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The allocation of resources during bacterial growth is strongly related to the availability of ribosomes and RNA polymerase molecules. Here, coarse-grained models offer a promising start due to their simple structure and the limited number of kinetic parameters. Based on published data sets for proteome and mRNA data in Escherichia coli, and together with mass balance equations describing gene expression, we are able to calculate the number of active molecules (that is, the number of ribosomes that are currently translating nascent and mature mRNA, as well as the number of RNA polymerase molecules on the DNA). This information is a prerequisite for meaningful coarse-grained models. In our approach, the cellular compartment is structured into a cytosolic region and a nucleoid region, and the processes of transcription and translation are assigned accordingly. The theoretical study reveals a quadratic relationship between the number of active ribosomes and the growth rate μ. While the overall available number of ribosomes follows the linear "bacterial growth law", the approach allows us to determine the growth limit for the chosen experimental environment (minimal medium, only one C source). The new approach is in good agreement with published experimental data, and, with a simple rule of thumb can be applied to other cellular systems.

A quantitative description of dynamical systems requires the estimation of uncertain kinetic parameters and an analysis of their precision. A method frequently used to describe the confidence intervals of estimated parameters is based on the Fisher-Information-Matrix. The application of this traditional method has two important shortcomings: (i) it gives only lower bounds for the variance of a parameter if the solution of the underlying model equations is non-linear in parameters. (ii) The resulting confidence interval is symmetric with respect to the estimated parameter. Here, we show that by applying the bootstrap method a better approximation of (possibly) asymmetric confidence intervals for parameters could be obtained. In contrast to previous applications devoted to non-parametric problems, a dynamical model describing a bio-chemical network is used to evaluate the method.

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.

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.

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.

The presumably high potential of a holistic design approach for complex biochemical reaction networks is exemplified here for the network of tryptophan biosynthesis from glucose, a system whose components have been investigated thoroughly before. A dynamic model that combines the behavior of the trp operon gene expression with the metabolic network of central carbon metabolism and tryptophan biosynthesis is investigated. This model is analyzed in terms of metabolic fluxes, metabolic control, and nonlinear optimization. We compare two models for a wild-type strain and another model for a tryptophan producer. An integrated optimization of the whole network leads to a significant increase in tryptophan production rate for all systems under study. This enhancement is well above the increase that can be achieved by an optimization of subsystems. A constant ratio of control coefficients on tryptophan synthesis rate has been identified for the models regarding or disregarding trp operon expression. Although we found some examples where flux control coefficients even contradict the trends of enzyme activity changes in an optimized profile, flux control can be used as an indication for enzymes that have to be taken into account in optimization.