- Research article
- Open Access
Towards a quantitative understanding of the MITF-PIAS3-STAT3 connection
© Thingnes et al; licensee BioMed Central Ltd. 2012
- Received: 23 October 2011
- Accepted: 8 February 2012
- Published: 8 February 2012
Expression of the two transcription factors microphthalmia-associated transcription factor (MITF) and signal transducer and activator of transcription 3 (STAT3) are tightly connected to cell proliferation and survival, and are important for melanocyte development. The co-regulation of MITF and STAT3 via their binding to a common inhibitor Protein Inhibitor of Activated STAT3 (PIAS3) is intriguing. A better quantitative understanding of this regulation is likely to be important for elucidation of the melanocyte biology.
We present a mathematical model describing the MITF-PIAS3-STAT3 signalling network. A default parameter set was developed, partly informed by the literature and partly by constraining the model to mimic reported behavioural features of the system. In addition, a set of experiment-specific parameters was derived for each of 28 experiments reported in the literature. The model seems capable of accounting for most of these experiments in terms of observed temporal development of protein amounts and phosphorylation states. Further, the results also suggest that this system possesses some regulatory features yet to be elucidated.
We find that the experimentally observed crosstalk between MITF and STAT3 via PIAS3 in melanocytes is faithfully reproduced in our model, offering mechanistic explanations for this behaviour, as well as providing a scaffold for further studies of MITF signalling in melanoma.
- Success Criterion
- Phosphorylation Rate
- System Biology Graphical Notation
- Tetradecanoyl Phorbol Acetate
- MITF Activity
The melanocytes are skin cells of neural crest origin that constitute 5% - 20% of the basal layer of human epidermis [1–6]. The cell type is responsible for the melanin pigment production and thus the colour patterning of skin and hair in mammals. Melanoma, a cancer originating in melanocytes, is in its later stages notoriously resistant to treatment, and although good prognostic markers exist, the understanding of the underlying biology is only slowly forthcoming . While knowledge about each single protein and gene involved in melanocyte development and regulation of homeostasis is important, developing an understanding of the signalling networks connecting the receptors on the surface to the regulating effect on gene transcription in the nucleus appears crucial in implementing efficient molecular treatment strategies in the dawning era of personalized cancer therapy.
Expression of microphthalmia-associated transcription factor (MITF), the signal transducer and activator of transcription 3 (STAT3), and their co-regulation via protein inhibitor of activated STAT3 (PIAS3), are all tightly connected to cell differentiation, proliferation and survival. MITF is considered to be a master regulatory gene for melanocytes, and has been shown to play important roles in the regulation of genes involved in cell cycle progression, including Bcl-2 and CDK2 [8–10]. MITF is also of clinical significance, as MITF mutations in humans cause Waardenburg syndrome type II , and a significant number of malignant melanomas harbour MITF amplifications. MITF has also been proposed to be important for both differentiation of melanocytes and for tumour transformation . MITF has two phosphorylation sites influencing the PIAS3 binding: S73 and S409. These sites are phosphorylated by different kinases in the MAPK pathway, the ERK and RSK, respectively [13, 14].
STAT3 is a transcription factor involved in signal transduction pathways that are activated by several extracellular stimuli, including the IL-6 family of cytokines. It is tyrosine phosphorylated by the Janus kinase (JAK) or SRC. The resulting signal mediates cell growth, differentiation, and survival [15–17]. The underlying molecular details have only partly been elucidated .
PIAS3 has been identified as an inhibitor of both activated STAT3 and MITF [19–23]. PIAS3 can bind activated STAT3, as well as non-activated MITF in one of its two inactive complexes. The phosphorylation of MITF at S409 results in MITF dissociation from the complex, and more PIAS3 is thereby made available. As a result, more STAT3 is bound in complex with PIAS3 and is thus prevented from binding DNA and activating target genes [22, 24, 25]. Similarly, expression of constitutively active STAT3 will complex with unbound PIAS3, resulting in less PIAS3 being available for binding to MITF. Consequently, more active MITF is observed .
