Mathematical Modeling of Cellular Processes

Many important biological properties arise from the dynamic interplay of a large number of different cellular components. New properties emerge from that interplay, that are not apparent from the component list alone. We use mathematical modeling to simulate and understand complex cellular processes, with the ultimate aim to interfere with the respective processes, for example to combat viral infection, cancer or detrimental effects of cellular and organismal ageing.

We use different mathematical tools and a variate of methods for this purpose, e.g. Agent-based Models (ABMs) or models based on systems of ordinary or partial differential equations.

Virus-Host Interactions

HIV Virus (Image source)
HIV Virus

Viruses depend on their host cells for their replication and spread, understanding virus-host interactions is therefore an important component of a model-driven development of new anti-viral therapies. Targeting host factors required by the virus for its replication or spread my thus be an efficient strategy to combat infection, in particular for RNA viruses with their associated high mutation rates.

Based on time-resolved measurments of viral replication and spread, we develop quantitative and dynamic models describing virus-cell interactions. Our aim is to understand how viruses hijack cellular mechanisms, how they dynamically interact with the host cell, and which potential novel drug targets in the host cell can most efficiently combat the infection.

Modelling the Cellular Immune Response

In parallel to the infection, cells defend themselves with an intricate and well concerted immune response. Molecular sensors such as RIG-I or toll-like receptors (TLRs) recognize invading pathogens, and activate a strong antiviral defense through the nuclear factor kappa-B (NF-kB) and interferon regulatory factor 3. These in turn mediate the production of proinflammatory cytokines, the secretion of interferon, and ultimately the production of antiviral proteins that inhibit protein synthesis and viral replication.

To understand the dynamic interplay between viral replication on the one hand and the innate immune response on the other, we develop mathematical models of relevant immunity pathways. Using these approaches, we strive to elucidate what determines the outcome of the race between viral replication and the cellular antiviral response, and how the scales can be tipped in favor of the host cell.

Bacterial adaptation and bacterial infections

In contrast to viruses, which essentially carry only genetic information and cannot replicate outside of the host, bacteria are complete cells. They are thus far more complex, bringing their own cellular mechanisms and machinery. While some bacteria are harmful to humans, others are useful or even required commensals; some bacteria are pathogenic, others are not.

We employ mathematical modeling combined with high-throughput experimental data and sophisticated bioinformatics algorithms to characterize bacterial cells, e.g. to understand how they adapt to stress, how they regulate cellular mechanisms, how they respond to treatment or their host's immune response mechanisms, and how they interact with each other and with their host.

Systems Biology of Cancer

Cancer is a complex disease, typically characterized by a multitude of genetic abnormalities and multi-genic and environmental interactions. Oncogenic transformation of cells is accompanied by a disregulation of genetic networks, hence, in order to understand and combat cancer, we need to understand the systems level changes leading to tumor cell development and proliferation.

We develop computational and mathematical models of relevant regulatory and signal transduction processes involved in cell proliferation. As a recent example, we have developed a mathematical model of EGF receptor trafficking, a central process upstream of a number of anti-apoptotic and proliferative pathways, and study the influence of disturbances of EGF trafficking on cancer development using computational modeling.

Ageing and Age associated Diseases

Ageing is associated with a general deregulation of cellular processes and dysfunction of cell regeneration. For example, telomeres shorten in ageing cells, ultimately prohibiting the cell from dividing further. Furthermore, accumulation of genomic mutations in aged organisms can lead to functional impairment of important proteins or regulatory networks. Taken together, these processes lead to the typical phenotype of senescense, together with a plethora of age-associated diseases, such as Alzheimer's disease, cardiovascular disease, arthritis, cataracts, type 2 diabetes, hypertension, osteoperosis and Cancer.

We use high-throughput data analysis and network modeling tools to unravel and understand the systems biology of ageing and age-related diseases, with the aim to decipher the underlying mechanisms and develop new strateges to reverse or at least delay organismal ageing.