Methods
In our lab we combine computational and experimental methods in order to get the best possible understanding of our research. Our 'wet lab' enables us to measure our own data and test theoretically derived hypotheses.
MODELING METHODS

Ordinary differential equations
The use of ordinary differential equations (ODEs) is the most common approach to dynamic modeling. ODE modeling allows the deterministic and continuous simulation of a biological system. As such, ODEs describe the change of something in dependence to a certain variable, mostly time. ODEs are used, for example, to describe concentration changes of cellular entities, such as metabolites, mRNAs, and proteins. 
Partial differential equations
A partial differential equation (PDE) is an equation that contains partial derivatives in one or more variable(s). For instance, a PDE can be used to describe changes in time and space. Therefore, systems of PDEs can be considered as a natural extension of ODEs (ordinary differential equations). PDEs can be applied to a wide range of biological processes such as spatial signal transduction and cellcell communication, mechanical forces in plant or fungal cell walls as well as membrane bending and stretching. While linear PDEs can often be invesigated analytically, solutions to nonlinear PDE systems are usually obtained numerically by using the finite element method (FEM). 
Agentbased modeling
In agentbased modeling (ABM), a system is described as a collection of decisionmaking entities (agents) and a set of rules, which defines the agents' behaviour. The set of rules determines how agents interact which each other and/or their environment. Often, ABMs contain random elements, e.g. probabilistic decision making and initial agent placement. ABM provides a natural description of a biological system and is able to capture emergent (often unpredictable) behaviour. We use ABMs among others to model lipid metabolism, DNA repair or sperm migration. 
Boolean models
Boolean models are especially useful when rates and concentrations of a given system are unknown, as this type of model does not require kinetic parameters. It instead describes the system in a qualitative way. A Boolean network is defined as a set of nodes, which are influenced by other nodes in the network. Each node is defined by a Boolean variable, which can only take two values, TRUE and FALSE. To influence one another, nodes need transition functions, which dictate their behavior. In a biological system, the values TRUE and FALSE mostly represent the ON and OFF behavior of a biological component. Each node in a Boolean network represents such a biological component, for example a gene or a protein. The ON and OFF behavior signifies an activity, so ON means a protein or a gene is active, while OFF means it is inactive. In our group, we use Boolean models to represent large signaling networks. 
Stochastic models
Where molecule numbers are too small to be amenable to differential equation techniques, other modeling types have to be applied. This is the case in particular in protein translation, where both the number of mRNA transcripts and the number of produced protein molecules on biological time scales may be on the order of 1...10 for many genes. To avoid discretization errors, we treat every ribosome, mRNA transcript, tRNA molecule and protein individually and determine the reaction rates (initiation, elongation, termination) by means of random experiments. These models can accommodate timedependent transcriptomes, energy dependence and tRNA numbers. 
Constraintbased modeling
Constraintbased modeling is a static modeling approach applicable for largescale metabolic networks. A constraintbased reconstruction is a union of (i) a stoichiometrically balanced metabolic model, (ii) a set of constraints for metabolic fluxes, and possibly (iii) a list of genes responsible for the catalysis of reactions included in the model. Detailed knowledge on species quantities, reaction mechanisms and the respective kinetic parameters (which are usually unknown) is not required. The genes  if known  are connected with the reactions by logical expressions. The constraints commonly limit available nutrients by setting maximum values for the source or the uptake reactions of sparse or known growth limiting nutrients. In addition, constraints can be used to define essential functions of the modeled networks, such as detoxification from metabolic byproducts or the turnover of cellular entities such as mRNAs or proteins. Constraintbased models are commonly analyzed using flux balance analysis (FBA) or metabolic control analysis (MCA). Image from Yus et al., Science (2009). 
Reactioncontingency based modeling
Reactioncontingency based modeling is an approach to formalise molecular biology. It recognizes that we often have limited information of the exact nature of biochemical reactions. This is reflected by a separation between different possible events, “reactions”, and constraints on these events “contingencies”. The reactions capture the variables in the system by defining which state transitions may occur (e.g. proteinprotein interactions, covalent modifications). The contingencies capture the causalities between these state transitions, e.g. that a kinase must bind a coactivator before phosphorylating a target. By defining both reactions and contingencies in terms of (combinations of) decontextualized, sitespecific elemental states, the resolution of the model can be fully adapted to the underlying empirical data. In addition, the bipartite (reactions & contingencies) formalism makes the network definition scalable and composable, making it possible to accurately represent the state of the knowledge even for large networks. We have implemented this in the rxncon language, which is especially suited for formalising signal transduction. However, with the increasing awareness of metabolic regulation, it may also find its way into metabolic modeling.
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