# Data-driven Computational Modeling

## Dynamics of intracellular signaling

Mathematical models are widely used to describe intracellular signaling and metabolic pathways. In contrast to purely statistical methods, dynamical models facilitate the integration of a multitude of different data and data types using parameter estimation. Thereby, models allow for a holistic understanding of biological processes.

- In collaboration with groups from Berlin, Freiburg, Heidelberg, Köln, München and Stuttgart we work on dynamical models for signaling pathways. Among others, we are interested in Epo signaling and opioid signaling as well as a variety of cancer related pathways.
- To infer parameters of these models we successfully employed efficient maximum likelihood and Bayesian parameter estimation.
- As models for biological systems are subject to a significant degree of uncertainty in structure and parameter values, we develop methods for optimization, model selection and uncertainty analysis (Weber et al., 2011; Raue et al, 2015). In particular, we use Markov chain Monte Carlo sampling and profile likelihood methods to assess the uncertainties and the predictive power of models (Hug et al., 2013). Our methods are designed for large-scale and are often several orders of magnitude faster than existing methods. For some problems we were able to reduce the computation time from weeks to seconds. This allowed us the inference of genome-scale models with several thousand parameters from omics data.
- For small- and medium-scale models we developed methods for set-based methods for parameter estimation and uncertainty analysis (Hasenauer et al., 2010). In contrast to conventional methods which test a finite number of points in parameter space, set-based methods can examine complete parameter regimes. This allow for additional guarantees.
- We also developed iVUN, a visualization tool that support an in-depth study of biochemical reaction networks, their dynamics as well as parameter and prediction uncertainties (Vehlow et al., 2013). iVUN provides a large variety of different visualization options and linking between those. This turned out to be highly beneficial for the complex analysis tasks that come with the biological systems.

Collaboration partners: Tim Hucho , Ursula Klingmüller, Birgit Luber, Nicole Radde, Jens Timmer, Daniel Weiskopf, Alacris Theranostics GmbH, Bayer Technology Services GmbH

Selected publications:

- Raue A, Steiert B, Schelker M, Kreutz C, Maiwald T, Hass H, Vanlier J, Tönsing C, Adlung L, Engesser R, Mader W, Heinemann T, Hasenauer J, Schilling M, Höfer T, Klipp E, Theis FJ, Klingmüller U, Schöberl B, Timmer J. Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems. Bioinformatics, 2015.
- Vehlow C*, Hasenauer J*, Kramer A, Raue A, Hug S, Timmer J, Radde N, Theis FJ, Weiskopf D. iVUN: interactive Visualization of Uncertain biochemical reaction Networks. BMC Systems Biology, 14(Suppl 19):S2, 2013.
- Hug S, Raue A, Hasenauer J, Bachmann J, Klingmüller U, Timmer J, Theis FJ. High-dimensional Bayesian parameter estimation: Case study for a model of JAK2/STAT5 signaling. Mathematical Biosciences, 246(2):293-304, 2013.
- Weber P, Hasenauer J, Allgöwer F, Radde N. Parameter estimation and identifiability of biological networks using relative data. In Proceedings of the 18th IFAC World Congress, p. 11648-11653, 2011.
- Hasenauer J, Waldherr S, Wagner K, Allgöwer F. Parameter identification, experimental design and model falsification for biological network models using semidefinite programming. IET Systems Biology, 4(2):119-130, 2010.

## Modeling and analysis heterogeneous cell populations

## Stochastic and mixed-effect modeling

Functional cell-cell variability is omnipresent in multicellular organisms and microbial populations. Even genetically identical cells can respond differently to the same stimulation. Prominent examples are cancer cells, stem cells and neurons. The observed cell-to-cell variability can have different sources, i.e. intrinsic and extrinsic noise.

- In the presence of intrinsic noise the dynamics of individual cells are governed by a continuous-time discrete-state Markov chain. Accordingly, the population dynamics are captured by a chemical master equations (CME). As the CME is, for most processes, large, a direct numerical simulation of the CME is in general infeasible and parameter estimation is challenging.
- We introduced the method of conditional moments (MCM). The MCM provides an approximation to the statistics of the solution of the CME (Hasenauer et al., 2014). The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems.
- We developed methods to estimate the parameters of stochastic processes using (conditional) moment equations and system size expansions (Kazeroonian et al., 2013). These methods possess a significantly reduced computational complexity while exploiting most available information. This has been quantified using profile likelihoods.

