Non-markovian transport of DNA in microfluidic post arrays

Tilted post arrays for separating long DNA

Recent simulations by Chen and Dorfman [Electrophoresis 35, 405-411 (2014)] suggested that "tilting" the electric field with respect to the lattice vectors of a hexagonal post array would lead to a substantial improvement in electrophoretic DNA separations therein. We constructed such an array where the electric field is applied at an angle equidistant between the two lattice vectors. This tilted array leads to (i) baseline resolution of 20 kbp DNA and λ DNA (48.5 kbp) in a 4 mm channel and (ii) measurable separation resolutions for electric fields up to 50 V/cm, both of which are improvements over untilted post arrays of the same post density. The predicted time required to reach a resolution of unity is approximately 5 min, independent of electric field. The separations are more reproducible at higher fields.

Comparison of microfabricated hexagonal and lamellar post arrays for DNA electrophoresis

We used Brownian dynamics simulations to compare DNA separations in microfabricated post arrays containing either hexagonal or lamellar lattices. Contrary to intuition, dense hexagonal arrays with frequent DNA post collisions do not yield the optimal separation. Rather, hexagonal arrays with pore sizes commensurate with the radius of gyration of the DNA lead to increased separation resolution due to a molecular weight dependent collision probability that increases with molecular weight. However, when the hexagonal array is too sparse, this advantage is lost due to the low number of collisions. Lamellar lattices, such as the DNA nanofence, appear to be superior to a hexagonal array at the same post density, since the lamellar lattice combines regions for DNA relaxation with locally dense post regions for collisions. The relative advantages of different post arrays designs are explained in terms of the statistics for the number of collisions and the holdup time, providing guidelines for designing post arrays for separating long DNA.

Relationship between frequency and deflection angle in the DNA prism

The DNA prism is a modification of the standard pulsed-field electrophoresis protocol to provide a continuous separation, where the DNA are deflected at an angle that depends on their molecular weight. The standard switchback model for the DNA prism predicts a monotonic increase in the deflection angle as a function of the frequency for switching the field until a plateau regime is reached. However, experiments indicate that the deflection angle achieves a maximum value before decaying to a size-independent value at high frequencies. Using Brownian dynamics simulations, we show that the maximum in the deflection angle is related to the reorientation time for the DNA and the decay in deflection angle at high frequencies is due to inadequate stretching. The generic features of the dependence of the deflection angle on molecular weight, switching frequency, and electric field strength explain a number of experimental phenomena.

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

We used top-down fabrication techniques to create both an ordered hexagonal array and a disordered array of 1 μm diameter cylindrical posts in a silicon dioxide microchannel with the same number of posts per unit area. The electrophoretic mobility and dispersion coefficient of λ DNA in each of the arrays were obtained as a function of the electric field using ensembles of DNA molecules in a double channel device that minimizes experimental artifacts. To deepen our understanding of the transport, we also used fluorescence microscopy to examine the dynamics of single DNA molecules as they interact with the arrays at a fixed value of the electric field. Based on the results of these two types of experiments, we conclude that the electrophoretic mobility is not dependent on the array order but that band broadening in the device is greater in the disordered array.

DNA electrophoresis in a nanofence array

We present the design and implementation of an oxidized silicon "nanofence array" for long DNA electrophoresis. The device consists of a periodic array of post-filled regions (the nanofences) alternating with empty channel regions. Even in this prototype version, the nanofence array provides the resolving power of a hexagonal nanopost array without requiring any direct-write nanopatterning steps such as electron-beam lithography. Through detailed single molecule investigations, we demonstrate that the origin of the resolving power of the nanofence array is not a reduction in band broadening, which might be expected from the theories for DNA electrophoresis in post arrays. Rather, the enhanced stretching of the hooked DNA by the uniform electric field between nanofences increases the efficiency of the collisions.

Hydrodynamic manipulation of DNA in nanopost arrays: unhooking dynamics and size separation

Micro- or nanofabricated obstacle arrays are widely used as model matrices to perform fast DNA separations by electrophoresis. In this report, a gallery of obstacles of radii spanning from 40 to 250 nm are used to investigate the dynamics of hydrodynamic-field-driven DNA-nanopost collisions at the single-molecule level. The data shows that DNA disengagement dynamics are reasonably well described by conventional electrophoretic models in the limit of a large spacing between obstacles and for moderate migration velocities. It is also demonstrated that the use of hydrodynamic flow fields to convey DNA molecules is associated with changes in the configurational space of hooking events, and to altered relaxation dynamics between consecutive collisions. This study defines experimental conditions for the efficient separation of DNA fragments of tens of base pairs, and provides a complete framework by which to understand the behavior of DNA in the course of hydrodynamic-driven migrations through nanopost arrays.

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.

