Analysis of an apoptotic core model focused on experimental design using artificial data.

The activation of caspases is a central mechanism in apoptosis. To gain further insights into complex processes like this, mathematical modelling using ordinary differential equations (ODEs) can be a very powerful research tool. Unfortunately, the lack of measurement data is a common problem in building such kinetic models, because it practically constrains the identifiability of the model parameters. An existing mathematical model of caspase activation during apoptosis was used in order to design future experimental setups that will help to maximise the obtained information. For this purpose, artificial measurement data are generated in silico to simulate potential experiments, and the model is fitted to this data. The model is also analysed using observability gramian and sensitivity analyses. The used analysis methods are compared. The artificial data approach allows one to make conclusions about system properties, identifiability of parameters and the potential information content of additional measurements for the used caspase activation model. The latter facilitates to improve the experimental design of further measurements significantly. The performed analyses reveal that several kinetic parameters are not at all, or only scarcely, identifiable, and that measurements of activated caspase 8 will maximally improve the parameter estimates. Furthermore, we can show that many assays with inhibitor of apoptosis protein (IAP) knockout cells only provide redundant information for our needs and as such do not have to be carried out.

Multistability of signal transduction motifs.

Protein domains are the basic units of signalling processes. The mechanisms they are involved in usually follow recurring patterns, such as phosphorylation/dephosphorylation cycles. A set of common motifs was defined and their dynamic models were analysed with respect to number and stability of steady states. In a first step, Feinberg's chemical reaction network theory was used to determine whether a motif can show multistationarity or not. The analysis revealed that, apart from double-step activation motifs including a distributive mechanism, only those motifs involving an autocatalytic reaction can show multistationarity. To further characterise these motifs, a large number of randomly chosen parameter sets leading to bistability was generated, followed by a bifurcation analysis of each parameter set and a statistical evaluation of the results. The statistical results can be used to explore robustness against noise, pointing to the observation that multistationarity at the single-motif level may not be a robust property; the range of protein concentrations compatible with multistationarity is fairly narrow. Furthermore, experimental evidence suggests that protein concentrations vary substantially between cells. Considering a motif designed to be a bistable switch, this implies that fluctuation of protein concentrations between cells would prevent a significant proportion of motifs from acting as a switch. The authors consider this to be a first step towards a catalogue of fully characterised signalling modules.

A feed-forward loop guarantees robust behavior in Escherichia coli carbohydrate uptake.

MOTIVATION: In Escherichia coli, the phosphoenolpyruvate: carbohydrate phosphotransferase system acts like a sensory element which is able to measure the flux through glycolysis. Since the output of the sensor, the phosphorylated form of protein EIIA, is connected to the activity of the global transcription factor Crp, the kinetic and structural properties of the system are important for the understanding of the overall cellular behavior. RESULTS: A family of mathematical models is presented, varying with respect to their degree of complexity (number of reactions that are taken into account, number of parameters) that show a structurally and quantitatively robust behavior. The models describe a set of experimental data that relates the output of the sensor to the specific growth rate. A central element that is responsible for the structural robustness is a feed-forward loop in the glycolysis, namely the activation of the pyruvate kinase reaction by a metabolite of the upper part of the glycolysis. The robustness is shown for variations of the measured data as well as for variations of the parameters. AVAILABILITY: MATLAB files for model simulations are available on http://www.mpi-magdeburg.mpg.de/people/kre/robust/ A short description of the files provided on this site can be found in the Supporting information.

Using chemical reaction network theory to discard a kinetic mechanism hypothesis.

Feinberg's chemical reaction network theory (CRNT) connects the structure of a biochemical reaction network to qualitative properties of the corresponding system of ordinary differential equations. No information about parameter values is needed. As such, it seems to be well suited for application in systems biology, where parameter uncertainty is predominant. However, its application in this area is rare. To demonstrate the potential benefits from its application, different reaction networks representing a single layer of the well-studied mitogen-activated protein kinase (MAPK) cascade are analysed. Recent results from Markevich et al. (2004) show that, unexpectedly, multilayered protein kinase cascades can exhibit multistationarity, even on a single cascade level. Using CRNT, we show that their assumption of a distributive mechanism for double phosphorylation and dephosphorylation is crucial for multistationarity on the single cascade level.

Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli.