Constraining model behaviour and parameter domains
List of core parameters
MITF phosphorylation on S73, ERK dependent (Mol-1min-1)
MITF de-phosphorylation on S73 (min-1)
MITF auto-phosphorylation on S73 (min-1)
MITF phosphorylation on S409 (Mol-1min-1)
MITF de-phosphorylation on S409 (min-1)
MITF/PIAS3 association (Mol-1min-1)
MITF/PIAS3 dissociation (min-1)
MITFp79/PIAS3 association (Mol-1min-1)
MITFp79/PIAS3 dissociation (min-1)
MITFp409/PIAS3 association (Mol-1min-1)
MITFp409/PIAS3 dissociation (min-1)
MITFpp/PIAS3 association (Mol-1min-1)
MITFpp/PIAS3 dissociation (min-1)
STAT3 phosphorylation (Mol-1min-1)
STAT3 de-phosphorylation (min-1)
STAT3p/PIAS3 association (Mol-1min-1)
STAT3p/PIAS3 dissociation (min-1)
MITF production (Mol min-1)
MITF degradation (min-1)
MITFp73 degradation (min-1)
MITFp409 degradation (min-1)
PIAS3 production (Mol min-1)
PIAS3 degradation (min-1)
STAT3 production (Mol min-1)
STAT3 degradation (min-1)
RSK1 phosphorylation (Mol-1min-1)
RSK1 de-phosphorylation (min-1)
ERKp concentration (Mol)
JAKp concentration (Mol)
An overview of the biological experiments
Temporal development of ERK and RSK1 kinase activity
Distribution between MITF phosphorylation before stimulation
Figure 1 and 2
Temporal development of MITF phosphorylation states after stimulation
Figure 1 and 2
Temporal development of MITF degradation
Figure 1 and 2
MITF activity in response to PIAS3 transfection
Amount of MITF-PIAS3 complex in response to activation
 Figure 2A
Amount of MITF-PIAS3 complex in response to activation with transfected MITF and PIAS3
 Figure 2B
MITF activity in response to transfection of constitutively active RSK1
 Figure 3A
MITF activity in response to PIAS3
 Figure 3B, left, black
MITF activity in response to transfection of PIAS3 and active RSK1
 Figure 3B, left, grey
Activity of a MITF-S409A mutant in response to PIAS3
 Figure 3B, right, black
Activity of a MITF-S409A mutant in response to transfection of PIAS3 and active RSK1
 Figure 3B, right, grey
Activity of MITF in response to transfection of PIAS3
 Figure 6
Activity of MITF-S73D mutant in response to transfection of PIAS3
 Figure 6
Activity of MITF-S409D mutant in response to transfection of PIAS3
 Figure 6
Activity of MITF-S73/409D mutant in response to transfection of PIAS3
 Figure 6
MITF-PIAS3 association in response to activation
 Figure 3A
S409A mutated MITF-PIAS3 association in response to activation
 Figure 3A
STAT3 activity in response to activation
 Figure 3B
STAT3 activity in response to activation with transfected PIAS3
 Figure 3B
STAT3 activity in response to activation with transfected PIAS3 and small amount of MITF
 Figure 3B
STAT3 activity in response to activation with transfected PIAS3 and large amount of MITF
 Figure 3B
STAT3 activity in response to activation with transfected PIAS3 and small amount of S-409A mutated MITF
 Figure 3B
STAT3 activity in response to activation with transfected PIAS3 and large amount of S409A mutated MITF
 Figure 3B
MITF activity in response to transfection of Y705F mutated STAT3 and STAT3-C
 Figure 4B
MITF and STAT3 activity in response to activation compared between wild type and mutated MITF (unable to bind PIAS3)
 Figure 6D and E
STAT3 activity in response to transfection of MITF or S409D MITF mutation
 Figure 7C
MITF activity in response to transfection of STAT3-C
 Figure 7D
Robustness of fit between model results and experimental data
Interpretation and qualification of selected experiments
The focal melanocyte regulatory module may reflect the need for co-regulation of two transcription factors. It seems to provide one type of solution for obtaining different co-regulation effects on different time scales, from the immediate effects on the activity of one transcription factor upon activation of the other, to the long term effect of sequestering and later release. Because this module has components working on many different time scales, the history leading up to an event may be determinative. This may be of importance when interpreting results from experiments that operate on different time scales, such as transfection of constitutively active kinases compared to activation of pre-existing kinases.
The cross talk is going mostly one way
The asymmetry of the network, introduced by PIAS3 binding to activated STAT3, while most efficiently binding to non-activated MITF, yields a particular regulatory effect. We observe that in the model, STAT3 is more affected by the activation of MITF than MITF is affected by the activation of STAT3. This phenomenon, which is in accordance with earlier observations [19, 20], can be elucidated from some features of the model. In the resting cell, PIAS3 is to a larger extent bound to un-phosphorylated MITF and MITFp73, which are the major phosphorylation states in the resting cell. On the other hand, STAT3 only binds PIAS3 when activated. Thus, even if both transcription factors are able to alter the amount of free PIAS3, only STAT3 is affected by it: Activated MITF does not interact with PIAS3, and is therefore unaffected by the amount of free PIAS3. STAT3, on the other hand, binds PIAS3 only in activated state, and the strength of the signal is therefore highly affected by the level of free PIAS3. This is a mechanistic explanation for the observation that STAT3 does not associate with PIAS3 that is already associated with MITF .
