An embedding method for simulation of immobilized enzyme kinetics and transport in sessile hydrogel drops

A newly-developed embedding method for simulating enzyme kinetics and transport occurring within axisymmetric 3D domains is presented. The physical problem is pertinent to gel-pad microarrays for assessment of enzymatic activity. An enzyme is immobilized uniformly within a hydrogel which is spotted onto a solid surface in the form of a sessile drop, taking on a spherical cap shape. An aqueous solution containing substrate flows slowly past the porous drop. The substrate diffuses into the drop and is converted to product with the help of the enzyme. The product accumulates in and diffuses out of the drop and is taken away by the flow. Spatiotemporal distribution of the product, monitored via fluorescence, can be used to quantify the enzyme kinetics. This process is described by a system of nonlinear reaction-diffusion partial differential equations, modeling the diffusive transport and enzymatic reaction. The computational domain contains both the hydrogel drop and the bulk fluid phases. The embedding method is a computational technique that enables the use of finite differences on a regular Cartesian grid for simulation of multiphase problems with complex interfaces/boundaries. It uses a volume-fraction-based approach, similar to the volume-of-fluid (VOF) method, to implement the boundary conditions that must be applied at the interface between the phases. The main advantage of the embedding method is its simplicity, which results in code generation that can be highly optimized. In the present work, we apply the embedding method to the aforementioned two-phase reaction-diffusion problem and validate the results by comparing to a number of exact solutions available in simpler geometries and to results obtained using a finite-volume method on an unstructured body-fitted mesh. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)