- For the in-depth analysis of single-cell time-lapse data, we developed a computationally efficient framework for mixed-effect modeling. This method exploits the hierarchical structure of mixed-effect models for parameter optimization and uncertainty analysis. In combination with sigma-point approximations of the population statistics, this approach allows for a simultaneous estimation of population models from single-cell time-lapse, single-cell snapshot, population average and time-to-event data.
- The different modeling approaches are currently employed to study the dynamics of stem cells and neurons.

Collaboration partners: Roland Eils, Carsten Marr, Joachim Rädler, Verena Wolf

Selected publications:

- Hasenauer J, Wolf V, Kazeroonian A, Theis FJ. Method of conditional moments (MCM) for the chemical master equation. Journal of Mathematical Biology, 69(3):687-735, 2014.
- Kazeroonian A, Hasenauer J, Theis FJ. Parameter estimation for stochastic biochemical processes: A comparison of moment equation and finite state projection. In Proceedings of 10th International Workshop on Computational Systems Biology, pages 66-73, 2013.
- Hasenauer J, Waldherr S, Doszczak M, Radde N, Scheurich P, Allgöwer F. Identification of models of heterogeneous cell populations from population snapshot data. BMC Bioinformatics, 12(125), 2011.

## Multi-experiment and ODE-constrained mixture modeling

To understand the dynamics of heterogeneous cell populations, we have to unravel the structure of populations. If the subpopulations are very different, the subpopulation structure can be studied by analyzing a single experiment, however, in general this is not possible as the individual experiments are not very informative enough.

- We developed Multi-Experiment mixture MOdeling (MEMO) and ODE-cosntrained Mixture Modelling (ODE-MM). These methods facilitate the simultaneous analysis of several datasets and can be employed for the comparison of completing hypotheses.
- MEMO have been applied to study the spindle assembly checkpoint, a crucial cell cycle checkpoint. We quantify the influence of different quantitative perturbations and gained insights into the underlying biochemical network (Heinrich et al., 2013).
- We also studied heterogeneous populations of neurons using MEMO and ODE-MM. In collaboration with an experimental group, we could establish FGF as a modulator of pain sensitization and a potential drug target for the treatment of chronic pain. Furthermore, we revealed the causal difference between the neuronal subpopulation which responds to NGF stimulation and the neuronal subpopulation which does not, thereby providing novel insights into growth factor induced pain sensitizations (Andres et al., 2012; Hasenauer et al., 2014).

Collaboration partners: Nicole Radde, Silke Hauf, Tim Hucho

Selected Publications:

- Hasenauer J, Hasenauer C, Hucho T, Theis FJ. ODE constrained mixture modelling: A method for unraveling subpopulation structures and dynamics. PLoS Computational Biology, 10(7):2014.
- Heinrich S, Geissen EM, Trautmann S, Kamenz J, Widmer C, Drewe P, Knop M, Radde N, Hasenauer J, Hauf S. Determinants for robustness in spindle assembly checkpoint signaling. Nature Cell Biology, 15(11):1328-1339, 2013.
- Andres C, Hasenauer J, Ahn HS, Joseph EK, Theis FJ, Allgöwer F, Levine JD, Dib-Hajj SD, Waxman SG, Hucho T. Wound healing growth factor, basic FGF, induces Erk1/2 dependent mechanical hyperalgesia. Pain,154(10):2216-2226, 2013.
- Andres C, Hasenauer J, Allgöwer F, Hucho T. Threshold-free population analysis identifies larger DRG neurons to respond stronger to NGF stimulation. PLoS ONE, 7(3):e34257, 2012.

## Proliferation dynamics of cell populations

Cell proliferation plays an essential role in most biological processes. Therefor, a multitude of mathematical models has been developed to describe proliferation processes, covering the intracellular signal transduction as well as the population balance. Unfortunately, most models are either inflexible or a rigorous analysis is infeasible as the computational complexity is high.

