DNA electrophoresis in microfabricated devices

Kevin D. Dorfman

Rev. Mod. Phys. 82, 2903 – Published 6 October 2010

Abstract

Picking up at the conclusion of Viovy’s review of the physics of gel electrophoresis [J.-L. Viovy, Rev. Mod. Phys. 72, 813 (2000)], this review synthesizes the experimental data, theoretical models, and simulation results for DNA electrophoresis in microfabricated and nanofabricated devices appearing since the seminal paper by Volkmuth and Austin [Nature (London) 358, 600 (1992)]. Prototype versions of these devices separate DNA by molecular weight at a rate far superior to gel electrophoresis. After providing an overview of the requisite background material in polymer physics, electrophoresis, and microfluidic device fabrication, the focus is on the following three generic problems: (i) collision with an isolated post, (ii) transport in an array of posts, and (iii) entropic trapping and filtration in the slit-well motif. The transport phenomena are examined here in the context of the length and time scales characterizing the DNA, the device, and the applied electric field.

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DOI:https://doi.org/10.1103/RevModPhys.82.2903

Authors & Affiliations

Kevin D. Dorfman^*

Department of Chemical Engineering and Materials Science, University of Minnesota–Twin Cities, Minneapolis, Minnesota 55455, USA

^*dorfman@umn.edu

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Vol. 82, Iss. 4 — October - December 2010

