Research Area D3-5

Mathematics and life sciences

PIs: Bovier, Niethammer, Rumpf

Contributions by Garcke, Hölzel, Kolanus, Schultze, Velázquez



Topic and goals

The enormous progress made in recent years in the experimental life sciences provides a wealth of data on the functioning of living organisms. This is especially true for the immune system. There is general consensus that in order to turn these data into knowledge about the functioning of this system, mathematical modeling as well as theoretical and numerical analysis in conjunction with experimental data is essential for future progress. The two existing clusters of excellence at UBonn, ImmunoSensation and HCM, provide the ideal environment to make substantial advances in this direction. Based on encouraging achievements in the previous funding period, the clusters have decided to particularly strengthen this cooperation institutionally by the creation of three internationally visible junior research groups in the field of mathematical modeling in life and medical sciences, each endowed with a W2 professorship, a postdoc position, and a PhD position. Each group is expected to shape its own independent research agenda. They will be supported equally by HCM and ImmunoSensation. To support this initiative, the university has provided supplementary funding to establish these new teams in 2018. Based on the recommendation of the joint hiring committee, three offers were made in January 2018. The new research groups will be positioned at the interface of the two clusters. This provides a unique opportunity to develop new and challenging mathematical models with a significant impact on the understanding of the immune system and immune-mediated diseases. The range of research topics to be studied includes, but is not limited to, the analysis of information processing, the dynamics of the immune response, modeling and optimization of treatment protocols, sparse data problems in single cell approaches, predicting and modeling cell behavior from perturbation experiments, and the analysis of two to three-dimensional images including dynamic images in the context of immune responses. In what follows, we describe four directions of research which are already ongoing or in concrete planning. Depending on the recruitments, further directions will evolve.



State of the art, our expertise

Modeling immunotherapy. Shortly after the establishment of ImmunoSensation, a cooperation between Bovier, Hölzel, Tüting, and their groups was established on mathematical modeling of cancer immunotherapy; see Figure (a). The starting point was an experimental study of immunotherapy by adoptive cell transfer (ACT) of melanoma in a mouse model conducted in the lab of Tüting and published in Nature [LKR+12]. This therapeutic approach involves the injection of T-cells which recognize a melanocyte-specific antigen and are able to kill differentiated types of melanoma cells. The therapy induces an inflammation and the melanoma cells react to this by switching their phenotype, i.e., by passing from a differentiated phenotype to a dedifferentiated one where the expression of the antigen is downregulated and which therefore is not recognized by the T-cells. Thus, they are not capable of killing these cancer cells, and a relapse is often observed. It was shown that this phenotypic switch is enhanced by the presence of pro-inflammatory cytokines, in particular TNF-alpha. There is great interest in quantitative modeling of the dynamics of these processes with the ultimate goal of optimizing treatment protocols in order to minimize chances of relapse; see the discussion in [HBT13]. To this end, we developed a stochastic individual-based model that incorporates the key processes on the level of the individual agents (cells and cytokines). Mathematically, these are measure-valued Markov processes [BCM+16, BBC17]. A comparison of experimental data of Landsberg et al. with simulations for biologically reasonable parameters and different initial doses of T-cells is plotted in Figure (b). On the theoretical side, this has led us to introduce and analyze a generalized model that describes individuals simultaneously by their genotype and phenotype and allows for phenotypic switches without mutations. We have proved convergence to the so-called polymorphic evolution sequence (PES).        

Analysis of multi-spectral imaging. Recent advances in new fluorescent dyes and multi-spectral imaging technologies such as multiplex immunohistochemistry (IHC) allow for a comprehensive spatio-phenotypical analysis of tissue sections at unprecedented depth with important implications for clinical routine diagnostics. This technology provides high-dimensional data and imposes new challenges for image analysis. As an example, cancer immunotherapy requires the characterization of tumor-infiltrating immune cell phenotypes. New deep learning approaches for automated evaluation of tissue sections provide valuable information on patients’ response to therapy. First results on the classification of T-cells penetrating dense tumor cell environments were obtained in [EHK+]; see Figure (c).        

Data analysis for third generation sequencing. Technological progress in single-cell sequencing increased the size of the experimental data by several orders of magnitude. This requires scalable methods to separate the underlying biological signals from experiment-specific technical noise. Improved resolution of the sequencing technology shows that cell populations are not as homogeneous as was assumed. This is particularly prominent in the immune system where cell populations gradually adapt in response to external stimuli or specialize during the lifetime forming contiguous cell-lineages. The typical methodology currently used in single-cell RNA-sequencing analysis relies on several steps starting with dimensionality reduction, e.g., by a principal component analysis or more sophisticated methods like t-distributed stochastic neighbor embedding (t-SNE). Diffusion maps constitute an approach that has recently been introduced to single-cell analysis at the Helmholtz Zentrum München and at Yale University; they have been shown to work better than t-SNE on contiguous data.          

