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1.
Matrix A with characteristic polynomial Q(z) is defined positive or negative Hurwitz according to whether Q(z) or Q(-z) is a Hurwitz polynomial. Leading principle sections of the Tikhonova growth matrix have associated characteristic polynomials Pn(-z) which satisfy the recursionThat the Tikhonova growth matrix is negative Hurwitz is established through applying the Wall-Stieltjes theory of continued fraction expansions to show the Pn(-z) are Hurwitz polynomials. The Kayeya-Enestrom theorem and a procedure for refinement of the Gerschgorin estimate are used to obtain analytical bounds on spectral radii for the Tikhonova model, which provides estimates of maximal growth rates. The theory allows generalization to more complicated growth models. 相似文献
2.
Mathematical results are derived, which enable one to find a vector of parameters k0 such that (P1(s,k0)?H)∩(P2(k0)=0), where P1(s,k) is a polynomial in s and in the components of k,P2(k) is a polynomial in the components of k, and H is the set of Hurwitz polynomials. The algorithm is based on an extension of the root locus technique to the multiparameter case. The design problem of coupling networks between a resistive generator and a passive load, under prescribed power gain characteristics, is translated into the above formulation. A numerical example is provided. 相似文献
3.
Shih-Feng YangChyi Hwang 《Journal of The Franklin Institute》2002,339(2):129-144
In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p0(s)+λp1(s), where λ∈[0,1] and p0(s) and p1(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure. 相似文献
4.
P.A. Lee 《Journal of The Franklin Institute》1979,307(6):331-339
For the following mixed bivariate probability distribution between a discrete random variable X and a continuous random variable Λ: where α, β > 0, 0 < p = 1 ? q < 1, x=0,1,2,...,a canonical expansion is obtained in terms of the Laguerre and Meixner orthogonal polynomials. The chance mechanisms giving rise to this mixed bivariate distribution are also discussed. 相似文献
5.
《Journal of The Franklin Institute》2002,339(6-7):521-528
Basic properties of a new class of strictly positive real (SPR) functions are stated. Four problems are studied. The first deals with SPR preservation of transfer functions, obtained under the composition of polynomials with SPR0 functions. The second deals with Hurwitz stability preservation of the numerator of transfer functions, obtained under the composition of polynomials with SPR0 functions. The third deals with making a Hurwitz closed-loop plant, an SPR0 function by substituting s by SPR0 functions. The four deals with the synthesis of simultaneous SPR feedback plants. For the new class of SPR0 functions, a characterization is presented. For the first and second problems, sufficient conditions are presented using the new class of SPR0 functions. For the third and four problems, two examples are presented, the first being for simultaneous SPR closed-loop systems via constant controllers. The second is for simultaneous stabilization via universal feedback adaptive control. 相似文献
6.
V. Ramachandran C.S. Gargour M. Ahmadi M.T.H. Boraie 《Journal of The Franklin Institute》1984,318(6):407-413
In this paper we present an alternative approach to the direct design of 1-D recursive digital filters satisfying prescribed magnitude specifications with or without constant group delay characteristic. This method uses an iterative method to calculate the coefficients of the filter's transfer function and guarantees the stability of the designed filter using a new stability test reported by Ramachandran and Gargour. To illustrate the usefulness of the technique, examples are given. 相似文献
7.
