Biomolecular motor-driven molecular sorter.

We have developed a novel, microfabricated, stand-alone microfluidic device that can efficiently sort and concentrate (bio-)analyte molecules by using kinesin motors and microtubules as a chemo-mechanical transduction machine. The device removes hundreds of targeted molecules per second from an analyte stream by translocating functionalized microtubules with kinesin across the stream and concentrating them at a horseshoe-shaped collector. Target biomolecule concentrations increase up to three orders of magnitude within one hour of operation.

Nanomechanical model of microtubule translocation in the presence of electric fields.

Research efforts in recent years have been directed toward actively controlling the direction of translocation of microtubules on a kinesin-coated glass surface with E-fields (electric fields), opening up the possibility of engineering controllable nanodevices that integrate microtubules and motor proteins into their function. Here, we present a detailed, biophysical model that quantitatively describes our observations on the steering of microtubules by electric fields. A sudden application of an electric field parallel to the surface and normal to the translocation direction of a microtubule bends the leading end toward the anode, because Coulombic (electrophoretic) forces are dominant on negatively charged microtubules. Modeling this bending as a cantilever deflection with uniform loading requires accurate mechanical and electrical properties of microtubules, including their charge density, viscous drag, and flexural rigidity. We determined the charge density of microtubules from measurements of the electrophoretic mobility in a "zero flow" capillary electrophoresis column and estimate it to be 256 e(-) per micron of length. Viscous drag forces on deflecting microtubules in electroosmotic flows were studied theoretically and experimentally by directly characterizing flows using a caged dye imaging method. The flexural rigidity of microtubules was measured by applying E-fields to microtubules with biotinylated segments that were bound to streptavidin-coated surfaces. From the calculated loading, and the Bernoulli-Euler curvature and moment equation, we find that the flexural rigidity of microtubules depends on their length, suggesting microtubules are anisotropic. Finally, our model accurately predicts the biophysical properties and behavior of microtubules directed by E-fields, which opens new avenues for the design of biomolecular nanotransport systems.

Theoretical and numerical analysis of temperature gradient focusing via Joule heating.

We present a detailed theoretical and numerical analysis of temperature gradient focusing (TGF) via Joule heating-an analytical species concentration and separation technique relying upon the dependence of an analyte's velocity on temperature due to the temperature dependence of a buffer's ionic strength and viscosity. The governing transport equations are presented, analyzed, and implemented into a quasi-1D numerical model to predict the resulting temperature, velocity, and concentration profiles along a microchannel of varying width under an applied electric field. Numerical results show good agreement with experimental trials presented in previous work. The model is used to analyze the effects of varying certain geometrical and experimental parameters on the focusing performance of the device. Simulations also help depict the separation capability of the device, as well as the effectiveness of different buffer systems used in the technique. The analysis provides rule-of-thumb methodology for implementation of TGF into analytical systems, as well as a fundamental model applicable to any lab-on-a-chip system in which Joule heating and temperature-dependent electrokinetic transport are to be analyzed.

Biomolecular motor-driven microtubule translocation in the presence of shear flow: modeling microtubule deflection due to shear.

We have previously demonstrated that shear flow aligns microtubules moving on kinesin-coated microchannels with the flow direction, and statistically analyzed the rate of microtubule alignment under different concentrations of kinesin as well as strengths of shear flow. These data qualitatively support the hypothesis that the alignment results from the leading ends of translocating microtubules bending into the direction of the flow due to viscous drag force. Here, we present a cantilever-beam model that quantitatively shows agreement between this hypothesis and observation. Specifically, the model couples the exact nonlinear solution for cantilever-beam deflection with drag coefficients determined by numerical simulations of microtubules in the presence of shear flow near a wall. Coupled with flexural rigidity results of our previous study (which used electric fields), the established model successfully predicts new experimental data for microtubule bending in response to shear flow, further supporting our hypothesis for the mechanism of microtubule alignment. We expect that the newly-calculated drag coefficients and beam-bending model may be useful for biophysical studies as well as interpretation of in vivo data and the design of kinesin/microtubule-based devices.