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Images

Figure 1
(Color online) Coarse-grained picture of DNA in free solution. Depending on the length scale of interest, we treat the DNA as (a) a coil of radius of gyration $R_{g}$ at the largest scale, (b) a collection of beads connected by springs at intermediate scales, or (c) a connection of $N_{k}$ rigid segments of Kuhn length $l_{k} \approx 300 bp$ at the smallest scale. In order for the bead-spring description to be valid, each bead-spring pair must consist of a number of Kuhn segments.Reuse & Permissions
Figure 2
Free solution velocity as a function of $N_{bp}^{- 0.6}$ , where $N_{bp}$ is the number of base pairs. Adapted from 234.Reuse & Permissions
Figure 3
Experimental measurements of the free-solution electrophoresis of DNA during capillary electrophoresis. (Top) Free solution velocity as a function of the electric field for different sized DNA. (Bottom) Diffusion coefficient as a function of DNA length for different electric fields. From 164.Reuse & Permissions
Figure 4
(Color online) Schematic illustration of biased reptation during gel electrophoresis of DNA. The gel fibers confine the DNA of contour length $L$ to a tube of radius $a$ and length $L_{tube}$ . The projection of this tube in the direction of the electric field is $h_{x}$ . The blowup shows the blobs of DNA present in the shaded region of the chain. Each blob contains ${(a ∕ l_{k})}^{2}$ Kuhn segments.Reuse & Permissions
Figure 5
Electrophoretic mobility of different sized DNA in a 1.5% agarose gel as a function of the electric field. From 93.Reuse & Permissions
Figure 6
(Color online) Electrophoretic mobility for different degrees of polymerization $N$ of linear and star samples of polystyrene sulfonate. The circles and squares are different star samples; the linear samples are the + symbols. The inset shows the principle behind entropic trapping when the pore size $a$ is commensurate with the radius of gyration, $R_{g}$ . Data from 226.Reuse & Permissions
Figure 7
(Color online) Schematic overview of device fabrication. (a) Conventional microfabrication in silicon and glass. To provide high-resolution features, these systems usually use a positive photoresist. Exposed positive resist is removed during the developing stage. Oxidation is required for silicon substrates to prevent conduction through the silicon. (b) PDMS microfabrication. The negative photoresist SU-8 is commonly used; the exposed SU-8 remains after the developing step. The PDMS is normally oxidized in a plasma to render it hydrophilic and make a strong seal to glass. The first step of this figure is optical lithography, which is useful for producing features larger than $1 μ m$ . For smaller-scale features, electron-beam lithography, and nanoimprint lithography, among other methods, can replace the first step.Reuse & Permissions
Figure 8
(Color online) Self-assembly of superparamagnetic beads. (a) In the absence of a magnetic field, the beads form a homogenous suspension of particles. (b) In the presence of the magnetic field, the beads assemble into a quasihexagonal array of posts. The scale bar is $10 μ m$ . The schematic on top is complements of Michel Gauthier; the experimental images below are from 149.Reuse & Permissions
Figure 9
Colloidal crystal of $2 μ m$ polystyrene spheres packed by evaporation from the exit of a PDMS microchannel. The scale bar is $10 μ m$ and arrows indicate point defects. From 256.Reuse & Permissions
Figure 10
Visualization of the post-collision process for T4-DNA colliding with a $0.8 μ m$ radius PDMS post at a Péclet number $Pe = 8$ [see Eq. (28)]. The center-of-mass position is measured in the direction of the electric field (from left to right in the images). The hold-up time $t_{H}$ is computed from the offset between the slopes of the trajectories in the two regimes where the DNA moves with the free-solution mobility $μ_{0} E$ . The first open circle and its image correspond to the point where the DNA is wrapped around the post and reaches complete extension. The second open circle and its image correspond to the conformation of the DNA when it is released from the post. From 188.Reuse & Permissions
Figure 11
(Color online) Schematic of the rope-over-pulley collision for an extended chain. The instantaneous difference in length between the two arms is denoted $χ (t)$ and the length of the short arm is $χ_{1} (t)$ . The time $t = 0$ is the start of the unhooking process. An $(x, y)$ Cartesian coordinate system is fixed on the center of the obstacle such that the net DNA motion is in the $- x$ direction.Reuse & Permissions
Figure 12
(Color online) Unhooking dynamics for different length chains from molecular-dynamics simulations. The number $N$ is the number of beads used to represent the chain. The axis labels have been converted to the present notation assuming that the chain friction is independent of the chain conformation. From 108.Reuse & Permissions
Figure 13
(Color online) Visualization of the W collision of T4-DNA with a $0.8 μ m$ radius post at $Pe = 8$ . From 188.Reuse & Permissions
Figure 14
(Color online) Schematic depiction of an X collision. The length of the short arm is $χ_{1} (t)$ .Reuse & Permissions
Figure 15
(Color online) Plot of the hold-up time as a function of (a) the initial dimensionless offset between the two arms and (b) the initial dimensionless length of the short arm for T4-DNA colliding with a $0.8 μ m$ radius PDMS post at a Péclet number $Pe = 8$ . The circles are U/J collisions, the open squares are X collisions, and the stars are W collisions. The solid line in (a) is Eq. (32) and the line in (b) is Eq. (33). Data from 188.Reuse & Permissions
Figure 16
Universal scaling of the dimensionless collision time $⟨ t_{c} ⟩ μ_{0} E ∕ L$ vs the impact parameter for a point-sized post. In converting from the notation of 208 to the present one, we assumed the numerical constant $A = 1$ and that the degree of polymerization $N$ is equivalent to the contour length $L$ . From 208.Reuse & Permissions
Figure 17
Plot of the probability of $λ$ -DNA hooking with a $0.8 μ m$ radius post as a function the scaled impact parameter $b ∕ R_{g}$ for different values of the Deborah number De from (a) experiment and (b) Brownian dynamics simulations. The point-sized limit agrees with 208. From 185.Reuse & Permissions
Figure 18
