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Wolf Lab

Mathematical Modelling of Cellular Processes


Our group develops and analyses mathematical models of mammalian signaling pathways and gene-regulatory networks in normal and disease states. For our investigations we use tools such as simulations, bifurcation analyses and sensitivity analyses.

Complex diseases are often characterized by an accumulation of multiple perturbations, such as mutations or over-expression of proteins, in rather large and complex cellular networks. The consequences of these perturbations can hardly be analyzed by pure reasoning.

Here, mathematical modelling contributes to a deeper understanding of the regulatory systems and provides thus a better basis for the interpretation of high-throughput data and identification of effective drug targets. 

Main projects in the last years have focused on signal transduction, in particular on the NF-κB/IKK pathway and the Wnt/β-catenin pathway. In many of our projects we closely collaborate with experimental partners in and outside of the MDC.



NF-κB signaling pathway

Bifurcation analysis of the total NF-κB concentration. (A) The bifurcation diagram shows the dynamical changes of active NF-κB upon variation of the total NF-κB concentration. (B) Active NF-κB dynamics for three exemplary total NF-κB concentrations. (C) 3D representation of changes of dynamical behavior of active NF-κB upon changing total NF-κB concentrations.

NF-κB is one of the most important transcription factors for the regulation of cell differentiation, proliferation and survival. Dysregulation of NF-κB can lead to severe diseases, e.g. cancer, autoimmune diseases, neurodegenerative diseases, cardiovascular diseases and diabetes. Transcription factor NF-κB coordinates cellular responses by activating the transcription of numerous target genes, some of these act as regulators of NF-κB through feedback mechanisms. Using mathematical modeling, we analyze:

  • the effect of post-transcriptional regulation on the NF-κB pathway (Murakawa et al., 2015)
  • the interplay of NF-κB and the tumor suppressor p53 in context of DNA damage
  • the crosstalk between canonical and non-canonical NF-κB signaling (Yilmaz et al., 2014)
  • the capability of NF-κB in exhibiting different types of dynamics, e.g. oscillatory and non-oscillatory dynamics, in response to the same stimulus by bifurcation analyses (Mothes et al., 2015).



Murakawa Y, Hinz M, Mothes J, Schuetz A, Uhl M, Wyler E, Yasuda T, Mastrobuoni G, Friedel CC, Dölken L, Kempa S, Schmidt-Supprian M, Blüthgen N, Backofen R, Heinemann U, Wolf J, Scheidereit C, Landthaler M. RC3H1 post-transcriptionally regulates A20 mRNA and modulates the activity of the IKK/NF-κB pathway. Nat Commun. 2015 Jul 14; 6:7367. doi: 10.1038/ncomms8367.

Mothes J, Busse D, Kofahl B, Wolf J. Sources of dynamic variability in NF-κB signal transduction: a mechanistic model. Bioessays 2015 Apr; 37(4): 452-62. doi: 10.1002/bies.201400113.

Yilmaz ZB, Kofahl B, Beaudette P, Baum K, Ipenberg I, Weih F, Wolf J, Dittmar G, Scheidereit C. Quantitative dissection and modeling of the NF-κB p100-p105 module reveals interdependent precursor proteolysis. Cell Reports 2014 Dec 11;9(5):1756-69. doi: 10.1016/j.celrep.2014.11.014.

Metabolism and cancer

We are investigating the metabolism of cancer cells and how it is regulated by relevant oncogenes. For this aim, we apply methods such as statistical analysis of metabolic profiles, 13C-based flux estimation and disease-specific dynamical models of metabolism.

We started the analysis of the energy metabolism in yeast where we analyzed the spatial effects of nutrient gradients in cell layers in a combined theoretical and experimental setting (Schütze & Wolf, 2010, Schütze et al., 2011). We showed that metabolic processes introduce an additional level of local inter-cellular coordination.



Schütze J, Mair T, Hauser MJB, Falcke M, Wolf J. Metabolic Synchronization by Traveling Waves in Yeast Cell Layers. Biophysical Journal. 2011;100(4):809-813. doi: 10.1016/j.bpj.2010.12.3704.

Schütze J, Wolf J. Spatio-temporal dynamics of glycolysis in cell layers. A mathematical model. Biosystems. 2010 Feb;99(2):104-8. doi: 10.1016/j.biosystems.2009.10.002. Epub 2009 Oct 30. PubMed PMID: 19837130.

Regulation of gene expression by Wnt/β-catenin signalling under wild-type and mutant conditions

Mathematical modelling of Wnt/β-catenin signalling

Wnt proteins are secreted signalling molecules that control the intracellular concentration of the transcriptional regulator β-catenin. Target genes of the Wnt/β-catenin signalling pathway are involved in many different cellular processes ranging from pattern formation in embryogenesis, control of planar cell polarity, to maintenance of stem cells. Several target genes influence the dynamics of signal transduction by regulatory feedback mechanisms. Aberrant regulation of the pathway has been associated with several human diseases, especially cancer.

Using detailed ordinary differential equation models, we:

  • investigate the influence of individual feedback mechanisms and their combinations on signalling dynamics under wild-type conditions and in the presence of carcinogenic pathway mutations (Benary et al., 2015).
  • explore the impact of different gene regulatory mechanisms on the region-specific gene expression of hepatocytes that contributes to the zonation of the metabolic functions of the liver (Benary & Kofahl et al., 2013).
  • study the autocrine and paracrine impact of the secreted Wnt-inhibitor Dickkopf on the gene expression of adjoined hepatocytes (Hartung & Benary et al., 2017).



