Biomolecular Sensing Processing and Analysis - Rashid Bashir and Steve Wereley

for studying all reactions. Furthermore, it is a label-free approach, which can be easily multiplexed to study thousands of reactions simultaneously. In this chapter, we discuss the latest developments in the technology of cantilever arrays and how it can be used to study specific biomolecular reactions involving nucleic acids and proteins.

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3

An On-Chip Artificial Pore for Molecular Sensing

O. A. Saleh1 and L. L. Sohn2

1 Laboratoire de Physique Statistique, Ecole Normale Superieure,´ Paris, France 2 Dept. of Mechanical Engineering, University of California, Berkeley, CA. USA

3.1. INTRODUCTION

Currently, a variety of strategies for developing nanopores for molecular sensing exist— from engineering transmembrane protein pores so that they can detect sequence-specific DNA strands with single-base resolution [1, 2] to “drilling” molecular-scaled holes into silicon nitride membranes to detect the presence of single molecules of DNA [3, 4] to employing gold [5] or carbon [6] nanotubes as the ultimate artificial pores. While all of these strategies have shown early success in molecular sensing, there are major technological hurdles one must overcome: reproducibly creating an effective pore, maintaining a pore’s stability over a period of time, and integrating the pore into a device that is inexpensive and easy to fabricate and use. Here, we describe our group’s effort in developing a fullyintegrated artificial pore on chip for molecular sensing. As we will demonstrate, our pore addresses the technological hurdles with which other nanopore strategies are confronted. Equally important, we will show that our on-chip artificial pore is a flexible platform technology that has a number of diverse applications—from label-free immunoassays to single-molecule DNA sizing.

3.2. THE BASIC DEVICE: FABRICATION AND MEASUREMENT

The on-chip artificial pore we have developed is based on the Coulter counter technique of particle sizing [7]. Coulter counters typically consist of two reservoirs of particle-laden solution separated by a membrane and connected by a single pore through that membrane.

depositions of 50 Å/250 Å Ti/Pt in an electron-beam evaporator with the sample positioned 45 degrees from normal to the flux of metal to ensure that the electrodes are continuous down both walls of the reservoirs.

The device is sealed on top with a silicone-coated (Sylgard 184, Dow Corning Corp.) glass coverslip before each measurement. Prior to sealing, both the silicone and the substrate are oxidized in a DC plasma to insure the hydrophilicity [13] of the reservoir and pore and to strengthen the seal [14] to the quartz substrate. After each measurement, the coverslip is removed and discarded, and the substrate is cleaned by chemical and ultrasonic methods. Thus, each device can be reused many times.

3.2.2. Pore Measurement

We have measured solutions of negatively-charged (carboxyl-coated) latex colloids (Interfacial Dynamics, Inc.) whose diameters range from 87 nm to 640 nm using the device we just described. All colloids were suspended in a solution of 5x concentrated TBE buffer with a resistivity of 390 -cm and pH 8.2. To reduce adhesion of the colloids to the reservoir and pore walls, we added 0.05% v/v of the surfactant Tween 20 to every solution. The colloidal suspensions were diluted significantly from stock concentrations to avoid jamming of colloids in the pore; typical final concentrations were 108 particles/mL. The pore and reservoirs were filled with solution via capillary action.

The sensitivity of a Coulter counter relies upon the relative sizes of the pore and the particle to be measured. The resistance of a pore R p increases by δ R p when a particle enters since the particle displaces conducting fluid. δ R p can be estimated [9] for a pore aligned along the z-axis (see Fig. 3.2) by

where A(z) represents the successive cross sections of the pore containing a particle, and ρ is the resistivity of the solution. For a spherical particle of diameter d in a pore of diameter D and length L, the relative change in resistance is

Eqs. (3.1) and (3.2) assume that the current density is uniform across the pore, and thus is not applicable for cases where the cross section A(z) varies quickly, i.e. when d D. For that particular case, Deblois and Bean [10] formulated an equation for δ R p based on an approximate solution to the Laplace equation:

where F (d3/D3) is a numerical factor that accounts for the bulging of the electric field lines into the pore wall. When employing Eq. (3.3) to predict resistance changes, we find

FIGURE 3.2. Relative changes in baseline current δI/I vs time for (a) a monodisperse solution of 87 nm diameter latex colloids measured with an EBL-defined pore of length 8.3 µm and cross section 0.16 µm2, and (b) a polydisperse solution of latex colloids with diameters 460, 500, 560, and 640 nm measured with a PL-defined pore of length 0.5 µm and cross section 1.2 µm2. Each downward pulse represents an individual particular entering the pore. The four distinct pulse heights in (b) correspond as labeled to the four different colloid diameters. [From Ref. 12.]

an effective value for D by equating the cross sectional area of our square pore with that of a circular pore.