Large-library fluorescent molecular arrays remain limited in sensitivity (1 × 106 molecules) and dynamic range due to background auto-fluorescence and scattering noise within a large (20–100 μm) fluorescent spot. We report an easily fabricated silica nano-cone array platform, with a detection limit of 100 molecules and a dynamic range that spans 6 decades, due to point (10 nm to 1 μm) illumination of preferentially absorbed tagged targets by singular scattering off wedged cones. Its fluorescent spot reaches diffraction-limited submicron dimensions, which are 104 times smaller in area than conventional microarrays, with comparable reduction in detection limit and amplification of dynamic range.Commercially available fluorescent micro-arrays based on target labeling, northern blot, or enzyme-linked immunosorbent assay (ELISA) are limited to a detection threshold of 1 to 10 × 106 molecules per fluorescent spot,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 thus requiring cell culturing or Polymerase Chain Reaction (PCR) amplification for many applications. The low sensitivity is often due to broad illumination, which creates auto-fluorescence noise. Even if point illumination and pin-hole filtering of non-focal plane noise are implemented in a confocal setup, the large and non-uniform fluorescent spots create scattering noise over each 20–100 μm element, which degrades the detection limit.4 Smaller spots can, in theory, be introduced by nano-sprays and nano-imprinting. However, directing the targets to such small areas then becomes problematic. Real-time PCR is, in principle, capable of detecting a single molecule but is limited in its target number5 and is hence slow/expensive for large-library assays. A large-library platform with much better detection limit than the current fluorescent microarrays would transform many screening assays. Ideally, this platform would not use the confocal configuration. Instead, it would direct the target molecules to a submicron spot and illuminate them with a nearby point source that does not require scanning.A promising platform is the optical fiber bundle array,6 with more than 104 fibers and targets, in principle. With its endoscopic configuration, these fiber bundles are most convenient for in situ and real-time biosensing modalities in microfluidic biochips and microfluidic 3-D cell cultures. Consequently, the optical sensing is typically carried out in the transmission mode, with the optical signals transmitted through the optical fibers to a detector. Microwell arrays at the distal end of imaging fiber, with molecular targets captured and transported to the microwells by microbeads, are the most popular among these optical fiber arrays. Although detection limit better than 1 × 106 molecules per bead has been reported, the bar-coded beads limit the target number of this platform.7, 8Our previous work9, 10 has shown that plasmonics at nanotips can enhance local electric field by three orders of magnitude. However, conduction loss and quenching of fluorescence11, 12 by the metal substrates limit the use of plasmonic enhanced fluorescence for large-library assays. Only nano-molar sensitivity has been demonstrated using plasmonics from metal coated nanocone tips.13, 14 In this paper, we will extend the conical fiber array platform not by tip plasmonics but by another optical phenomenon with induced dipoles: singular scattering off dielectric wedges and tips.15 Instead of the surface plasmon resonance on metallic nanostructures,16 field focusing at the cone tip by the dielectric media (the silica fiber) is used to produce a localized and singularly large scattering intensity at the tip. Singular scattering from a wedge or a cone has been known for decades.17, 18 It is only recently that numerical simulation19 has revealed that field focusing by this singular scattering can effect a five-order intensity enhancement that is frequency independent. This intense tip scattering produces a local light source at the tip that does not suffer from conduction loss. Unlike plasmonic metal nanostructures, the dielectric tip would also not quench the fluorescent reporters excited by the light source. In fact, it will help scatter the fluorescent signal, with Rayleigh scattering intensity scaling with respect to wavelength. We hence utilize this phenomenon for diffraction-limit fluorescent sensing/imaging for the first time here.The local light source due to tip scattering minimizes background auto-fluorescence and scattering noise, provided the target molecules preferentially diffuse towards the dielectric vertices. If the targets do not preferentially hybridize with probes at the vertices, there would be significant target loss, with a concomitant loss in sensitivity, because the vertex regions are just a small fraction of the total area. Fortunately, like electromagnetic radiation at the electrostatic limit of the Maxwell equations for sharp (sub-wavelength) vertices,20 the steady-state diffusion of molecules also obey the Laplace equation and so do the DC or AC electric potentials that drive electrophoresis and dielectrophoresis of the molecules.21 Hence, the diffusive, electrophoretic, and dielectrophoretic fluxes of target molecules are also singularly large at the vertices and there will be preferential hybridization there until the tip is saturated. Previously, we have demonstrated preferential diffusive transport of colloids to channel corners22 and dieletrophoretic trapping of bacteria23 and DNA molecules24 around sharp nanostructures like carbon nanotubes. Hence, dielectric nanotips fabricated by low-cost techniques can potentially provide the smallest fluorescent spot, which can preferentially capture target molecules and whose fluorescent image is limited in size only by the diffraction limit, without a confocal configuration.Although the scattering singularity is stronger at the conic tip, the total increase in scattering area of this singularity of measure zero is not as high as that of a sharp wedge, thus rendering the signal relatively weak. We hence employ a well-defined multi-wedged silica cone fabricated by wet-etching, with the wedges introduced by non-uniform stress formed