- We developed a unifying modeling framework for proliferating cell populations. The proposed framework incorporates age structure and label dynamics, and allows for a direct comparison of model predictions and measurement data. While the resulting system of coupled partial differential equations is highly complex, we prove that it can be decomposed into two lower-dimensional systems. This reduces the computational effort for simulation division-, age- and label-structured population (DALSP) models and allows for sophisticated parameter estimation procedures.
- In combination with sophisticated parameter estimation and uncertainty analysis tools, our unifying modeling framework could be used to verify the age- and the division-dependence of T lymphocytes. These methods are implemented in the software toolbox ShAPE-DALSP .
- In cooperation with our experimental partner, we use proliferation models to study the in vivo proliferation dynamics of leukemia cells. Using model-based approaches we could verify significant differences between the in vivo proliferation of different patient cell lines.

Collaboration partners: Irmela Jeremias, Frank Allgöwer

Selected Publications:

1. Hasenauer J, Schittler D, Allgöwer F. Analysis and simulation of division- and label-structured population models: A new tool to analyze proliferation assays. Bulletin of Mathematical Biology, 74(11): 2692-2732, 2012.

2. Metzger P, Hasenauer J, Allgöwer F. Modeling and analysis of division-, age-, and label-structured cell populations. In Proceedings of 9th International Workshop on Computational Systems Biology, p. 60-63, 2012.

## Spatio-temporal dynamics of intercellular signaling

Intercellular communication is a key component in many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Such processes demand for models involving time and space leading to system of coupled partial differential equations, which are theoretically well understood but a quantitative, data-driven analysis is challenging due to the computational complexity.

- In corporation with experimentalists at the Helmholtz Zentrum München we developed a model for the lateral line development in zebrafish and the mid-hindbrain boundary formation during embryonic development. By applying a data-driven analysis methods to the latter we established a new post-transcriptional regulation mechanisms by miRNAs.
- In cooperation with experimentalist at the IST Austria we developed a gradient model for dendritic cell movement and successfully estimated the parameters and performed a practical identifiability analysis.
- We developed methods for spatio-temporal model and uncertainty analysis. In particular we use PDE-constrained optimization and accelerated methods for profile likelihood calculation.

Collaboration partners: Nilima Praksh, Hernán López-Schier, Michael Sixt

Selected publications:

- Hock S, Hasenauer J, Theis F. Modeling of 2D diffusion processes based on microscopy data: Parameter estimation and practical identifiability analysis. BMC Bioinformatics, 14(Suppl 10):S7, 2013.
- Hock S, Ng Y.K., Hasenauer J, Wittmann D, Lutter D, Trümbach T, Wurst W, Prakash N, Theis F. Sharpening of expression domains induced by transcription and microRNA regulation within a spatio-temporal model of mid-hindbrain boundary formation, BMC Systems Biology, 7:48, 2013.

## Dynamics of growing, heterogeneous tissues

Biological tissues are multi-scale systems composed of cells, fibers and extracellular matrices surrounded by fluid. Key building blocks are individual cells which process information and divide, die or differentiate. Furthermore, the individual cells communicate via direct cell-cell interaction and indirectly via the surrounding fluid. The different biological processes take place on different spatial and temporal scales. To understand the resulting stochastic processes across scales using a minimal set of assumptions, agent-based models are required.

- We used this multi-scale modeling framework to simulate tumor spheroids growth. Using imaging data we confirmed the qualitative properties of the model and refined the model parameters manually. Furthermore, we find indication for an unknown dependence of the division rate on the density of extracellular matrices. As a manual calibration of models is usuals not feasible, we developed a paralleled Approximate Bayesian Computing (ABC) methods to infer the parameters of computationally intensive model automatically.
- To deepen our understanding of in vivo differentiation processes in the gastrointestinal epithelium we developed an agent-based model mimicking the process. The model will be used to unravel the differences between healthy and diabetic individuals and to provide potential explanations for the differences.

Collaboration partners: Dirk Drasdo,Heiko Lickert

Selected Publications:

- Hasenauer J, Jagiella N, Hross S, Theis FJ. Data-driven modelling of biological multi-scale processes. Journal of Coupled Systems and Multiscale Dynamics, 2015.