This model cannot explain the result of experiment #26
Our results indicate that it is not possible to mimic experiment 26 with this model. This finding contradicts the mechanism suggested in  as an explanation for the observed data. In our opinion, these observations must either be caused by un-expected properties in the MITF mutant, and/or by un-modelled connections in the network. The latter is supported by the fact that the module modelled here is an abstraction of a small part of a vastly complex regulatory network. Mechanisms not accounted for in the present model include regulation of MITF [10, 27, 28] and upstream co-regulators in the JAK-STAT  and the SRC-STAT pathways.
The sensitivity of simulation results to parameter value perturbations
In the sensitivity analysis the model parameters were perturbed in a range from half to double their default value. Some of the parameters exposed negligible effect on the simulation results under these perturbations. For instance there are no experiments that show high sensitivity to the association and dissociation constants kMp409ass, kMp409diss. A possible explanation for this is that the affinity of S409 phosphorylated MITF to PIAS3 is so low that PIAS3-MITFp409 is rare compared to the other PIAS3-MITF complexes, and modest perturbations of the association and dissociation constants does not change this situation. The MITF and STAT3 production rates (P MITF andPSTAT3) are affecting the total amount of protein, but still none of the experiments are particularly sensitive to these parameters. The reason for this seems to be that the relative response measured in the experiments is not affected much by this total amount.
The broader context
In the skin, the major contributors to melanocyte signalling are dermal fibroblasts and epidermal keratinocytes [30, 31]. For MITF, the major regulatory pathways are thought to be the TGF-β and the POMC derivatives ACTH and α-MSH signalling pathways . The TGF-β pathway, which is often dysregulated in melanoma [33, 34], down-regulates MITF, while the α-MSH pathway up-regulates MITF expression [28, 35, 36]. The up-regulation occurs via α-MSH binding and activation of MC1R, which leads to cAMP/PKA activation and activation of MAPK [36, 37]. Thus, the effect of the MAPK pathway on MITF is complex, including up-regulation, activation and tagging for degradation. For STAT3, in addition to the IL-6 cytokine family, growth factors such as EGF, PDGF and KITL have been reported to activate STAT3 [38–40]. Here, KITL is of special interest in melanocyte biology. In addition to being essential for melanocyte development, it has recently been reported that the hereto unidentified coupling of MC1R activation to MAPK proceeds via MC1R-coupled KIT activation of MAPK . With a focus on developing potential therapies toward melanoma, both MITF and STAT3 have been implicated in neoplastic progression. MITF has been classified as a bona fide context dependent oncogene . STAT3 has been implicated in neoplastic progression with an increased contribution especially in metastatic melanoma . Strikingly, no spontaneous or inherited mutations have been isolated . Targeting STAT3 is, however, feasible from both upstream and downstream elements. In addition to being a melanoma oncogene, depletion of MITF has been reported to induce arrest, senescence and cell death in melanoma identifying it as a potential target for therapy [43, 44]. Indeed, a PIAS3 based peptide has been developed to target both MITF and STAT3 via a PIAS3 23-aa mimic [21, 23].
Applicability of the Model
With regards to MITF and STAT3 and their roles in melanocyte biology, it is intriguing that α-MSH signalling is somewhat equivalent to KITL signalling with the additional activation of the cAMP/PKA axis. This leads to an increase in MITF production and dual phosphorylation of both MITF and STAT3. Likewise, α-MSH signalling in melanoma predisposing MC1R RHC (red hair colour) mutant backgrounds, which does not elevate cAMP, would alone be equivalent to KITL signalling in a wild type background with regards to MITF and STAT3, the outcome being STAT3 phosphorylation and MITF activation and subsequent depletion. With this in mind, the emergence of MITF's role in melanoma and its high frequency of duplication, it seems contradictory that MC1R mutants predispose individuals to this disease. It will be interesting to see if compensatory mutations in cAMP elevating factors such as G protein-coupled receptors (e.g. the histamine receptor H2) are found to be necessary for progression and if so to model the outcomes [45–47].
Special conditions like JAK-STAT3 activation duration due to SOCS feedback inhibition versus SRC-STAT3 activation, which is not influenced by SOCS , may be simulated through the model. In addition, other relevant factors such as NF-κ-B, which is also regulated by PIAS3 binding , may be added by incorporating an NF-κ-B module. Another interesting module would, for example, be GM-CSF/KITL or GM-CSF/α-MSH signalling. GM-CSF activates MAPK, but has been reported to inhibit KIT signalling via direct binding of CSF2RA to KIT .
With this model at hand, more detailed issues in this network can be addressed. The previously posed question on which phosphorylation states of MITF are represented by the upper band interpreted to be phosphorylated MITF in Western blot analysis [13, 14], is such an issue. With the ability to test different hypothesis in simulations, both the experiment design and the interpretation of the experimental results could benefit.
