Transient Convection, Diffusion, and Adsorption in Surface-Based Biosensors

Abstract

This paper presents a theoretical and computational investigation of convection, diffusion, and adsorption in surface-based biosensors. In particular, we study the transport dynamics in a model geometry of a surface plasmon resonance (SPR) sensor. The work, however, is equally relevant for other microfluidic surface-based biosensors, operating under flow conditions. A widely adopted approximate quasi-steady theory to capture convective and diffusive mass transport is reviewed, and an analytical solution is presented. An expression of the Damkoḧler number is derived in terms of the nondimensional adsorption coefficient (Biot number), the nondimensional flow rate (Pećlet number), and the model geometry. Transient dynamics is investigated, and we quantify the error of using the quasi-steady-state assumption for experimental data fitting in both kinetically limited and convection-diffusionlimited regimes for irreversible adsorption, in specific. The results clarify the conditions under which the quasi-steady theory is reliable or not. In extension to the well-known fact that the range of validity is altered under convection-diffusion-limited conditions, we show how also the ratio of the inlet concentration to the maximum surface capacity is critical for reliable use of the quasi-steady theory. Finally, our results provide users of surface-based biosensors with a tool for correcting experimentally obtained adsorption rate constants.

A quantitative model for lateral flow assays

“…This result, in apparent contradiction with the previous one (Fig. 3), is the trend typically expected in the kinetic analysis of advection-diffusion-reaction systems (Gervais and Jensen 2006;Kockmann 2008;Hansen et al 2012;Aguirre et al 2014). The rationale is that flow rate must be increased to improve the analyte flux and hence attain better capture efficiency in a given assay time.…”

“…In fact, integrating with the initial condition C AS = 0, t k = 0, yields It should be mentioned that a solution analogous to Eq. 10 has been reported (Hansen et al 2012) for pseudo steady state operation of open flow-cells with surface reactions. Precisely, the kinetic timescale t k is more suitable for systems without sample volume limitations.…”

“…Comprehensive theoretical models for surface binding in microfluidic systems are available (Hu et al 2005;Gervais and Jensen 2006;Parsa et al 2008;Squires et al 2008;Hansen et al 2012;Aguirre et al 2014), which involve the coupling of advective transport, molecular diffusion, and chemical reactions. These formulations are very useful to understand the physicochemical basis of the general Abstract A simple mathematical model that quantitatively describes the dynamics of analyte capture in lateral flow assays is presented.…”

Transport of biomolecules to binding partners displayed on the surface of microbeads arrayed in traps in a microfluidic cell

“…As Da decreases, the slowing of the kinetic rate decreases the binding, and the initial reduction in the sublayer concentration in the earliest times is much smaller than the case for Da ¼ 10 Alternatively when Da/Pe 1=3 ) 1, the sublayer concentration tends to zero, at least initially, and the target flux to the surface is controlled solely by the diffusive mass transfer. The characteristic time for the target to bind to an equilibrium surface density (t eq;D ) is given by t eq;D et al, 36 for a patch of probes on one wall of a two dimensional microfluidic channel, have examined, by comparison to numerical simulations, the validity of reproducing the entire binding curve of the target to the patch for Pe ) 1 by a boundary layer approximation in which D…”

“…While the analysis of the binding of targets to surface probes as a screening platform has been studied in detail for the case of probe "patches" situated on a microchannel wall (e.g., Refs. [34][35][36], the binding of target to microbeads captured in traps has received very limited attention. Bau et al [37][38][39][40] studied the geometry of microbeads sandwiched between the top surface of a flow channel and a shallow well at the bottom of the channel (the microbeads were preassembled in the shallow wells before closing the cell), and obtained solutions for the target concentration on the microbead surface as a function of the stream velocity and target-probe kinetic rate constants.…”