Continuous‐time random walk models of DNA electrophoresis in a post array: Part I. Evaluation of existing models

Abstract

Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.

Tilted post arrays for separating long DNA

“…This concordance further underscores the quality of the simulation model, as evidenced in previous work. 18 While we expect that the device should continue to reach unity resolution at a reasonable length even up to 50 V/cm, we did not observe the exponential decay in the required time as a function of electric field that was seen in simulations. 24 Rather, to within the experimental error, the time required to reach R ¼ 1 should be approximately 300 s. This is clearly much improved over the untilted post array, which requires around 10-15 min to reach the same resolution for this range of molecular weights.…”

“…In the latter cases, the analytes tend to move at an angle with respect to the driving force, a method known as deterministic lateral displacement. 54 Since the DNA loses memory of its previous transport upon collision with a post, 18 it is not deflected by the post and thus does not exhibit deterministic lateral displacement. Rather, the separation proceeds in a manner similar to the separation in a conventional post array, with the DNA all moving in the direction of the applied voltage drop.…”

“…3 Unfortunately, due to the slow migration of long DNA in the net direction of the applied field, pulsed field separations take hours to days to achieve a baseline separation; 3 this time is compared to minutes needed to separate long DNA in post arrays. [4][5][6] Regular arrays of micro-and nano-sized posts, fabricated by semiconductor methods, have been the subject of substantial experimental work [6][7][8][9][10][11][12][13][14][15][16][17][18][19] using a wide variety of materials, post sizes, and post spacing. In addition to microfabricated arrays with perfectly ordered features, results also exist for self-assembled magnetic beads, 4,5,20 which form quasihexagonal arrays, microfabricated arrays with intentional disorder, 21 and nanowire-based posts.…”

“…24 The model used for these simulations has been well parameterized with post array experiments and has been shown to match single molecule experiments in normal hexagonal post arrays very well. 18 To date, Brownian dynamics simulations 24 are the only evidence supporting the efficacy of tilted post arrays compared to their untilted counterparts. In the present contribution, we test these simulation results by experiments in a post array with a 15 tilt, as illustrated in Fig.…”

Experimental study of the effect of disorder on DNA dynamics in post arrays during electrophoresis

“…Moreover, Brownian dynamics simulations that included the perturbations in the electric field caused by insulating posts matched the experimentally measured electrophoretic mobility [17,18], indicating that the disturbance in the electric field due to the posts qualitatively alters the transport in this relatively tight array. These experiments and simulations showed that DNA makes enough collisions in an ordered array to yield a size based separation [19].…”