Further work could include refinement of various parts of the model by integrated wet-lab modelling efforts. The three parts of the model that could benefit the most from structural enhancement, are the following: (i) The mapping function from the MITF phosphorylation states to the MITF transcriptional activity could be represented on a higher resolution level. This is needed for the model to address quantitative data with absolute values. (ii) The production regime of MITF, PIAS3, STAT3 and RSK1 could be represented by both transcription and translation. (iii) The enzymatic equations could be represented by Michaelis-Menten kinetics. All these structural changes will introduce more state variables and model parameters, thus nothing would be gained by these efforts without the generation of accurate quantitative data to pin down both the model structure and the parameter values.
In this work, we have provided a mathematical model of the MITF-PIAS3-STAT3 network and have mimicked a representative selection of lab experiments that explore the features of this network. The analyses of this model have revealed explanations to the observed phenomena, as well as recommended reconsideration of previously proposed explanations. This model provides a framework for further investigation of this interesting crosstalk, and can be used as a tool for experimental design and as starting point for further modelling efforts.
We have developed an ordinary differential equation (ODE) model of the MITF-PIAS3-STAT3 system. The graphical representation of the model given in Figure 2 is represented in Systems Biology Graphical Notation as implemented in CellDesigner . The ODE-model was implemented in MATLAB (Additional file 2 - MATLABcode.zip). In the following the model is presented in terms of the chemical reaction equations and the ordinary differential equations. All protein amounts represented by the state variables in the model are presented in an arbitrary unit (au).
A signal propagating through the JAK-STAT3-pathway is represented in the model simulations by an elevation of the constant representing the amount of phosphorylated JAK.
These chemical reactions were translated into an ODE model by anticipating simple mass action reaction kinetics. See Table 2 for a comprehensive list of parameters. Equation (11), describing the dynamics of unbound and un-phosphorylated MITF, is provided in detail below. One differential equation for each phosphorylation and complex state of each protein is given. These equations are in the same way determined from the chemical equations and are therefore only commented when features differ.
The readouts of the model are the amounts of the different phosphorylation and complex states of the proteins involved. To be able to view this model in the light of available experimental results, these levels have to be interpreted in a way comparable to the lab-generated data. The transcriptional activity of MITF and STAT3 is measured either as luciferase activity of a transfected reporter gene or as mRNA-levels of downstream genes.
Values for the transcriptional activity of different MITF mutants are given in . From these we have calculated the factors to be A M = -0.11, AM73 = 0.44, AM409 = 0.11 and A Mpp = 0.56. This simple representation of MITF transcriptional activity is able to take negative values, which does not make sense biologically; therefore, A0 is set to the relative high arbitrary value 10, which is sufficiently high to avoid negative MITF activity in this study.
Parameterizing the model
While this model contains a large number of parameters, we can make at least a reasonable order of magnitude estimate for most of them from empirical biological data. In the experiments used for model development and parameter fitting, neither implicit nor explicit absolute protein amounts have been provided. The cells are either transfected, activated or both, and thus the input protein amounts and perturbations will by this fact be qualitative. The results are presented as qualitative protein or complex amounts (Western blot) or transcriptional activity for MITF and PIAS3 (measured by luciferase assays or PCR-measurements of target genes mRNA levels). These results are quantified relative to a control, but not in absolute terms.
An estimate for the degradation rates of PIAS3 and STAT3 is calculated directly from the protein stability index (PSI) as presented in  (γSTAT3 = 0.002 and γPIAS3 = 0.008). The PSI derived degradation rate for MITF is 0.008, but MITF is known to be relatively stable in un-phosphorylated form while ERK mediated phosphorylation on S73 also tags MITF for proteasome mediated degradation [13, 14]. To match degradation time series data [13, 14] MITF was assigned a low degradation rate in the un-phosphorylated state, γ MITF = 0.0012, and relatively high degradation rate when phosphorylated on S409 (regardless of phosphorylation status on S73), γMITFp73 = 0.01. The proportion of MITF phosphorylated on S73 (regardless of phosphorylation status on S409) is degraded only when ubiquitinated (and then with a rather high degradation rate, γMITFp73 = 0.02). The ubiquitination rate constant is adjusted to k u = 0.0001 to yield degradation in accordance with data [13, 14]. When the proteins are in complex, they are thought to be more stable than as free molecules. As an approximation the degradation rates of all complexes were set to 20% of the average of the degradation rate of the two components.
