Nabil Laachi

Continuous-time random walk models of DNA electrophoresis in a post array: Part II. Mobility and sources of band broadening†

Using the two‐state, continuous‐time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 μm posts with a 3 μm center‐to‐center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. On the contrary, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well described by a single post rope‐over‐pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device.

Statistics of tethered self-avoiding chains under spherical confinement and an external force

We compute the partition function of self-avoiding chains tethered inside a confining sphere using Monte Carlo simulations on a three-dimensional lattice. Two cases are considered: (i) single-tethered chains with one end anchored and one end free and (ii) double-tethered chains where both ends are tethered at a distance equal to the diameter of the sphere. The self-avoidance, confinement, and tethering constraints dramatically decrease the number of allowed configurations when compared with an unconstrained random coil, thereby affecting the sampling method used in the Monte Carlo procedure. The effect of an external applied force and the bias it introduces in the partition function are also investigated. Our method involves a decomposition of the partition function into the product of several terms that can be evaluated independently. For short chains, we demonstrate the validity of our approach through a direct evaluation of the partition function using an exact enumeration of the appropriate paths on the lattice. In the case of long chains, scaling laws for the behavior of the partition function are identified.

DNA Electrophoresis in Confined, Periodic Geometries: A New Lakes-Straits Model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimms approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.

Band Broadening During High-Throughput Mutation Detection in Microchannels

Cycling temperature gradient electrophoresis represents a promising method for performing high-throughput DNA mutation detection in a microfluidic platform. Sweeping the temperature between an “all denatured” and “all annealed” state eliminates difficulties introduced by the low thermal mass of the system, while still preserving a mobility difference between the wild type and mutant alleles. We describe a theoretical analysis of this method of mutation detection, based on a multiple-time scales analysis that is valid when the DNA experience many temperature cycles before reaching the detector [1]. We focus on the band-broadening incurred by the interplay between the relaxation time of the chemical system and the thermal oscillations. New results are presented for the case where the denaturing and annealing reactions proceed at identical rates. Our analysis indicates that this separation would be best operated at low electric fields.Copyright