A mathematical model for the KdpD/KdpE two-component system is presented and its dynamical behavior is analyzed. KdpD and KdpE regulate expression of the kdpFABC operon encoding the high affinity K+ uptake system KdpFABC of Escherichia coli. The model is validated in a two step procedure: (i) the elements of the signal transduction part are reconstructed in vitro. Experiments with the purified sensor kinase and response regulator in presence or absence of DNA fragments comprising the response regulator binding-site are performed. (ii) The mRNA and molecule number of KdpFABC are determined in vivo at various extracellular K+ concentrations. Based on the identified parameters for the in vitro system it is shown, that different time hierarchies appear which are used for model reduction. Then the model is transformed in such a way that a singular perturbation problem is formulated. The analysis of the in vivo system shows that the model can be separated into two parts (submodels which are called functional units) that are connected only in a unidirectional way. Hereby one submodel represents signal transduction while the second submodel describes the gene expression.

Modeling and experimental validation of the signal transduction via the Escherichia coli sucrose phospho transferase system.

Bacterial signal processing was investigated concerning the sucrose phosphotransferase system (sucrose PTS) in the bacterium Escherichia coli as an example. The about 20 different phosphotransferase systems (PTSs) of the cell fulfill besides the transport of various carbohydrates, also the function of one signal processing system. Extra- and intracellular signals are converted within the PTS protein chain to important regulatory signals affecting, e.g. carbon metabolism and chemotaxis. A detailed dynamical model of the sucrose PTS was developed describing transport and signal processing function. It was formulated using a detailed description of complex formation and phosphate transfer between the chain proteins. Model parameters were taken from literature or were identified with own experiments. Simulation studies together with experimental hints showed that the dynamic behavior of phosphate transfer in the PTS runs within 1 s. Therefore a description of steady state characteristics is sufficient for describing the signaling properties of the sucrose PTS. A steady state characteristic field describes the degree of phosphorylation of the PTS protein EIIACrr as a function of the input variables extracellular sucrose concentration and intracellular phosphoenolpyruvate (PEP):pyruvate ratio. The model has been validated with different experiments performed in a CSTR using a sucrose positive E. coli W3110 derivative. A method for determining intracellular metabolite concentrations has been developed. A sample preparation technique using a boiling ethanol buffer solution was successfully applied. The PTS output signal degree of phosphorylation of EIIACrr was also measured. Steady state conditions with varying dilution rate and dissolved oxygen concentration and dynamical variations applying different stimuli to the culture were considered. Pulse, and stop feeding experiments with limiting sucrose concentrations were performed. Simulation and experimental results matched well. The same holds for the expanded sucrose PTS and glycolysis model.

Time hierarchies in the Escherichia coli carbohydrate uptake and metabolism.

The analysis of metabolic pathways with mathematical models contributes to the better understanding of the behavior of metabolic processes. This paper presents the analysis of a mathematical model for carbohydrate uptake and metabolism in Escherichia coli. It is shown that the dynamic processes cover a broad time span from some milliseconds to several hours. Based on this analysis the fast processes could be described with steady-state characteristic curves. A subsequent robustness analysis of the model parameters shows that the fast part of the system may act as a filter for the slow part of the system; the sensitivities of the fast system are conserved. From these findings it is concluded that the slow part of the system shows some robustness against changes in parameters of the fast subsystem, i.e. if a parameter shows no sensitivity for the fast part of the system, it will also show no sensitivity for the slow part of the system.

Reduction of mathematical models of signal transduction networks: simulation-based approach applied to EGF receptor signalling.

Biological systems and, in particular, cellular signal transduction pathways are characterised by their high complexity. Mathematical models describing these processes might be of great help to gain qualitative and, most importantly, quantitative knowledge about such complex systems. However, a detailed mathematical description of these systems leads to nearly unmanageably large models, especially when combining models of different signalling pathways to study cross-talk phenomena. Therefore, simplification of models becomes very important. Different methods are available for model reduction of biological models. Importantly, most of the common model reduction methods cannot be applied to cellular signal transduction pathways. Using as an example the epidermal growth factor (EGF) signalling pathway, we discuss how quantitative methods like system analysis and simulation studies can help to suitably reduce models and additionally give new insights into the signal transmission and processing of the cell.

Modular modeling of cellular systems with ProMoT/Diva.

