Modeling and optimization of a multi-enzyme electrokinetically driven multiplexed microchip for simultaneous detection of sugars

Abstract

A model-based methodology was developed to optimize microfluidic chips for the simultaneous enzymatic quantification of sucrose, D-glucose and D-fructose in a single microfluidic channel with an integrated optical detection system. The assays were based on measuring the change in concentration of the reaction product NADH, which is stoichiometrically related to the concentration of those components via cascade of specific enzymatic reactions. A reduced order mathematical model that combines species transport, enzyme reaction, and electrokinetic bulk flow was developed to describe the operation of the microfluidic device. Using this model, the device was optimized to minimize sensor response time and maximize signal output by manipulating the process conditions such as sample and reagent volume and flow rate. According to this simulation study, all sugars were quantified within 2.5 min in the optimized microchip. A parallel implementation of the assays can further improve the throughput. In addition, the amount of consumed reagents was drastically reduced compared to microplate format assays. The methodology is generic and can easily be adapted to other enzymatic microfluidic chips.Keywords Lab-on-a-chip Á Reduced order model Á CFD Á Food Á Michaelis-Menten Á Microfluidics List of symbolsA c cross-sectional area of the channel (m 2 ) h height of microchannel (lm) w width of microchannel (lm) C i concentration of species i (mol m -3 ) D i diffusion coefficient of the ith species (m 2 s -1 ) I electric current (A) k cat rate constant (s -1 ) r rate of reaction (mol m -3 s -1 ) R electrical resistance (X) K M Michaelis-Menten constant (mol m -3 ) K S dissociation constant (mol m -3 ) L length (m) M S molecular weight of molecule (g/mol) V molar volume at its boiling point (m 3 /kg mol) t time (s) u eo electroosmotic slip velocity (m s -1 ) u ep electrophoretic velocity (m s -1 ) Q flow rate (m 3 s -1 ) / applied potential (V) e 0 permittivity of vacuum (C 2 N -1 m -2) l eo electroosmotic mobility (m 2 V -1 s -1 ) q density of the fluid (kg m -3 ) g dynamic viscosity of fluid (kg m -1 s -1 ) r electrical conductivity of fluid (S m -1 ) f zeta potential (V) k D thickness of electric double layer (nm) e r dielectric constant of the medium l ep, i electrophoretic mobility of the ith species (m 2 V -1 s -1 ) M number of junctions N number of branches Abbreviations EDL

Design and optimization of a double-enzyme glucose assay in microfluidic lab-on-a-chip

“…5,6,19,22,24 The governing equations for the electrokinetic fluid flow are the conservation equations for mass ͓continuity equation, Eq. ͑2͔͒ and momentum ͓Navier-Stokes equation, Eq.…”

“…22,24 Hence, the slip velocity at the channel wall can be calculated from the local potential gradient by the HelmholtzSmoluchowski equation 6,21…”

“…The general mass transport equation in microfluidic chips includes terms for convection, diffusion, migration, and reaction, 5,6 …”

“…28 For in-depth analysis on the kinetic mechanism of two substrate enzymatic process we refer to Marangoni. 31 The initial rate equation for such mechanism is given by 6,27 …”

“…22 To save the computational resource, the reaction channel beyond 20 mm is neglected during the computation and the corresponding potential in this artificial boundary is recalculated. 5,6 Using mesh sensitivity analysis, mesh size that governs a meshindependent solution was chosen. Accordingly the mesh that consists of 44 308 triangular elements has been computed for an absolute and relative tolerance of 1 ϫ 10 −6 .…”