Theoretical Article

Immunology and Cell Biology (2011) 89, 100–110; doi:10.1038/icb.2010.69; published online 18 May 2010

Inferring relevant control mechanisms for interleukin-12 signaling in naïve CD4+ T cells

Stacey D Finley1, Deepti Gupta2, Ning Cheng3 and David J Klinke II3,4

  1. 1Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA
  2. 2Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA
  3. 3Department of Chemical Engineering, West Virginia University, Morgantown, WV, USA
  4. 4Department of Immunology, Microbiology, & Cell Biology, West Virginia University, Morgantown, WV, USA

Correspondence: Professor DJ Klinke, Department of Chemical Engineering, West Virginia University, PO Box 6102, Morgantown, WV 26506-6102, USA. E-mail:

Received 11 September 2009; Accepted 15 April 2010; Published online 18 May 2010.



Interleukin-12 (IL-12) is a key cytokine involved in shaping the cell-mediated immunity to intracellular pathogens. IL-12 initiates a cellular response through the IL-12 signaling pathway, a member of the Janus kinase/signal transducer and activator of transcription (JAK/STAT) family of signaling networks. The JAK/STAT pathway includes several regulatory elements; however, the dynamics of these mechanisms are not fully understood. Therefore, the objective of this study was to infer the relative importance of regulatory mechanisms that modulate the activation of STAT4 in naïve CD4+ T cells. Dynamic changes in protein expression and activity were measured using flow cytometry and these data were used to calibrate a mathematical model of IL-12 signaling. An empirical Bayesian approach was used to infer the relative strengths of the different regulatory mechanisms in the system. The model predicted that IL-12 receptor expression is regulated by a dynamic, autonomous program that was independent of STAT4 activation. In summary, a mathematical model of the canonical IL-12 signaling pathway used in conjunction with a Bayesian framework provided high-confidence predictions of the system-specific control mechanisms from the available experimental observations.


interleukin-12; Bayesian inference; CD4+ T cells; signal transduction; ordinary differential equations

The immune response provides the human body with natural defenses against infectious diseases and wreaks havoc on human health when dysfunctional.1 These natural defenses are coordinated by specialized cells, called CD4+ T helper cells, that release chemical messengers called cytokines.2, 3 T helper (Th) cells become polarized into one of the three subtypes: Th1 cells coordinate the response to intracellular pathogens, Th2 cells defend against extracellular pathogens and Th17 cells coordinate the autoimmune response.4 Each of these subsets can be identified by the unique profile of cytokines that they produce. In addition, specific cytokines influence the polarization of naïve T helper cells into the different subtypes. Understanding the role of cytokines in shaping the cellular response is essential for engineering immunotherapies tailored to individuals.5, 6, 7

Interleukin-12 (IL-12) is a key cytokine known to promote the differentiation of T cells into Th1 cells.8 IL-12 is a heterodimer (IL-12p70) consisting of a 35kDa subunit (p35) and a 40kDa subunit (p40) that is expressed in both monomeric (IL12p40) and homodimeric (IL12(p40)2) forms. IL-12 initiates a cellular response by recognizing and binding to its receptor, IL-12R, which is composed of two subunits: IL-12Rβ1 and IL-12Rβ2.9 The β1 subunit is involved in other cytokine signaling pathways such as IL-23,10 whereas β2 is specific to the IL-12 signaling pathway and has been shown to be dynamically regulated during T-cell activation.9 Both IL12p40 and IL12(p40)2 can bind to IL-12R, acting as antagonists to IL12p70 binding. A mathematical model of this competitive binding reveals the importance of measuring all forms of IL-12 in understanding the bioactivity of IL-12.11 Ultimately, regulation of the IL-12 pathway is critical for Th differentiation,12 and polarization of Th cells into Th1 cells requires sustained IL-12 signaling.13

The IL-12 signaling network is a member of the Janus kinase (JAK) and signal transducer and activator of transcription (STAT) family of signaling pathways. Signaling through JAK/STAT pathways activates STAT proteins that subsequently translocate to the nucleus, initiating gene expression and protein translation.14 The suppressors of cytokine signaling (SOCS) family of proteins act as negative regulators of signaling in the JAK/STAT pathway. Additional regulators have been found to inhibit signaling through the JAK/STAT pathway, including protein tyrosine phosphatases, which are known to dephosphorylate activated JAK, STAT, or cytokine receptors15 and protein inhibitors of activated STATs (PIAS) that interact with phosphorylated STATs in the nucleus to inhibit their activity.16 TC45, a nuclear protein tyrosine phosphatase, has also been shown to deactivate phosphorylated STAT4 dimers within the nucleus for export back to the cytoplasm.17 In addition, it has been shown that cellular context has an important role in influencing the strength of signaling through particular reaction pathways.18 The canonical JAK/STAT pathway incorporates the regulatory mechanisms described above; however, the dynamic role of these different feedback mechanisms in regulating signaling in the IL-12 pathways remains unclear.14 Therefore, the objectives of the current study were to (1) develop an experimentally validated mathematical model to describe signaling in the IL-12 pathway in naïve CD4+ T helper cells and (2) use the model to infer the relative importance of feedback mechanisms in STAT4 activation within naïve CD4+ T cells.