MOTIVATION: Need for software to setup and analyze complex mathematical models for cellular systems in a modular way, that also integrates the experimental environment of the cells. RESULTS: A computer framework is described which allows the building of modularly structured models using an abstract, modular and general modeling methodology. With this methodology, reusable modeling entities are introduced which lead to the development of a modeling library within the modeling tool ProMot. The simulation environment Diva is used for numerical analysis and parameter identification of the models. The simulation environment provides a number of tools and algorithms to simulate and analyze complex biochemical networks. The described tools are the first steps towards an integrated computer-based modeling, simulation and visualization environment Availability: Available on request to the authors. The software itself is free for scientific purposes but requires commercial libraries. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/promot

The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

The organization of metabolic reaction networks. III. Application for diauxic growth on glucose and lactose.

A mathematical model to describe carbon catabolite repression in Escherichia coli is developed and in part validated. The model is aggregated from two functional units describing glucose and lactose transport and degradation. Both units are members of the crp modulon and are under control of a global signal transduction system which calculates the signals that turn on or off gene expression for the specific enzymes. Using isogenic mutant strains, our model is validated by a set of experiments. In these experiments, substrate composition of the preculture and of the experimental culture are varied in order to stimulate the system in different ways. With the obtained measurements (three states in the liquid phase and one intracellular component) a part of the model parameters could be estimated. Therefore all experiments could be sufficiently described with a single set of parameters.

Modeling of inducer exclusion and catabolite repression based on a PTS-dependent sucrose and non-PTS-dependent glycerol transport systems in Escherichia coli K-12 and its experimental verification.

We used genetically engineered sucrose positive Escherichia coli K-12 derivatives as a model system for the modeling and experimental verification of regulatory processes in bacteria. These cells take up and metabolize sucrose by the phosphoenolpyruvate (PEP)-dependent sucrose phosphotransferase system (Scr-PTS). Expression of the scr genes, which cluster in two different operons (scrYAB and scrK), is negatively controlled by the ScrR repressor. Additionally, expression of the scrYAB operon, but not of the scrK operon is positively controlled by the cAMP-CRP complex. Modeling of sucrose transport and metabolism through the Scr-system and of the scr gene expression has been performed using a modular and object-orientated new approach. To verify the model and identify important model parameters we measured in a first set of experiments induction kinetics of the scr genes after growth on glycerol using strains with single copy lacZ operon fusions in the scrK or scrY genes, respectively. In a second set of experiments an additional copy of the complete scr-regulon was integrated into the chromosome to construct diplogenotic strains. Differences were observed in the induction kinetics of the cAMP-CRP-dependent scrY operon compared to the cAMP-CRP independent scrK operon as well as between the single copy and the corresponding diplogenotic strains.

The organization of metabolic reaction networks. II. Signal processing in hierarchical structured functional units.

Based on the analysis of molecular interactions of proteins with DNA binding sites, a new approach to developing mathematical models describing gene expression is introduced. Detection of hierarchical structures in metabolic networks can be used to decompose complex reaction schemes. This will be achieved by assigning each regulator protein to one level in the hierarchy. Signals are then transduced from the top level to the lower level, but not vice versa. The method is shown by a simple example with two interacting proteins. A comparison of simulation results shows good agreement between a model taking all interactions into account and a model developed with the new approach. Finally, the method is applied to the crpA modulon in Escherichia coli, which controls uptake and metabolism for a number of carbohydrates. Here, RNA polymerase represents the top level, CrpA the second level, and the lactose-specific repressor LacI the lowest level, respectively. Besides the lactose operon, the method is applied to the adenylate cyclase gene and the gene for the regulator CrpA.

The organization of metabolic reaction networks: a signal-oriented approach to cellular models.

Complex metabolic networks are characterized by a great number of elements and many regulatory loops. The description of these networks with mathematical models requires the definition of functional units that group together several cellular processes. The approach presented here is based on the idea that cellular functional units may be assigned directly to mathematical modeling objects. Because the proposed modeling objects have defined inputs and outputs, they can be connected with other modeling objects until eventually the whole metabolism is covered. This modular approach guarantees a high transparency for biologists as well as for engineers. Three criteria are introduced to demarcate functional units. The criteria consider the physiological pathways, the organization of the corresponding genes, and the observation that cellular systems can be structured into units showing a hierarchy of signal transduction and processing. As an example, the carbon catabolic reactions in Escherichia coli are discussed as members of a functional unit catabolism.

Carbazole antibiotics synthesis in a Streptomyces tendae bald mutant, created by acriflavine treatment.