Active alignment of microtubules with electric fields.

The direction of translocation of microtubules on a surface coated with kinesin is usually random. Here we demonstrate and quantify the rate at which externally applied electric fields can direct moving microtubules parallel to the field by deflecting their leading end toward the anode. Effects of electric field strength, kinesin surface density, and microtubule translocation speed on the rate of redirection of microtubules were analyzed statistically. Furthermore, we demonstrated that microtubules can be steered in any desired direction via manipulation of externally applied E-fields.

Low-power concentration and separation using temperature gradient focusing via Joule heating.

We present an experimental study of temperature gradient focusing (TGF) exploiting an inherent Joule heating phenomenon. A simple variable-width PDMS device delivers rapid and repeatable focusing of model analytes using significantly lower power than conventional TGF techniques. High electric potential applied to the device induces a temperature gradient within the microchannel due to the channel's variable width, and the temperature-dependent mobility of the analytes causes focusing at a specific location. The PDMS device also shows simultaneous separation and concentration capability of a mixture of two sample analytes in less than 10 min. An experiment combining Joule heating with external heating/cooling further supports the hypothesis that temperature is indeed the dominant factor in achieving focusing with this technique.

Electrokinetic protein preconcentration using a simple glass/poly(dimethylsiloxane) microfluidic chip.

We discovered that a protein concentration device can be constructed using a simple one-layer fabrication process. Microfluidic half-channels are molded using standard procedures in PDMS; the PDMS layer is reversibly bonded to a glass base such as a microscope slide. The microfluidic channels are chevron-shaped, in mirror image orientation, with their apexes designed to pass within approximately 20 microm of each other, forming a thin-walled section between the channels. When an electric field is applied across this thin-walled section, negatively charged proteins are observed to concentrate on the anode side of it. About 10(3)-10(6)-fold protein concentration was achieved in 30 min. Subsequent separation of two different concentrated proteins is easily achieved by switching the direction of the electric field in the direction parallel to the thin-walled section. We hypothesize that a nanoscale channel forms between the PDMS and the glass due to the weak, reversible bonding method. This hypothesis is supported by the observation that, when the PDMS and glass are irreversibly bonded, this phenomenon is not observed until a very high E-field was applied and dielectric breakdown of the PDMS is observed. We therefore suspect that the ion exclusion-enrichment effect caused by electrical double layer overlapping induces cationic selectivity of this nanochannel. This simple on-chip protein preconcentration and separation device could be a useful component in practically any PDMS-on-glass microfluidic device used for protein assays.

Rapidly prototyped three-dimensional nanofluidic channel networks in glass substrates.

Microfluidic and nanofluidic technologies have long sought a fast, reliable method to overcome the creative limitations of planar fabrication methods, the resolution limits of lithography, and the materials limitations for fast prototyping. In the present work, we demonstrate direct 3D machining of submicrometer diameter, subsurface fluidic channels in glass, via optical breakdown near critical intensity, using a femtosecond pulsed laser. No postexposure etching or bonding is required; the channel network (or almost any arbitrary-shaped cavity below the surface) is produced directly from "art-to-part". The key to this approach is to use very low energy, highly focused, pulses in the presence of liquid. Microbubbles that result from laser energy deposition gently expand and extrude machining debris from the channels. These bubbles are in a highly damped, low Reynolds number regime, implying that surface spalling due to bubble collapse is unimportant. We demonstrate rapid prototyping of three-dimensional "jumpers", mixers, and other key components of complex 3D microscale analysis systems in glass substrates.

Timescales for relaxation to Boltzmann equilibrium in nanopores.

In most models for electrokinetic phenomena at charged interfaces, Boltzmann equilibrium is assumed to be established. Here we show that a long nanopore with significant double layer overlap establishes equilibrium quite slowly and that centimeter-long nanopores can take O(10(5)) s to establish Boltzmann equilibrium. The timescale is determined not by diffusion across the double layer, but by diffusion or convective transport along the length of the pore to reservoirs at its ends. An "intermediate equilibrium" state described by Qu and Li (J. Colloid Interface Sci. 224 (2000) 397) may exist for times between the (fast) EDL establishment timescale and (slow) axial transport timescale.

Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations.

This paper summarizes theory, experimental techniques, and the reported data pertaining to the zeta potential of silica and silicon with attention to use as microfluidic substrate materials, particularly for microchip chemical separations. Dependence on cation concentration, buffer and cation type, pH, cation valency, and temperature are discussed. The Debye-Hückel limit, which is often correctly treated as a good approximation for describing the ion concentration in the double layer, can lead to serious errors if it is extended to predict the dependence of zeta potential on the counterion concentration. For indifferent univalent electrolytes (e.g., sodium and potassium), two simple scalings for the dependence of zeta potential on counterion concentration can be derived in high- and low-zeta limits of the nonlinear Poisson-Boltzman equation solution in the double layer. It is shown that for most situations relevant to microchip separations, the high-zeta limit is most applicable, leading to the conclusion that the zeta potential on silica substrates is approximately proportional to the logarithm of the molar counterion concentration. The zeta vs. pH dependence measurements from several experiments are compared by normalizing the zeta based on concentration.

Zeta potential of microfluidic substrates: 2. Data for polymers.

Zeta potential data are reviewed for a variety of polymeric microfluidic substrate materials. Many of these materials currently used for microchip fabrication have only recently been employed for generation of electroosmotic flow. Despite their recent history, polymeric microfluidic substrates are currently used extensively for microchip separations and other techniques, and understanding of the surface zeta potential is crucial for experimental design. This paper proposes the use of pC (the negative logarithm of the counterion concentration) as a useful normalization for the zeta potential on polymer substrates in contact with indifferent univalent counterions. Normalizing zeta by pC facilitates comparison of results from many investigators. The sparseness of available data for polymeric substrates prevents complete and rigorous justification for this normalization; however, it is consistent with double layer and adsorption theory. For buffers with indifferent univalent cations, normalization with the logarithm of the counterion concentration in general collapses data onto a single zeta/pC vs. pH curve, and (with the exception of PMMA) the repeatability of the data is quite encouraging. Normalization techniques should allow improved ability to predict zeta potential performance on microfluidic substrates and compare results observed with different parameters.

Voltage-addressable on/off microvalves for high-pressure microchip separations.

We present a microchip-based, voltage-addressable on/off valve architecture that is fundamentally consistent with the pressures and solvents employed for high-pressure liquid chromatography. Laser photopatterning of polymer monoliths inside glass microchannels is used to fabricate mobile fluid control elements, which are opened and closed by electrokinetic pressures. The glass substrates and crosslinked polymer monoliths operate in water-acetonitrile mixtures and have been shown to hold off pressures as high as 350 bar (5000 p.s.i.). Open/closed flow ratios of 10(4) to 10(6) have been demonstrated over the pressure range 1.5-70 bar (20-1000 p.s.i.), and the pressure-leak relationship shows the potential for valving control of flow through packed or monolithic chromatography columns. We expect that this valve platform will enable multiplexing of multiple chromatographic separations on single microchips.

High-pressure microfluidic control in lab-on-a-chip devices using mobile polymer monoliths.

We have developed a nonstick polymer formulation for creating moving parts inside of microfluidic channels and have applied the technique to create piston-based devices that overcome several microfluidic flow control challenges. The parts were created bycompletely filling the channels of a glass microfluidic chip with the monomer/ solvent/initiator components of a nonstick photopolymer and then selectively exposing the chip to UV light in order to define mobile pistons (or other quasi-two-dimensional shapes) inside the channels. Stops defined in the substrate prevent the part from flushing out of the device but also provide sealing surfaces so that valves and other flow control devices are possible. Sealing against pressures greater than 30 MPa (4,500 psi) and actuation times less than 33 ms are observed. An on-chip check valve, a diverter valve, and a 10-nL pipet are demonstrated. This valving technology, coupled with high-pressure electrokinetic pumps, should make it possible to create a completely integrated HPLC system on a chip.