If R p is the dominant resistance of the measurement circuit, then relative changes in the current I are equal in magnitude to the relative changes in the resistance, |δ I /I | = |δ R p /R p |, and Eqs. (3.2) and (3.3) can both be directly compared to measured current changes. This comparison is disallowed if R p is similar in magnitude to other series resistances, such as the electrode/fluid interfacial resistance, Re/ f , or the resistance Ru of the reservoir fluid between the inner electrodes and the pore. We completely remove Re/ f from the electrical circuit by performing a four-point measurement of the current (see Fig. 3.1a). We minimize Ru by placing the inner electrodes close to the pore (50 µm away on either side), and by designing the reservoir with a cross section much larger than that of the pore. For a pore of dimensions 10.5 µm by 1.04 µm2 we measured R p = 36 M , in good agreement with the 39 M value predicted by the pore geometry and the solution resistivity. This confirms that we have removed Ru and Re/ f from the circuit.

Fig. 3.2 shows representative data resulting from measuring a monodisperse solution of colloids 87 nm in diameter with an EBL-defined pore (Fig. 3.1a), and from measuring a polydisperse solution containing colloids of diameters 460 nm, 500 nm, 560 nm, and 640 nm with a PL-defined pore (Fig. 3.1b). Each downward current pulse in Fig. 3.2, corresponds to a single colloid passing through the pore. For the data shown, 0.4 V was applied to the pore. In other runs, the applied voltage was varied between 0.1 and 1 V to test the electrophoretic response of the colloids. We found that the width of the downward current pulses varied

FIGURE 3.3. A histogram of pulse heights resulting from measuring the polydisperse solution shown in Figure 3.2(b). The resolution of this particular device is ±10 nm in diameter for the particles measured. [From Ref. 12.]

approximately as the inverse of the applied voltage, as is expected for simple electrophoretic motion.

Fig. 3.3 shows a histogram of 3000 events measured for the polydisperse solution. The histogram shows a very clear separation between the pore’s response to the differentlysized colloids. The peak widths in Fig. 3.3 represent the resolution of this device, which we find to be ±10 nm in diameter for the measured colloids. This precision approaches the intrinsic variations in colloid diameter of 2–4%, as given by the manufacturer. In this run, the maximum throughput was 3 colloids/s, a rate easily achievable for all of our samples. Event rates are limited by the low concentrations needed to avoid jamming.

We used a device whose pore size was 10.5 µm by 1.04 µm2 to measure colloids ranging from 190 nm to 640 nm in diameter. Figure 3.4 shows the comparison between the measured mean pulse heights and those predicted by Eqs. (3.2) and (3.3). As shown, there is excellent agreement between the measured and calculated values, with the measured error insignificant compared to the range of pulse heights. In addition, the measurements more

FIGURE 3.4. Comparison of measured δI/I values (circles) those predicted by Eq. (3.2) (dotted line) and Eq. (3.3) (dashed line). The measured data were taken over several runs on a single PL-defined pore of length 10.6 µm and cross section 1.04 µm2. Error bars for the larger colloid sizes are obscured by the size of the plotted point. As the colloid diameter increases, there is a transition from agreement with Eq. (3.3) to Eq. (3.2). This reflects the fact that the derivation of Eq. (3.3) assumes the colloid diameter d is much less than the pore diameter D; conversely Eq. (3.2) relies on an assumption that holds only as d approaches D, and breaks down for smaller colloids. [From Ref. 12.]

FIGURE 3.6. Schematic of the measurement geometry for a pore of diameter D and length L containing a colloid of diameter d that travels a distance b off the pore axis. Inset: Typical trace of the measured resistance vs time showing the passage of a single colloid that produces a resistance pulse of width τ and height R. [From Ref. 16.]

size that travel on-axis, off-axis particles take longer to transit the pore (causing wider pulses) and produce larger electrical resistance changes. The former effect, which we refer to as the hydrodynamic off-axis effect, is simply due to the parabolic distribution of fluid velocity within the pore. The latter effect, which we refer to as the electrical off-axis effect, occurs because off-axis particles enhance the non-uniformity in the distribution of electrical current density and consequently increase further the electrical resistance. Here, we discuss two main results [16]: first, we show how off-axis particles affect data taken on populations of colloidal particles and propose a method to remove these effects. Second, we point out that a device utilizing pressure-driven flow will have an increased resolution over one using electrophoretic flow, since the algorithm we have developed to remove off-axis effects can only be performed for pressure-driven flow. As we will demonstrate, both results should increase the precision of the resistive-pulse technique in future applications.

To describe quantitatively our data, we follow the work of Berge et al. [17] who formulated phenomenological equations to describe the two aforementioned off-axis effects. For the hydrodynamic effect, they found that previous experimental data [18] on the time τ for a particle to pass through the pore are well described by

where τ0 = 16η(L/D)2/ P is the on-axis transit time for an infinitely small particle, η is the fluid viscosity, L is the pore length, D is the pore diameter, P is the pressure drop across the pore, x = 2b/D is the fractional radial position for a particle centered a distance b off of the pore axis, c1 = 1 − (2/3)(d/D)2, c2 = 23.36(1 − c1), and d is the particle diameter (see Fig. 3.6). Berge et al. [17] then utilized Eq. 3.4 to describe empirically the variation in the change in electrical resistance R with an off-axis coordinate x as

where R0(d, D, L) is the change in resistance for the on-axis particle (see Ref. 18 for its functional form) and α is a constant whose value varies between 4.2 and 7.5.