and developing an experimentally validated computational model. Our model quantitatively characterized the effects of IL-6 classic and trans-signaling in activating the signal transducer and activator of transcription 3 (STAT3), phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt), and mitogen-activated protein kinase (MAPK) signaling to phosphorylate STAT3, extracellular regulated kinase (ERK) and Akt, respectively in endothelial cells under HSS condition. The trained and validated experiment-based computational model was used to characterize the dynamics of phosphorylated STAT3 (pSTAT3), Akt (pAkt), and ERK (pERK) in response to IL-6 classic and/or trans-signaling under HSS conditions. The model predicts that IL-6 classic and trans-signaling induced responses are dose dependent. In addition, IL-6 trans-signaling induces greater downstream signaling responses compared to classic signaling and plays a dominant role in the overall effects due to a tighter binding of the ligand and receptors and an abundant supply of soluble receptor sIL-6R because of the experimental setting. Moreover, our model identifies the species and kinetic parameters that specifically have a significant impact on the phosphorylation of STAT3, Akt, and ERK, which represent potential targets for the inflammatory cytokine mediated signaling and angiogenesis-based therapies under HSS conditions. Overall, the model predicts the effects of IL-6 classic and/or trans-signaling stimulation under HSS condition quantitatively and provides a framework for analyzing and integrating experimental data. More broadly, this model can be applied to identify potential targets that influence inflammatory cytokine mediated signaling in endothelial cells under HSS conditions and to investigate the effects of angiogenesis- and inflammation-based therapies specific to PAD.

Graphical Abstract

INTRODUCTION

Angiogenesis is the formation of new blood capillaries from pre-existing blood vessels (1) and it plays an important role in many diseases, such as peripheral arterial disease (PAD), cancer, and ocular diseases, as well as regenerative medicine and tissue engineering. As blood vessels are essential for the delivery of nutrients, proper angiogenesis is critical for cell survival within tissues, including tumors. Targeting angiogenesis is an important strategy in many contexts including PAD. PAD is a sequalae of systemic atherosclerosis, which leads to an obstruction in arteries and further limits blood flow to distal tissues (2). Promoting angiogenesis has been an important investigational strategy for PAD treatment; however, it has not been successful. At least one potential explanation for this clinical failure is that angiogenesis triggers inflammation (2,3) and inflammation usually causes malfunctional vessel development (3), which limits the angiogenesis-base strategy due to the inability to avoid producing leaky, mal-formed, vessels that are incapable of increasing perfusion to the ischemic limb. Also, inflammation can promote angiogenesis in various ways. Specifically, inflammatory tissues are often hypoxic which induces angiogenesis (4). Also, cells involved in inflammatory processes such as macrophages and fibroblasts secrete angiogenic factors that promote vessel formation (4). In addition, pro-inflammatory cytokines such as interleukin-6 (IL-6) and tumor necrosis factor alpha (TNFα) have been shown to promote angiogenesis (4–6). Therefore, inflammation is often associated with angiogenesis (4) and it plays a vital role in the development of various diseases, including PAD. Thus, the goal of this study is to investigate IL-6 mediated signaling in vascular endothelial cells under hypoxia serum starvation (HSS) conditions using a computational model and associated experimental data to understand the mechanism involved in the PAD microenvironment.

There have been various experimental and computational studies that explored the range of responses to inflammatory cytokines in different cell types such as macrophages (7), T cells (8,9), and cancer cells (10,11). Also, recent reviews have focused on computational models and analysis of angiogenic signaling (12,13). However, there is limited quantitative analysis of inflammatory together with angiogenic responses in endothelial cells under PAD-specific HSS conditions to inform potential treatments that target inflammation and angiogenesis. Therefore, we aim to focus on characterizing endothelial inflammatory and angiogenic responses under HSS conditions. Many cytokines, such as IL-6, TNFα, and interleukin-1β (IL-1β) regulate inflammatory signaling (14–18). The role of many circulating biomarkers, such as selectins and interleukins in PAD has been reviewed (19,20). In this study, we will focus on the intracellular signaling mediated by one of the major inflammatory cytokines, IL-6, as it has been identified as an important biomarker in inflammation in many diseases such as cardiovascular disease including PAD and cancer (19–22). In addition, elevated levels of IL-6 (23–28) and soluble IL-6 receptors (sIL-6R) (28,29) have been demonstrated in pathological conditions, including PAD and cancer.

It is noteworthy that IL-6 has the potential to have roles as both a pro- or an anti-inflammatory factor (22). IL-6 signaling transduces via binding to its membrane bound receptor (IL-6R), known as classic signaling, or through binding to its soluble receptor sIL-6R, and then recruiting glycoprotein 130 (gp130), this is referred to as trans-signaling (22). It has been shown that IL-6 classic signaling is associated with anti-inflammatory and regenerative responses, while IL-6 trans-signaling is involved in pro-inflammatory responses (22,30). Specifically, IL-6 binds to its receptors (IL-6R and/or sIL-6R) and gp130 and initiates signaling through the signal transducer and activator of transcription 3 (STAT3), mitogen-activated protein kinase (MAPK) and phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt) pathways to phosphorylate STAT3, extracellular regulated kinase (ERK) and Akt. The reason why we focus on the phosphorylation of STAT3, ERK, and Akt is that the phosphorylated STAT3 (pSTAT3) and Akt (pAkt) are important signaling species in the inflammatory responses (31), while pAkt is believed to play an important role in cell survival (32–36) and phosphorylated ERK (pERK) is critical in cell proliferation (37,38), which are important processes involved in angiogenesis. Thus, we mainly focus on IL-6 trans-signaling mediated pSTAT3 and pAkt responses as indicators for pro-inflammatory signaling, and IL-6 classic signaling mediated Akt and ERK activation as signaling species for pro-angiogenic responses.

Previously, we studied the response of phosphorylated STAT3 (pSTAT3), Akt (pAkt), and ERK (pERK) upon the stimulation of IL-6 in the presence or absence of sIL-6R in endothelial cells in the normal condition by constructing a computational model to gain insight into angiogenic and inflammatory signaling in endothelial cells (39). However, it is not clear how IL-6 quantitatively regulates the intracellular signaling in endothelial cells under PAD-specific HSS conditions. Thus, we performed in vitro experiments on HUVECs to study pSTAT3, pAkt, and pERK time course and dose response in response to the stimulation of varying concentrations from 0 to 50 ng/ml of IL-6 and 0 to 100 ng/ml sIL-6R under HSS condition at varying time points from 0 to 4 hours by immunoblotting and ELISA. We adapted our previous general model in the normal conditions (39) and calibrated and validated against these experimental measurements to develop a predictive model specific to HSS conditions.

In order to improve current anti-inflammatory strategies that target endothelial cells, it is beneficial to have a quantitative understanding of the dynamics of the complex biochemical reactions involved in inflammatory signaling networks. Computational modeling is a powerful tool that can be used to investigate molecular responses mechanistically and systematically. For instance, Reeh et al. developed a mathematical model to investigate IL-6 trans- and classic signaling in human hepatoma cells on a molecular level (40). Their model provided a mechanistic explanation for differential cellular responses to IL-6 and underscored the importance of receptor expression levels in modulating signal strength and duration (40). In addition, Sadreev et al. built a mathematical model to describe the multisite phosphorylation for inflammatory signaling in T cells to study the mechanism of STAT3 and Interferon Regulation factor 5 (IRF-5) signaling in T cell differentiation (41). The study showed how phosphorylation site occupancy modulates downstream signaling intensity, offering insights into how T cell differentiation is controlled by post-translational modifications in the context of inflammation (41). Furthermore, Zhao et al. developed a large-scale mechanistic model that focused on seven driving pathways including interferon gamma (IFNγ), IL-1β, IL-10, IL-4, TNFα, hypoxia, and VEGF to characterize macrophage polarization (42). Their model predicted macrophage phenotypic outcomes in response to diverse microenvironmental cues, identifying key signaling crosstalk nodes that govern polarization dynamics (42). Later, Zhao et al. constructed a multiscale model that takes into account inflammatory signaling and includes intracellular, cellular, and tissue-level features to study the dynamic reconstitution of perfusion during post hindlimb ischemia (43). This model showed how inflammatory signaling affects vascular remodeling and perfusion recovery, highlighting the interplay between immune response and tissue regeneration. The study identified critical time windows and cellular processes influencing vascular repair which are important in therapeutic strategies for peripheral arterial disease (43).

Therefore, we constructed the first computational model that focuses on IL-6 mediated signaling in endothelial cells to characterize endothelial inflammatory and angiogenic responses under HSS conditions. The model predicts the dynamics of pSTAT3, pAkt and pERK in response to IL-6 classic and trans-signaling. The model predicts that that IL-6 classic and trans-signaling induced responses are dose dependent. In addition, IL-6 trans-signaling induces greater downstream signaling responses compared to classic signaling and plays a dominant role in the overall effects due to a tighter binding of the ligand and receptors and an abundant supply of sIL-6R because of the experimental setting. Using this model, we also identified the influential species and kinetic parameters that specifically modulate the pSTAT3, pAkt, and pERK responses, which represent potential targets for inflammation- and angiogenesis-based therapies and investigated their efficacy. The model predictions provide mechanistic insight into IL-6 signaling in endothelial cells under HSS conditions. More broadly, this model provides a framework to study the efficacy of inflammation- and angiogenesis-based therapies for endothelial cells under PAD-specific HSS conditions.