Hartung N, Benary U, Wolf J, Kofahl B. Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes. BMC Syst Biol. 2017 Oct 13;11(1):98. doi: 10.1186/s12918-017-0470-9.

Benary U, Kofahl B, Hecht A, Wolf J. Mathematical modelling suggests a differential impact of β-transducin repeat-containing protein paralogues on Wnt/β-catenin signalling dynamics. FEBS J. 2015 Mar;282(6):1080-96. doi: 10.1111/febs.13204.

Benary U, Kofahl B, Hecht A, Wolf J. Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions. Front Physiol. 2013 Feb 25;4:21. doi: 10.3389/fphys.2013.00021.

Kofahl B, Wolf J. Mathematical modelling of Wnt/β-catenin signalling. Biochem Soc Trans. 2010 Oct;38(5):1281-5. doi: 10.1042/BST0381281.

Robustness of cellular rhythms

Sensitivities for randomly sampled parameter sets of a circadian and a calcium oscillations model

Oscillations occur in a wide variety of cellular processes, such as signaling, metabolism, or within gene-regulatory networks. Thereby, the period or amplitude as oscillatory characteristics differ in their robustness, i.e. in their susceptibility to perturbations. What makes the period of circadian oscillations so robust; which design principles render that of intracellular calcium oscillations so variable?

Systematical examination of prototype oscillator models and models of various cellular rhythms emphasizes the need to consider feedback type and reaction kinetics as design principles when establishing predictive oscillator models (Wolf et al., 2005, Baum et al., 2016).



Baum K, Politi AZ, Kofahl B, Steuer R, Wolf J: Feedback, mass conservation and reaction kinetics affect the robustness of cellular oscillations. PLOS Comput Biol. 2016 Dec 27;12(12):e1005298. doi: 10.1371/journal.pcbi.1005298.

Wolf J, Becker-Weimann S, Heinrich R: Analysing the robustness of cellular rhythms. Syst Biol (Stevenage). 2005 Mar;2(1):35-41.

Using mechanistic models of gene expression to mine high-throughput data

Analysis of diverse high-throughput data using mechanistic models of gene expression

Generation of high-throughput data (‘omics’) is a central approach of today’s research in systems biology and systems medicine. Bioinformatic tools and biostatistical methods are commonly used to analyse omics data. We develop ordinary differential equation models of detailed molecular processes to extract novel insights into the regulation of gene expression from high-throughput data.

We developed a quantitative model of mammalian gene expression to obtain a first genome-scale prediction of synthesis rates of mRNAs and proteins from transcriptomic and proteomic data (Schwanhäusser et al., 2011; Schwanhäusser et al., 2013).

Based on chromatin-immunoprecipitation sequencing (ChIP-seq) data and transcriptomics data, we modelled MYC-dependent gene regulation to demonstrate that cell type-specific gene expression profiles arise from differential affinities of target gene promoters for MYC (Lorenzin et al., 2016; Benary et al., 2017).

We are currently establishing an easy-to-apply theoretical framework that links high-throughput population-based mRNA and protein measurements with single cell gene expression dynamics in dividing cells (Baum et al., submitted).



Benary U, Wolf E, Wolf J. Mathematical modelling of promoter occupancies in MYC-dependent gene regulation. Genomics and Computational Biology, [S.l.], v. 3, n. 2, p. e54, jan. 2017. ISSN 2365-7154. doi: 10.18547/gcb.2017.vol3.iss2.e54.

Lorenzin F, Benary U, Baluapuri A, Walz S, Jung LA, von Eyss B, Kisker C, Wolf J, Eilers M, Wolf E. Different promoter affinities account for specificity in MYC-dependent gene regulation. Elife. 2016 Jul 27;5. pii: e15161. doi: 10.7554/eLife.15161.

Schwanhäusser B, Wolf J, Selbach M, Busse D. Synthesis and degradation jointly determine the responsiveness of the cellular proteome. Bioessays. 2013 Jul;35(7):597-601. doi: 10.1002/bies.201300017. Epub 2013 May 22.

Schwanhäusser B, Busse D, Li N, Dittmar G, Schuchhardt J, Wolf J, Chen W, Selbach M. Global quantification of mammalian gene expression control. Nature. 2011 May 19;473(7347):337-42. doi: 10.1038/nature10098.


Former lab members

  • Antonio Politi, Postdoc, went to EMBL Heidelberg
  • Jana Schütze, PhD student, went to Humboldt-University Berlin
  • Christian Brettschneider, Postdoc, went to Atos Consulting
  • Alexandra Iovkova, scientist, went to TU Munich
  • Dorothea Busse, Postdoc, went to IRI LifeSciences, Humboldt-University Berlin
  • Bente Kofahl, PhD student and Postdoc, went to Freiburg University  
  • Laura Stumpf, Master student, went to Insilico Biotechnology
  • Janina Mothes, PhD student and Postdoc, went to Bayer AG

Guests and internships

  • Niklas Hartung, guest PhD student
  • Kristin Meisel, internship 2011
  • Dominik Otto, internship 2014
  • Luis Martini, internship 2015
  • Maria Trofimova, internship 2016
  • Pia Brechmann, internship 2016
  • Mirjam van Bentum, Charité MoIMed rotation student 2016
  • Janosch Brandhorst, Bachelor student 2017/ 2018
Dr. Jana Wolf
Dr. Jana Wolf
Phone: 9406-2641
Max-Delbrück-Centrum für Molekulare Medizin (MDC)
Robert-Rössle-Str. 10
13092 Berlin, Deutschland
Building 31.1, Room 5016