Modeling of motion of immune cells. Immune cells migrate on the basis of dynamic cell shape changes and directional force coupling of the migrating cell to extracellular substrates. The precise regulation via fast cytoskeletal changes in response to extracellular cues is insufficiently understood. The Kolanus group has a long-standing interest in the regulation of immune and tumor cell migration [BQL+14, EQK17]. Recently, an in vivo imaging system was established based on microfluidic pumps, which enables us to generate complex visualizable extracellular cues, such as chemokine gradients, and allows us to subject cells to conflicting or paradoxical cues occurring all the time in physiological settings. The system permits precise cellular path tracking, as well as the dynamic observation of subcellular signaling and of quantitative cytoskeletal alterations. Mathematical modeling is required to analyze the resulting cell behavior and to understand regulatory principles, which can readily be subjected to experimental testing in both qualitative and quantitative settings. The aim is to understand how under those circumstances, chemotactic signals can yield a directional cell Motion.



Research program

Modeling immunotherapy. We will expand the joint project on modeling cancer immunotherapy

and focus on effects of treatment protocols involving several agents, e.g., ACT plus chemotherapies

[LKR+12, G+17]. Another crucial aspect will be to understand the interplay of therapy with

the clonal evolution of cancer. Again in the melanoma mouse model, Glodde [G+17] provided

experimental data on immunotherapy combined with a c-MET inhibitor whose main effect is to

reduce the proficiency for phenotypic switches. She also studied the fate of resistant genetic

variants of the melanoma cells.

The combined therapy showed significantly improved therapy results, while therapy leads

to a selection for the genetic variants. We will use these data to improve the precision of the

model by improving parameter fits, but also by incorporating effects such as the geometry of

tumor–T-cell interactions and T-cell exhaustion. To identify model parameters, efficient numerical

simulations are required. We are developing an adaptive hybrid simulation tool which uses the

fact that the dynamics of large populations can be well approximated by deterministic differential

equations while correctly accounting for stochastic effects due to small sub-populations.

One of the key objectives will be to analyze the effects of therapy on clonal evolution of

tumors. This is highly significant for strategies that try to minimize the chance of the development

of therapy resistant mutants, a phenomenon that is widely discussed in the literature, e.g., in

[GVG12]. In the long term, we also intend to extend our models to be able to deal with tumors,

such as prostate carcinoma, where the underlying geometry is more complex.


Data analysis for third generation sequencing. For the analysis of big data generated by singlecell

sequencing, we will follow different approaches. We will integrate domain-specific knowledge

into diffusion maps by the appropriate determination of similarity measures exploiting biological

prior information, which will also lead to interpretations of the observed patterns. Furthermore,

we aim for high-performance methods which scale up to very large data sets and will cooperate

closely with RA B2 in this respect. In particular, we will make use of Bayesian inference

with Markov chains, already applied to small single-cell RNA-sequencing data. To extend this to

data sets of millions of cells, we will apply recent developments in variational inference, prominently

used in neural networks. These techniques include graph optimization, stochastic gradient

descent, variational autoencoders, and the acceleration via minibatch training and GPU computation,

as studied by Garcke et al. [LFX+16].


Analysis of multi-spectral imaging. So far, there is little mathematical understanding of the observed

effectiveness of deep learning in the context of tissue pattern classification. We will use

tools from the calculus of variations and from gradient flows on shape manifolds [RW15] in the

analysis of deep learning approaches, and combine recent advances on non-smooth optimization

with primal-dual methods and stochastic descent schemes. In addition, we plan to incorporate

recently developed principal geometric shape statistics [ZHRS15] in the classification of cell vari-

ability using problem adapted dissimilarity measures. In close cooperation with members of the

cluster ImmunoSensation, we will work on the application of this technology to cell and tissue

classification problems. For instance, we aim for the automatic detection of cell infiltration of specific

T-cell phenotypes in the tumor microenvironment or the identification of T-cell clustering in

the vicinity of blood vessels, the extracellular matrix, or the connective tissue. We will design a

flexible and easy-to-use toolbox to describe the desired classification together with the generation

of stochastic training data for a variety of tissue classification problems.