Flow cytometry results

Magnetic bead enrichment from the starting population of Balb/c splenocytes was used to obtain a population of cells that were >96% positive for CD4+ and >90% positive for both CD4+ and CD62Lhigh (that is, naïve CD4+ T cells). As the population of CD4+ CD62Lhigh splenocytes may contain a mixture of both central memory and naïve T cells, the activation marker CD44 was used to assess the contribution of the central memory pool. Greater than 95% of CD4+CD62Lhigh cells were observed by flow cytometry to express intermediate to low levels of CD44, consistent with a naïve T-cell population (that is, CD4+CD62LhighCD44low). The results suggest that the contribution of the central memory population (that is, CD4+CD62LhighCD44high) was minor. In comparison, high levels of CD44 expression were observed in the CD4+CD62Llow population, consistent with an effector T-cell population (that is, CD4+CD62LlowCD44high) (data not shown).

The dynamics of IL-12 signaling leading to STAT4 activation were assessed in naïve CD4+ T cells extracted from murine splenocytes. Following a pre-activation period, cells were stimulated and subsequently fixed at various time points ranging from 15min to 24h. Flow cytometry was used to measure the extent of cell staining by fluorescence intensity of the markers for IL-12Rβ1, IL-12Rβ2 and phosphorylated STAT4 (pSTAT4). Cells that exhibited non-specific staining were removed by partitioning the population of cells into live and dead cells based on forward scatter and side scatter characteristics of the sample. On an average, 2 × 104 cells were analyzed at each time point, with 60±9% of the population remaining after gating on forward and side scatter characteristics.

The activity of STAT4 (pSTAT4) with respect to IL-12β2 is shown in Figure 1. We have defined a data-driven threshold, indicated by the vertical line in all panels, for whether a cell was positive for IL-12Rβ2, below which 95% of the unstained cells exhibited a lower level of expression. In addition, the dotted horizontal line indicates the upper limit of pSTAT4 mean fluorescent intensity (MFI) for 95% of the cell population before IL-12 stimulation (see 0min panel). These data-driven thresholds compared with the normalized histograms of IL-12Rβ1, IL-12Rβ2 and pSTAT4 for unstained, unstimulated and IL-12-stimulated populations are shown in Figure 2 (panels a, c, and e). The pairwise comparison shown in Figure 1 indicates that the MFI for pSTAT4 was correlated with cells that express IL-12β2.

Figure 1.
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Pairwise density plots for phosphorylated STAT4 versus IL-12Rβ2. Each sub-panel corresponds to a different time following IL-12 stimulation. The solid line indicates the expression threshold for a cell to be associated with positive expression of IL-12Rβ2. Ninety-five percent of the unstained cell fraction was contained below the threshold. The dotted line indicates the upper limit of pSTAT4 MFI for 95% of the CD4+ CD62L+ fraction prior to IL-12 stimulation.

Full figure and legend (312K)

Figure 2.
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Marginalized probability distribution function (PDF) for IL-12Rβ1 (a, b), IL-12Rβ2 (c and d), and pSTAT4 (e, f). Data from the 6-h time point is shown for Balb/c primary cells (a, c, e) and 2D6 cell line (b, d, f). Three cell populations are shown: unstained cells (gray shaded), cells receiving no stimulation (black solid line), and cells stimulated with IL-12 (red dashed line). The dotted line indicates the upper limit of the protein expression or activity for 95% of the unstained (ad) or unstimulated (e, f) CD4+ CD62L+ fraction. A full colour version of this figure is available at the Immunology and Cell Biology journal online.

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Evolution of IL-12Rβ2 and pSTAT4 over time

The protein expression and activity were presented using probability distribution functions (PDFs), enabling a comparison across different samples (Supplementary Figure S1A–C). This analysis showed that the MFI of IL-12Rβ1, IL-12Rβ2 and pSTAT4 varied with time. PDFs for IL-12Rβ2 at each time point exhibited a unimodal distribution (see Supplementary Figure S1B). In contrast, pSTAT4 exhibited a bimodal distribution (Supplementary Figure S1C), revealing a heterogeneous population of cells: responsive cells expressing pSTAT4 in response to IL-12 and unresponsive cells that did not activate STAT4. To investigate the cause of the bimodality in pSTAT4 MFI, we stimulated the 2D6 T cell line with recombinant IL-12p70 (20ngml−1), stained for IL-12Rβ1, IL-12Rβ2 and pSTAT4, and used flow cytometry to assay for changes in cellular expression and activity (Figure 2). In contrast to the Balb/c primary cells, the PDF for pSTAT4 for the 2D6 cell line exhibited a unimodal distribution (Figure 2f), indicating that the presence of responsive and unresponsive cells may be attributed to the heterogeneity in the cell population or stimulation conditions, rather than an inherent characteristic of IL-12 signaling. On the basis of this result, we analyzed the flow-cytometry data in order to parse out unresponsive cells and track pSTAT4 in the remaining cells as a function of time. A gaussian distribution was fit to the unresponsive population and subtracted from the PDF for the total population. The resulting density function was used to characterize the change in pSTAT4 MFI within the responsive population (an example of this analysis is given in Supplementary Figure S1D).

Using the flow-cytometry data, we estimated the median protein expression/activity as a function of time (see Figures 3a–c). The control cells, those receiving no stimulation or anti-IL-4 only, were found to exhibit a similar dynamic change in the expression of IL-12Rβ1 as cells treated with both IL-12 and anti-IL-4 (Figure 3). Similarly, control cells and cells stimulated with IL-12 exhibited similar expression profiles for IL-12Rβ2, suggesting a dynamic program for IL-12 expression not associated with IL-12 stimulation. This initial signaling phase that is independent of IL-12 is consistent with the work of Afkarian et al.,19 who show that early activation of interferon-γ, a promoter of IL-12Rβ2 expression, by the transcription factor T-bet is independent of stimulation by IL-12. Recently, Schulz et al.20 also reported variations in the sensitivity of naïve CD4+ T cells to respond to IL-12. Therefore, we obtained a basal profile of IL-12R expression (Reaction Class 18) from the control experiments using a superposition of gaussian distributions (Supplementary Figure S2). Control cells exhibited negligible activity of STAT4 as expected, and cells stimulated with IL-12 exhibited changes in STAT4 activity, which also varied with time (Figure 3). The activity of STAT4 increased with time, up to 2–3h after stimulation with IL-12, at which point maximum pSTAT4 MFI occurred.

