The spread of an infection within an organism and the development of counteracting immune responses represent a complex dynamical system: Pathogens have to find appropriate target cells to multiply, while immune responses are activated and try to clear the invading pathogen. The outcome of these dynamics depends on the interaction of various molecular and cellular processes across multiple scales in space and time.

Combining experimental and clinical data with mathematical models and computational methods is essential for a systematic and quantitative understanding of the underlying biology. These analyses allow to identify key processes of disease progression and to determine therapeutic targets.

In this talk, I will present mathematical and computational methods to analyze spatio-temporal dynamics of host-pathogen interactions and the development of immune responses. These approaches allow the integration of multivariate data from different scales, combining single-cell information and population dynamics measurements.

I will demonstrate how these methods can be used to advance our understanding of infection and immunity. In addition, I will describe experimental and mathematical challenges that still need to be solved.

Deciphering the regulatory mechanisms that control the establishment and maintenance of cellular programs is an essential task in computational biology. Transcription Factors (TFs) are key players in these mechanisms. To avoid costly TF ChIP-seq assays the binding of TFs to cell-specific regulatory regions is often deduced from open-chromatin measurements. Thus, it is important to develop computational methods for accurate TF binding prediction in open-chromatin regions (OCRs).

I will introduce our method, TEPIC, for the prediction of TF binding by combining sets of OCRs with a biophysically inspired TF binding model. Estimates for the number of bound TF molecules per gene (TF affinities) are obtained by considering distance-weighted far-away enhancer regions. I will illustrate the usefulness of TF binding predictions with TEPIC in different integrative applications of gene expression analyses: discovery of key regulatory factors in cell types, prediction of TFs that regulate cell differentiation in CD4+ T-cells and inference of stem cell regulators from time-series epigenomic data. At the end I will outline a set of current challenges, which are roadblocks to enable personalized systems medicine.

Gene regulation is central to cellular information processing. However, the mechanism of gene regulation and how they are encoded in the genome are still not fully understood. Here, we present approaches from machine learning and statistics that leverage the potential of large biomedical data to shed light on these mechanisms and their genomic encoding.

Furthermore, we show application of the developed methods in various settings. Finally, we will give an outlook on our future work on the analysis and modelling of biomedical data.

Increasing computing power has made it possible to study drug-target interactions by means of molecular dynamics simulations. However, the characterization of bound/unbound states and the estimation of binding kinetics from these data remains a challenging task. I will briefly explain how Markov state modelling can be used to estimate drug affinity and binding rates, thereby supporting drug design. In addition, I will demonstrate how this approach can be adapted to compute transition rates in general biological switches.

Once the binding kinetics have been estimated, reaction rate equations can be used to describe the time course of concentrations of occupied receptor binding sites. Coupled to a mathematical model that quantifies the ligand's efficacy, this approach allows to study the potency of a drug and the effect of treatment strategies by computer simulations. I will illustrate this method in terms of a mathematical model for the administration of GnRH analogues in reproductive endocrinology.

Immunoepidemiology is a quite recent discipline which combines individual- and populationoriented approaches to provide new perspectives on infectious diseases and pathogens transmission.

When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment boosts the immune system thus prolonging the time in which a recovered individual is immune. Such an interplay of within host processes and population dynamics poses significant challenges in rigorous mathematical modeling of immunoepidemiology.

The main goal of this talk is to study the influence of the immune status and immune response of single hosts on epidemiological patterns applying appropriate and innovative mathematical models and methods. I will propose a framework to model disease dynamics in a population, monitoring the immune status of individuals and including both waning immunity and immune system boosting.

Mathematical models are powerful tools in modern life sciences. Similar to experimental techniques, models facilitate the study of biological processes and hypothesis testing. Furthermore, models allow for the integrative assessment of multiple datasets as well as the prediction of latent variables and the design of future experiments. To achieve this, the model structure has to be defined and the unknown model parameters have to be estimated from experimental data. These tasks are challenging for a wide range of application problems.

In this presentation, I will outline some of our work on data-driven mathematical modelling. Firstly, I will talk about the modelling of intracellular signalling using large-scale ordinary differential equations (ODEs). I will present a scalable optimization framework we developed to calibrate ODEs with thousands of state variables and parameters, and how our models outperform established statistical models. Secondly, I will talk about the modelling of heterogeneous cell populations using the chemical master equation. I will present the conditional moment equation, a computationally tractable approximation we introduced, and how it enables us to infer latent variables and sources of cell-to-cell variability. Thirdly, I will talk about multi-scale models for biological processes, in particular hybrid discrete-continuum models. I will present our work on the calibration of these models using Approximate Bayesian Computing, and how we use these methods for model-based integration and filtering of imaging data. In the presentation, I will describe the mathematical approaches, outline how the approaches rendered previously infeasible problems feasible and present applications of the approaches in the life sciences.