Brownian-motion based simulation of stochastic reaction–diffusion systems for affinity based sensors

Abstract

In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.

Stochastic Time Response and Ultimate Noise Performance of Adsorption-Based Microfluidic Biosensors

“…Figure 6a shows that the steady-state variance obtained by using the model that takes into account the AD process, diffusion, and convection has a maximum at a certain concentration. This result for the MT-influenced binding of target particles is in accordance with the computer simulation results obtained for the variance of silicon nanowire fieldeffect biosensors whose response fluctuates due to the coupling of the AD process and mass transfer by diffusion [29,30].…”

“…The dependence SNR e (C) obtained by using the derived analytical expression and shown in Figure 6a is in accordance with that obtained in [30] by computer simulation for the case of diffusion-influenced binding. Diagrams of this kind (Figure 6a) enable the determination of the concentration detection and quantification limits for a given sensor and given experimental conditions, as the values of C at which the SNR has the minimal required values for reliable analyte detection and quantification, respectively.…”

“…Approximate mathematical models that enable the analysis of statistical parameters (expected value, standard deviation, and variance) of the stochastic time response of adsorption-based (both chemical and biological) sensors and their noise performance metrics (AD noise power spectral density and signal-to-noise ratio) have been developed for some practically significant cases [15,16,18,20,21,[24][25][26][27][28][29][30]. Based on these references, it can be concluded that the closed-form solutions for the mentioned quantities are only devised for simplified cases, during the transient regime of the binding process on the sensing surface, or after the steady state of the binding process is reached.…”

“…In [18,29,30], a stochastic simulation was used for the analysis of the change in the expected value and variance of the number of adsorbed particles, and the sensor signalto-noise ratio in time, considering the transport of analyte particles by diffusion. The emphasis was on the influence of the target substance concentration and probe density on the mentioned time dependences, while MT influence was not analyzed in particular.…”