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.

A model describing the effect of enzymatic degradation on drug release from collagen minirods.

A drug delivery system, named minirod, containing insoluble non-cross-linked collagen was prepared to investigate the release of model drug compounds. To characterise the complete drug release process properly, a mathematical model was developed. Previously, a mathematical model describing water penetration, matrix swelling and drug release by diffusion from dense collagen matrices has been introduced and tested. However, enzymatic matrix degradation influences the drug release as well. Based on experimental data, a model was developed which describes drug release by collagenolytic matrix degradation based on enzyme diffusion, adsorption and cleavage. Data for swelling, collagen degradation and FITC dextran release from insoluble equine collagen type I minirods were collected. Sorption studies demonstrated a tight sorption of collagenase on collagen surfaces that follows a Freundlich sorption isotherm and results in a degradation constant of 3.8x10(-5) mol/l for the minirods. The diffusion coefficients of FITC dextran 20 and 70 (3x10(-3) and 2.4x10(-3) cm2/h) in water were analyzed by fluorescence correlation spectroscopy (FCS). Using these data, the mathematical model was verified by two-dimensional simulations. The numerical results agreed well with the measurements.

Simulation of carrier-facilitated transport of phenanthrene in a layered soil profile.

The appropriate prediction of the fate of the contaminant is an essential step when evaluating the risk of severe groundwater pollutions-in particular in the context of natural attenuation. We numerically study the reactive transport of phenanthrene at the field scale in a multilayer soil profile based on experimental data. The effect of carrier facilitation by dissolved organic carbon is emphasized and incorporated in the model. Previously published simulations are restricted to the saturated zone and/or to homogeneous soil columns at the laboratory scale. A numerical flow and transport model is extended and applied to understand and quantify the relevant processes in the case of a strongly sorbing hydrophobic organic compound that is subject to carrier facilitation in the unsaturated zone. The contaminant migration is investigated on long- and short-term time scales and compared to predictions without carrier facilitation. The simulations demonstrate the importance of carrier facilitation and suggest strongly to take this aspect into account. By carrier facilitation breakthrough times at the groundwater level decreased from 500 to approximately 8 years and concentration peaks increased by two orders of magnitude in the long-term simulation assuming a temporary spill in an initially unpolluted soil with a non-sorbing carrier.

Modeling of drug release from collagen matrices.

Drug release from collagen matrices is in most cases governed by diffusion from swollen matrices but also enzymatic matrix degradation or hydrophobic drug/collagen interactions may contribute. To reduce water uptake and to prolong the release, insoluble collagen matrices have been chemically or dehydrothermally crosslinked. Assuming Fickian diffusion a one-dimensional model was developed and tested that allows description of water penetration, swelling and drug release and that may be expanded considering a subsequent erosion process or interactions. Swelling is described by a volume balance. For dry collagen matrices crosslinked by thermal treatment the existence of a moving front separating the polymer from a gel phase was considered, and a convective term induced by the volume expansion was incorporated. The resulting moving boundary problem was solved using a method based on biquadratic finite elements in both space and time that is stable, shows high accuracy, and is suitable for solving problems with a singularity at the initial time point. The model was verified for insoluble collagen matrices at different crosslinking degrees for both chemical and thermal treatment. For constant diffusion coefficients a close form of the solution was derived yielding equivalent results to the numerical approach.