MATERIAL AND METHODS

In vitro experiments

Cell culture and treatment

Human Umbilical Vein Endothelial Cells (HUVECs, Cell Application, USA) with 3×10⁵ cells/well for 6-well plate were plated and grown overnight in 10% FBS (Cat. S11550H, RD system, USA) endothelial growth medium (Cat. 211-500, Cell Application) at 37°C and 5% CO₂ incubator, the next day, the medium was removed, and the cells were briefly washed with warm endothelial cell serum-free defined medium (Cat 113-500, Cell Application) to completely remove remained serum. The endothelial cell serum-free defined medium was then replaced with the warm endothelial starvation medium (Cat. 209-250), the cells were grown in the endothelial starvation medium in 2% O₂ hypoxia chamber at 37°C incubator for 2 hours. Subsequently, the cells under HSS medium were untreated (control) or treated with different concentrations of IL-6 (Cat. 206-IL-200/CF, R&D system), or IL-6 combined with sIL-6R (227-SR-025/CF, R&D system) for different times, at the experiment time-points, cell supernatants were collected and saved in −80°C for future ELISA assay. The cells being washed with cold PBS were harvested and lysed with RAPA lysis buffer (Millipore, USA) containing protease cocktail inhibitors complete mini (Millipore, USA) and phosphatase cocktail inhibitors (sodium fluoride, sodium orthovanadate, sodium pyrophosphate, self-made) for Western blot. At the parallel experiment, the cells were harvested and lysed with ELISA lysis buffer (100 mM Tris HCl, pH 7.4, 150 mM NaCl, 1 mM EDTA, 1% Triton-100 and 0.5% sodium deoxycholate) containing protease cocktail inhibitors and phosphatase cocktail inhibitors for ELISA assay. The experiments were set in quadruplicate on per time-point/per dose and repeated under the same experimental condition.

Western blot

Total protein concentrations in cell lysates were quantitated with Pierce BCA Protein Assay (ThermoScientific, USA), equal total proteins in the same final volume were mixed with reducing 4X Laemmli sample buffer (BioRad, USA) and boiled for 10 min, then boiled samples were fractioned with 4–20% Criterion^™ TGX^™ Precast Gel (Bio-Rad), the proteins in gel were electronically transferred to nitrocellulose membrane by using Trans-Blot Turb (Bio-Rad). After the membrane was blocked with 5% BSA in TBST buffer at room temperature for 1 hour, the membrane was incubated with primary antibodies in 5% BSA TBST buffer at 4°C overnight, primary antibodies were used as followings in present study: anti-phospho-STAT3Tyr⁷⁰⁵ antibody (Cell Signaling Technology, USA, #9131; 1:1000 dilution), anti-phospho-AKT Ser⁴⁷³ antibody (Cell Signaling Technology, USA, #4060; 1:1000 dilution), anti-phospho-ERK1/2Thr²⁰²/Tyr²⁰⁴ antibody (Cell Signaling Technology, USA, #9106; 1:1000 dilution), anti-STAT3 antibody (Cell Signaling Technology, USA, #4904; 1:1000 dilution), anti-AKT antibody (Cell Signaling Technology, USA, #2920; 1:1000 dilution), HRP-conjugated β-actin (Cell Signaling Technology, USA, #5125; 1:1000 dilution), anti-ERK1/2 antibody (Santa Cruz Biotechnology, USA, #SC-514302, 1:1000 dilution), the next day, after being washed three times with TBST buffer at room temperature, the membrane was incubated with HRP-conjugated secondary antibody at room temperature for 1 hour. The signal was detected with ECL (ThermoScientific) and scanned with imager iBright 1500 (Invitrogen).

Sandwich enzyme linked Immuno-sorbent assay-ELISA assay

DuoSet^® ELISA kits (R&D systems, USA) were used for measuring protein concentrations in cell supernatants or cell lysates by following manufacturer’s manual; specifically, the concentrations of IL-6, soluble IL-6R, and soluble gp130 in cell supernatants and IL-6, soluble IL-6R, IL-6R, and gp130 in cell lysates were determined by ELISA assay.

Computational model

Model construction

We constructed a molecular-detailed model that describes the intracellular network of IL-6 classic and trans-signaling induced STAT3, Akt, and ERK phosphorylation in endothelial cells under HSS condition. The molecular interactions involved in the network (Figure 1) were adapted from our previous work studying IL-6 induced signaling in endothelial cells under normal conditions (39). It is noteworthy that although STAT3 has been shown to have two phosphorylation sites, Tyr705 and Ser727 (44), it has been shown that IL-6 induced tyrosine phosphorylation depends on JAKs, while the mechanism of serine phosphorylation is not clear (45). Thus, we only considered the singly phosphorylated STAT3 (pSTAT3) in our model. In addition, we consider that activated Akt and ERK include both singly and doubly phosphorylated forms of each species since they have been reported to get activated at two phosphorylation sites (46,47). The model can be expanded when additional data are available. For simplicity, we collectively refer to these species as phosphorylated STAT3, Akt, and ERK (pSTAT3, pAkt, and pERK), respectively. The model reactions, initial conditions, and parameter values are provided in Supplementary Tables S1–3.

Figure 1.

Schematic of IL-6 signaling network under HSS conditions. IL-6 classic and trans-signaling is induced by IL-6 binding to membrane-bound and soluble IL-6 receptors, respectively, and recruiting gp130, which activates STAT3, PI3K/Akt, and MAPK pathways and phosphorylates STAT3, Akt, and ERK, respectively.

The network is implemented as an ordinary differential equation (ODE)-based model using MATLAB (MathWorks, Natick, MA). The main model includes 55 reactions, 65 species, and 68 parameters. The initial variable settings of the initial conditions and parameters are taken from the best fit values from our previous work (39). The reactions, initial conditions, and parameter values are listed in Supplementary Tables S1 to S3. We listed four representative reactions below that describe the ligand-receptor binding as an example.

$$\text{IL6}+\text{IL6R}\stackrel{\text{p1cl,p2cl}}{⟷}\text{IL6:}\text{IL6R}$$

$$\text{IL6:}\text{IL6R}+\text{IL6:}\text{IL6R}+\text{gp130}+\text{gp130}\stackrel{\text{p3cl,p4cl}}{⟷}\text{Rcomplex}$$

$$\text{IL6}+\text{sIL6R}\stackrel{\text{p1tr,p2tr}}{⟷}\text{IL6:}\text{sIL6R}$$

$$\text{IL6:}\text{sIL6R}+\text{IL6:}\text{sIL6R}+\text{gp130}+\text{gp130}\stackrel{\text{p3tr,p4tr}}{⟷}\text{Rcomplex}$$

Because the simulated time is within four hours, we do not consider the degradation of the ligands or signaling species. The complete model is available in Supplemental File 3.

To set the initial conditions, since the expression of IL-6R in human endothelial cells under HSS is unclear (48), we corelated the IL-6R level with the gp130 level, which were measured in HUVEC lysates by one factor: ratio4 (gp130/IL-6R = 0.087 nM/0.00069 nM = 126) (Supplementary Table S2). Also, we assumed a negligible basal sIL-6R in the system since the basal sIL-6R level (0.00012 nM) measured in HUVEC medium is much lower than IL-6R and gp130 measured in the HUVEC lysates, specifically the basal sIL-6R level is approximately 5.8-fold lower than IL-6R (0.00069 nM) and 725-fold lower than gp130 (0.087 nM).

Sensitivity Analysis

To determine the parameters and initial concentrations that have a significant impact on the model outputs, we performed the sensitivity analysis by calculating the Partial Rank Correlation Coefficients (PRCCs), which indicate the correlation between the model inputs and model outputs (49). All targeted parameters and initial values were sampled simultaneously within specified bounds using Latin Hypercube Sampling (LHS); PRCC values for all targeted parameters and initial values were computed to evaluate the correlation between the model inputs (kinetic parameters or initial conditions) and the pSTAT3, pAkt, and pERK concentrations. In addition, the p-values from a t-distribution test corrected with Bonferroni correction were calculated. The PRCC values of the sensitive variables that are statistically significant (p-value < 0.05) were compared. The PRCC values range from −1 to 1, where a higher positive PRCC value and a lower negative PRCC value indicate a stronger positive and negative correlation, respectively, between the input and output.

Prior to model training, we calculated PRCC values for all the parameters and initial values. All model parameters and initial values were sampled within two orders of magnitude above and two orders of magnitude below the baseline values, where the baseline values were obtained from the best fit from our previous work (39) listed in Supplementary Tables S2–3. The PRCC values were then calculated using the same concentrations and time points as those used in the experimental data used for model training. For each variable, the sensitivity index was selected by the highest PRCC value (PRCC_max) across all of the concentrations and time points.

We also performed sensitivity analysis for the calibrated and validated model to identify potential targets for inflammation- and angiogenesis-based strategies.

Identifiability analysis

In addition to parameter sensitivity, we also performed structural parameter identifiability analysis (50,51) to consider the uncertainty caused by the model structure in a dynamical system to study molecular signal transduction. We adapted the methods from Berthoumieux et al., 2013’s work and used differential algebra techniques to transform the systems of ODEs into input-output equations and applied symmetry detection to find transformations of parameters that leave the model’s input-output behavior unchanged. This was implemented by adapting publicly available MATLAB code for ODEs (Garcia Molla, 2025). The original implementation is accessible via MATLAB Central File Exchange (https://www.mathworks.com/matlabcentral/fileexchange/1480-sensitivity-analysis-for-odes-and-daes). By identifying the symmetries, we determined which parameters were structurally identifiable. The identifiability analysis identifies the parameters that have one unique model output for each parameter value. In this method, pair-wise correlation coefficients between parameters were calculated. A correlation coefficient close to 1 or −1 means two parameters are highly colinear, which suggest that they can’t be estimated independently, while lower correlation suggest the independence of the parameters. As a rule of thumb, pair-wise correlation coefficients within (−0.9,0.9) indicate no strong collinearity. Thus, the parameters that are identifiable have correlations between −0.9 and 0.9 with all other parameters while unidentifiable parameters have correlations of > 0.9 or < −0.9 with at least one other parameter.