Figure 3.
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Median protein MFI as a function of time. Median values for all experimental groups: cells receiving no stimulation (blue squares), cells stimulated with anti-IL4 (black triangles), and cells stimulated with anti-IL-4 and IL-12 (red circles). Changes in fluorescent intensity (see Figure S1) correspond to changes in protein expression or activity: (a) IL-12Rβ1 expression, (b) IL-12Rβ2 expression, and (c) Phosphorylated STAT4 activity. Two experimental replicates are shown. A full colour version of this figure is available at the Immunology and Cell Biology journal online.

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As the flow cytometry results provided relative measurements, we determined the basal level of IL-12R as 130nM based on an estimate of the number of receptors per cell (7500 membrane receptors per cell) in PHA-stimulated lymphoblasts, the fraction of receptors present on the cell surface (75%), and a cell radius of 3.5μm.11 The activity of STAT4 was also normalized for each cell by dividing the observed fluorescence intensity of pSTAT4 by the observed fluorescence intensity of IL-12Rβ2 receptor expression. Normalizing STAT4 activity with respect to IL-12β2 expression provided an estimate of the activity of the receptor on a cellular basis as a function of time. Changes in the activity of the receptor could be due to partitioning of IL-12R within the cell in response to positive feedback mechanisms or due to inhibition by negative feedback mechanisms.

Parameter estimation and model calibration

The mathematical model was used to infer the relative contribution of positive and negative feedback loops in regulating receptor activity. Given that the 33 model parameters were being fit to 44 experimental data points (4 observables, each with 11 time points), the problem is well posed in theory, and the system is overdetermined. In practice, only a subset of the model parameters can be uniquely defined, and parameter identifiability is useful in determining the identifiable parameters a priori (that is, given unlimited information). The correlation coefficients listed in Supplementary Table S5 show that estimates of the forward binding rate (for example, kf6, kf7, kf8 and kf16) were unique if the corresponding dissociation constants, KD, were specified. Therefore, we fixed the KD values according to the values reported by Yamada et al.21 We equated kf6 to kf7, as was done in the model developed by Yamada et al.21 The Michaelis–Menten constant, KM, was correlated to the Vm parameter for reaction classes 15 and 17. Specifying one of these redundant parameters helps improve the coefficient for estimating the contribution of the pathway, and we set the KM value based on a previous model of IL-12 signaling.21 In total, 14 parameters were selected to be fit to experimental data based on their correlation coefficients and values available in the literature.

In contrast to a priori parameter identifiability, an empirical Bayesian approach was used to estimate the sensitivity of the model parameters with respect to the available data. An adaptive Markov chain Monte Carlo (AMCMC) algorithm22 was used to estimate the expectation values of the model parameters, wherein simulated annealing provided an initial estimate of the parameter values. Three parallel chains, each containing 1 × 106 steps, were used to estimate the posterior distributions. The simulation of each chain took approximately 720h on a single core of a 2.66-GHz Dual-Core Intel Xeon 64-bit processor (Dell, Round Rock, TX, USA) with 8GB RAM. The trace and cumulative distributions of the acceptance fraction show that the scaling factor was adjusted in order to maintain the acceptance fraction around 0.2 (Supplementary Figure S3A and B). The trace of the scaling factor suggests that 1 × 105 steps were required to establish an appropriate proposal distribution (Supplementary Figure S3C). To minimize the effect of autocorrelation, the chains were thinned by selecting every 500th iteration. A graphical summary of the Gelman–Rubin statistics was used as a diagnostic to determine the convergence of the Markov chains to the posterior distribution in the model predictions (Figure 4). An initial sequence of 2 × 105 AMCMC steps was required for the three chains to converge. This initial sequence was used as the ‘burn-in’ period.

Figure 4.
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Convergence of the model predictions among the three parallel Markov chains. The y-axis corresponds to the model simulation time. The x-axis corresponds to the cumulative range of AMCMC steps for which the Gelman–Rubin statistic is calculated. (a) Phosphorylated STAT4 normalized to the level of IL-12Rβ2 expression on a cellular basis. (b) IL-12 bound to IL-12R (data from Chizzonite54). (c) Phosphorylated form of STAT4 reported as a percentage of the maximum STAT4 activity. (d) Total IL-12Rβ2 expression. Values less than 1.2 suggest convergence of the chains.

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Traces for each of the parameters were used to estimate the degree of mixing among the three chains (Supplementary Figure S4). The optimal parameter values were determined using the expectation maximum and are listed in Supplementary Table S4. Pairwise scatter plots obtained from the three chains following the burn-in period were used to estimate the posterior identifiability of the model parameters (Figure 5). The scatter plots were colored based on the marginal posterior probability density obtained by kernel density estimation. A high value for the correlation coefficient suggests that the parameters were not independently identifiable given the calibration data. There were differences between a priori identifiability (Supplementary Table S5) and posterior distribution in parameter values (Figure 5). For example, kf1 and kf5 exhibit a higher correlation given the available data, and Vm17 and k18 were not correlated based on the available data (Figure 5).