The production rates for MITF, PIAS3 and STAT3 are complex functions of the concentration of a large number of substances, of which none are involved in this model. Therefore these production rates are represented here by constants whose values are relative to the corresponding degradation rates determined by the steady state levels of each of the three proteins. It is important for the proper function of this module that these three proteins are present at approximately equimolar levels. The values are therefore set to p MITF = 1, p PLAS3 = 1.262 and pSTAT3 = 0.211 to meet this criterion. This yields a steady state amount of approximately 100 (au). The level of phosphorylated ERK in the resting cell is set to ERKp = 10 and is elevated to approximately 1000 whenever a MAPK signal is simulated. The total amount of RSK1 is set to 500 of which the phosphorylation is determined dynamically (equation (12) and (13)). The phosphorylation speed for RSK1 is found in , and the phosphorylation and de-phosphorylation rate constants calculated to kRp+ = 0.0004 and kRp- = 0.04, respectively. The Western blot analysis of MITF presented in  and  has one band interpreted as un-phosphorylated MITF and one band interpreted as phosphorylated MITF. No interpretation is provided on which phosphorylation states this latter band may represent. By interpreting this band as the sum of all phosphorylated MITF, we have adjusted the phosphorylation rate constants of MITF to make the model behaviour fit the experimental data. The rate constants are set to kMp73E+ = 0.00015, kMp73- = 0.03, kMp73a+ = 0.025, kMp409+ = 0.0001 and kMp409- = 0.04. With no direct measurements of the STAT3 phosphorylation rate, we assigned the same values to the STAT3 phosphorylation/de-phosphorylation rate constants as we did for RSK1: kSp+ = 0.0002 and kSp- = 0.04. The constant representing phosphorylated JAK is set to 10 in the un-activated state and approximately 1000 in the activated state.
With no direct measurements of the MITF-PIAS3 and STAT3-PIAS3 association and dissociation rate constants, they were inferred from qualitative results and assumptions. We anticipated that this process is faster than the phosphorylation process, which means that both association and dissociation rate constants should be relatively high. MITF has lower affinity to PIAS3 when phosphorylated at S409 and higher affinity when phosphorylated at S73, compared to un-phosphorylated MITF . The double phosphorylated MITF exhibits an intermediate affinity comparable to that of un-phosphorylated MITF . When the MITF-PIAS3 association/dissociation rate constants were adjusted so that the model emulated the results from , they were assigned the following values: k Miss = 0.01, k Mdiss = 1, kMp73ass= 0.03, kMp73diss= 0.5, kMp409ass= 0.0001, kMp409diss= 1, k Mppass = 0.01 and k Mppdss = 1. The STAT3-PIAS3 association/dissociation rate constants were adjusted in the same way to data from  and are assigned the values k Spass = 0.005 and k Spass = 0.2.
Formalizing the experiments
We extracted a set of representative experiments from four relevant publications [14, 19, 20, 22] (Table 2). The numbering in the table provided a unique ID for each experiment, and was used throughout the article. The perturbations of the cells that were reported in the published experiments, like transfection of mutated genes or receptor activation, were assigned digital counterparts in the model through alterations of the input values, starting values, or some of the parameters. In the following, these details, as well as the criteria used for the sensitivity analysis, are given for each of the experiments.
Experiment # 1 is a simulation of the experiment presented in  Figure 5B. Here, the authors use kinase assays to investigate the temporal development of ERK and RSK1 kinase activity after stimulation of melanoma cells. The stimulation was simulated by elevation of the amount of phosphorylated ERK to 1000 from the default value of 10. The success criterion used in the sensitivity analysis was that the phosphorylated RSK1 level should reach 90% of its maximum between 3 and 10 minutes after activation.
Experiment #2 simulates the pre-stimulation distribution among the MITF phosphorylation states in the experiments presented in , Figure 1 and 2. To emulate the growing cell culture the level of phosphorylated ERK was elevated from the default value of 10 to the intermediate level of 80. Steady state values were found for the state variables and the total amount of phosphorylated and un-phosphorylated MITF was compared. The success criterion used in the sensitivity analysis was that both categories should be between 25% and 75% of the total amount.
Experiment #3 is also based on , Figure 1 and 2. Here, the phosphorylation state of MITF after 30 minutes of activation is considered. The cell stimulation is simulated by elevation of the levels of phosphorylated ERK and JAK from the default value of 10 to 1000. The success criterion used in the sensitivity analysis was that more than 80% of the MITF is phosphorylated after 30 minutes.
Experiment #4 is also based on , Figure 1 and 2. Here, the degradation profile is considered. The cell stimulation is simulated by elevation of the levels of phosphorylated ERK and JAK from the default value of 10 to 950. The success criterion used in the sensitivity analysis is that less than 50% of the MITF is degraded after 1 h and at least two thirds are degraded after 5 h.