Parameterization

A total of 36 influential variables with PRCC_max values greater than 0.46 and less than −0.46 were identified by sensitivity analysis. Of these, 21 identifiable variables were identified by identifiability analysis (Supplementary Table S4, highlighted in red) Thus, we held the 15 nonidentifiable variable constant and estimated a total of 21 influential and identifiable variable values by fitting the model to experimental measurements using Particle Swarm Optimization (PSO) implemented by Iadevaia et al. (52). The PSO algorithm was implemented using MATLAB. Initially, a population of particles, which represent parameter sets was created. As the algorithm explores the parameter space, at each particle location, an objective function is evaluated. Through communication among particles, the one has the lowest objective function value is determined. The objective function for each parameter set was used to identify optimal parameter values by minimizing the weighted sum of squared residuals (WSSR) using PSO:

$$\mathrm{W}\mathrm{S}\mathrm{S}\mathrm{R}(\theta )=min\sum _{i=1}^n{\left(\frac{V_{\mathit{pred},i}(\theta )-V_{\mathit{exp},i}}{V_{\mathit{exp},i}}\right)}^2$$

where ${\mathrm{V}}_{\mathit{exp},i}$ is the ith experimental measurement, ${\mathrm{V}}_{\mathit{pred},i}$ is the $i$th predicted value at the corresponding time point, and $n$ is the total number of experimental data points. The minimization is subject to $\mathrm{\theta }$, the set of upper and lower bounds on each of the fitted parameters. The bounds for the model parameters and initial values were set to be two orders of magnitude above and below the baseline parameter values, which were taken from the best fit from our work (39) and listed in Supplementary Tables S2–3.

The model was fitted using three experimental datasets, specifically: 1) relative change of pSTAT3, ppAkt, and pERK time course responses from 0 to 240 min stimulated by 50 ng/ml IL-6 alone and in combination with 100 ng/ml sIL-6R compared with reference points (pSTAT3, ppAkt, and pERK stimulated by 50 ng/ml IL-6 in combination with 100 ng/ml sIL-6R at 5 min, respectively); 2) varying concentrations IL-6 from 0 to 50 ng/ml alone induced pSTAT3, ppAkt, and pERK relative change dose responses at 10 min compared with reference points (pSTAT3, ppAkt, and pERK stimulated by 50 ng/ml IL-6 alone, respectively); 3) varying concentrations IL-6 from 0 to 50 ng/ml in combination with doubled concentrations of sIL-6R induced pSTAT3, ppAkt, and pERK relative change dose responses at 10 min compared with reference points (pSTAT3, ppAkt, and pERK stimulated by 50 ng/ml IL-6 in combination with 100 ng/ml of sIL-6R at 10 min, respectively). All experiments were conducted using HUVECs.

Model simulations were compared to experimental measurements. Specifically, the relative change of the responses was calculated as follows:

$$\text{relative}\text{change}\left(\mathrm{t},c_{IL6},c_{sIL6R}\right)=\frac{response\left(\mathrm{t},c_{IL6},c_{sIL6R}\right)-response\left(t_{ref},c_{re{f}_{-}IL6},c_{ref\_sIL6R}\right)}{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{e}\left(t_{ref},c_{re{f}_{-}IL6},c_{re{f}_{-}sIL6R}\right)}$$

where $\mathit{response}(\mathrm{t},c_{\mathit{IL}6},c_{\mathit{SIL}6\mathit{R}})$ is the level of pSTAT3, ppAkt, or pERK upon the stimulation of concentration $c_{\mathit{IL}6}$ IL-6 in combination of concentration $c_{\mathit{SIL}6\mathit{R}}$ sIL-6R at time t, and $\mathit{response}\left(t_{\mathit{ref}},c_{\mathit{ref\_IL}6},c_{\mathit{ref\_sIL}6\mathit{R}}\right)$ is the response (pSTAT3, ppAkt, or pERK) upon the stimulation of a reference concentration combination of $c_{\mathit{ref\_IL}6}$ IL-6 and $c_{\mathit{ref\_sIL}6\mathit{R}}$ sIL-6R at a reference time point $t_{\mathit{ref}}$.

Those reference points were randomly selected to serve as normalization anchors in order to avoid biasing the model calibration toward specific experimental conditions and to ensure that the normalization did not preferentially weight certain regions of the data. Random selection provided an unbiased baseline for comparing simulated and experimental trends, while still ensuring that the chosen points fell within physiologically relevant ranges observed in the experiments. Systematic selection strategies for example mid-range or max points could be explored in future work to test robustness.

Here, the pSTAT3 in the model simulation includes all free and bound forms of singly-phosphorylated STAT3. Also, ppAkt includes all free and bound forms of doubly-phosphorylated Akt, since anti-phospho-AKT^Ser473 antibody was used for detecting phosphorylated Akt and it has been reported that Akt gets phosphorylated at S473 as a secondary event (53–55). Thus, we compared the predicted doubly phosphorylated Akt (ppAkt) to experimental data. In addition, pERK in the model simulation includes all free and bound forms of singly- and doubly-phosphorylated ERK.

We first fitted the model 100 times to the experimental data. However, from the parameter set that has the lowest errors, many fitted values were found at one of the bounds (Supplementary Table 5). To exclude the possibility of arbitrary bounds limiting the parameter search space, we adjusted the bounds to be two orders of magnitude above and below the set of parameter values that has the lowest errors (Supplementary Table 6). The identified influential variables were estimated another 50 times with the new bounds. With the second round of fitting, none of the parameters were estimated to be at one of the bounds (Supplementary Table 6). After model training, we validated the model with two datasets not used in the fitting. We predicted that the varying concentrations IL-6 from 0 to 50 ng/ml in combination with 50 ng/ml sIL-6R induced pSTAT3, ppAkt, and pERK relative change dose responses at 10 min compared with reference points (pSTAT3, ppAkt, and pERK stimulated by 50 ng/ml IL-6 and 50 ng/ml sIL-6R at 10 min, respectively). Also, the relative change of pSTAT3, ppAkt, and pERK dose responses stimulated by 50 ng/ml IL-6 in combination with varying concentrations sIL-6R from 0 to 50 ng/ml at 10 min compared with reference points (pSTAT3, ppAkt, and pERK stimulated by 50 ng/ml IL-6 and 50 ng/ml sIL-6R at 10 min, respectively). The experiments used for validation were also performed using HUVECs.

Goodness of fit

The performance of the model was assessed as WSSR between the model predictions and experimental data and a Runs test to determine if the predicted curve deviates systematically from the experimental data.

The Runs test is a nonparametric statistical method used to assess whether the residuals from a model fit are randomly distributed (56). When a model fits well, residuals, differences between observed and predicted values, should represent only experimental noise and should be randomly scattered above and below zero (56). The Runs test evaluates the sequence of positive and negative residuals (“runs”) to determine whether there is an unexpected clustering of same-sign residuals, which would indicate systematic deviation between the model and the data. A p-value less than 0.05 suggests that the residuals are not random and the fit may be inadequate, while a p-value greater than 0.05 supports the hypothesis that the residuals are randomly distributed.

For the two datasets used for validation, we simulated the experimental conditions without any additional model fitting and compared to the experimental measurements. A total of 12 parameter sets with the smallest errors and p-values greater than 0.05 by performing the Runs test were taken to be the “best” sets based on the model fitting and validation (Supplementary Table S6) and were used for all model simulations.

Monte Carlo simulations

To study the robustness of the system, the fitted model was run 1000 times by generating 1000 values for all parameters and non-zero initial concentrations, sampling from normal distributions, respectively. For initial concentrations and parameters that were estimated by fitting to the experimental data, the mean values (μ) were the best fit, and for all other model variable values, we set μ to be the baseline values. The variances for the initial concentrations were set as an estimate of 10%μ. For all the parameters, we calculated the standard deviation (σ) to capture 99.7% of the possible values given the range of μ ± 50%μ (i.e., μ ± 3σ). It is worth noting that with this sampling, it is possible to get negative values, though this is unlikely to occur. However, if any negative values were selected, we resampled until all the sampled variables are positive.

We used normal distributions for parameter sampling to explore variability around literature-based or nominal values, under the assumption of symmetric uncertainty. While we recognize that some biological parameters may follow skewed (e.g., log-normal) distributions, we limited the range of variation to avoid sampling non-physical values. Incorporating alternative distributions (e.g., log-normal) or more advanced sampling techniques (e.g., Latin Hypercube Sampling) is a promising direction for future work to further improve the robustness of our uncertainty analysis.

Signaling responses

We investigated the STAT3, Akt, and ERK phosphorylation responses upon stimulation by IL-6 classic and/or trans-signaling under HSS conditions.

Maximum pSTAT3, pAkt, and pERK.

We calculated the maximum STAT3, Akt, and ERK phosphorylation levels induced by the stimulation by IL-6 classic and/or trans-signaling within four hours.

Area under the curve (AUC) of pSTAT3, pAkt, and pERK.

We calculated the AUC of STAT3, Akt, and ERK phosphorylation levels induced by the stimulation by IL-6 classic- and/or trans-signaling within four hours.