Figure 5.
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Pairwise comparison of rate parameters. Parameter names are given on the diagonal. Above the diagonal are the pairwise correlation coefficients of the parameters obtained from the thinned Markov chains. Pairwise projections of the marginalized probability density are given below the diagonal. Coloring is based upon the estimated 2-D posterior density distributions. The values in each scatter plot are centered at the mean values determined from three parallel Markov Chains, and each plot axis spans O(1016). A full colour version of this figure is available at the Immunology and Cell Biology journal online.

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The posterior distribution in the model predictions was obtained by marginalizing the model predictions over all of the parameter values from the Markov chain following the burn-in period. Model simulation revealed that the model was able to capture the long-range dynamics of the IL-12 signaling pathway (Figure 6), and convergence of the Markov chains resulted in a small range of predictions.

Figure 6.
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The mathematical model for early signaling events reproduces the early dynamics for activation of the STAT4 pathway downstream from the IL-12 receptor. Stimulated results from three Markov chains (black, blue, and red lines) are compared against the experimental observations (squares) used to calibrate the mathematical model. Dashed lines indicate 95% confidence interval for the posterior predictions; solid lines indicate the median value. (a) Phosphorylated STAT4 normalized to the level of IL-12Rβ2 expression on a cellular basis. (b) IL-12 bound to IL-12R (data from Chizzonite54). (c) Phosphorylated form of STAT4 reported as a percentage of the maximum STAT4 activity. (d) Total IL-12Rβ2 expression. The initial conditions used in the stimulation are listed in Supplementary Table S1. A full colour version of this figure is available at the Immunology and Cell Biology journal online.

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Understanding how biochemical cues are integrated by cells of the immune system to shape immunity remains a major question in the field.14 To address one aspect of this question, we have developed a mathematical model of the IL-12 signaling pathway and calibrated the model to dynamic measurements of IL-12Rβ2 expression and STAT4 activation in naïve CD4+ T cells derived from Balb/c mice. Given these dynamic calibration data, we also estimated the uncertainty in the model predictions using an empirical Bayesian approach. We incorporated the natural programming of the cellular signaling pathway, as well as feedback loops to describe the control mechanisms at work within the IL-12 signaling network. To our knowledge, this is the first model that integrates kinetic measurements of the dynamic intracellular signaling response of the IL-12 pathway and that establishes a level of confidence in the model predictions. In the following paragraphs, we will describe our predictions related to the relative contributions of postulated regulatory mechanisms that influence sustained IL-12 signaling.

Inference of regulatory mechanisms

The mathematical model developed here was used to infer the relative contributions of different regulatory mechanisms within the IL-12 signaling pathway. We first studied the relative rate of receptor downregulation by activated (ligand-bound receptors) and by inactive receptors. These signaling events were associated with rate parameters k1 and k2 and calibrated to the experimental data. The distribution in these parameters indicated very little difference between downregulation of the active and inactive receptor population (Figure 7a), implying that downregulation due to the activation of the receptor was not a major factor in regulation of IL-12R expression.

Figure 7.
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Comparison of regulation mechanisms predicted from the posterior distribution. (a) Distribution in the logarithm of the rate parameters (Logi)) associated with receptor down regulation for inactive (black—parameter k1) and active (gray—parameter k2) IL-12 receptors. (b) Distribution of rates of reaction for autonomous program for IL-12Rβ2 expression (black—reaction class 18 in Figure 1) and positive feedback where pSTAT4 promotes increased expression of IL-12Rβ2 (gray—reaction class 17 in Figure 1) shown as a function of time. Solid line is median value for cumulative Markov chain; dashed lines enclose 95% of the model predictions (i.e., a 95% confidence interval). (c) Range of model predictions for the concentration of IL-12Rβ2 bound to SOCS (reaction class 16 in Figure 1) shown as a function of time. Solid line is median value for predictions obtained from the cumulative Markov chain; dashed lines indicate 95% confidence interval in the model predictions, given the postulated mathematical model and experimental data.

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Becskei and Grusby23 recently reported a positive feedback loop for IL-12-induced IL-12Rβ2 expression, whereby activation of STAT4 by IL-12 results in increased IL-12Rβ2 expression in naïve CD4+ T cells obtained from 129 mice. Moreover, Becksei and Grusby implicitly assume that, in the absence of IL-12 stimulation, the level of IL-12Rβ2 expression remains constant. As shown in Bi et al.4 and in Schulz et al.,20 the basal expression of IL-12Rβ2 is not constant but changes with time in primary naïve CD4+ T cells. Assuming that the basal expression of IL-12Rβ2 is constant and cellular expression of this receptor is measured only under stimulation conditions, the logical interpretation of the dynamic response is that (1) active receptors exhibit a higher degradation rate (as illustrated in Figure 3 by the decline in IL-12Rβ2 in the first 3h following stimulation) and (2) the increase in receptors from 4h is due to a positive feedback loop. In the work by Becskei and Grusby,23 the contributions of this positive feedback loop (that is, pSTAT4-induced IL-12Rβ2 expression) and an autonomous program were quantified by the parameters vx4 and bx, respectively. The reported maximum likelihood values of these parameters imply that the positive feedback pathway is 3500 times greater that the autonomous program pathway. Therefore, we also investigated the relative source of IL-12Rβ2, comparing IL-12Rβ2 expression by the programmed synthesis of IL-12Rβ2 mRNA and the positive feedback loop whereby pSTAT4 promotes increased expression of IL-12Rβ2. As we measured cellular response under unstimulated and stimulated conditions, we reached a different conclusion. The distributions of the reaction rates of the pathways corresponding to an autonomous program for basal synthesis of receptor mRNA and feedback by pSTAT4 revealed that the average reaction rate of pSTAT4 feedback was at least 100 times less than that of the autonomous program of IL-12Rβ2 synthesis (Figure 7b). This difference suggests that the positive feedback was not a major factor in regulating IL-12Rβ2 expression in our system. This observation is consistent with the reported inability of Balb/c T cells to maintain IL-12 responsiveness despite previous STAT4 activation.24 In contrast, T cells derived from the B10.D2 strain increase the expression of IL-12Rβ2 in response to IL-12 stimulation. This suggests that the contribution of the STAT4-mediated positive feedback loop may be different among inbred mouse strains.