Experiment #5 is a simulation of the experiment presented in , Figure 6. Here, the authors have transfected MITF, a MITF reporter gene, and different amounts of PIAS3 into NIH 3T3 fibroblasts (endogenously not expressing MITF). To mimic MITF transfection, the MITF production rate is increased from 1 to 18. To mimic the four different amounts of PIAS3 transfection, the PIAS3 production rate was increased from 0.211 to 0.5, 1, 2 and 4. The model was simulated for 2880 minutes (2 days) for each perturbation and the resulting MITF activity was compared for the four PIAS3 levels. The success criterion used in the sensitivity analysis was that MITF activity should be monotonically decreasing with increasing PIAS3 and that the MITF activity at the highest PIAS3 amount should be less than the half that of the lowest PIAS3 amount.
In experiments #6 and #7, we have mimicked the experiments presented in , Figure 2. Here the authors have investigated the association between MITF and PIAS3 in BL6-B16 cells before and after 10 and 30 minutes of activation with c-kit ligand. In experiment #6 only GFP-PIAS3 was transfected, while in experiment #7, the cells were transfected with both MITF and PIAS3. In experiment #6, activation is performed by increase of the levels of phosphorylated ERK and JAK from 10 to 500 and 50, respectively. In experiment #7, transfection was simulated by elevation of the MITF production rate from 1 to 10 and the PIAS3 production rate from 1.262 to 10 and simulated for 2880 minutes (2 days). Thereafter, activation was simulated by increase of the amount of phosphorylated ERK and JAK from 10 to 1200 and 250, respectively. The success criterion used for the sensitivity analysis in both experiments was that the total amount of MITF-PIAS3-complex should be higher after 10 minutes of stimulation compared to before stimulation and that the amount of complex should be lower after 30 minutes of stimulation than after 10 minutes.
Experiment #8 simulated the experiment from , Figure 3A, left. The authors co-transfected NIH 3T3 cells using MITF, with a constitutively active RSK1 plasmid and with a reporter gene to read MITF activity. To simulate transfection of MITF, the MITF production rate was elevated from 1 to 7. The amount of RSK1 is not dynamically determined in the model, and thus the transfection of this product is approximated with an elevation of the static amount from 500 to 5000. The manipulated model was simulated for 2880 minutes (2 days), and the MITF activities with and without RSK1 were compared. The success criteria used in the sensitivity analysis was that the two cases should not differ more than twofold.
Experiments #9 to #12 represent simulations of the experiment presented in  Figure 3B. Here, the authors transfected NIH 3T3 cells with MITF or the MITF-S409A mutant, with constitutively active RSK1 and with a reporter gene to monitor MITF transcriptional activity. To simulate the transfection of MITF, the MITF production rate was elevated from 1 to 7. To simulate the transfection of PIAS3, the PIAS3 production rate was elevated from 1.262 to 4. The amount of RSK1 is not dynamically determined in the model, and thus the transfection of this product is approximated with an elevation of the static amount from 500 to 5000. The activation level was elevated from 10 to 20 to emulate the activity in growing cells. After simulation for 2880 minutes (2 days), the MITF activities, with and without PIAS3 were compared for each of the four experiments. For each experiment the manipulations were as follows: without RSK1, with wild-type MITF (experiment #9), with RSK1 and wild-type MITF (experiment #10), without RSK1, with mutant MITF (experiment #10) and with RSK1, with mutant MITF (experiment #11). The success criterion used in the sensitivity analysis was for each experiment: Experiment #9: MITF activity in the case with PIAS3 is less than 42% and greater than 2% of that without PIAS3. Experiment #10: MITF activity in the case of PIAS3 is less than 84% and greater than 44% of that without PIAS3. Experiment #11: MITF activity in the case of PIAS3 is less than 55% and greater than 15% of that without PIAS3. Experiment #12: MITF activity in the case of PIAS3 is less than 50% and greater than 10% of that without PIAS3.