RESULTS

Experimental:

Activation of signaling pathways in HUVECs under HSS by IL-6 with or without sIL-6R

Prior to measuring the phosphorylation of STAT3, Akt, and ERK induced by IL-6 alone or IL-6 combined with sIL-6R in HUVECs under HSS condition, HUVECs biological responses and the efficacy of the reagents IL-6 and sIL-6R were tested by detecting MCP-1 mRNA regulation in HUVECs stimulated by 100 ng/ml IL-6 alone or 100 ng/ml IL-6 in combination with 200 ng/ml sIL-6R in normoxia from 0 to 4 hours. Previous studies have reported increased MCP-1 mRNA and protein levels in HUVECs treated with IL-6 in combination with sIL-6R (31). The mRNA was a read out of the ligand receptor activity. MCP-1 mRNA in HUVECs reached a maximum of 170-fold after one-hour treatment of 100 ng/ml IL-6 combined with 200 ng/ml sIL-6R. In addition, MCP-1 mRNA was highly upregulated within 4 hours, a slight increase of MCP-1 mRNA in HUVECs was observed when HUVECs were treated by 100 ng/ml IL-6 alone (Supplementary Figure S1). Next, we measured the phosphorylation of STAT3Tyr⁷⁰⁵, ERK Thr²⁰²/Tyr²⁰⁴ and AKT Ser⁴⁷³ in HUVECs under 2-hour HSS condition before the stimulation of 50 ng/ml IL-6 alone or 50 ng/ml IL-6 in combination with 100 ng/ml sIL-6R for different time-points including 0, 5, 10, 15, 30, 60, 120 and 240 minutes. The phosphorylation of STAT3Tyr⁷⁰⁵, AKT Ser⁴⁷³ and ERK Thr²⁰²/Tyr²⁰⁴ was dramatically activated to reach their maximum with an increase of 316-fold for pSTAT3Tyr⁷⁰⁵, 24.5-fold for pAKT Ser⁴⁷³ and 164-fold for pERK Thr²⁰²/Tyr²⁰⁴ after 15-minute stimulation of 50 ng/ml IL-6 combined with 100 ng/ml sIL-6 (Figure 2A–F). On the other hand, in response to 50 ng/ml IL-6 stimulation alone, pSTAT3Tyr⁷⁰⁵ reached the maximum of 107-fold increase at 15 minutes (Figure 2A–B), pAKT Ser⁴⁷³ and pERK Thr²⁰²/Tyr²⁰⁴ have the maximum of 3.3-fold and 30-fold increase, respectively, at 10 minutes (Figure 2C–F). When 100 ng/ml sIL-6R was applied together with 50 ng/ml IL-6R, the highly phosphorylation of pSTAT3Tyr⁷⁰⁵ was maintained above 95-fold after 4-hours (Figure 2A–B), while the phosphorylation of AKT Ser⁴⁷³ and ERK Thr²⁰²/Tyr²⁰⁴ Ser⁴⁷³ was reduced to approximately the basal level within one-hour (Figure 2C–F).

Figure 2.

Experimental: Phosphorylation of STAT3, AKT and ERK in HUVECs under 2-hour HSS before the treatment with IL-6 (50 ng/ml) or in combination with sIL-6R (100 ng/ml) was determined by Western blot. The alterations of phosphorylated kinase were calculated as the ratios of phosphorylated kinase to its total kinase and normalized to control. The graph shows the relative fold changes as mean ± SEM from representative quadruplicate samples in one experiment out of two independent experiments with the similar results. (A) phosphorylation of STAT3Tyr⁷⁰⁵ and (B) its quantification. (C) phosphorylation of AKT Ser⁴⁷³ and (D) its quantification. (E) phosphorylation of ERK Thr²⁰²/Tyr²⁰⁴ and (F) its quantification. Statistics uses One-Way ANOVA VS HUVECs without treatment. p<0.05, significant. *p < 0.05, **p < 0.01, ***p < 0.005 and ****p < 0.001.

Expression and regulation of some factors in IL-6 signaling pathways in HUVECs under HSS condition

It is undefined whether the HSS condition regulates the expression levels of IL-6 and sIL-6R in HUVECs, we measured the concentrations of IL-6, sIL-6R and gp130 in the cellular culture supernatant and cell lysate from HUVECs using ELISA. We also assessed the concentration of IL-6R associated with membrane in cell lysate. We found increased IL-6 (1.31-fold), gp130 (1.39-fold) in cellular culture supernatant, reduced IL-6 (1.19-fold), gp130 (1.19-fold) and sIL-6R (1.30-fold) in cell lysate of HUVECs under 2-hour HSS condition compared to control (Figure 3A–G).

Figure 3.

Experimental: Basal concentrations in the cellular culture supernatant and cell lysate of HUVECs. (A) IL-6 concentration in the cellular culture supernatant. (B) IL-6 concentration in cell lysate. (C) sIL-6R concentration in the cellular culture supernatant. (D) sIL-6R concentration in cell lysate. (E) IL-6R concentration in cell lysate. (F) gp130 concentration in the cellular culture supernatant. (G) gp130 concentration in cell lysate. The graphs show the relative fold changes as mean ± SEM from representative quadruplicate samples in one experiment out of two independent experiments with the similar results. Statistics uses One-Way ANOVA vs HUVECs without treatment. p<0.05, significant. *p < 0.05, ***p < 0.005 when compared to control, ns is non-significant.

Dose-dependent activation of signaling pathways in HUVECs in response to IL-6 with or without sIL-6R stimulation

Next, we addressed the dose response of HUVECs to the stimulation by 0 – 50 ng/ml IL-6 alone or in combination with doubled concentrations of sIL-6R on the phosphorylation of the three kinases. We found that the phosphorylation of STAT3Tyr⁷⁰⁵ in HUVECs under 2-hour HSS is the dose-dependent of IL-6 alone or in combination with sIL-6R (Figure 4A). When combined with 20 ng/ml sIL-6R, a lower dose of 10 ng/ml IL-6 was needed to reach the same level of pSTAT3Tyr⁷⁰⁵ induced by 50 ng/ml IL-6 alone (Figure 4A). Additionally, the phosphorylation of AKT Ser⁴⁷³ had no obvious changes in response to IL-6 stimulation alone or a low dose of the combination of 0.5 – 10 ng/ml IL-6 and doubled concentrations of sIL-6R (Figure 4B). However, the phosphorylation of AKT Ser⁴⁷³ was induced by the stimulation of IL-6 (50 ng/ml) combined with sIL-6R (100 ng/ml) (Figure 4B). While pERK Thr²⁰²/Tyr²⁰⁴ was highly induced by the stimulation of 5 ng/ml IL-6 alone (Figure 4C) and was induced in a dose-dependent manner by the combination of IL-6 and sIL-6R (Figure 4C).

Figure 4.

Experimental: Phosphorylation of STAT3, AKT and ERK in HUVECs under 2-hour HSS before the treatment with varying doses of IL-6 or IL-6 combined with sIL-6R was determined by Western blot. One representative blot from two independent experiments run in quadruplicate. The alterations of phosphorylated kinase were calculated as the ratio of phosphorylated kinase to its total kinase and normalized to control. The graph shows the relative fold changes as mean ± SEM from representative quadruplicate samples in one experiment out of two independent experiments with the similar results. (A) phosphorylation of STAT3Tyr⁷⁰⁵ in HUVECs treated with IL-6 alone (a) or IL-6 combined with sIL-6R (c) and their quantifications (b) and (d), respectively. (B) phosphorylation of pAKT Ser⁴⁷³ in HUVECs treated with IL-6 alone (e) or IL-6 combined with sIL-6R (g) and their quantifications (f) and (h), respectively. (C) phosphorylation of ERK Thr²⁰²/Tyr²⁰⁴ in HUVECs treated with IL-6 alone (i) or IL-6 combined with sIL-6R (k) and their quantifications (j) and (l), respectively. Statistics uses unpaired t-test VS control. p<0.05, significant. *p < 0.05, **p < 0.01, ***p < 0.005 and ****p < 0.001.

Specific role of IL-6 or sIL-6R in IL-6 signaling in HUVECs under HSS conditions by the stimulation of IL-6 alone or combined with sIL-6R

To characterize the specific impact of IL-6 or sIL-6R on IL-6 signaling, we investigated the effects of IL-6 or sIL-6R by stimulating HUVECs with a fixed 50 ng/ml IL-6 in combination with a range of 0.5 to 50 ng/ml sIL-6R or a fixed 50 ng/ml sIL-6R combined with a range of 0.5 to 50 ng/ml IL-6. Western blot indicated that phosphorylation of STAT3Tyr⁷⁰⁵ and ERK Thr²⁰²/Tyr²⁰⁴, not AKT Ser⁴⁷³, was induced by the combination of 0.5–5 ng/ml sIL-6R plus 50 ng/ml IL-6, at the fixed dose of IL-6 or sIL-6R condition, a low dose of sIL-6R (0.5–1.0 ng/ml) caused a larger induction pSTAT3Tyr^705, pERK Thr²⁰²/Tyr²⁰⁴ and AKT Ser⁴⁷³ compared with the low dose of IL-6 (0.5–1.0 ng/ml) induced (Figure 5A–F). The concentration of intersection points in Figure 5B, D and F showed around 8 ng/ml IL-6 with fixed 50 ng/ml sIL-6R or 8 ng/ml sIL-6R with 50 ng/ml IL-6 induced similar level phosphorylation of STAT3Tyr⁷⁰⁵ (Figure 5B), while 5 ng/ml IL-6 or sIL-6R induced the same level of pERK Thr²⁰²/Tyr²⁰⁴ (Figure 5F).

Figure 5.

Experimental: Phosphorylation of STAT3, AKT and ERK in HUVECs under 2-hour HSS before the treatment with fixed 50 ng/ml IL-6 with varying doses of sIL-6R or fixed 50 ng/ml sIL-6R with varying doses of IL-6 was determined by Western blot. One representative blot from two independent experiments run in quadruplicate. The alterations of phosphorylated kinase were calculated as the ratio of phosphorylated kinase to its total kinase and normalized to control. The graph shows the relative fold changes as mean ± SEM from representative quadruplicate samples in one experiment out of two independent experiments with the similar results. (A) phosphorylation of STAT3Tyr⁷⁰⁵ and (B) its quantification. (C) phosphorylation of AKT Ser⁴⁷³ and (D) its quantification. (E) phosphorylation of ERK Thr²⁰²/Tyr²⁰⁴ and (F) its quantification. Statistics uses One-Way ANOVA VS HUVECs without treatment. p<0.05, significant. *p < 0.05, **p < 0.01, ***p < 0.005 and ****p < 0.001.