We also evaluated the effect of SOCS binding on the signaling pathway, finding that the fraction of receptor bound by SOCS was quite small (Figure 7c). The average response showed that less than 0.1% of the total IL-12R was bound by SOCS and 97.5% of the predictions estimated that less than 0.6% of IL-12R was bound by SOCS, with the maximum occurring at 2h following stimulation by IL-12. In addition, the correlation coefficients among the posterior distribution in the parameters, as shown in Figure 5, suggest that an increase in binding of inactive STAT4 to IL-12R (kf8) can partially compensate for an increase in SOCS synthesis rate (kf23). Under these conditions, SOCS has a limited effect on receptor expression and activation of STAT4. Singh et al.25 suggest strong negative feedback by SOCS species following activation of the JAK–STAT signal transduction pathway induced by the IL-6 signal; however, we observed that this negative feedback loop was not a major contributor to alterations in IL-12R expression. Given the minimal contribution of SOCS, we were unable to assess the particular mechanism by which SOCS regulated IL-12 signaling. By obtaining experimental data from a positive control (that is, stimulating cells with IL-4, which promotes the synthesis of SOCS), it may be possible to infer the mechanism of action of SOCS, that is, whether the protein acts to increase IL-12R degradation or decreases the ability of IL-12R to phosphorylate STAT4.

Limitations of the analysis

The results presented here were influenced by the assumptions made a priori in developing the model. In particular, we did not explicitly account for the distribution of IL-12-bound receptor among different endosomal trafficking compartments, which has recently been reported to be important for effective IL-5 signaling.26 In addition, we assumed that the rate of ligand–receptor binding and IL-12R mRNA translocation and degradation observed by others was applicable to our system.

Our data suggested cyclical IL-12R expression driven by a cell-autonomous program. Cell-autonomous maintenance of IL-12Rβ2 expression has been associated with a genomic region within chromosome 11 called Tpm1 (T-cell phenotype modifier 1).27 The particular genes associated with this locus remain unresolved. Similar oscillations in protein expression resulting from feedback loops have been observed in other biological systems.28, 29, 30 If we assume that the observed dynamics reflects two sinusoidal functions with periods of 7 and 3.5h, respectively, and interpolate system behavior between the 7.5 and 24h time points, the predicted regulatory mechanisms are similar to the ones shown in Figure 7 (data not shown). A counter-regulatory cytokine, IL-4, also promotes the expression of SOCS3 and inhibits IL-12-induced STAT4 activation in polarized CD4+ Th2 cells.31 The addition of anti-IL-4 to the stimulation conditions ruled out the contribution of an autocrine negative feedback loop attributed to enhanced IL-4 production by Balb/c T cells32 leading to the downregulation of IL12Rβ2.33 Regulation of IL-12Rβ2 expression in Balb/c T cells by interferon-γ34 still remains a possible explanation. In future studies, it will be important to include experimental measurements of IL-12R synthesis and degradation and SOCS expression in order to address these limitations and further support the model predictions. The model does not exactly reproduce early oscillations in STAT4 activity (Figure 4c), which is closely related to the input function IL-12Rβ2. We chose to represent this IL-12-independent expression profile using 14 evenly spaced gaussians; including more gaussians may result in a better fit of STAT4 activity. In addition, non-convergence of pSTAT4 during early time points (Figure 4c) may be an artifact of simulation response as this figure reflects variations in STAT4 activity (plotted on the y-axis), and the simulation response is nearly vertical during that time period. Slight variations in parameter values that are consistent with later times would provide large differences in predictions during these early time points.

Concluding thoughts

Mathematical models are tools used to rationalize about the intracellular signaling mechanisms that underpin biological response.35 Mathematical models that describe biochemical kinetics are explicit statements about molecular–molecular interactions that are presumed to be important in a system and the corresponding dynamics of these interactions. These interactions give rise to a flow of molecular information in the form of reaction pathways.36 The primary goal of the analysis of these reaction pathways is to make predictions: what do we expect to happen in a particular reacting mixture under particular reaction conditions, given our current understanding of molecular interactions? Similarities confirm our explicit statements whereas differences between the expected behaviors and new data highlight the areas of uncertainty in our understanding and provide the engine for scientific progress.37 Analogous to experimental studies, the ability of a particular mathematical model to describe a system of interest must include a statement of belief.

Belief derived from a mathematical model is expressed commonly in terms of a single point estimate for the predictions, obtained from the set of parameters that minimizes the variance between model and data.38 Given that a model constrains the set of possible states of the system, it is essential to provide an estimate of the uncertainty associated with the model predictions given the available data. A Bayesian view of statistics is a mathematical expression of our beliefs.39 Beliefs are established based on the observation of data and the interpretation of that data within the context of our previous knowledge37 Mathematical models provide a quantitative framework for representing previous knowledge of the detailed biochemical interactions that comprise a signaling network. The unknown parameters of the model can be calibrated against the observed network dynamics. Given the calibration data and the postulated model, the uncertainty in the model predictions can be obtained using an empirical Bayesian approach for model-based inference.22

This work applied an empirical Bayesian approach to infer the relative importance of postulated mechanisms that control IL-12 signaling in naïve CD4+ T cells obtained from Balb/c mice. In particular, this work revealed that an IL-12-independent, dynamic program for IL-12R expression was the major contributor to regulating signaling through the IL-12 pathway. The degradation rate for activated receptors was not significantly different from the degradation rate for inactive receptors. The similarity in degradation rates suggested that the downregulation of receptor expression was not by a mechanism directly related to the activity of the receptor. Finally, direct negative regulation of IL-12 signaling by SOCS expression was not a major factor in regulating IL-12 signaling. More generally, this model-based approach can be used to infer control mechanisms in other cell signaling pathways.