Modeling of motion of immune cells. The experiments with the in vitro imaging system are a basis

to formulate modeling hypothesis for the driving mechanisms and the resulting motion patterns

of individual cells and cell aggregates. With Bovier, Niethammer, and Velázquez, there is already

expertise in HCM on stochastic particle systems [BdH15], as well as on PDE models for pattern

formation [HNV16] and chemotaxis [LSV12]. In close cooperation with the experimental partners

at ImmunoSensation, the first task will be to identify mathematical models that can capture the

biological mechanisms and appropriately reflect experimental observations. In particular, we will

model the concentration of chemicals in the interior of the cell and of signal molecules on its surface

via partial differential equations. Thereby, we will explore if these models allow us to explain

the rich type of cell behavior observed in the experiments. At a later stage, the mathematical

analysis and numerical simulation will be used to understand complex cell behavior and to work

out regulatory principles which can be subjected to experimental testing in both qualitative and

quantitative Settings.


New experimental methods in the life sciences provide new types of data and large datasets. Mathematical modeling, analysis, and simulation are required to analyze these data and to advance our understanding of the functioning of living organisms. We strive for a quantitative modeling of immunotherapy, the analysis of multi-spectral images of malignant tissue, an advanced analysis of single-cell sequencing data, and the modeling of cell motion and migration. With the creation of the three junior research groups, we expect to reinforce these directions while broadening the cooperation between mathematics and the life sciences.




[BBC17] M. Baar, A. Bovier, and N. Champagnat. From stochastic, individual-based models to the canonical equation of adaptive dynamics in one step. Ann. Appl. Probab., 27(2):1093–1170, 2017.

[BCM+16] M. Baar, L. Coquille, H. Mayer, M. Hölzel, M. Rogava, T. Tüting, and A. Bovier. A stochastic model for immunotherapy of cancer. Sci. Rep., 6:24169, 2016.

[BdH15] A. Bovier and F. den Hollander. Metastability: A potential-theoretic approach, volume 351 of Grundlehren der Mathematischen Wissenschaften. Springer, Cham, 2015.

[BQL+14] T. Bald, T. Quast, J. Landsberg, M. Rogava, N. Glodde, L.-R. D., J. Kohlmeyer, S. Riesenberg, D. van den Boorn-Konijnenberg, et al. Ultraviolet-radiation-induced inflammation promotes angiotropism and metastasis in melanoma. Nature, 507:109–113, 2014.

[EHK+] A. Effland, M. Hölzel, T. Klatzer, E. Kobler, J. Landsberg, L. Neuhäuser, T. Pock, and M. Rumpf. Variational networks for joint image reconstruction and classification of tumor immune cell interactions in melanoma tissue sections. In Proceedings of the workshops ‘Bildverarbeitung für die Medizin’. Springer. to appear.

[EQK17] F. Eppler, T. Quast, and W. Kolanus. Dynamin2 controls Rap1 activation and integrin clustering in human T lymphocyte adhesion. PLoS ONE, 12:e0172443, 2017.

[G+17] N. Glodde et al. Reactive neutrophil responses dependent on the receptor tyrosine kinase c-MET limit cancer immunotherapy. Immunity, 47:789–802, 2017.

 [GVG12] R. Gillies, D. Verduzco, and R. Gatenby. Evolutionary dynamics of carcinogenesis and why targeted therapy does not work. Nat. Rev. Cancer, 12:487–493, 2012.

[HBT13] M. Hölzel, A. Bovier, and T. Tüting. Plasticity of tumour and immune cells: a source of heterogeneity and a cause for therapy resistance? Nat. Rev. Cancer, 13:365–376, 2013.

[HNV16] M. Helmers, B. Niethammer, and J. J. L. Velázquez. Mathematical analysis of a coarsening model with local interactions. J. Nonlinear Sci., 26(5):1227–1291, 2016.

[LFX+16] J. Liu, D. Feld, Y. Xue, J. Garcke, T. Soddemann, and P. Pan. An efficient geosciences workflow on multi-core processors and GPUs: a case study for aerosol optical depth retrieval from MODIS satellite data. Int. J. Digital Earth, 9(8):748–765, 2016.

[LKR+12] J. Landsberg, J. Kohlmeyer, M. Renn, T. Bald, M. Rogava, M. Cron, M. Fatho, V. Lennerz, T. Wölfel, M. Hölzel, and T. Tüting. Melanomas resist T-cell therapy through inflammationinduced reversible dedifferentiation. Nature, 490(7420):412–416, 10 2012.

[LSV12] S. Luckhaus, Y. Sugiyama, and J. J. L. Velázquez. Measure valued solutions of the 2D Keller- Segel system. Arch. Rat. Mech. Anal., 206(1):31–80, 2012.

[RW15] M. Rumpf and B. Wirth. Variational time discretization of geodesic calculus. IMA J. Numer. Anal., 35(3):1011–1046, 2015.

[ZHRS15] C. Zhang, B. Heeren, M. Rumpf, and W. Smith. Shell PCA: statistical shape modelling in shell space. In Proc. of IEEE International Conference on Computer Vision, 2015.