Computational:

The fitted and validated molecular-detailed computational model captures the main characteristics of IL-6 induced STAT3, Akt, and ERK phosphorylation dynamics in endothelial cells under HSS conditions

To train the model, we initially identified the model variables including kinetic rates and initial concentrations that significantly influence the model outputs, pSTAT3, pAkt, and pERK. This was achieved by performing sensitivity analysis using PRCC as detailed in the Methods. We analyzed the PRCC values for all the species concentrations and kinetic rates. The highest PRCC values were determined across all of the input concentrations and time points for a total of 65 species, 68 parameters, and 1 factor (ratio4: gp130/IL-6R) that affect model outputs. To identify influential variables, we set a threshold of |PRCC| > 0.46. This cutoff was selected empirically by testing different thresholds and evaluating their effect on the model’s ability to capture experimental data without overfitting. The value of 0.46 provided a balance between sensitivity (detecting important variables) and specificity (excluding weakly influential variables) and enabled robust model performance. Under this criterion, variables with PRCC values above 0.46 (positive influence) or below −0.46 (negative influence) were considered to have a significant impact on the outputs. Of these, 35 variables (Supplementary Table S4 and Figure S3) were identified as influential to pSTAT3, pAkt, and pERK in response to IL-6 alone (ranging from 0 to 50 ng/ml) and/or with additional sIL-6R (ranging from 0 to 100 ng/ml), mirroring the experimental conditions. Among the influential variables, 21 of them were uncorrelated (highlighted in red, Supplementary Table S4 and Figure S4). Their values were then estimated by calibrating the model to experimental data using PSO (52) as elaborated in the Methods.

The calibrated model showed consistency with experimental results, as depicted in Figure 6A. It quantitatively captures the dynamics of pSTAT3, ppAkt, and pERK in response to the stimulation of 50 ng/ml IL-6 alone (Figure 6A–C, light gray) and in combination with 100 ng/ml sIL-6R (Figure 6A–C, dark gray). Furthermore, varying concentrations of IL-6 and in combination with doubled concentrations of sIL-6R induced-pSTAT3, ppAkt, and pERK dose responses (Figure 6D–F) aligned well with experimental measurements. The weighted errors for the 12 best fits range from 32.6 to 34.3 (Supplementary Table S6).

Figure 6.

Computational model comparison to training data for IL-6 stimulation. 50 ng/ml IL-6 with or without additional 100 ng/ml sIL-6R induced relative pSTAT3 (A), ppAkt (B), and pERK (C) dynamics within 4 hours under HSS. Varying concentrations of IL-6 in combination with doubled concentrations of sIL-6R induced relative pSTAT3 (D), ppAkt (E), and pERK (F) under HSS at 10 min. The circles are experimental data. Bars are mean ± SEM. Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Curves are model training results. Light gray: 50 ng/ml IL-6 (A-C) stimulation and 0 – 50 ng/ml IL-6 (D-F) stimulation; Dark gray: 50 ng/ml IL-6 + 100 ng/ml sIL-6R (A-C) and 0 – 50 ng/ml IL-6 + 0 – 100 ng/ml sIL-6R (D-F) stimulation.

In addition to model fitting, the model predictions showed a good agreement with separate experimental observations that were not utilized during the model training process (Figure 7). To validate the model, we compared the model predictions to two independent sets of experimental data. Specifically, varying concentrations of IL-6 in combination with additional 50 ng/ml sIL-6R induced-pSTAT3, ppAkt, and pERK dose responses (Figure 7A–C) shows an agreement with experimental measurements. In addition, varying concentrations of sIL-6R in combination with 50 ng/ml IL-6 induced-pSTAT3, ppAkt, and pERK dose responses (Figure 7D–F) match the experimental observations.

Figure 7.

Model comparison to validation data for IL-6 stimulation. Varying concentrations of IL-6 in combination with 50 ng/ml sIL-6R induced relative pSTAT3 (A), ppAkt (B), and pERK (C) under HSS at 10 min. Varying concentrations of sIL-6R in combination with 50 ng/ml IL-6 induced relative pSTAT3 (D), ppAkt (E), and pERK (F) under HSS at 10 min. The circles are experimental data. Bars are mean ± SEM. Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Curves are model predictions.

We evaluated the predicted doubly phosphorylated Akt (ppAkt) against experimental data for both model fitting and validation (see Methods for more details). However, given the significant roles demonstrated by both Akt T308 and S473 phosphorylation in the downstream signaling (46), we considered both singly and doubly phosphorylated forms of Akt in our analyses for the remainder of this work.

To assess the model’s robustness, we performed Monte Carlo simulations (see Methods) by introducing variability in the initial concentrations and parameters. We then analyzed the predicted pSTAT3, pAkt, and pERK levels. The model predictions with randomly varied parameters values within the estimated range can continue to capture pSTAT3, pAkt, and pERK dynamics in response to IL-6 stimulation alone and in combination with sIL-6R (Figures S5–6). These simulations indicate that the overall dynamics of the model outputs, pSTAT3, pAkt, and pERK, are relatively robust to variations or uncertainties in initial concentrations and parameters in the signaling network.

IL-6 classic and trans-signaling induced responses are dose-dependent

We first applied the experimentally validated model to investigate the effects of IL-6 classic and trans-signaling on STAT3, Akt, and ERK phosphorylation under HSS condition. Our model predicts that the maximum pSTAT3 and pAkt levels increase with the increase of IL-6 concentrations within four hours (Figure 8A–B). IL-6-induced pSTAT3 exhibits the optimal ligand levels required to elicit maximal responses as their dose response plateaus at approximately 20 nM IL-6 in the range of 0 – 50 nM (Figure 8A). In addition, STAT3 showed a greater activation than Akt and ERK in response to 0 – 50 nM IL-6 stimulation alone (Figure 8A–C). It is worth noting that there is only slight activation in Akt and no obvious activation in ERK in response to IL-6 within the same concentration range (Figure 8B–C). Moreover, the area under the curve (AUC) is quantified for pSTAT3, pAkt, and pERK dynamics within four hours as well and they exhibit a similar dose-dependent behavior (Supplementary Figure S7A–C).

Figure 8.

Predicted maximum pSTAT3, pAkt, and pERK in response to IL-6 classic and trans-signaling under HSS conditions. Maximum pSTAT3 (A), pAkt (B), and pERK (C) in response to IL-6 concentrations varying from 0 to 50 nM without sIL-6R. In the absence of IL-6R, 20 nM IL-6 in combination with sIL-6R concentrations varying from 0 to 50 nM induced maximum pSTAT3 (D), pAkt (E), and pERK (F). Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Orange: classic signaling responses; Yellow: trans-signaling responses.

We then eliminated the effect of IL-6 classic signaling by setting IL-6R level to be zero and simulated the phosphorylation of STAT3, Akt, and ERK in response to 20 nM IL-6 in combination with varying concentrations of sIL-6R to examine the effects of IL-6 trans-signaling. A dose-dependent increase in STAT3, Akt, and ERK activation with the increase of sIL-6R concentrations and plateau within 50 nM sIL-6R in combination with 20 nM IL-6 was also observed when considering the maximal phosphorylation levels (Figure 8D–F) and AUC (Supplementary Figure S7D–F), respectively. Similar to IL-6 stimulation alone, STAT3 exhibited a greater activation than Akt and ERK in response to 20 nM IL-6 stimulation combined with 0 – 50 nM sIL-6R. However, in contrast with the minimal activation in Akt and ERK in response to IL-6 stimulation alone, pAkt and pERK induced by IL-6 trans-signaling at the plateau level showed a 54- and 6.3-fold increase compared to classic signaling level, respectively.

Furthermore, given the same trends exhibited by the maximum levels and AUCs (Figure 8 and Supplementary Figure S7), we utilized the maximum pSTAT3, pAkt, and pERK levels within four hours as indicators for pSTAT3, pERK and pAkt responses in this study for simplification.

IL-6 trans-signaling induces stronger responses than classic signaling effects

To compare the effects of classic and trans-signaling on the phosphorylation of STAT3, Akt, and ERK, we next set the concentration of sIL-6R to be the same level as IL-6R for each fit, averaging at 8 nM among the 12 best fits. We then simulated the dynamics of pSTAT3, pAkt, and pERK in response to 20 nM IL-6 alone in the presence of IL-6R (orange) and 20 nM IL-6 combined with the mean value of 8 nM sIL-6R in the absence of IL-6R (yellow) (Figure 9). Given the presence of both IL-6R and sIL-6R in the physiological and pathological conditions, we also investigated the overall effects of the stimulation of 20 nM IL-6 in combination with 8 nM sIL-6R (mean) in the presence of IL-6R on pSTAT3, pAkt, and pERK responses (Figure 9, gray curves). The model showed that the IL-6 trans-signaling and overall effects induced significantly higher levels of max pSTAT3, pAkt, and pERK than the corresponding responses induced by classic signaling (Figure 9). Moreover, IL-6 trans-signaling exhibited a dominant role in the overall responses induced by the overall effects overlapped with those induced by IL-6 trans-signaling (Figure 9).

Figure 9.

Predicted time courses of pSTAT3 (A), pAkt (B), and pERK (C) following stimulation by 20 nM IL-6 alone with a mean value of 8 nM IL-6R (orange), 20 nM IL-6 in combination with a mean value of 8 nM sIL-6R in the absence of IL-6R (yellow), and 20 nM IL-6 with a mean value of 8 nM of both IL-6R and sIL-6R (gray). Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Orange: classic signaling responses; Yellow: trans-signaling responses; Gray: overall responses.

