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Making it stick: convection, reaction and diffusion in surface-based biosensors


The past decade has seen researchers develop and apply novel technologies for biomolecular detection, at times approaching hard limits imposed by physics and chemistry. In nearly all sensors, the transport of target molecules to the sensor can play as critical a role as the chemical reaction itself in governing binding kinetics, and ultimately performance. Yet rarely does an analysis of the interplay between diffusion, convection and reaction motivate experimental design or interpretation. Here we develop a physically intuitive and practical understanding of analyte transport for researchers who develop and employ biosensors based on surface capture. We explore the qualitatively distinct behaviors that result, develop rules of thumb to quickly determine how a given system will behave, and derive order-of-magnitude estimates for fundamental quantities of interest, such as fluxes, collection rates and equilibration times. We pay particular attention to collection limits for micro- and nanoscale sensors, and highlight unexplained discrepancies between reported values and theoretical limits.

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Figure 1: Model system studied here.
Figure 2: Purely diffusive flux to sensors of three different sizes (λ = L/H): λ = 10 (top), λ = 1 (middle), and λ = 1/10 (bottom), computed using COMSOL.
Figure 3: Mass transport and steady-state flux.
Figure 4: Example sensors: a microscale sensor (left) and a nanowire sensor (right).
Figure 5: The equilibration time τCRD, normalized by the reaction time τR, plotted as a function of the Damkohler number Da, as in equation 20 in the main text.

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T.M.S. gratefully acknowledges National Science Foundation CAREER support (CBET- 0645097) and support from the Los Alamos National Laboratory/UCSB Institute for Multiscale Materials Science for R.J.M. S.R.M. gratefully acknowledges the National Institutes of Health Center for Cell Decision Process Grant (P50-GM68762) and the National Cancer Institute Platform Partnership Grant (R01-CA119402). We gratefully acknowledge T. Burg, J. Han, R. Kamm, S. Quake and H. Stone for critical readings and helpful suggestions.

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Correspondence to Todd M Squires.

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Squires, T., Messinger, R. & Manalis, S. Making it stick: convection, reaction and diffusion in surface-based biosensors. Nat Biotechnol 26, 417–426 (2008).

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