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Our research group pursuits focuses in research projects in the following areas:

Dynamics of intracellular signaling

Biological processes are usually studied under several experimental conditions using a variety of experimental techniques. Mechanistic mathematical models allow the integration of the collected – often heterogeneous – data and facilitate a holistic understanding. We use this in cooperation projects to assess biological properties that are not directly measurable and to compare competing hypotheses.

Two key challenges of data-driven mathematical modeling of intracellular processes are parameter estimation and uncertainty analysis.

1. We develop Frequentists and Bayesian parameter estimation methods (Hug et al., Mathematical Biosciences, 2013). To assess parameter and prediction uncertainties, we advanced Monte Carlo and profile likelihood methods by exploiting the problem structure.

We applied these methods for instance:

  • to develop a holistic model of pain sensitization that takes into account different growth factors, opioids and other influencing factors.
  • to describe EGF signaling in gastric cancer patients and derive biomarkers for treatment with trastuzumab and cetuximab.

2. We develop scalable methods for the optimization of large-scale models, e.g. using adjoint sensitivity analysis (Fröhlich et al, PLoS Computational Biology, 2017). These methods are computationally feasible for models with thousands of state variables and parameters. Implementations are provided in the software toolboxes AMICI and PESTO.

We applied these methods for instance to develop a large-scale mechanistic mathematical model of cancer signaling (>1200 molecular species and >2600 biochemical reactions) and to parameterize it using exome, transcriptome and proteome data for 120 cancer cell lines. Our parameterization method reduced the computing time from 200,000 years to about one week.

Dynamics of intracellular signaling


Modeling and analysis heterogeneous cell populations

Functional cell-cell variability is omnipresent in multicellular organisms as well as microbial populations. Even genetically identical cells can respond to the same stimulation differently. In collaboration with experimental groups we investigate the role of cell-to-cell variability and its consequences using experimental techniques with single-cell resolution, e.g. single-cell RNA sequencing and flow cytometry. Methodologically, we are concentrating on the development of statistical methods and population models, which allow efficient parameterization and an efficient hypothesis test, while facilitating the integration of different types of single-cell data.

 1. We develop methods for the data-driven modeling of heterogeneous populations and introduce novel data analysis approaches to study the cell-to-cell variability (Loos et al., Cell Systems, 2018). This includes ODE-constrained mixture modeling (ODE-MM) and multi-experiment Mixture Modeling (ME-MM) to investigate subpopulation structures in heterogeneous populations. These approaches enable the integrated analysis of many data sets and can be used to test hypotheses or to process data. Implementations are provided in CERENA , ODEMM and NEMO.

We applied these methods

  • to quantify the influence of perturbations on the spindle assembly checkpoint, a crucial cell cycle checkpoint, in S. pombe and provide an explanation for its robustness (Heinrich et al., Nature Cell Biology, 2013),
  • to study heterogeneous populations of neurons and established FGF as a modulator of pain sensitization and a potential drug target for the treatment of pain (Andres et al., Pain, 2013), and
  • to determine the causal difference of NGF responsive and non-responsive neuronal subpopulations (Hasenauer et al., PLoS Computational Biology, 2014)

2. We advance and employ sigma-point approximations and moment equations (Hasenauer et al., Journal of Mathematical Biology, 2014) to study biological processes in which single cells are subject to intrinsic and/or extrinsic cell-cell variability. Furthermore, we developed methods to adapt mechanistic mathematical models at the same time to molecular data for single cells and populations as well as to phenotype data. This allowed us to examine the link between signal transmission and decision making.
We applied these methods for instance

  • to infer the parameters and the network structure of the spindle assembly checkpoint signaling in S. pombe from phenotypic data, and
  • to investigate the heterogeneous behavior of human cell lines after TRAIL and TNF stimulation and revealed potential causes for cell-cell variability.

Modeling and analysis heterogeneous cell populations


Spatio-temporal dynamics of intercellular signaling

Biological tissues are built of many different cells and cell types that communicate. This cell-cell communication forms the basis for biological processes such as chemotaxis, immune defense and morphogenesis. A quantitative description of such processes requires spatially and temporally resolved models, whose simulation is computationally demanding.

1) We develop models for several spatio-temporal processes to integrate heterogenous data about the respective processes, e.g.

  • the mid-hindbrain boundary formation during embryonic development and found indications for a post-transcriptional regulation mechanism by miRNAs (Hock et al., BMC Systems Biology, 2013), and
  • a model for the establishment of chemokine gradient, which are essential for the guidance of dendritic cells towards lymphoid vessels, directly from imaging data (Hross et al., Royal Society Interface, 2018).

Depending the biological application, we employ partial different equation, agent-based or hybrid discrete-continuum models. 

2) We develop flexible statistical inference method for parameterizing computationally intensive spatio-temporal processes (Jagiella et al., Cell Systems, 2017). The problem of the computing time -- single simulations often take hours or even days -- is addressed by the use of high-performance computing (HPC). The software toolbox pyABC we develop has been used in a variety of project, for instance the study tumour growth.


Spatio-temporal dynamics of intercellular signaling


In vitro and in vivo proliferation dynamics of cell populations

One of the most important biological processes is cell proliferation. The dysregulation of cell proliferation results in various diseases. A variety of mathematical models have been developed to describe proliferation processes. However, the established model disregard biological knowledge and are too inflexible / time-consuming to be applied in practice.

1) We develop flexible modeling approach for labeled cell populations (Hasenauer et al., Bulletin of Mathematical Biology, 2012) to allow a rigorous analysis of in vitro and in vivo proliferation. The corresponding class of partial differential equation models takes into account the essential properties of individual cells, allows a direct comparison of simulation and measuring results, and enables efficient numerical simulation. By means of these models,

  • we investigated the proliferation of T lymphocytes and demonstrated that existing models yielded incorrect results as they did not take into account the cell age (Hross & Hasenauer, Bioinformatics, 2016), and
  • we quantified the in vivo proliferation of acute lymphocytic leukemia cells in patient-\newline derived xenograph mouse models (Ebinger et al., Cancer Cell, 2016). We were able to identify a dramatic difference in the growth behavior of cells from different patients. Furthermore, we were able to detect a resistant subgroup of cells, which probably inhabits a niche.

2) We develop continuous partial differential equation model for the integration of multiple single-cell datasets, e.g. single-cell RNA sequencing. The models capture complex population structures and decision making by accounting for the underlying tree structure. A manageable complexity is achieved be performing the modeling in reduced space, using e.g. pseudo-time ordering.


In vitro and in vivo proliferation dynamics of cell populations



 In this context we also develop software toolboxes

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