To provide a mechanistic explanation of the higher responses induced by IL-6 trans-signaling compared to classic signaling and its dominant role in the overall effects, we explored the model structure and identified that it is primarily resulted from an assumption of a constant sIL-6R as our model input (dsIL6R/dt = 0). This assumption arises from the abundant presence of sIL-6 in the cell culture media in typical in vitro experimental conditions. A similar assumption was also made in Reeh et al.’s model, specifically, Hyper-IL-6, a fusion protein comprising sIL-6R and IL-6 was utilized to investigate the effects of IL-6 trans-signaling (40), which was assumed to be a constant model input as its concentration remained constant in the supernatant during in vitro experimentation (40). A sustained availability of soluble receptor leads to greater downstream responses compared to IL-6 classic signaling as the quantity of IL-6R is limited.

To verify this hypothesis, we configured IL-6R as a constant input, mirroring the behavior of sIL-6R, and compared the effects of classic and trans-signaling. We found that max pSTAT3, pAkt, and pERK induced by IL-6 classic signaling increased by 1.5-fold, 19.8-fold, and 4.0-fold when IL-6R and sIL-6R are set at the same level and remain constant within four-hour simulation time (Supplementary Figure S8A) compared to the baseline levels (Figure 9). However, in comparison with the responses induced by trans-signaling and overall effects, max pSTAT3 level induced by classic signaling when IL-6R is constant and at the same level as the sIL-6R is only slightly lower (0.99-fold), while classic signaling under the same condition induced pAkt and pERK levels are still somewhat lower (0.31-fold and 0.64-fold, respectively) (Supplementary Figure S8A). It suggests that the sustained availability of sIL-6R is one of the key factors contributing to the stronger downstream responses induced by trans-signaling compared to classic signaling, especially STAT3 phosphorylation.

We also observed some differences in the dissociation constant (Kd) for the ligand-receptor binding reactions induced by the IL-6 classic and trans-signaling. Specifically, the Kd values for reaction 1 (R1: IL-6 + IL-6R ↔ IL-6:IL-6R; mean Kd = 7.2 × 10⁴ nM) and the Kd for reaction 2 (R2: 2 IL-6:IL-6R + 2 gp130 ↔ Rcomplex; Kd = 0.05 nM) are higher than those for reaction 3 (R3: IL-6 + sIL-6R ↔ IL-6:sIL-6R; Kd = 17.9 nM and the Kd for reaction 4 (R4: 2 IL-6:sIL-6R + 2 gp130 ↔ Rcomplex; Kd = 0.02 nM), respectively (Supplementary Figure S9). It suggests a tighter binding for the reactants involved in the trans-signaling reactions compared to classic signaling. However, when we set the kinetic rates governing the ligand-receptor binding reactions for classic signaling (R1 and R2) to be the same as the corresponding kinetic rates for trans-signaling (R3 and R4), only slight increases in classic signaling-induced responses was observed, specifically, 4.3% increase in pSTAT3, 32.9% increase in pAkt, and 1.1% increase in pERK compared with baseline model predictions (Supplementary Figure S8B and Figure 9). It indicates that the tighter binding of IL-6 and sIL-6R and gp130 compared to IL-6 and IL-6R and gp130 also contributes to the stronger downstream responses induced by trans-signaling, especially Akt activation.

Furthermore, in our previous work that studied IL-6 signaling under normal conditions, a Kd value of 479.6 nM was predicted for reaction 1 (39), which is 0.0067-fold lower than the Kd in the HSS conditions. This suggests a tighter binding for IL-6 to IL-6R under normal condition compared to HSS condition, leading to stronger competition for IL-6 binding to sIL-6R and it moves towards more inflammatory signaling in the HSS conditions.

Last, we set IL-6R and sIL-6R at the same level and remain constant within four hours, and adjusted the kinetic rates governing R1 and R2 to be the same as those of R3 and R4. We then predicted the dynamics of pSTAT3, pAkt, and pERK (Supplementary Figure S8C). The activation of STAT3, Akt, and ERK induced by IL-6 classic was found to coincide with the corresponding responses induced by IL-6 trans-signaling.

Overall, the model suggests that IL-6 trans-signaling elicits stronger downstream responses, specifically, pSTAT3, pAkt, and pERK, than classic signaling, and it plays a dominant role in the overall effects. It is primarily attributed to the abundant availability of sIL-6R and the tighter binding of IL-6 to sIL-6R and gp130.

sIL-6R enhances the downstream signaling

We next compared reaction rates for reactions 1–4 with or without IL-6R and sIL-6R (Figure 10). We found that IL-6 binds to sIL-6R and gp130 more rapidly than IL-6R and gp130 in the beginning (Figure 10A–D). Notably, the presence of additional sIL-6R makes reactions rates for R1 and R2 become negative (Figure 10A–B and E–F), indicating a faster dissociation of IL6:IL6R and Rcomplex compared to the association of IL-6, IL-6R, and gp130. It suggests that more IL-6 and gp130 are released from binding to IL-6R and become available for binding to sIL-6R, thus promote trans-signaling. Also, reactions rates for R3 and R4 are more sustained when both IL-6R and sIL-6R were present compared to the reactions rates for trans-signaling (Figure 10C–D and G–H) as more IL-6 were released from classic signaling. Taken together, these findings indicate that the presence of additional sIL-6R shifts the signaling towards trans-signaling, thereby promoting inflammatory responses. This is consistent with the dominant role of trans-signaling in the overall effects.

Figure 10.

Reaction rates for ligand-receptor binding following stimulation by 20 nM IL-6 alone with a mean value of 8 nM IL-6R (orange) (A-B), 20 nM IL-6 in combination with a mean value of 8 nM sIL-6R in the absence of IL-6R (yellow) (C-D), and 20 nM IL-6 with a mean value of 8 nM of both IL-6R and sIL-6R (gray) (E-H). R1: IL-6 + IL-6R ↔ IL-6:IL-6R; R2: 2 IL-6:IL-6R + 2 gp130 ↔ Rcomplex; R3: IL-6 + sIL-6R ↔ IL-6:sIL-6R; R4: 2 IL-6:sIL-6R + 2 gp130 ↔ Rcomplex. Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Orange: classic signaling responses; Yellow: trans-signaling responses; Gray: overall responses.

To further study the intricacies of the model, we compared the time courses of relevant species involved in R1-R4 with or without IL-6R and sIL-6R (Supplementary Figure S10). The model predicts a higher formation of IL-6:sIL-6R compared to IL-6:IL-6R (Supplementary Figure S10A and C). Also, the predicted level of signaling Rcomplex induced by trans-signaling is higher than that of classic signaling (Supplementary Figure S10B and D). These model predictions further affirm that IL-6 trans-signaling promotes stronger responses than classic signaling. Moreover, we observed an accumulation of IL-6:IL-6R and a higher consumption of IL-6:sIL-6R induced by the overall effects compared to classic and trans-signaling respectively (Supplementary Figure S10A compared to E, and C compared to F). It aligns with our predictions that additional sIL-6R shifts the signaling towards trans-signaling. Additionally, the Rcomplex induced by the overall effects is approximately at the same level as the Rcomplex induced by trans-signaling (Supplementary Figure S10D compared to G), which corroborates the dominant role of trans-signaling in the overall effects.

Generally, the model suggests that in the presence of abundant sIL-6R, IL-6 trans-signaling induces stronger responses and the presence of additional sIL-6R shifts the signaling towards trans-signaling

Both IL-6 and sIL-6R levels regulate signaling strength

We then varied IL-6 and sIL-6R simultaneously from 0 to 50 nM and examined their combination effects on STAT3, Akt, and ERK activation. We found that there is a gradient towards the diagonal direction with increasing concentrations of both IL-6 and sIL-6R in promoting the activation of each signaling species (Figure 11). As we observed previously, the phosphorylation of STAT3, Akt, and ERK reached a plateau at approximately 20 nM IL-6 stimulation (Figure 8A–C), while additional sIL-6R further promotes the downstream signaling (Figure 11). Also, at certain levels of sIL-6R, additional IL-6 led to increased activation of STAT3, Akt, and ERK as well (Figure 11). Upregulation of IL-6 (26) and sIL-6R (58) has been reported in the peripheral arterial disease conditions, which leads to greater inflammatory responses. It is consistent with our model predictions as elevated levels of IL-6R and sIL-6R lead to greater phosphorylation of STAT3, Akt, and ERK (Figure 11).

Figure 11.

Predicted maximum pSTAT3, pAkt, and pERK responses with varying concentrations of IL-6 and sIL-6R under HSS conditions. Maximum pSTAT3 (A), pAkt (B), and pERK (C) in response to the stimulation of 0 – 50 nM IL-6 in combination with 0 – 50 nM sIL-6R.

Model identifies potential targets for influencing STAT3, Akt, and ERK activation and quantitively evaluates their efficacy

We performed sensitivity analysis using PRCC (see Methods for more details) for the experimentally validated model and identified influential initial concentrations (Supplementary Figure S11A-C) and parameters (Supplementary Figure S11D) affecting STAT3, Akt, and ERK activation. Specifically, all model parameters and initial values were sampled within two orders of magnitude above and below the baseline values. In this case, the baseline values for the fitted variables were determined as the best fit estimated from model fitting. Considering the behaviors of max pSTAT3, pAkt, and pERK that approximately reach a plateau as the IL-6 concentration increases (Figure 8), 20 nM IL-6 was selected as a representative concentration to capture the optimal responses induced by classic signaling. Additionally, to compare the effects of IL-6 classic and trans-signaling, we selected 8 nM sIL-6 as a representative concentration as it is the same level as the IL-6R concentration from the best fit. Consequently, we calculated the PRCC values for pSTAT3, pAkt, and pERK in response to the stimulation of 20 nM IL-6 in combination of 8 nM sIL-6R at eight time points (0, 5, 10, 15, 30, 60, 120, and 240 min) ranging from zero to 240 min. Again, the PRCC_max across all the concentrations and time points was assessed for all the variables.