Experimental aspects


Eight- to 12-week-old female Balb/c mice were obtained from Hilltop Lab Animals (Scottsdale, PA, USA). Mice were housed in sterilized microisolator cages in the university vivarium, and facility sentinel animals were regularly screened for specific pathogenic agents. All studies were conducted in accordance with all federal and institutional guidelines for animal use and were approved by the West Virginia University Animal Care and Use Committee guidelines.

Antibodies and reagents

Hamster anti-mouse IL-12 receptor β2 (HAM10B9), FITC-conjugated mouse anti-hamster IgG1 (G94-56), biotinylated anti-mouse IL-12 receptor β1 (114), allophycocyanin (APC)-streptavidin, and phycoerythrin-conjugated mouse anti-mouse phosphorylated STAT4 (38/p-Stat4 Y693), BD Phosflow Lyse/Fix buffer, BD Phosflow Perm Buffer III and FcBlock were purchased from BD Biosciences (San Diego, CA, USA). The CD4+ CD62L+ T-cell isolation kit was purchased from Miltenyi Biotec (Auburn, CA, USA). Recombinant mouse IL-12p70, FITC-conjugated rat anti-mouse CD4 (GK1.5), phycoerythrin-conjugated rat anti-mouse CD44 (IM7), allophycocyanin-conjugated rat anti-mouse CD62L (MEL-14), affinity-purified hamster anti-mouse CD28 (37.51) and rat anti-mouse IL-4 (11B11) were purchased from eBioscience (San Diego). Monoclonal hamster anti-mouse CD3 (145-2C11) was purchased from R&D Systems (Minneapolis, MN, USA). Unless otherwise noted, all primary cell cultures were maintained at 37°C in 5% CO2 in RPMI 1640 plus supplements (referred to as complete RPMI or cRPMI). The RPMI supplements were 10% heat-inactivated fetal bovine serum (FBS) (Hyclone, Logan UT, USA), 2mM of L-glutamine (Medtech Inc., Herndon, VA, USA), 50mM HEPES (Sigma Chemical, St Louis, MO, USA), 49μM β-mercaptoethanol (Sigma Chemical) and 100μgml−1 of streptomycin and 100Uml−1 penicillin (Hyclone).

Cell isolation and tissue culture

Spleens from Balb/c mice were isolated and a cell suspension was made by mashing the spleens through a nylon screen. Following lysis of red blood cells using Tris ammonium chloride, the cells were pooled and washed twice in cRPMI containing 1.5% FBS. Mouse splenocytes were resuspended at 2.5 × 108ml−1. Unpolarized CD4+CD62L+ (that is, naïve) T cells were subsequently isolated through negative selection by automated magnetic cell sorting, following the manufacturer's instructions (Miltenyi Biotec). Briefly, mouse splenocytes were enriched for CD4+ T cells by negative selection through indirect magnetic labeling of non-CD4+ T cells using a cocktail of biotin-conjugated monoclonal anti-mouse antibodies against CD8a, CD45R, CD11b, CD25, CD49b, TCRγ/δ and Ter-119 and magnetic microbeads conjugated to a monoclonal anti-biotin antibody. CD4+CD62L+ T cells were subsequently enriched from CD4+ splenocytes by positive selection using magnetic microbeads conjugated to a monoclonal rat anti-mouse CD62L antibody. Enrichment for CD4+CD62L+ T cells was confirmed by flow cytometry using anti-CD4, anti-CD62L and anti-CD44 antibodies. 2D6 cells, an IL-12-responsive mouse Th1-cell clone provided by Dr MJ Grusby (Harvard Medical School, Boston, MA, USA), were maintained in cRPMI supplemented with 100mM sodium pyruvate (Fisher Scientific, Pittsburgh, PA, USA), 1% MEM non-essential amino-acid solution (100 × Fisher Scientific) and 6.7ngml−1 IL-12p70.

Pre-activation of naïve CD4+ T cells

Signaling via the IL-12 pathways requires the co-expression of both components of the IL-12 receptor: IL-12Rβ1 and IL-12Rβ2.9, 40 IL-12Rβ1 is expressed constitutively on CD4+ T cells. Naïve CD4+ T cells were stimulated for 44h with plate-bound anti-CD3 and anti-CD28 to upregulate IL-12Rβ2.41 Anti-CD3-coated plates were prepared by adding 10μgml−1 of monoclonal anti-mouse CD3 (R&D Systems) to 96-well culture plates and incubating for 90min at 37°C followed by storage overnight at 4°C. Before the addition of the cells, the unbound anti-CD3 was aspirated out of the wells and the wells were washed three times with sterile phosphate buffered saline (PBS). Naïve CD4+ T cells (2 × 104cells per well) and 2μgml−1 of anti-mouse CD28 (eBioscience, San Diego) were added to each of the anti-CD3-coated wells. All primary cell cultures were performed in cRPMI supplemented with 10% FBS, 37°C and 5% CO2.

