Dynamical Systems

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 Freiburg, Heidelberg, Stuttgart and Berlin we work on dynamical models for TNF, TRAIL, NFkB and JAK/STAT signaling.
  • 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 model selection and uncertainty analysis. In particular, we use Markov chain Monte Carlo sampling and profile likelihood methods to assess the uncertainties and the predictive power of models.
  • 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. 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 as presented here.

Collaboration partners: Nicole Radde, Peter Scheurich, Jens Timmer, Daniel Weiskopf, Jana Wolf

Publications:

1. 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, 2013.

2. Raue A, Kreutz C, Theis FJ, Timmer J. Joining forces of Bayesian and Frequentist methodology: A study for inference in the presence of non-identifiability. Phil. Trans. Roy. Soc. A, 2013.

3. 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. 

Modeling and analysis heterogeneous cell populations

Stochastic modeling using hybrid methods

Even genetically identical cell populations are known to exhibit cell-to-cell variability. Prominent examples are cancer cells, stem cells and neurons. The observed cell-to-cell variability can have different sources, but in particular stochastic fluctuations play a crucial role. In the presence of stochastic fluctuations the dynamics of individual cells are described by the chemical master equation (CME). As the CME is, for most processes, large, a direct numerical simulation of the CME is in general infeasible.

  • We introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. 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 moment equations. This approach possesses a significantly reduced computational complexity while exploiting most available information. This has been quantified using profile likelihoods.
  • These moment equation based approaches are currently employed to study the dynamics of stem cells and neurons.

 Collaboration partners: Carsten Marr, Verena Wolf, Heinz Koeppl 

 Publications:

1.     Hasenauer J, Wolf V, Kazeroonian A, Theis FJ. Method of conditional moments (MCM) for the chemical master equation. Journal of Mathematical Biology, 2013. [Epub ahead of print].

2.     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.

3.     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 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 a multi-experiment mixture modeling approach, which allows for the simultaneous analysis of several datasets. Furthermore, our approach can be employed for model comparison as well as data preprocessing.
  • The multi-experiment mixture modeling approaches 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.
  • We also studied heterogeneous populations of neurons using these methods. Together with different experimental groups, we could establish FGF as a modulator of pain sensitization and a potential drug target for the treatment of chronic pain.

 

Collaboration partners: Nicole Radde, Silke Hauf, Tim Hucho

 Publications:

1.     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, November 2013.

2.     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.

3.     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 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.
  • 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

 

References:

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 Center Munich we developed a model for the mid-hindbrain boundary formation during embryonic development. Using data-driven analysis methods we could establish 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 profile likelihood methods.

Collaboration partners: Nilima Praksh, Michael Sixt

 References:

1. 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.

2. 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. 

  • In cooperation with the group of Dirk Drasdo we developed and implemented a multi-scale modeling framework for biological tissues. Cells are represented as individuals (cellular automaton), diffusing molecules as a continuum (PDE) and blood vessels as graph structure (0D model).
  • We used this multi-scale modeling framework to simulate tumor spheroids and vascularized tissues describing the growth of lung cancer cells in vitro and in vivo. 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.
  • 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.
  • The simulation of agent-based models is computationally demanding (> 20 CPU hours for the tumor growth model), rendering parameter estimation and hypothesis testing challenging. We investigate novel optimization strategies, based on Gaussian processes, which reduce the number of model evaluations.

Collaboration partners: Dirk Drasdo,Anika BötcherDiana Mateus 

References:

  1. Drasdo D, Jagiella N, Ramis-Conde I, Vignon-Clementel I, Weens W. Modeling steps from a benign tumor to an invasive cancer: examples of intrinsically multi-scale problems, in Cell Mechanics: From Single Scale-Based Models To Multiscale Modeling, pp. 379-417, 2010.

 

 

 

 

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