To quantitatively analyze their effects in pSTAT3, pAkt, and pERK, we systematically varied each of identified influential variables within a finite range, specifically 10-fold above and below the baseline levels and compared with the baseline model predictions (Figure 12). A ratio greater than one suggests that varying the variable enhances the response; a ratio equal to one shows no effects on the response; and a ratio less than one indicates an inhibitory effect on the response. We consider the perturbations to be effective when the change in response is greater than 2-fold or less than 0.5-fold.

Figure 12.

Predicted targets for modulating pSTAT3, pAkt, and pERK responses under HSS conditions. 0.1-fold/baseline (blue) and 10-fold/baseline (orange) for 20 nM IL-6 with a mean value of 8 nM of IL-6R and 6.4 nM sIL-6R induced pSTAT3/total STAT3 (A, D), pAkt/total Akt (B, E), and pERK/total ERK (C, F) when varying identified influential initial concentrations (left) and parameters (right) by 0.1- and 10-fold of their baseline values. Bars are mean ± 95% confidence intervals of model predictions.

We found that the initial STAT3 concentration positively influences STAT3 phosphorylation as its direct relevance to the signaling species of interest (Figure 12A). Also, no parameter was observed to significantly affect STAT3 phosphorylation (Figure 12B). In addition, Akt phosphorylation is positively regulated by Akt, PI3K, and PIP2 levels (Figure 12C), and parameter p5, and negatively regulated by PP2A and PTEN levels, and parameter p6 (Figure 12D). This is intuitive as Akt, PI3K, and PIP2 are important signaling upstream species for Akt phosphorylation. PP2A and PTEN are phosphatases for pAkt and PIP3. Also, parameters p5 and p6 are the activation and deactivation rates of Rcomplex, respectively. Last, basal pERK and Ptase2 are predicted to positively and negatively regulate the phosphorylation of ERK, respectively (Figure 12E) and no parameter was observed to affect ERK phosphorylation significantly (Figure 12F). This is because basal pERK level directly contributes to the total pERK level and Ptase2 is the phosphatase for pMEK and ppMEK.

Thus, our model delineates potential targets for modulating downstream responses, pSTAT3, pAkt, and pERK upon the stimulation of the overall effects of IL-6 classic and trans-signaling under HSS conditions and quantitively evaluates their efficacy.

Comparison of the predicted targets under HSS and normal conditions

We then listed and compared the predicted targets for modulating pSTAT3, pAkt, and pERK responses under HSS and normal conditions (39) (Table 1). Here, the predicted targets under HSS conditions are results from the present study, generated using our computational model under the specified HSS parameter set. The predicted targets under normal conditions are taken from our previous computational predictions (39). We found that STAT3 is predicted to be influential to STAT3 activation under HSS conditions but not under normal conditions. In addition, several variables including Akt, PI3K, PIP2, PP2A, PTEN, p6 are predicted to be important in Akt activation under both normal and HSS conditions, while p5 is only influential to pAkt under HSS conditions, and IL-6R, STAT3, k_aAkt, and k_aPP2A are only important in Akt activation under normal conditions. Finally, the model predicts that basal pERK and Ptase2 levels are important regulators for ERK activation under HSS condition, while IL-6R, STAT3, p5 and p6 are influential variables to pERK under normal conditions. Overall, the model suggests the potential targets for modulating pSTAT3, pAkt, and pERK under HSS conditions are different than under normal conditions and our model can identify the potential targets specific to HSS conditions.

Table 1.

Comparison of the predicted targets for modulating pSTAT3, pAkt, and pERK responses under HSS and normal conditions. The predicted targets under HSS conditions are results from the present study, generated using our computational model under the specified HSS parameter set. The predicted targets under normal conditions are taken from our previous computational predictions (39).

pSTAT3		pAkt		pERK
HSS	normoxia	HSS	normoxia	HSS	normoxia
STAT3	-	Akt	Akt	pERK_basal	IL6R
		PI3K	IL6R	Ptase2	STAT3
		PIP2	PI3K		p5
		PP2A	PIP2		p6
		PTEN	PP2A
		p5	PTEN
		p6	STAT3
			k_aAkt
			k_aPP2A
			p6

Discussion

IL-6 as a pleiotropic cytokine in diverse organs mediates cellular biological function by pro- or anti-inflammatory procedure in the paracrine and autocrine fashion, IL-6 has its effect on cells or tissues by its classic signaling and trans-signaling pathway to influence cell migration, proliferation and apoptosis. Two decades ago, ischemia or hypoxia induced IL-6 production was linked to PAD (59), IL-6 was found as a main trigger in the formation and progression of atherosclerosis, the following investigations also demonstrated that elevated IL-6 in the serum of PAD patients is the biomarker for PAD (60,61), and increasing IL-6 concentration was associated with adverse outcomes in patients with PAD outcome (62–66). Although IL-6 biological function was described as IL-1ß/IL-6/C-reactive protein pathway, IL-6 signals through the IL-6 classical signaling or trans-signaling pathway were undefined in PAD, especially, the alterations of kinase activities downstream of IL-6 classic and trans-signaling pathways in the hypoxia/ischemia biological procedure. In present study, we elucidated the difference of IL-6 classic and trans-signaling in HUVECs under 2-hour HSS condition, and showed the IL-6 trans-signaling induced a strong phosphorylation of pSTAT3Tyr⁷⁰⁵, pERK1/2Thr²⁰²/Tyr²⁰⁴ and pAKT Ser⁴⁷³ than IL-6 classic signaling caused. Among pSTAT3Tyr⁷⁰⁵, pERK1/2Thr²⁰²/Tyr²⁰⁴ and pAKT Ser⁴⁷³, both IL-6 classic signaling and trans-signaling affect their alterations in the order of pSTAT3Tyr⁷⁰⁵, pERK1/2Thr²⁰²/Tyr²⁰⁴ and pAKT Ser⁴⁷³ in HUVECs under HSS condition, affecting that gene expression and regulation downstream of these kinases activity which changes HUVECs biological function.

We mimicked the PAD ischemia procedure by establishing HUVECs growing in HSS condition, a cellular culture model inducing HUVECs injury, we found that HSS caused the IL-6 and sIL-6R basal accumulation in the cellular culture supernatant of HUVECs, and increased IL-6 and sIL-6R in the cellular culture supernatant of HUVECs were HSS time-dependent. Simultaneously, bound to membrane IL-6R were gradually reduced with the HSS exposure, IL-6 classic signaling pathway is via IL-6 binding to IL-6R to initiate signaling, thus, the IL-6 classic signaling was weakened in the HSS condition. With the stimulation of IL-6 alone and IL-6 in combination of sIL-6R, the HUVECs under HSS exhibit a marked increase of kinase activities, and HSS increased the production of IL-6 and sIL-6R.

IL-6 elevation has different roles in normal and pathophysiology. The phosphorylation of pSTAT3Tyr⁷⁰⁵, pERK1/2Thr²⁰²/Tyr²⁰⁴ and pAKT Ser⁴⁷³ induced by IL-6 alone or IL-6 in combination of sIL-6R was recently documented at normal growth environment in HUVECs; the pERK1/2Thr²⁰²/Tyr²⁰⁴ and pAKT Ser⁴⁷³ in HUVECs treated by IL-6 alone have not increased (31). In contrast, HUVECs under HSS have dramatic increase of pERK1/2Thr²⁰²/Tyr²⁰⁴ when cells were treated by 5 ng/ml IL-6 compared with control. HUVECs under HSS have no increase in pAKT Ser⁴⁷³ which is similar to HUVECs under normal physiological condition. A missense variant pAsp358Ala in the IL-6 receptor had been reported to reduce the risk of PAD (67), the explanation for this result is the missense variant impairs IL-6 classic signaling from reducing membrane-bound IL-6R.

We constructed an intracellular signaling model delineating IL-6 mediated inflammatory pathways in endothelial cells under HSS conditions. The computational model represents the reaction network of interactions on a molecular level. The model incorporates molecular interactions, kinetic parameters, and initial concentrations documented in literature, which are provided in the supplementary materials (Supplementary Tables 1–3). Influential parameters were estimated by fitting the model to our experimental measurements. Subsequently, we validated the model using six independent experimental datasets. All experimental data utilized for model training and validation are from in vitro studies conducted on HUVECs under HSS conditions. Thus, this model is constructed specifically to characterize in vitro HUVEC responses under HSS conditions and serves as the foundational framework for prospective modeling work that is based on in vivo experiments. For example, Zhao et al. constructed a virtual mouse model to study the revascularization and tissue perfusion for mouse hindlimb ischemia (43). Our model can provide a framework of an additional critical angiogenic and inflammatory pathway in endothelial cells to gain a more comprehensive understanding of the inflammatory signaling networks in endothelial cells.

The calibrated model predicts pSTAT3, pAkt, and pERK responses upon the stimulation by IL-6 classic and/or trans-signaling under HSS conditions. Overall, the model suggests that the max pSTAT3, pAkt, and pERK levels are IL-6 and sIL-6R dose-dependent under HSS conditions, which is consistent with our previous work on IL-6 induced signaling in endothelial cells under normal conditions (39). Also, our model predicts slight activation in Akt and no activation in ERK upon the stimulation of 0 – 50 nM IL-6 alone (Figure 8B and C), which is consistent with experimental observations (Figure 4Bf and Cj) that pAkt and pERK induced by 0.5 – 50 ng/ml IL-6 alone showed no significant difference compared to control. Also, our model predicts that IL-6 trans-signaling induces stronger responses and the presence of additional sIL-6R shifts the signaling towards trans-signaling and promotes inflammatory responses. This is also consistent with our experimental observations, which showed a greater activation in pSTAT3, pAkt, and pERK in response to 50 ng/ml IL-6 in combination with 100 ng/ml sIL-6R compared to 50 ng/ml IL-6 stimulation alone (Figure 2). Importantly, our molecularly detailed model mechanistically examined this phenomenon, which could be hard to differentiate experimentally, and found that IL-6 trans-signaling induces greater downstream signaling, pSTAT3, pAkt, and pERK than classic signaling due to the abundant availability of sIL-6R and tighter binding of ligand and receptors. Furthermore, our model identified the influential species and kinetic parameters that specifically modulate downstream inflammatory and/or angiogenic signals, pSTAT3, pAkt, and pERK responses, which could aid in relevant experimental design to investigate the effects of potential targets.