Stimulation of IL-12 signaling

Pre-activated naïve CD4+ T cells were divided into three treatment groups. In the first group, cells were stimulated with recombinant IL-12p70 (20ngml−1) and anti-mouse IL-4 (10μgml−1). The addition of anti-IL-4 to the stimulation conditions ruled out the contribution of an autocrine-negative feedback loop attributed to enhanced IL-4 production by Balb/c T cells.32 The second and third groups functioned as negative controls and were exposed to anti-IL-4 and PBS, respectively. The experiments were performed in duplicate. Before IL-12p70 stimulation, 2D6 cells (4 × 104cells per well) were cultured in 96-well u-bottomed culture plates for 12h in the absence of IL-12p70. Cells were assayed by flow cytometry following a 6h exposure to IL-12p70 (20ngml−1) or PBS, as a negative control. The experiments were performed in triplicate. Cells were appropriately stimulated and re-incubated for a series of time points at 37°C at 5% CO2.

Flow cytometry

Unsorted splenocytes and isolated naïve CD4+ T cells were prepared, as described above, and stained with fluorophore-conjugated antibodies specific for the mouse T-cell markers CD4, CD62L and CD44. For extracellular staining, single-cell suspensions were washed with ice-cold PBS containing 0.2% sodium azide (Sigma-Aldrich Chemical Co., MO, USA) (PBSaz) and then incubated with purified rat immunoglobulin and purified mouse immunoglobulin (BD Biosciences, San Jose, CA, USA) for 30min on ice to prevent nonspecific binding. Subsequently, the cells were washed, and incubated with buffer containing the appropriate antibody reagent for 30min on ice. The cycle was repeated for any additional antibodies. Finally, the cells were washed twice in PBSaz and fixed in 0.4% paraformaldehyde. For intracellular staining, stimulated cells at the different time points were centrifuged and fixed at the appropriate times by incubating with BD Phosflow Lyse/Fix buffer (BD Biosciences) pre-warmed to 37°C for 10min. Following fixing, cells were washed in PBS and incubated with buffer containing the appropriate antibody reagent for 30min on ice. The cycle was repeated for any additional antibodies. Cells were assayed for total cellular expression of the components of the IL-12 receptor (that is, anti-mouse IL-12Rβ1 and anti-mouse IL-12Rβ2, BD Pharmingen, San Jose, CA, USA) and intracellular activation of STAT4 (that is, phosphorylated STAT4, BD Pharmingen) by flow cytometry. Finally, the cells were washed three times in PBSaz and analyzed using a FACSAria flow cytometer (Becton Dickinson, Franklin Lakes, NJ, USA). The fluorescent intensity for each parameter was reported as a pulse area using 18-bit resolution. Single-stain controls were used to establish fluorescent compensation parameters. Unstained cells were used as negative flow cytometry controls. Flow cytometry data was analyzed using R/Bioconductor.42

Mathematical modeling

A mathematical model of IL-12 signaling was developed to describe the early signaling events following stimulation of IL-12R and to represent the regulatory aspects of the IL-12 pathway. Our model expands upon a model of T-helper-cell differentiation that was aimed at simulating the Th1/Th2 balance in cytokine signaling networks, including the IL-12 pathway, along with IL-4 and interferon-γ pathways.21 However, the previous model of IL-12 signaling was based on the dynamics of the interferon-γ pathway. The objectives of our study required the synthesis of a new mathematical model that builds upon elements of this previous work.

Developing a mathematical model for a reaction network involves two aspects. First, one must construct the topology of the reaction network (i.e., the series of biochemical interactions between reacting species). Once the reaction topology is specified, one must select values of the model parameters and initial conditions that are consistent with the experimental data used to calibrate the model. Once calibrated, the model can be used to describe the evolution in species’ concentration as a function of time and to explore the dynamic implications of different regulatory mechanisms. In the following paragraphs, each of these components of the IL-12 signaling network will be discussed in more detail.

Topology of the IL-12 signaling network

As depicted in Figure 8, a series of reaction classes that represent a canonical JAK–STAT signaling pathway were assembled to create a chemical kinetic model for IL-12 signaling. The collection of molecular species included in the model is listed in Supplementary Table S1. The kinetics of the reactions were defined using reaction classes based on specific protein–protein interactions (Table 1 and Supplementary Table S2).43 Although a protein can be part of a larger complex, only a short peptide sequence, a protein motif, provides the point of interaction between proteins.44 From this perspective, the kinetics are governed by the interactions between protein motifs on the various protein complexes. The relationships among all of the biochemical species represented in the model were compiled into a reaction mechanism. The corresponding 28 differential equations were used to describe the evolution of the system with time (Supplementary Table S3).

Figure 8.
Figure 8 - Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, please contact or the author

A simplified schematic diagram of the reaction classes represented in the mathematical model. The model represents IL-12R synthesis and degradation; IL-12 binding to IL-12R; STAT4 dimerization and phosphorylation; JAK2 and TYK2 association with the receptor; activation of the signaling pathways associated with the interaction between STAT4 and the bound receptor complex (LRTJ); dimerization and localization of phosphorylated STAT4; deactivation following the dephosphorylation by STAT4 protein phosphatase; and negative feedback by SOCS and protein phosphatase.

Full figure and legend (165K)

Signaling through the IL-12 signaling pathway is initiated by IL-12p70 binding to its receptor, IL-12R. The IL-12 receptor is represented implicitly as a complex of both IL-12Rβ1 and IL-12Rβ2. IL-12p70 (L), IL-12R (R) and the IL12-IL12R (LR) complex interact with JAK245 and tyrosine kinase 2 (TYK2). Binding of JAK2 and TYK2 imparts kinase activity to this activated receptor complex (LRTJ) and activates the STAT4 protein by phosphorylation.46 Phosphorylated STAT4 then dimerizes and translocates to the nucleus, where it promotes the transcription of IL-12R mRNA.23 Nuclear IL-12R mRNA is exported to the cytosol, enabling the synthesis of new IL-12 receptors. In the absence of specific knowledge regarding trafficking of IL-12R,47 IL-12R is assumed to exhibit basal turnover with enhanced receptor degradation following receptor ligation.48 In addition, we have accounted for steady-state synthesis of JAK2, TYK2 and IL-12R mRNA, and protein degradation.

