Microtech2010 2010

Mathematical modeling and computer simulation of Brownian motion and hybridization of nanoparticle-bioprobe-polymer complexes in the low concentration limit

A. Toth, D. Banky, V. Grolmusz
Eotvos University, HU

Keywords: hybridization, incubation time, computer simulation


We present a mathematical model and the computer simulation of Brownian motion of nanoparticle-bioprobe-polymer contrast agent complexes and their hybridization to immobilized targets. Our model is a stochastic counterpart of the continuous model presented in Ericson et al. Anal BioChem 317 (2003). We present results for the dependence of incubation times on the number of particles available for detection, and the geometric layout of the biochip. We derive values for the time necessary for a single particle hybridization within a prescribed probability error, as well as values for maximal hybridization concentration in many particle systems. We use both explicit computations with the Fokker-Planck equation for the probability distributions, and computer simulations for docking to targets. The parameters of our model can be derived from these theoretical values and fast Monte Carlo simulations. Knowledge of the proper incubation times in advance makes it possible to assess the feasibility of single detection systems, and gives optimal incubation times for quality assurance of a prescribed statistical error leading to cost reduction of such systems. There are many published results on measured data of various hybridization experiments. Our model is consistent with these observed values.
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