# Raia et al., (2010). Dynamic Mathematical Modeling of IL13-Induced Signaling in Hodgkin and Primary Mediastinal B-Cell Lymphoma Allows Prediction of Therapeutic Targets.

April 2016, model of the month by *Thawfeek Mohamed Varusai*

Original model: BIOMD0000000313.

**Introduction:**

Lymphomas are tumours of the lymphatic system and are quite heterogeneous in nature. There are several types of clinical malignancies of lymphomas, which include primary mediastinal B-cell lymphoma (PMBL) and classical Hodgkin lymphoma (cHL). The Janus kinase signalling pathway (JAK/STAT) is known to signal a range of cytokines and growth factors, which primarily trigger the downstream transcriptional process, thereby regulating several vital cellular functions such as cell proliferation and apoptosis. Consequently, the JAK/STAT pathway is found to be aberrant in many cancers including blood malignancies. In this paper, the authors use a combination of experimental and mathematical modelling approach to study the role of JAK/STAT signalling pathway in PMBL and cHL classes of lymphomas [1].

Figure 1The process diagram of MedB-1 dynamic signaling network model consisting of reactions (arrows) with enzymatic, mass action, or custom kinetics. Round-headed arrows indicate reaction catalysis, whereas bar-ended arrows reaction inhibition. IL13 is used as input function of the system. Reactions and species colored in gray are omitted in the L1236 model. Figure taken from [1].

**Motivation:**

The JAK/STAT signalling pathway is known to be deregulated in PMBL and cHL cases by being constitutively active. Pathway activating factors in PMBL and cHL include hyperphosphorylated STAT5 and STAT6 proteins, over-expression of JAK2 gene and stimulation of the JAK/STAT pathway by the secreted interleukin 13 (IL13). Some of the pathway aberrations in lymphoma are less clear such as the role of non-mutated negative regulators like SOCS3, constitutive expression of SHP1 and the differential roles of STAT5 and STAT6. For these reasons, the authors consider JAK/STAT signalling as a promising pathway to study in the context of lymphomas. Since the system involved is complex and non-linear, a quantitative dynamic model-based approach is required. Previous JAK/STAT pathway modelling attempts are mainly literature-based or focused on non-pathological systems. This reduces the predictive power of the resultant model for pathological conditions. Very few other studies include empirical and modelling approach to understand the JAK/STAT pathway. The authors, therefore, use a combination of experiments and mathematical modelling in PMBL and cHL derived cell lines for their study.

**Mathematical Modelling:**

The authors describe the JAK/STAT pathway for PMBL and cHL conditions using a mathematical model. MedB-1 cells (derived from PMBL) and L1236 cells (derived from cHL) were used to generate the experimental data required to describe the corresponding models. The two models were generated slightly different from each other to accommodate the different experimental observations in the two cell types. The MedB-1 model has few additional components than L1236 model - the IL13Ra2 decoy receptor (DecoyR) and the SOCS3-mediated negative feedback (Fig.1). Ordinary differential equations were used to represent the reactions. The authors use data from the time course experiments from IL13 treated cell lines to estimate the model parameters. Sensitivity analysis has been performed on the model parameters to identify the parameters that can serve as therapeutic interventions. Subsequently, the authors have experimentally validated a potential drug target in the system.

**Results:**

The heterogeneous nature of lymphoma have been emprically established by identifying the molecular stoichiometric differences in the JAK/STAT signalling components in MedB-1 and L1236 cell lines. Experimental data show that the signalling pathway is more aberrant in L1236 cells than in MedB-1, suggesting that the former is more aggressive than the latter. Experiments also shed light on the differential role of STAT family members in IL13 signalling – STAT5 is more responsive than STAT6 in both MedB-1 and L1236 cell types. Data-based mathematical modelling of the JAK/STAT pathway was used to gain a quantitative understanding of two systems. Sensitivity analysis of the models reveal that L1236 cells are more susceptible to perturbations than MedB-1. Furthermore, sensitivity analysis show potential intervening points in the pathway that can be exploited for drug targeting in the lymphoma. Finally, the authors empirically validate model predictions by testing a potential drug target that is common to both lymphomas – STAT5 phosphorylation.

**Predictive Power of the Model:**

The predictive power of a mathematical model depends upon how well the model represents the real biological system of interest. Parameter values are key deciding factors of the model predictive power. In this study, the authors take several measures to accurately estimate the model parameters in the MedB-1 and L1236 systems.

- Model parameters were estimated using empirical data from the corresponding malignant cell types as opposed to data from literature or from a non-pathological system.
- The authors empirically determine the ligand receptor dynamics in each system ensuring constant extracellular ligand concentration.
- Alternate model structures were tested for parameter estimation and the best fit model network was chosen for the analysis.
- Global optimal parameter set for the model was obtained using random scanning of the parameter space, including the initial species concentrations.
- The empirical data points are much higher than the model parameters in both the models, solving the over-parameterization problem.
- The authors also address the parameter identifiability issue in the model ensuring that almost all parameters are identifiable.

Therefore, the models can be claimed to have a high predictive power for the MedB-1 and L1236 systems. This is corroborated by the observation that drug inhibition experiments on the JAK/STAT pathway in cells match with the sensitivity analysis of the models. However, to truly gain insight on the differential impact of tumour cells relative to normal cells, a JAK/STAT pathway model of a normal B cell would be required. The authors admit this but were not able to perform the task due to technical difficulties.

**Significance of the Model:**

Using mathematical models to understand the JAK/STAT pathway has been a fruitful approach in this study. As mentioned in the discussion section of the paper, the models reveal important biological knowledge about the JAK/STAT network. Model simulations show that IL13Ra2 decoy receptor has more impact on IL13 signalling in MedB-1 cells than L1236 cells despite the fact that the expression of the receptor is higher in the latter than the former. Another observation in the study is that the empirical STAT5 phosphorylation peak could not be fully represented by the L1236 model, suggesting the involvement of non-modeled factors such as cross talks from other pathways. Obtaining such information about the biological system using only experiments may either not be possible due to technological limitations or may involve laborious work.

**Scientific Value Added:**

The impact of a study on the scientific community is proportional to the degree of usage of its results by other researchers. The value that this study adds is as follows:

- The primary contribution is a data-based model of MedB-1 and L1236 cells that can be reused/repurposed by other researchers for predictive purposes.
- In the process of parameter estimation, the authors experimentally derive some parameters of the JAK/STAT pathway in MedB-1 and L1236 cells, such as ligand binding rates and molecular stoichiometry, that can be exploited by scientists for their research.
- The biological knowledge from this study such as the functional role of IL13Ra2 decoy receptor in MedB-1 and L1236 can be useful for researchers.

## Bibliographic references

- Raia et al. Dynamic Mathematical Modeling of IL13-Induced Signaling in Hodgkin and Primary Mediastinal B-Cell Lymphoma Allows Prediction of Therapeutic Targets . Cancer Res February 1, 2011 71; 693.