To assess the mechanisms for control of IL-12 signaling, we have incorporated three negative regulatory mechanisms: (1) ligand-induced receptor downregulation, (2) inhibition of the activity of activated IL-12R by SOCS and (3) deactivation of phosphorylated STAT within the nucleus. As discussed above, activating a receptor commonly results in an increase in the rate of receptor degradation (that is, receptor downregulation). IL-12 promotes the expression of SOCS1 and SOCS3.13 However, the particular mechanism by which SOCS proteins regulate cytokine signaling remains elusive.49 In addition, protein inhibitors of activated STATs and protein tyrosine phosphatases inhibit the activity of activated STATs within the nucleus.50 To represent this mechanism, a generic protein phosphatase (XPP) was included in the model that dephosphorylated STAT4 dimers in the nucleus to form STAT4 monomers. Unactivated STAT4 monomers were exported back to the cytosol.

Reactions took place in three locations: extracellular environment, cytosol and nucleus, and the kinetic constants corresponding to reactions that involved reactants located in different compartments were scaled to account for the different respective volumes,51 with the cytosol serving as the reference volume. Signaling events that occurred at the cell membrane were assumed to be well dispersed within the cytosol. The initial receptor concentration was determined by dividing the total number of receptors present on the cell surface by the average volume of incubation medium per cell, Vm (10−5ml). However, the cytoplasmic water volume, Vcw (1.26 × 10−10ml), is the reference volume, and the receptor concentration was scaled by multiplying by Vm/Vcw.51 Initial concentrations were taken from the literature21 or determined using algebraic constraints on conserved species (Supplementary Table S1).

Model calibration

The resulting biochemical kinetic reaction network specified interactions between proteins (that is, a set of coupled non-linear differential equations) and was coupled with parameters for each reaction to simulate the concentration changes with time. The literature provided an initial source of parameter values for each reaction.21, 52 The binding rates and kinetic constants for STAT4 phosphorylation and translocation were obtained from the work of Koster and Hauser.53 The rates of degradation and translocation of IL-12R mRNA were based on the data from Hoffman et al.,28 assuming degradation and translocation rates are independent of the transcription factor (that is, NF-κB versus STAT4). Mass balances provided the rate of steady-state synthesis of nuclear IL-12R mRNA.

The experimental data measuring the expression of IL-12Rβ2, the activity of STAT4 (that is, phosphorylated STAT4) and activity of STAT4 normalized to IL-12Rβ2 expression were used to calibrate the mathematical model. In addition, ligand–receptor binding in human lymphoblastoid cells was used,54 assuming that ligand–receptor binding is cell-type independent. The model equations were encoded and evaluated in MatLab V7.0 (The MathWorks, Natick, MA, USA). Summed squared error between experimental and simulated measurements was used to determine the goodness-of-fit. Estimates for unknown parameter values were determined using these experimental data and were guided by parameter identification analysis. Ultimately, all parameter values, tabulated in Supplementary Table S4, were determined to be consistent with observed experimental data using a combination of simulated annealing55 and an empirical Bayesian approach discussed in more detail in the following sections.

Parameter identification

An important aspect of model development is to identify parameters that can be uniquely determined from the available data. We have used parameter identification analysis to determine whether the parameter calibration problem was initially well posed.56 The correlation coefficients between model parameters were calculated, where parameters that were locally identifiable had correlations with all other parameters between −0.965 and 0.965 (that is, between –1 and 1). Parameters that were not locally identifiable, termed a priori unidentifiable, had correlations of >0.965 or <−0.965 with at least one other parameter (see Supplementary Table S5).

Bayesian confidence interval estimation

A computational Bayesian approach was used to estimate the uncertainty associated with the model parameters given the available experimental data and to determine the interdependence of the parameter values.22 We used an adaptive Markov chain Monte Carlo (AMCMC) algorithm to generate a sequence of states that represent samples drawn from the posterior distribution of the model predictions, given the uncertainty in the model parameters and the specific calibration data. A starting point in the parameter space was obtained by simulated annealing.55 Using an unbiased prior distribution, a learning period of 100000 steps was used to establish the covariance of the proposal distribution. The proposed steps within parameter space were evaluated using a Metropolis–Hastings algorithm with a targeted acceptance fraction equal to 0.2. The Gelman–Rubin potential scale reduction factor was applied to the model predictions to estimate the convergence of the Markov chain to the posterior distribution of the model predictions.57, 58 In addition, representative samples from the posterior distribution were obtained by retaining every 500th step of the cumulative chain.


Conflict of interest

The authors declare no conflict of interest.



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We thank Kathy Brundage for assistance with the experimental techniques and John Barnett for providing access to laboratory facilities. This work was supported by grants from the PhRMA Foundation, the National Cancer Institute (NCI) R15CA123123 and the National Institute of Allergy and Infectious Disease (NIAID) R56AI076221. The content is solely our responsibility and does not necessarily represent the official views of the NCI, the NIAID or the National Institutes of Health. Author contributions: DJK conceived the study; DG and NC performed the experiments; SDF, DG, NC and DJK analyzed the data; and SDF and DJK wrote the paper.

Supplementary Information accompanies the paper on Immunology and Cell Biology website