DNA electrophoresis in a sparse ordered post array

We present a study of the electrophoresis of long DNA in a strong electric field through a hexagonal array of cylindrical microscale posts spaced such that the pore size is commensurate with equilibrium coil size of the DNA. Experimental mobility, dispersivity, and videomicroscopy data indicate that the DNA frequently collide with the posts, contradicting previous Brownian dynamics studies using a uniform electric field. We demonstrate via simulations that the frequent collisions, which are essential to separations in these devices, are due to the nonuniform electric field, highlighting the importance of accounting for electric-field gradients when modeling DNA transport in microfluidic devices.

Effect of the matrix on DNA electrophoretic mobility

DNA electrophoretic mobilities are highly dependent on the nature of the matrix in which the separation takes place. This review describes the effect of the matrix on DNA separations in agarose gels, polyacrylamide gels and solutions containing entangled linear polymers, correlating the electrophoretic mobilities with information obtained from other types of studies. DNA mobilities in various sieving media are determined by the interplay of three factors: the relative size of the DNA molecule with respect to the effective pore size of the matrix, the effect of the electric field on the matrix, and specific interactions of DNA with the matrix during electrophoresis.

DNA unhooking from a single post as a deterministic process: insights from translocation modeling

Using stochastic methods developed for DNA translocation through nanopores, we study the unhooking of a long DNA chain from an isolated stationary micropost. Such methods quickly and efficiently furnish both the full probability distribution of the unhooking time and the ensuing moments for a wide range of chain and field parameters. The results compare favorably to more realistic but computationally intense Brownian dynamics simulations. For typical chain lengths and applied electric fields used in experiments, the unhooking process is effectively deterministic; diffusive fluctuations make a negligible contribution to the first and second moments of the unhooking time. This result lends credence to continuous-time random-walk models of the overall transport process that treat the unhooking as a convective process.

Detection of FITC-cortisol via modulated supraparticle lighthouses

Hormones are important bioactive compounds in blood and tissue that vary in concentration in response to stress and certain disease states. Establishing the changes in physiological hormone concentrations over time can lead to more effective diagnoses and perhaps a better understanding of the evolution of stress and disease. To monitor concentration over time, the sampling must be rapid and noninvasive; specimens such as saliva that require little effort to collect are preferred. However, more sensitive assay techniques are needed when compared to blood analysis since free hormone concentration in saliva is only a small fraction of the concentration in circulating blood. In this work, magnetic field-induced structures of paramagnetic particles are used as a solid substrate to demonstrate improved detection limits for a separation-free assay of cortisol. Once formed, the structures are subjected to a rotating magnetic field and this leads to two important features. First is the ability to utilize frequency and phase filtering (lock-in amplification) for the signal generated from surface-bound labeled species. Second is the improved mass transport of the antigen to the surface of the rotating structures. These two unique capabilities result in a quantifiable signal at a relatively low target antigen concentration. This method has been demonstrated with the detection of fluorescein isothiocyanate-labeled cortisol (FITC-cortisol) at a concentration of 300 pM.

A Brownian dynamics-finite element method for simulating DNA electrophoresis in nonhomogeneous electric fields

The objective of this work is to develop a numerical method to simulate DNA electrophoresis in complicated geometries. The proposed numerical scheme is composed of three parts: (1) a bead-spring Brownian dynamics (BD) simulation, (2) an iterative solver-enhanced finite element method (FEM) for the electric field, and (3) the connection algorithm between FEM and BD. A target-induced searching algorithm is developed to quickly address the electric field in the complex geometry which is discretized into unstructured finite element meshes. We also develop a method to use the hard-sphere interaction algorithm proposed by Heyes and Melrose [J. Non-Newtonian Fluid Mech. 46, 1 (1993)] in FEM. To verify the accuracy of our numerical schemes, our method is applied to the problem of lambda-DNA deformation around an isolated cylindrical obstacle for which the analytical solution of the electric field is available and experimental data exist. We compare our schemes with an analytical approach and there is a good agreement between the two. We expect that the present numerical method will be useful for the design of future microfluidic devices to stretch and/or separate DNA.

DNA electrophoresis in microfluidic post arrays under moderate electric fields

The dynamics of long DNA moving through microfluidic arrays of micron-sized posts under a moderate electric field are modeled by a Scher-Lax continuous-time random walk. The microscale model consists of a repetitive sequence of three steps: (i) collision with the post and extension into two arms, (ii) electric-field-driven unhooking from the post, and (iii) uniform translation until the next collision. The model features two random variables: the initial offset between the two arms of the polymer during a given collision and the distance traveled between collisions. For experimentally realistic values of the electric field strength and DNA molecular weight, scaling laws indicate that the chain will generally be in a stem-flower conformation when unhooking from the post. Compared to a taut-chain model at the same field strength, the stem-flower conformation reduces the time engaged with the post and increases the collision frequency. Analytical expressions for the mean velocity and dispersivity are derived as a function of the post density, post spacing, free-solution mobility, Kuhn length, and sequence length. The incomplete extension of the chain does not strongly affect the mean velocity, but tends to increase the dispersivity relative to a taut chain. As a result, the separation resolution decreases as the field decreases for a moderate field, in agreement with experiments. The quantitative agreement between the model and experimental data is satisfactory, especially considering that the model contains no adjustable parameters.