Acriflavine treatment on Streptomyces tendae generated a bald mutant (bld-1) with an altered antibiotic pattern. The parental strain produced nikkomycins and juglomycins, whereas the mutant bld-1 was only capable of juglomycin synthesis. The existence of a mutant defective in morphogenesis and in nikkomycin biosynthesis suggests a common regulation of these processes. An interesting finding of this study is that mutant bld-1 produced two carbazole derivatives, hitherto never seen in cultures of the parental strain. It seems likely that the DNA intercalating dye acriflavine, by mutagenesis, had activated cryptic genes which are involved in carbazole synthesis. The two carbazole derivatives were identified as the neuronal cell protecting compounds CS-79B and carquinostatin A, recently isolated from a wild-type of S. exfoliatus. We found that both substances showed antibacterial activity.

Morphological characterization of filamentous microorganisms in submerged cultures by on-line digital image analysis and pattern recognition.

The morphology of filamentous microorganisms in submerged culture is of great interest. On the one hand, morphology influences rheology and mass transfer in the fermentation broth. On the other hand, morphology could be a visible expression of physiology and metabolism of the microorganisms. An algorithm for the morphological characterization and the estimation of biomass of filamentous microorganisms by means of digital image analysis has been developed. After measurement of eight features the objects in the broth are classified into different morphological classes, i.e., pellet aggregates, rough pellets, smooth pellets, mycelial flocks, and medium components. The classification is based on the measured object parameters and a knowledge base, which was generated in a preceding training phase. The method was tested on Streptomyces tendae Tü 901/8c. A typical batch fermentation in a defined medium is presented. It could be shown that both morphology and physiology have been changed in the course of the fermentation, especially during the transition from trophophase to idiophase. In order to supervise the fermentation processes continuously, an on-line image analysis system has been developed. Sampling, dilution, and image acquisition of the culture were performed under the control of a personal computer. (c) 1997 John Wiley & Sons, Inc.

Model-based monitoring and control of a monoclonal antibody production process.

A structured mathematical model describing the dynamics of hybridoma growth and monoclonal antibody (mAb) production in suspension cultures is presented. The model fits well to experimental data obtained from batch, fed-batch, and continuous cultures with hybridoma cells. Applications of the model for process control are demonstrated. 1. An extended Kalman filter (EKF) was designed to estimate the state of the process. The oxygen consumption rate of the cell culture is monitored on-line and is used as the only measurement information for the EKF. This EKF is able to provide good estimates for living and dead cell densities and the medium composition. 2. The mathematical model can be applied for the optimization of fed-batch cultures.

Measurement and simulation of the morphological development of filamentous microorganisms.

Growth of Streptomyces tendae was investigated in submerged culture. Images of several mycelia were analyzed by means of an image-processing system. The studies revealed that tip growth angles and branching outgrowth angles could be regarded as normally distributed. Based on these results, a random model for directional growth of hyphal tips as well as directional growth of branches is proposed. This model shows curved elongation of hyphal tips, so that the morphological development of a mycelium up to the formation of a pellet is predicted, similar to that observed in nature.

Mathematical model for apical growth, septation, and branching of mycelial microorganisms.

A mathematical model for apical growth, septation, and branching of mycelial microorganisms is presented. The model consists of two parts: the deterministic part of the model is based on fundamental cellular and physical mechanisms; it represents the kinetics for growth of hyphal tips and septation of apical as well as intercalary compartments. In regard to random occurrences of hyphal growth and branching, the stochastic part deals with branching processes, tip growth directions, and outgrowth orientations of branches. The model can explain the morphological development of mycelia up to the formation of pellets. The results, as predicted by the model, correspond very closely to those observed in experiments. In addition, some unmeasured states can be ascertained, such as the distribution functions of hyphal length (biomass) and tips along pellet radii.

Characterization of pellet morphology during submerged growth of Streptomyces tendae by image analysis.

Many filamentous bacteria and fungi tend to form pellets, or mixtures of dispersed mycelium and pellets in liquid fermentation broths. In some cases, a specific kind of morphology is required for optimum product yield. When quantitative analysis and characterization of the pellet morphology are needed, an image processing system can be used. It allows a fast and reproducible analysis of the frequency distribution of pellet size, mean pellet size, contents of pellets, or their shape. The use of such a system allows for an on-line analysis. For a demonstration of the method, results of two fermentations of Streptomyces tendae are shown.