Efficient numerical solution of micro-macro models for multicomponent transport and reaction problems in porous media - Elbinger, Tobias; Knabner, Peter (Applicable Analysis, 2022)
Transport and reaction of dissolved species in hierarchically structured complex media, e.g. porous media, can be described by micro-macro models (models with distributed micro-structure, FE2 models). These models offer advantages compared to pure micro- or pure macroscale models but exhibit, compared to pure macroscale models, a strongly increased numerical complexity. We show how parallel computing together with Schur complement techniques can make those models numerically feasible.
CRIS-Team WoS Importer:2022-08-19

Model-Based Design of Biochemical Microreactors - Elbinger, Tobias; Gahn, Markus; Hante, Falk; Voll, Lars; Leugering, Günter; Knabner, Peter; Neuss-Radu, Maria (Frontiers in Bioengineering and Biotechnology, 2016)
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-phosphat

Simulation of Processes in Living Cells: Towards the Modelling of Metabolic Channeling - Elbinger, Tobias; Gahn, Markus; Neuss-Radu, Maria; Knabner, Peter (2nd International Conference on Multi-scale Computational Methods for Solids and Fluids, 2015)
We consider a two-scale homogenized model for processes in living cells including reaction and diffusion inside and on the surface of organelles. The resulting equations are fully coupled and the number of biochemical species in applications is large. We developed numerical schemes in order to rcomputation time by means of better scaling on parallel machines and reduction of the problemsize. A combination of those schemes provides a suitable numerical framework for our problem.
Keywords: Multiscale Finite Element Methods; Decoupling Algorithm; Newton’s Method

Upscaling the flow and transport in an evolving porous medium with general interaction potentials - Ray, Nadja; Elbinger, Tobias; Knabner, Peter (SIAM Journal on Applied Mathematics, 2015)
The objective of this research is to investigate the upscaling of flow and transport models including both an evolving solid-liquid interface and a quite general potentially even oscillating interaction potential. Starting from a comprehensive pore-scale model, formal, two-scale, asymptotic expansion in a level set framework is applied. In doing so, the interplay between flow, transport, interaction potential, and evolving geometry becomes evident. As a result of an averaging procedure, a fully coupled micro-macro model is established with new main variables. Moreover, time-and spacedependent coefficient functions are explicitly characterized by means of supplementary, fully coupled cell problems. The theoretical results obtained are complemented by the numerical computations of a heterogeneous multiscale scenario with a focus on the development of anisotropic transport. Because of the general framework considered in this research, numerous application are expected, such as in biology or colloidal dynamic
Keywords: Evolving porous medium; Flow; Interaction potential; Level set; Transport; Two-scale asymptotic expansion; Upscaling