Experiment #13 to #16 are simulations of the experiment presented in  Figure 6. In this experiment the authors investigate the inhibition of transcriptional activity of S/D mutants of MITF by PIAS3. This is achieved by transfection of wild-type MITF (experiment #13), MITF-S73D (experiment #14), MITF-S409D (experiment # 15) or MITF-S73/409D (experiment #16) and PIAS3 and a reporter gene into NIH 3T3 cells. We simulated the MITF transfection by elevation of the MITF production rate from 1 to 1.5, and the PIAS3 transfection was simulated by elevation of the PIAS3 production rate from 1.262 to 4.5. Here we have also set all MITF levels to zero before starting the simulation, since NIH 3T3 fibroblasts do not express endogenous MITF. To simulate MITF-S73D mutation we have set the MITF S73 de-phosphorylation rate constant to zero while the MITF S73 auto-phosphorylation rate constant is elevated from 0.025 to 5. To simulate MITF-S409D mutation, the RSK1 phosphorylation rate constant is elevated form 0.0004 to 0.04, the RSK1 de-phosphorylation rate constant is decreased from 0.04 to 0.004, the MITF S409 phosphorylation rate constant is elevated from 0.0001 to 0.01 and the MITF S409 de-phosphorylation rate constant is set to zero. The model was simulated for 2880 minutes (2 days) and the MITF transcriptional activity with PIAS3 was compared with the case without PIAS3 for wild-type MITF, and for each mutation form. The success criterion used for the sensitivity analysis was for each experiment: Experiment #13: MITF activity in the case of PIAS3 is less than 70% and greater than 30% of that without PIAS3. Experiment #14: MITF activity in the case of PIAS3 is less than 50% and greater than 10% of that without PIAS3. Experiment #15: MITF activity in the case of PIAS3 is less than 115% and greater than 75% of that without PIAS3. Experiment #16: MITF activity in the case of PIAS3 is less than 85% and greater than 45% of that without PIAS3.
Experiments #17 and #18 are simulations of the experiment presented in  Figure 3A. Here, the authors investigate PIAS3-STAT3 association in response to stimulation of NIH 3T3 cells transfected with STAT3, PIAS3 and MITF or the MITF S409A-mutant. The transfection is simulated by elevation of the MITF production rate from 1 to 10, the PIAS3 production rate from 1.262 to 10 and the STAT3 production rate from 0.211 to 10. The MITF S409A mutation was simulated by setting the MITF S409 phosphorylation rate constant to zero. The activation was simulated by elevation of the amount of phosphorylated ERK and JAK from 10 to 1000. In experiment #17, wild-type MITF, PIAS3 and STAT3 were all transfected and simulated for 2880 minutes (2 days), thereafter simulated for 15 more minutes with and without stimulation. The amount of PIAS3-STAT3-complex was compared. The success criterion used in the sensitivity analysis was that the amount of PIAS3-STAT3-complex should be at least 25% higher with stimulation compared to the case without stimulation. In experiment #18, S409A MITF, PIAS3 and STAT3 were transfected and simulated for 2880 minutes (2 days), and thereafter simulated for 15 more minutes with or without stimulation. The amount of PIAS3-STAT3-complex was compared with the stimulated case in experiment #17. The success criterion used in the sensitivity analysis was that the amount of PIAS3-STAT3-complex in the stimulated case in experiment #17 should be at least 25% higher than the amount of PIAS3-STAT3-complex in any of the two cases in #18.
Experiments #19 to #24 are simulations of the experiment presented in  Figure 3B. Here, the authors have investigated STAT3 transcriptional activity as a response to activation, transfection of PIAS3, and transfection of various amounts of wild-type and S409A mutated MITF in NIH T3T cells. The activation was simulated by elevation of the amounts of phosphorylated ERK and JAK from 10 to 1000. The transfections of PIAS3, STAT3 and the two different MITF amounts were simulated by elevation of the PIAS3 production rate from 1.262 to 7, the STAT3 production rate from 0.262 to 5, and the MITF production rate from 1 to 10 or 50, respectively. The S409A mutation was simulated by setting the MITF phosphorylation rate constant to zero. The model was run for 2880 minutes to simulate the incubation and then for 360 minutes to simulate the activation. The background luciferase activity of STAT3 was determined by elevation of the STAT3 production rate and running a model simulation for 3240 (2880+360) minutes. The amount of phosphorylated STAT3 in the end was interpreted as an estimate for the luciferase activity of STAT3 without activation and without PIAS3 or MITF. For experiments #19 to #24, the amount of phosphorylated STAT3 was compared to this background level. In experiment #19, the cells were transfected with STAT3 and activated. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 10 and 20 times the background level. In experiment #20, the cells were transfected with STAT3 and PIAS3 and activated. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 2.67 and 5.33 times the background level. In experiment #21 the cells were transfected with STAT3, PIAS3 and the smaller amount of MITF and activated. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 2.67 and 5.33 times the background level. In experiment #22 the cells were transfected with STAT3, PIAS3 and the larger amount of MITF and activated. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 6.67 and 13.33 times the background level. In experiment #23 the cells were transfected with STAT3, PIAS3 and the smaller amount of S409A mutated MITF and activated. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 5.67 and 11.33 times the background level. In experiment #24 the cells were transfected with STAT3, PIAS3 and the larger amount of S409A mutated MITF. The success criterion used in the sensitivity analysis was the level of phosphorylated STAT3 between 10 and 20 times the background level.
