Mathematical modelling and computer simulation of Brownian motion and hybridisation of nanoparticle–bioprobe–polymer complexes in the low concentration limit

Abstract

A wide variety of nano-biotechnological applications are being developed for nanoparticles based on in vitro diagnostic and imaging systems. Some of these systems allow highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes very difficult the mathematical simulation of the motion of nanoparticles based on classical, partial differential equations. We address the issue of incubation times for low concentration systems using Monte Carlo simulations. We describe a mathematical model and computer simulation of Brownian motion of nanoparticle–bioprobe–polymer contrast agent complexes and their hybridisation to immobilised targets. We present results for the dependence of incubation times on the number of particles available for detection, and the geometric layout of the DNA-detection assay on the chip.

Keywords:

• Brownian motion
• first passage time
• incubation time
• hybridisation
• Monte Carlo simulation

Acknowledgement

The authors acknowledge the partial support of an OTKA grant CNK-77780 and EU FP7 project ‘NANO-MUBIOP’.