In systems biology, one of the major tasks is to tailor model complexity to information content of the data. A useful model should describe the data and produce well-determined parameter estimates and predictions. Too small of a model will not be able to describe the data whereas a model which is too large tends to overfit measurement errors and does not provide precise predictions. Typically, the model is modified and tuned to fit the data, which often results in an oversized model. To restore the balance between model complexity and available measurements, either new data has to be gathered or the model has to be reduced. In this manuscript, we present a data-based method for reducing non-linear models. The profile likelihood is utilised to assess parameter identifiability and designate likely candidates for reduction. Parameter dependencies are analysed along profiles, providing context-dependent suggestions for the type of reduction. We discriminate four distinct scenarios, each associated with a specific model reduction strategy. Iterating the presented procedure eventually results in an identifiable model, which is capable of generating precise and testable predictions. Source code for all toy examples is provided within the freely available, open-source modelling environment Data2Dynamics based on MATLAB available at http://www.data2dynamics.org/, as well as the R packages dMod/cOde available at https://github.com/dkaschek/. Moreover, the concept is generally applicable and can readily be used with any software capable of calculating the profile likelihood.
Lung cancer, with its most prevalent form non-small-cell lung carcinoma (NSCLC), is one of the leading causes of cancer-related deaths worldwide, and is commonly treated with chemotherapeutic drugs such as cisplatin. Lung cancer patients frequently suffer from chemotherapy-induced anemia, which can be treated with erythropoietin (EPO). However, studies have indicated that EPO not only promotes erythropoiesis in hematopoietic cells, but may also enhance survival of NSCLC cells. Here, we verified that the NSCLC cell line H838 expresses functional erythropoietin receptors (EPOR) and that treatment with EPO reduces cisplatin-induced apoptosis. To pinpoint differences in EPO-induced survival signaling in erythroid progenitor cells (CFU-E, colony forming unit-erythroid) and H838 cells, we combined mathematical modeling with a method for feature selection, the L1 regularization. Utilizing an example model and simulated data, we demonstrated that this approach enables the accurate identification and quantification of cell type-specific parameters. We applied our strategy to quantitative time-resolved data of EPO-induced JAK/STAT signaling generated by quantitative immunoblotting, mass spectrometry and quantitative real-time PCR (qRT-PCR) in CFU-E and H838 cells as well as H838 cells overexpressing human EPOR (H838-HA-hEPOR). The established parsimonious mathematical model was able to simultaneously describe the data sets of CFU-E, H838 and H838-HA-hEPOR cells. Seven cell type-specific parameters were identified that included for example parameters for nuclear translocation of STAT5 and target gene induction. Cell type-specific differences in target gene induction were experimentally validated by qRT-PCR experiments. The systematic identification of pathway differences and sensitivities of EPOR signaling in CFU-E and H838 cells revealed potential targets for intervention to selectively inhibit EPO-induced signaling in the tumor cells but leave the responses in erythroid progenitor cells unaffected. Thus, the proposed modeling strategy can be employed as a general procedure to identify cell type-specific parameters and to recommend treatment strategies for the selective targeting of specific cell types.
Receptor tyrosine kinases (RTKs) are high-affinity cell surface receptors for growth factors that are frequently deregulated in cancer. Signaling through these receptors has been associated with increased cancer cell proliferation and resistance to cytotoxic therapies. To block this detrimental signaling, many companies are developing inhibitory antibodies against various RTKs. A key challenge in clinical studies is the optimal stratification of patients who may benefit from these therapies. For an RTK targeted antibody, the detection of the respective growth factor in the tumor microenvironment may be an important bio-marker. Beyond the physical presence of the growth factor, the decision whether a cancer cell will respond to growth factor-induced signals is governed by complex intra-cellular signaling networks. We compared different approaches to predict cellular responses and will highlight a hybrid approach that combines mechanistic modeling based on ordinary differential equations with a machine learning algorithm. The models are trained on in vitro drug response screens and then applied to predict response in patient samples. The mechanistic models are trained on quantitative data from signal transduction studies as well as RNAseq data for cellular characterization. Using the hybrid approach, a correlation between growth factor expression in the tumor microenvironment and its predicted response was identified. This supports the hypothesis of addiction of tumors to growth factors abundant in the tumor microenvironment, and might enable more robust patient stratification in the future.
For successful treatment of cancer patients, it is crucial to identify subgroups that respond to certain types of targeted therapy. A key element for tumor growth is the abundance of receptors and binding of growth factors, which can be diminished via therapeutic antibodies. Here, a mechanistic signaling network model is linked to patient-specific ribonucleic acid sequencing data (RNAseq), enabling the prediction of individuals susceptible to a particular medication. The mechanistic model comprises multiple receptors and their dimerization, and is calibrated using time-resolved in-vitro data. Further, the model is combined with in-vitro cell viability measurements via a machine learning algorithm and ultimately applied to patient-derived data to predict ligand dependence of tumors. For this purpose, RNA sequencing data are exploited to constrain model parameters and generalize model response. Mathematical modeling of signal transduction is used as a mediator, performing a non-trivial transformation of initial protein expression levels and ligand conditions to cell-type specific response. Thereby, it allows for bridging the gap between studies of signal transduction on a short time scale and cell fate decisions in the long term, potentially aiding in drug development, patient stratification, and prediction of tumor response. This chapter is based on work previously published in Hass et al. (NPJ Syst Biol Appl 3(1):27, 2017) and Hass (Quantifying cell biology: mechanistic dynamic modeling of receptor crosstalk. PhD thesis, Albert-Ludwigs-Universität Freiburg, 2017).
Targeted therapies have shown significant patient benefit in about 5–10% of solid tumors that are addicted to a single oncogene. Here, we explore the idea of ligand addiction as a driver of tumor growth. High ligand levels in tumors have been shown to be associated with impaired patient survival, but targeted therapies have not yet shown great benefit in unselected patient populations. Using an approach of applying Bagged Decision Trees (BDT) to high-dimensional signaling features derived from a computational model, we can predict ligand dependent proliferation across a set of 58 cell lines. This mechanistic, multi-pathway model that features receptor heterodimerization, was trained on seven cancer cell lines and can predict signaling across two independent cell lines by adjusting only the receptor expression levels for each cell line. Interestingly, for patient samples the predicted tumor growth response correlates with high growth factor expression in the tumor microenvironment, which argues for a co-evolution of both factors in vivo.
