Applicability of Birth–Death Markov Modeling for Single-Molecule Counting Using Single-Walled Carbon Nanotube Fluorescent Sensor Arrays

Abstract

In recent work, we have shown that d(AT)15 DNA-wrapped single-walled carbon nanotubes (SWNTs) are able to detect the adsorption and desorption of single molecules of nitric oxide (NO) from the surface by quenching of the near-infrared fluorescence (Zhang et al. J. Am. Chem. Soc. 2011, 133, 567−581). A central question is how to estimate the local concentration from stochastic dynamics for these types of sensors. Herein, we employ an exact solution to the birth–death Markov model to estimate the local analyte concentration from the stochastic dynamics. Conditions are derived for the intrinsic variance displayed by identical sensor elements, and the homogeneity of the environment is assessed by comparing experimental sensor-to-sensor variance with this limit. We find that d(AT)15 DNA-wrapped SWNTs demonstrate variances that are close to the idealized limit at relatively high NO concentrations (19.4 μM). At 780 nM, the sensor-to-sensor variance is approximately double the idealized value, indicating marginal variation in the SWNT array. An NO adsorption coefficient of 2.6 × 10–4 [μM–1] is identified, and we outline how to predict the local analyte concentration from the sensor dynamics.