IL-6 has emerged as an important biomarker in inflammation across various diseases such as cardiovascular disease and cancer (19–22). In addition, pathological conditions including peripheral arterial disease and cancer have been associated with elevated levels of IL-6 (23–28) and soluble IL-6 receptors (sIL-6R) (28,29). Although a number of computational models that studied IL-6-induced signaling in many cell types such as hepatoma cells (40), cardiac fibroblasts (68,69), macrophages (70,71), and cancer stem cells (72), there is a scarcity of quantitative understanding of IL-6 signaling in endothelial cells and non from PAD relevant, conditions. Our work is the first computational model that specifically focuses on IL-6 mediated signaling in endothelial cells under HSS conditions to elucidate endothelial cytokine-mediated inflammatory and angiogenic responses.

This model can be beneficial to assess the efficiency of angiogenesis- and inflammation-based therapies. Our model can identify the influential variables to the pSTAT3, pAkt and pERK levels induced by IL-6 signaling under HSS conditions and predict the alterations in these levels with perturbations in these variables. This model can provide quantitative insights into investigating the effectiveness of targeting specific variables as angiogenesis- and inflammation-based strategies.

We acknowledge certain limitations in our model. We assumed constant levels of IL-6 and sIL-6 over four hours given the sufficient nutrients in the cell culture media. Reeh et al. in their IL-6 signaling model to study human hepatoma cells have used a similar approach (40). Also, we estimated the receptor number as the expression of IL-6R is human endothelial cells conditions is uncertain (48). Furthermore, as the model was calibrated to fold change experimental data, the model can predict the relative change with minor variations (Figures 6–7). However, it showed large variations when predicting absolute values (Figures 8–9). It can be improved when additional data on the receptor expression become available.

In our current study, the predicted role of IL-6 under both normal and HSS conditions in HUVECs reflects the specific parameterization of the network using HUVEC-derived data, including experimentally informed rate constants, initial concentrations, and protein–protein interaction parameters. While the core signaling pathways are expected to be conserved across similar endothelial cell lines (e.g., HAECs, HMECs), quantitative differences in pathway activation could arise from cell-type–specific variations in receptor expression levels, intracellular signaling protein abundance, and feedback regulation. The proposed network framework is modular and can be adapted to other endothelial systems by re-estimating parameters (e.g., kinetic rate constants, binding affinities, degradation rates) and adjusting initial conditions based on cell-type–specific experimental measurements. Similarly, protein–protein interaction strengths can be updated to reflect alternative isoforms or differential post-translational modifications observed in other contexts. Such recalibration would allow the model to capture cell-specific signaling dynamics while maintaining the general mechanistic structure, thereby enabling broader application to study IL-6 signaling and related pathways in varied vascular and inflammatory settings.

In conclusion, we developed an experimentally validated computational model to characterize the dynamics of pSTAT3, pERK, and pAkt upon the stimulation of IL-6 in endothelial cells under HSS conditions. The model offers quantitative insights into the phosphorylation of STAT3, ERK, and Akt in response to IL-6 and sIL-6R and provides mechanistic understanding of inflammatory and angiogenic signaling in endothelial cells under HSS conditions. The understanding of the regulation of inflammatory and angiogenic signals on a molecular scale can better aid the development of strategies targeting inflammation and angiogenesis.

Supplementary Material

1

Table S1. List of model reactions.

Table S2. List of species with non-zero initial concentrations.

Table S3. List of model parameters.

Table S4. PRCC values

Table S5. Fitted initial concentrations and parameters.

Table S6. Fitted initial concentrations and parameters with adjusted bounds.

3

Figure S1. MCP1 mRNA expression in HUVECs. Quantitative PCR analysis of relative MCP1 mRNA expression in HUVECs treated with IL-6 (100 ng/ml) alone or in combination with sIL-6R (200 ng/ml) in 10% FBS endothelial growth medium with RPLP0 used for normalization. Data is presented as relative fold alterations with mean ± SEM from representative quadruplicate samples in one experiment with replicate by setting non-treated HUVEC as 1. Statistics uses One-Way ANOVA VS HUVECs without treatment. p<0.05, significant. *p < 0.05, **p < 0.01, ***p < 0.005 and ****p < 0.001.

Figure S2. Results of sensitivity analysis for model training. PRCC values for influential initial concentrations (A) and parameters (B). Y axes indicate PRCC values.

Figure S3. Distribution of fitted values. Each circle represents one fitted value.

Figure S4. Monte Carlo simulations for training data. 50 ng/ml IL-6 with or without additional 100 ng/ml sIL-6R induced relative pSTAT3 (A), ppAkt (B), and pERK (C) dynamics within 4 hours under HSS. Varying concentrations of IL-6 in combination with doubled concentrations of sIL-6R induced relative pSTAT3 (D), ppAkt (E), and pERK (F) under HSS at 10 min. The circles are experimental data. Bars are mean ± SEM. Curves are the mean values of the 1,000 Monte Carlo simulations. Shaded regions show 95% confidence intervals. Light gray: 50 ng/ml IL-6 (A-C) stimulation and 0 – 50 ng/ml IL-6 (D-F) stimulation; Dark gray: 50 ng/ml IL-6 + 100 ng/ml sIL-6R (A-C) and 0 – 50 ng/ml IL-6 + 0 – 100 ng/ml sIL-6R (D-F) stimulation.

Figure S5. Monte Carlo simulations for validation data. Varying concentrations of IL-6 in combination with 50 ng/ml sIL-6R induced relative pSTAT3 (A), ppAkt (B), and pERK (C) under HSS at 10 min. Varying concentrations of sIL-6R in combination with 50 ng/ml IL-6 induced relative pSTAT3 (D), ppAkt (E), and pERK (F) under HSS at 10 min. The circles are experimental data. Bars are mean ± SEM. Curves are the mean values of the 1,000 Monte Carlo simulations. Shaded regions show 95% confidence intervals.

Figure S6. Predicted AUC of pSTAT3, pAkt, and pERK in response to IL-6 classic and trans-signaling under HSS conditions. Maximum pSTAT3 (A), pAkt (B), and pERK (C) in response to IL-6 concentrations varying from 0 to 50 nM without sIL-6R. In the absence of IL-6R, 20 nM IL-6 in combination with sIL-6R concentrations varying from 0 to 50 nM induced maximum pSTAT3 (D), pAkt (E), and pERK (F). Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Orange: classic signaling responses; Yellow: trans-signaling responses.

Figure S7. Predicted time courses of pSTAT3, pAkt, and pERK following stimulation by 20 nM IL-6 alone with a mean value of 8 nM IL-6R (orange), 20 nM IL-6 in combination with a mean value of 8 nM sIL-6R in the absence of IL-6R (yellow), and 20 nM IL-6 with a mean value of 8 nM of both IL-6R and sIL-6R (gray) when IL-6R and sIL-6R are set at the same level and remain constant within four-hour simulation time (A), when kinetic rates governing R1 and R2 to be the same as the corresponding kinetic rates for R3 and R4 (B), and when both IL-6R was set as a constant input and kinetic rates governing R1 and R2 to be the same as the corresponding kinetic rates for R3 and R4 (C). Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits. Orange: classic signaling responses; Yellow: trans-signaling responses; Gray: overall responses. R1: IL-6 + IL-6R ↔ IL-6:IL-6R; R2: 2 IL-6:IL-6R + 2 gp130 ↔ Rcomplex; R3: IL-6 + sIL-6R ↔ IL-6:sIL-6R; R4: 2 IL-6:sIL-6R + 2 gp130 ↔ Rcomplex.

Figure S8. Dissociation constants (Kd) of ligand-receptor binding. R1: IL-6 + IL-6R ↔ IL-6:IL-6R; R2: 2 IL-6:IL-6R + 2 gp130 ↔ Rcomplex; R3: IL-6 + sIL-6R ↔ IL-6:sIL-6R; R4: 2 IL-6:sIL-6R + 2 gp130 ↔ Rcomplex. Each circle represents one fit. Orange: classic signaling responses; Yellow: trans-signaling responses.

Figure S9. Dynamics of relevant species involved in ligand-receptor binding following stimulation by 20 nM IL-6 alone with a mean value of 8 nM IL-6R (orange) (A-B), 20 nM IL-6 in combination with a mean value of 8 nM sIL-6R in the absence of IL-6R (yellow) (C-D), and 20 nM IL-6 with a mean value of 8 nM of both IL-6R and sIL-6R (gray) (E-G). Curves are the mean values of the 12 best fits. Shaded regions show 95% confidence intervals of the fits.

Figure S10. Results of sensitivity analysis for the trained and validated model. PRCC values that are greater than 0.5 or less than −0.5 for influential initial concentrations pSTAT3 (A), pAkt (B), and pERK, and influential parameters to pSTAT3 (D). Y axes indicate PRCC values. Note, no parameters were identified as influential for pAkt and pERK.

Highlights.

• IL-6 induces dose dependent signaling responses

• IL-6 trans-signaling induces higher signaling responses compared to classic signaling

• IL-6 trans-signaling plays a dominant role in the overall effects

• Model identified potential targets for the inflammatory cytokine mediated signaling

Data availability

All data generated or analyzed during this study are included in this published article and its supplementary materials.

Code availability

The model has been constructed using MATLAB (version R2023a). All model reactions, initial conditions, and values of parameters are provided in Supplementary Tables 1 to 3 in Supplementary Data. MATLAB.m file containing model code is available in the Supplementary File.