Experiment #25 simulated the experiment presented in  Figure 4B. Here, the authors have investigated MITF transcriptional activity in response to transfection of PIAS3, STAT3-Y705F mutant and a constitutively active STAT3 mutant (STAT3-C) in NIH 3T3 cells. The transfections were simulated by elevation of the production rate of MITF from 1 to 2, PIAS3 from 1.262 to 2 and STAT3 from 0.211 to 20. The NIH 3T3 cells were simulated by decreasing the starting values of all MITF and PIAS3 states to 1 and in simulations where MITF or PIAS3 were not transfected; their production rate were set to zero. The STAT3-Y705F mutant was simulated by setting the STAT3 phosphorylation rate constant to zero. STAT3-C was simulated by increase the STAT3 phosphorylation rate constant from 0.0002 to 0.02 and setting the de-phosphorylation rate constant to zero. Six different simulations were performed and the MITF transcriptional activity was compared: (i) Cells transfected with STAT3-Y705F, (ii) cells transfected with STAT3-C, (iii) cells transfected with MITF and STAT3-Y705F, (iv) cells transfected with MITF and STAT3-C, (v) cells transfected with MITF, PIAS3 and STAT3-Y705F and (vi) cells transfected with MITF, PIAS3 and STAT3-Y705F. The success criterion used in the sensitivity analysis was that the MITF transcriptional activity from simulation (i) should be between 50% and 150% of the MITF activity form (ii) and the MITF activity from (iii) should be between 80% and 120% of the MITF activity from (iv) and the MITF activity from (v) should be between 12.5% and 100% of the MITF activity from (vi) and the MITF activity from (i) should be less than the MITF activity from (iii) and the MITF activity from (iii) should be greater than 200% of the MITF activity from (v).
Experiment #26 simulates the experiment presented in  Figure 6D and 6E. Here, the authors use mRNA levels of MITF and STAT3 target genes to investigate MITF and STAT3 transcriptional activity after stimulation of mast cells derived from wild type or mutant mice. The MITF protein from the mutated mice lacks its ability to bind PIAS3. The activation is simulated by elevation of the amounts of phosphorylated ERK and JAK from 10 to 1000. The mutation is simulated by setting all four MITF-PIAS3 association rate constants to zero. The success criterion used in the sensitivity analysis was for cells from wild type mice: MITF activity after 30 minutes should be more than twice the MITF activity without stimulation, STAT3 activity at 4 hours should be more than twice the STAT3 activity without stimulation and for cells from mutated mice: MITF activity at 30 minutes and at 4 hours should be less than twice the MITF activity without stimulation and STAT3 activity at 30 minutes and 4 hours should be less than twice the STAT3 activity without stimulation.
Experiments #27 and #28 are simulations of the experiments presented in  Figure 7C and 7D. In experiment #27 the authors have investigated the STAT3 transcriptional activity in response to transfection of wild type MITF and a MITF mutant emulating MITF phosphorylated at S409. In experiment #28 the authors have investigated MITF transcriptional activity in response to transfection of constitutively active STAT3 (STAT3-C). The transfections were simulated by elevation of the STAT3 production rate from 0.211 to 5 and the MITF production rate from 1 to 5. The MITF mutant was simulated by setting the MITF-S409 phosphorylation rate constant to 5 and the MITF-S409 de-phosphorylation rate constant to zero. The STAT3-C mutant was simulated by increasing the STAT3 phosphorylation rate by 25 times and setting the de-phosphorylation rate to zero. The model was simulated for 2880 minutes without and with each of the three transfections. The success criterion used in the sensitivity analysis was for experiment #27 that the STAT3 activity had increased when the cells were transfected with MITF or the MITF mutant compared to without transfection and that the increase was higher when cells were transfected with wild type MITF compared to mutated MITF. The success criterion used in the sensitivity analysis for experiment #28 was MITF activity increased by at least 10%.
The ability of the model to mimic the experiments described above was tested for values of the core parameters in the multidimensional neighbourhood of the default values. Each parameter was sampled from a distribution being uniform on the logarithmic scale, with a sampling area reaching from one half to double the default value. For each set of values of the core parameters, the experiments were simulated and the result (success or failure) was recorded for each experiment. This procedure was repeated 106 times resulting in 106 parameter sets, each with a corresponding result vector recording success or failure for each experiment.
In order to study the sensitivity of each experiment i's success rate to variation in a parameter j, we sorted all parameter sets according to parameter j and divided them into 100 bins of 10000 parameter sets each. We used f i , the o verall success rate of experiment i (see Table 2, column 6) and , the success rate in bin k to computed the sensitivity measure . In order to remove clearly insensitive parameters, we set to zero all s i, j that did not exceed the maximum value observed under 10000 permutations of the parameter values.
This study was supported by The National Programme for Research in Functional Genomics (FUGE) in the Research Council of Norway
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