Computational modeling of biological molecule separation in nanofluidic devices

Abstract

Separation of biological molecules such as DNA and protein is of great importance for the chemical and pharmaceutical industries. In recent years, several researchers focused on fabricating patterned regular sieving nanostructures instead of using porous gel media to separate various types of biological molecules. Theoretical modeling of the separation process is very desirable for gaining fundamental understanding, device optimization and parameter exploration. Despite their small sizes, these devices contain a very large number of solvent molecules making ab-initio molecular modeling intractable. In other words, for an efficient model, some degree of coarse-graining is required. In this Thesis, we focus on the development of Brownian Dynamics (BD) simulation tools for modeling the performance of nanofluidic devices for the separation of short, Ogston-regime, dsDNA molecules. The first part of this Thesis focuses on the development of Brownian Dynamics models to predict the electrophoretic velocity of dsDNA molecules in nanoscale separation devices. The most general model developed here is based on the Worm-Like- Chain (WLC) model which includes the effects of bending and stretching stiffness and provides the most accurate mechanical description of the DNA molecule. The resulting Brownian Dynamics formulation includes hydrodynamic interactions within the molecule, and closely models the experimental set up of Fu et al. whose data are used for validation. For molecules that are sufficiently short (length on the order of, or smaller than, the persistence length), we developed a BD model which treats DNA molecules as rigid rods; this results in significantly reduced computational requirements. Finally, we present a further simplified BD model which treats the DNA molecules as point particles while accounting for their orientational degrees of freedom through an entropic energy barrier. This model is the most efficient and simplest to implement, but also is limited to short, essentially rigid molecules. Both the rigid-rod and the point particle model agree well with the experimental data of Fu et al. for appropriately short molecules. In the second part of this Thesis we present a variance reduction methodology for reducing the statistical uncertainty of Brownian Dynamics simulations. Our formulation is based on the recent method of Al-Mohssen and Hadjiconstantinou which uses importance weights within a control variate formulation. Variance reduction is achieved by subtracting the results of an equilibrium simulation using the same random numbers from the non-equilibrium results. Significant variance reduction is achieved for small electric fields, while very little additional computational cost is incurred.