Daniel Kaschek

Due to the high complexity of biological data it is difficult to disentangle cellular processes relying only on intuitive interpretation of measurements. A Systems Biology approach that combines quantitative experimental data with dynamic mathematical modeling promises to yield deeper insights into these processes. Nevertheless, with growing complexity and increasing amount of quantitative experimental data, building realistic and reliable mathematical models can become a challenging task: the quality of experimental data has to be assessed objectively, unknown model parameters need to be estimated from the experimental data, and numerical calculations need to be precise and efficient. Here, we discuss, compare and characterize the performance of computational methods throughout the process of quantitative dynamic modeling using two previously established examples, for which quantitative, dose- and time-resolved experimental data are available. In particular, we present an approach that allows to determine the quality of experimental data in an efficient, objective and automated manner. Using this approach data generated by different measurement techniques and even in single replicates can be reliably used for mathematical modeling. For the estimation of unknown model parameters, the performance of different optimization algorithms was compared systematically. Our results show that deterministic derivative-based optimization employing the sensitivity equations in combination with a multi-start strategy based on latin hypercube sampling outperforms the other methods by orders of magnitude in accuracy and speed. Finally, we investigated transformations that yield a more efficient parameterization of the model and therefore lead to a further enhancement in optimization performance. We provide a freely available open source software package that implements the algorithms and examples compared here.

Inferring knowledge about biological processes by a mathematical description is a major characteristic of Systems Biology. To understand and predict system's behavior the available experimental information is translated into a mathematical model. Since the availability of experimental data is often limited and measurements contain noise, it is essential to appropriately translate experimental uncertainty to model parameters as well as to model predictions. This is especially important in Systems Biology because typically large and complex models are applied and therefore the limited experimental knowledge might yield weakly specified model components. Likelihood profiles have been recently suggested and applied in the Systems Biology for assessing parameter and prediction uncertainty. In this article, the profile likelihood concept is reviewed and the potential of the approach is demonstrated for a model of the erythropoietin (EPO) receptor.

Cellular signal transduction is governed by multiple feedback mechanisms to elicit robust cellular decisions. The specific contributions of individual feedback regulators, however, remain unclear. Based on extensive time-resolved data sets in primary erythroid progenitor cells, we established a dynamic pathway model to dissect the roles of the two transcriptional negative feedback regulators of the suppressor of cytokine signaling (SOCS) family, CIS and SOCS3, in JAK2/STAT5 signaling. Facilitated by the model, we calculated the STAT5 response for experimentally unobservable Epo concentrations and provide a quantitative link between cell survival and the integrated response of STAT5 in the nucleus. Model predictions show that the two feedbacks CIS and SOCS3 are most effective at different ligand concentration ranges due to their distinct inhibitory mechanisms. This divided function of dual feedback regulation enables control of STAT5 responses for Epo concentrations that can vary 1000-fold in vivo. Our modeling approach reveals dose-dependent feedback control as key property to regulate STAT5-mediated survival decisions over a broad range of ligand concentrations.

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.

Quantitative systems pharmacology (QSP), a mechanistically oriented form of drug and disease modeling, seeks to address a diverse set of problems in the discovery and development of therapies. These problems bring a considerable amount of variability and uncertainty inherent in the nonclinical and clinical data. Likewise, the available modeling techniques and related software tools are manifold. Appropriately, the development, qualification, application, and impact of QSP models have been similarly varied. In this review, we describe the progressive maturation of a QSP modeling workflow: a necessary step for the efficient, reproducible development and qualification of QSP models, which themselves are highly iterative and evolutive. Furthermore, we describe three applications of QSP to impact drug development; one supporting new indications for an approved antidiabetic clinical asset through mechanistic hypothesis generation, one highlighting efficacy and safety differentiation within the sodium-glucose cotransporter-2 inhibitor drug class, and one enabling rational selection of immuno-oncology drug combinations.