# Model classification under uncertainties for cellular signaling networks (Project A-CH5)

Prof. Dr. Heike Siebert, Prof. Dr. Susanna Röblitz (ZIB), Prof. Dr. Alexander Bockmayr, Adam Streck, Stefanie Kasielke (ZIB)

This research is carried out in the framework of Matheon supported by Einstein Foundation Berlin

Mathematical modeling in biological and medical applications is almost always faced with the problem of incomplete and often noisy data. Rather than adding unsupported assumptions to obtain a unique model, a different approach generates a pool of models in agreement with all available observations. Analysis and classification of such models allow linking the constraints imposed by the data to essential model characteristics and showcase different implementations of key mechanisms. The results are exploitable for experimental design, may uncover specificity due to cell lines, tissues or environmental conditions and can be utilized for designing control strategies under model uncertainty.

Approaches to tackle this problem have been developed for different modeling formalisms.

For discrete models such as boolean networks it is possible to generate model pools based on uncertainty both in the network topology and the logical parameters. Further analysis focuses on filtering the pool for models in agreement with available data, e.g., time series data, utilizing formal verification methods.

For ordinary differential equation models, clustering and Bayesian approaches allow one to evaluate the impact of data uncertainty.

Within the project, we aim at combining the advantages of logical and continuous modeling to arrive at a comprehensive system analysis under data uncertainty. Model classification will integrate qualitative aspects such as characteristics of the network topology with more quantitative information extracted from clustering of joint parameter distributions derived from Bayesian approaches. The theory development is accompanied by and tested in application to oncogenic signaling networks.

**Background**

**Logical approach**

We provide methods and tools for generating and analyzing pools of logical models consistent with the given data. Tools from graph theory and formal verification enable us to comprehensively investigate the state transition systems encoding the dynamical behavior for large sets of such models. Different preprocessing techniques allow us to further increase efficiency, e.g., by identifying dynamically equivalent models.

In the pool analysis, topological characteristics are of particular interest, since they constitute usable constraints for a corresponding pool of continuous models (see below). We developed an approach for extracting and visualizing data pertaining the network structure based on correlations of the activity levels of regulators and targets. Our approaches for model pool construction, pool filtering using model checking techniques and the methods for topological analysis and visualization have been implemented in the tool TREMPPI (Toolkit for Reverse Engineering of Molecular Pathways and Parameter Identification).

**Continuous modeling**

Starting from a pool of given network topologies, a generic ODE model is generated comprising all previously identified logical connections in terms of sums of products of Hill functions. Coefficients of Hill functions can be interpreted as weighting factors of the underlying logical functions. Their values are obtained by parameter identification using quantitative time series data.

We apply both multi-start local optimization (Gauss-Newton methods) as well as Bayesian approaches to derive the joint probability distribution. Datasets of different cell lines probably result in different parametrizations of the model. An analysis of these models, e.g clustering in parameter space, will reveal similarities and differences between the cell lines.

**Integrating logical and continuous approaches**

To exploit the complementary strengths of both modeling approaches in concert, we develop a pipeline where the efficient analysis using logical models is used to obtain constraints for the network structure as well as the regulatory logic. These constraints are the basis for constructing consistent continuous models that in turn are confronted with quantitative data not fully exploitable in a discrete modeling framework. Analysis both for the logical and the continuous model pool are then done in parallel. In a last step, results are matched to obtain characterizations of the uncertainties integrating quantitative and qualitative aspects.

**Application**

In cooperation with Christine Sers from Charité Berlin we apply our methods to investigate crosstalk effects in the MAPK-mTor signaling network in the context of oncogenic signaling. In particular aspects of the integrated modeling are also used in elucidating the mechanisms of bacterial stress signaling.

**Software**

TREMPI - Toolkit for Reverse Engineering of Molecular Pathways through Parameter Identification

ODEtoBNet: Matlab toolbox for automatic transformation of a given ODE system into a Boolean network

**Publications**

Thobe K, Sers C, Siebert H: Unraveling the regulation of mTORC2 using logical modeling. Cell Communication and Signaling, 15:6, Jan 2017.

Streck A, Thobe K, Siebert H: Data-driven optimizations for model checking of multi-valued regulatory networks. Biosystems, 149, 125–138, 2016.

Becker K, Gebser M, Schaub T, Bockmayr A: Answer Set Programming for Logical Analysis of Data. *Workshop on Constraint based Methods for Bioinformatics*, WCB'16, Toulouse, 15-26, 2016.

Becker K., Blüthgen N., Bockmayr A: Logical analysis of perturbation data. International Workshop on Bioinformatics and Systems Biology, IBSB 2015, Boston, 2015.

Deuflhard P., Röblitz S.: A Guide to Numerical Modeling in Systems Biology. Texts in Computational Science and Engineering, volume 12, Springer International Publishing, 2015.

Streck A, Siebert H: Extensions for LTL model checking of Thomas networks. Strasbourg Spring School on Advances in Systems and Synthetic Biology, Strasbourg, 101-114, Mar 2015.

Yousef KP, Streck A, Schütte Ch, Siebert H, Hengge R, von Kleist M: Logical-continuous modelling of post-translationally regulated bistability of curli fiber expression in Escherichia coli. BMC Systems Biology, 9:39, Jul 2015.

Streck A, Thobe K, Siebert H: Analysing Cell Line Specific EGFR Signalling via Optimized Automata Based Model Checking. Computational Methods in Systems Biology, 13th International Conference, CMSB 2015, Nantes, France. Springer International, LNCS 9308, 264-276, Sept 2015.

Stötzel C, Röblitz S, Siebert H: Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation, PLoS ONE 10(10):e0140954, Oct 2015.

Streck A, Lorenz T, Siebert H: Minimization and equivalence in multi-valued logical models of regulatory networks. Natural Computing, 14(4): 555-566, Dec 2015.

Streck A, Thobe K, Siebert H: Comparative Statistical Analysis of Qualitative Parametrization Set. Hybrid Systems Biology, 4th International Workshop, HSB 2015, Madrid, Spain, September 4-5, 2015. Revised Selected Papers. Lecture Notes in Bioinformatics, 9271, 20-34, 2015.

Streck A, Siebert H: Equivalences in Multi-valued Asynchronous Models of Regulatory Networks. Cellular Automata, ACRI 2014, Krakow, Poland, Springer, LNCS 8751, 571-575, Sep 2014.

Thobe K, Streck A, Klarner H, Siebert H: Model Integration and Crosstalk Analysis of Logical Regulatory Networks. Computational Methods in Systems Biology, 12th International Conference, CMSB 2014, Manchester, UK. Springer, LNCS 8859, 32-44, Nov 2014.