Computational Systems Biology aims at the construction and analysis of predictive, mainly mechanistic, mathematical models for the description of complex interactions in biological systems. Such models are characterized by a large number of variables, parameters and constraints, which requires the application of efficient numerical algorithms and computational techniques for high-dimensional problems. Current research in our group comprises the following topics.
Parameter identification and uncertainty quantification
Experimental measurement data in biology are usually sparse and noisy. Therefore, we combine local optimization methods for parameter identification with new algorithmic approaches to Bayesian inverse problems. Recently, we suggested a new transformation invariant penalty term for the maximum penalized likelihood estimator within the empirical Bayes framework, see our article on arXiv on Objective Priors in the Empirical Bayes Framework.
Due to the multi-scale nature of biological systems, we increasingly consider hybrid models that combine different mathematical formalisms, e.g. ODEs for metabolic networks with discrete dynamical systems for regulatory processes, or ODEs for signaling pathways with partial differential equations describing biomechanical processes. We also consider different mathematical formalism for describing one and the same system. Here, we are particularly interested in transforming one formalism into another one, e.g. ODEs into Boolean networks, and in property conservation across formalism, see, e.g., our publication on Correspondance of Trap Spaces in Different Models of Bioregulatory Networks.
Application include biological and (bio)chemical processes on different levels of organization, e.g.,
- molecular conformation dynamics: Robust Perron Cluster Analysis (PCCA+), Markov state modelling for non-equilibrium dynamics
- chemical reaction kinetics: inference of binding rates from kinITC experiments; reaction rate equation modelling of multivalent binding processes
- bovine fertility and metabolism: follicular wave patterns, follicular competition, potassium balance
- the human menstrual cycle: pharmacokinetic/pharmacodynamic modelling of GnRH analogues; treatment computation in reproductive endocrinology