Collision of $λ$ -DNA with a large insulating post. (a) Extension at $De = 2$ in $1.3 cP$ buffer. Time step $Δ t$ between frames is $0.17 s$ unless noted. (b) Extension at $De = 9$ in $6 cP$ buffer. The time step between frames is $0.33 s$ unless noted. In both images, the DNA motion is from right to left. From 186.Reuse & Permissions
Figure 19
(Color online) Schematic of the different types of dynamics in a post array as a function of the size of the obstacles and the gap between obstacles. These regimes are only valid for a time-independent electric field. For clarity, a representative trajectory is included for the small DNA molecule during Ogston sieving in an array of large posts.Reuse & Permissions
Figure 20
(Color online) Steps in the geometration process in an array of small posts with small gaps.Reuse & Permissions
Figure 21
(Color online) Schematic of a continuous-time random-walk model for DNA electrophoresis in a post array. The numbers indicate different points in time during the cyclic process. The hexagonal array has a center-to-center spacing $a$ and post diameter $d$ . The DNA radius of gyration $R_{g}$ is indicated. The excluded row parameter $n^{*}$ is defined in Eq. (57). The role of the highlighted channel in a sparse array is discussed in Sec. 4A4.Reuse & Permissions
Figure 22
(Color online) Electrophoretic mobility as a function of the electric field in an array of $1.2 μ m$ diameter PDMS posts in a hexagonal array with spacing $a = 3 μ m$ . The solid squares correspond to the experimental data, the circles correspond to Brownian dynamics simulations using a nonuniform electric field, and the open squares correspond to Brownian dynamics simulations using a uniform electric field. Data from 178.Reuse & Permissions
Figure 23
Videomicroscopy images of $λ$ -DNA and T4-DNA in a nanopost array under an electric field of $7 V ∕ cm$ . From 105.Reuse & Permissions
Figure 24
(Color online) Histogram of the relative electrophoretic velocity before and after collisions of T4-DNA in a magnetic bead array at a macroscopic electric field $E = 26.8 V ∕ cm$ . The inset is a schematic of a trajectory of a DNA molecule’s center of mass $x_{com}$ as a function of time. The speed before the collision is computed from the slope of the trajectory prior to the plateau (the collision); the speed after the collision is computed from the slope of the trajectory after the plateau. Adapted from 149.Reuse & Permissions
Figure 25
(Color online) Brownian ratchet separation in a post array. (a) Schematic illustration of the principle behind the separation. (b) Illustration of the transport of a small (left) and large (right) particles approaching the gap between the obstacles. (c) Separation of $λ$ and T2 $(164 kbp)$ DNA in an optimal system. (a) From 70 by Michel Gauthier, (b) from 100, and (c) from 98.Reuse & Permissions
Figure 26
Videomicroscopy data for $λ$ -DNA moving in a hexagonal array of $10 μ m$ high, $15 μ m$ diameter PDMS pillars with a minimum separation distance of $1 μ m$ under a nominal electric field of $50 V ∕ cm$ . The post boundaries, which do not appear in fluorescence, are added for clarity. From 102.Reuse & Permissions
Figure 27
Second-generation anisotropic array for continuous separation by entropic trapping, size exclusion, or electrostatic exclusion. The insets show different portions of the device and different zoom levels. The gaps between the posts are different in the vertical and horizontal directions. By applying the average electric field at an angle to the lattice vectors of the array, the DNA moves freely in the vertical direction but can make horizontal jumps. Depending on the size of the gap, the jump frequency is due to entropic trapping, steric hindrances, or charge exclusion (see Sec. 5). From 139.Reuse & Permissions
Figure 28
(Color online) Schematic illustration of the switchback mechanism in a post array. The gray shaded region corresponds to the electric field direction $E_{1}$ and the clear region corresponds to an electric field rotated by the angle $θ$ . The symbols $h$ and $t$ refer to the head and tail of the chain for a given electric field direction.Reuse & Permissions
Figure 29
Continuous separation in the DNA prism. (a) Schematic illustration of the separation mechanism for a DNA prism. (b)–(d) Separation results for (1) 61, (2) 114, (3) 158, and (4) $209 kbp$ in a hexagonal array of $2 μ m$ diameter posts with a gap of $2 μ m$ . Image (b) corresponds to $250 ms$ square pulse of 32 and $20 V ∕ cm$ alternating at $2 Hz$ . Images (c) and (d) correspond to $40 ms$ square pulses of 240 and $150 V ∕ cm$ alternating at $12.5 Hz$ . From 101.Reuse & Permissions
Figure 30
(Color online) Principle behind an entropic recoil separation of different sized DNA in a dense post array under a pulsed electric field. Adapted from 23.Reuse & Permissions
Figure 31
(Color online) Schematic illustration of the slit-well motif. The relevant geometric length scales and electric field strengths are indicated. The deep region (the well) is generally larger than the equilibrium size the DNA in the device.Reuse & Permissions
Figure 32
Elution time as a function of molecular weight for $d_{w} = 1.8 μ m$ , $d_{s} = 75 nm$ , $l_{s} = l_{w} = 2 μ m$ , and $E = 80 V ∕ cm$ in a second-generation device developed by 89. The black circles and gray squares correspond to experiments performed with two different DNA ladders. The scaling law is based on Eq. (70) assuming that $t_{travel}$ is independent of $N_{k}$ (253). Data from 89.Reuse & Permissions
Figure 33
Probability of end-first (linear) hairpin to linear or hairpin insertion as a function of the chain size using the model of 253 with a dimensionless force of 0.08 and slit width of 1.5. From 253.Reuse & Permissions
Figure 34
Plot of the trapping time for $λ$ -DNA as a function of the inverse of the electric field for entropic trap arrays with different pitches. From 91.Reuse & Permissions
Figure 35
Normalized velocities (relative to a typical velocity in the dc separation regime) as a function of the time ratio $r_{t} = t_{1} ∕ t_{2}$ for the dimensionless electric field $ϵ_{1}$ and electric field ratio $ϵ_{2} = - r_{ϵ} ϵ_{1}$ . The inset shows two representative trajectories. From 240.Reuse & Permissions
Figure 36
(Color online) Schematic illustration of filtration of small rigid DNA by size in a slit-well motif, the so-called nanofilter. At low electric fields, the reduced configurational entropy in the slit leads to an effective partitioning between the two regimes. At high electric fields, the torque due on a molecule near the partition governs the separation.Reuse & Permissions

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