Model-Based Design of Biochemical Microreactors.

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate.

Material and shape optimization for multi-layered vocal fold models using transient loadings.

Commonly applied models to study vocal fold vibrations in combination with air flow distributions are self-sustained physical models of the larynx consisting of artificial silicone vocal folds. Choosing appropriate mechanical parameters and layer geometries for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In earlier work by Schmidt et al. [J. Acoust. Soc. Am. 129, 2168-2180 (2011)], the authors presented an approach in which material parameters of a static numerical vocal fold model were optimized to achieve an agreement of the displacement field with data retrieved from hemilarynx experiments. This method is now generalized to a fully transient setting. Moreover in addition to the material parameters, the extended approach is capable of finding optimized layer geometries. Depending on chosen material restriction, significant modifications of the reference geometry are predicted. The additional flexibility in the design space leads to a significantly more realistic deformation behavior. At the same time, the predicted biomechanical and geometrical results are still feasible for manufacturing physical vocal fold models consisting of several silicone layers. As a consequence, the proposed combined experimental and numerical method is suited to guide the construction of physical vocal fold models.

Painting by numbers: nanoparticle-based colorants in the post-empirical age.

The visual appearance of the artificial world is largely governed by films or composites containing particles with at least one dimension smaller than a micron. Over the past century and a half, the optical properties of such materials have been scrutinized and a broad range of colorant products, based mostly on empirical microstructural improvements, developed. With the advent of advanced synthetic approaches capable of tailoring particle shape, size and composition on the nanoscale, the question of what is the optimum particle for a certain optical property can no longer be answered solely by experimentation. Instead, new and improved computational approaches are required to invert the structure-function relationship. This progress report reviews the development in our understanding of this relationship and indicates recent examples of how theoretical design is taking an ever increasingly important role in the search for enhanced or multifunctional colorants.

Material parameter computation for multi-layered vocal fold models.

Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.

Registration of PE segment contour deformations in digital high-speed videos.

Oncologic therapy of laryngeal cancer may necessitate a total excision of the larynx which results in loss of voice. Voice rehabilitation can be achieved using mucosal tissue vibrations at the upper part of the esophagus which serves as substitute voice generating element (PE segment). The quality of the substitute voice is closely related to vibratory characteristics of the PE segment. By means of a high-speed camera the dynamics of the PE segment can be recorded in real-time. Using image processing the deformations of the PE segment are extracted from the image series as deforming contours. Commonly, the characterization of PE dynamics bases on the spectral analysis of the time varying contour area. However, this constitutes an integral approach which masks most of the specific dynamics of PE deformations. We present an algorithm that automatically registers one segmented contour in a frame of the video sequence to the contour in the next frame to derive discrete 2-D trajectories of PE vibrations. By concatenation of the obtained transformations this approach provides a total registration of PE segment contours. We suggest a mixed-integer programming formulation for the problem that combines an advanced outlier and deformation handling with the introduction of dummy points in regions that newly open up, and that includes normal information in the objective function to avoid unwanted deformations. Numerical experiments show that the implemented alternate convex search algorithm produces robust results which is demonstrated at the example of five high-speed recordings of laryngectomee subjects.