Moment Dynamics of Zirconia Particle Formation for Optimizing Particle Size Distribution.

We study the particle formation process of Zirconia ( ZrO 2 )-based material. With a model-based description of the particle formation process we aim for identifying the main growth mechanisms for different process parameters. After the introduction of a population balance based mathematical model, we derive the moment dynamics of the particle size distribution and compare the model to experimental data. From the fitted model we conclude that growth by molecular addition of Zr-tetramers or Zr-oligomers to growing particles as well as size-independent particle agglomeration takes place. For the purpose of depositing zirconia-based material (ZrbM) on a substrate, we determine the optimal process parameters such that the mineralization solution contains preferably a large number of nanoscaled particles leading to a fast and effective deposition on the substrate. Besides the deposition of homogeneous films, this also enables mineralization of nanostructured templates in a bioinspired mineralization process. The developed model is also transferable to other mineralization systems where particle growth occurs through addition of small molecular species or particle agglomeration. This offers the possibility for a fast determination of process parameters leading to an efficient film formation without carrying out extensive experimental investigations.

Analysis of primitive genetic interactions for the design of a genetic signal differentiator.

We study the dynamic and static input-output behavior of several primitive genetic interactions and their effect on the performance of a genetic signal differentiator. In a simplified design, several requirements for the linearity and time-scales of processes like transcription, translation and competitive promoter binding were introduced. By experimentally probing simple genetic constructs in a cell-free experimental environment and fitting semi-mechanistic models to these data, we show that some of these requirements can be verified, while others are only met with reservations in certain operational regimes. Analyzing the linearized model of the resulting genetic network, we conclude that it approximates a differentiator with relative degree one. Taking also the discovered nonlinearities into account and using a describing function approach, we further determine the particular frequency and amplitude ranges where the genetic differentiator can be expected to behave as such.

A resource dependent protein synthesis model for evaluating synthetic circuits.

Reliable in silico design of synthetic gene networks necessitates novel approaches to model the process of protein synthesis under the influence of limited resources. We present such a novel protein synthesis model which originates from the Ribosome Flow Model and among other things describes the movement of RNA-polymerase and ribosomes on mRNA and DNA templates, respectively. By analyzing the convergence properties of this model based upon geometric considerations, we present additional insights into the dynamic mechanisms of the process of protein synthesis. Further, we demonstrate how this model can be used to evaluate the performance of synthetic gene circuits under different loading scenarios.