during the fiber assembly process, to produce maximum scattering at the tip where three to four wedges converge (see inset of Fig. Fig.1A).1A). Using the reflection mode to fully exploit this singular scattering to excite fluorescent reporters at the tip and transmit the resulting signal, we report a nanocone array that can detect down to 100 molecules per cone tip with a large dynamic range from femtomolar to nanomolar concentrations. Although quantification for a single target is reported in this preliminary report, multi-target assays can readily be developed.Open in a separate windowFigure 1(A) A SEM image of the silica cone array where the single cone inset image shows three wedges converging into a 10 nm junction at the tip. (B) The optical setup of measurement. (C) The diffraction-limited fluorescent spot images.Amine-modified 35-base oligo-probes were functionalized onto both unetched silica fibers (as a control) and etched conic silica tips. The sample of 35-base ssDNA targets (corresponding to a primer for a segment of the Serotype 2 dengue genome) with a 5′ tagged Cy3 fluorophore was inserted into a microfluidic chip housing the fiber bundle (Fig. (Fig.1B)1B) and left overnight (see the supplementary material25 for exact sequence). After a standard rinsing protocol, fluorescent images were taken with an Olympus IX-71 fluorescent microscope for target concentrations ranging from 1 fM to 1 nM. A typical fluorescent image after hybridization is shown in Fig. Fig.1c,1c, where each micron-sized bright spot corresponds to a single tip in the cone array. The intensity profile shown in the supplementary material25 indicates a fluorescent spot smaller than 1 μm, indicating that the fluorescent light source is sub-wavelength and the resolution is close to diffraction limit. The size of this bright spot at the conic tip does not vary much with respect to the concentration but its intensity does, as shown in Fig. Fig.2A.2A. It was found that for flat fibers, only concentrations higher than 1 nM produced significant signals above the background. However, for etched conic fibers, 10 fM is clearly distinguishable from the background, which indicates that an improvement of sensitivity up to five orders can be realized by simply etching the flat surface into cone arrays. It also suggests very little target loss due to preferential hybridization onto the cone at sub-nM concentrations. We estimated the number of molecules per cone from the total number of molecules in target solution divided by the number of pixels on each fiber (104), which suggests less than 100 molecules per cone for a 10 fM bulk concentration, four orders better than any existing technology.Open in a separate windowFigure 2(A) Fluorescent intensity of etched conic fiber and unetched fiber for different concentrations of target molecules from 1 fM to 1 nM. (B) Fluorescent intensity increases linearly with exposure time. Non-target molecules with 1 μM concentration do not produce significant signal compared to lower concentrations of target molecules such as 1 nM and 10 nM (see the supplementary material25 for details of image analysis).Selectivity of the platform was also examined. Fig. Fig.2B2B presents the fluorescent intensity of the tips for non-target (1 μM) and target (1 nM and 10 nM) at different exposure times, which shows that fluorescent intensity increases linearly with exposure time. Beyond 5 s, saturation of images prevents further increase in the signal. For non-target, the intensity is much lower than 1 nM Target and 10 nM Target, which means non-target do not bind to the probes at the wedged tip as effectively as target molecules. Non-specific binding can be further removed by using more stringent buffers and higher flow rates.26 This platform can be extended to detect 70 000 targets, in theory, by functionalizing different probes onto each cones using localized photochemistry via masking, micro-mirror directed illumination, or direct laser writing. Extension to ELISA type protein assays is also straight forward. Integration of a transmission-mode optical fiber endoscope into a microfluidic biochip and into a 3-D cell culture for real-time monitoring of multiple molecular targets at near-single molecule resolution is currently underway. 相似文献
8.
9.
Plasmonic hot spots, generated by controlled 20-nm Au nanoparticle (NP) assembly, are shown to suppress fluorescent quenching effects of metal NPs, such that hair-pin FRET (Fluorescence resonance energy transfer) probes can achieve label-free ultra-sensitive quantification. The micron-sized assembly is a result of intense induced NP dipoles by focused electric fields through conic nanocapillaries. The efficient NP aggregate antenna and the voltage-tunable NP spacing for optimizing hot spot intensity endow ultra-sensitivity and large dynamic range (fM to pM). The large shear forces during assembly allow high selectivity (2-mismatch discrimination) and rapid detection (15 min) for a DNA mimic of microRNA.Irregular expressions of a panel of microRNAs (miRNA) in blood and other physiological fluids may allow early diagnosis of many diseases, including cancer and cardiovascular diseases.1 However, quantifying all relevant miRNAs (out of 1000), with similar sequences over 22 bases2 and large variations in expression level (as much as 100 fold) at small copy numbers, requires a new molecular diagnostic platform with high-sensitivity, high-selectivity, and large dynamic range. Current techniques for miRNA profiling, such as Northern blotting,3 microarray-based hybridization,4 and real-time quantitative polymerase chain reaction5 are expensive and complex. A simple and rapid miRNA array would allow broad distribution of molecular diagnostic devices for cancer and chronic diseases, eventually into homes for frequent prescreening of many diseases.At their low concentrations in untreated samples, optical sensing of miRNA is most promising. Plasmonically excited Raman scattering (SERS) and fluorescence sensors from metallic nanoparticles (NPs) or surfaces have enhanced the sensitivity of optical molecular sensors by orders of magnitude.6, 7, 8, 9 However, probe-less SERS sensing or fluorescent sensing of unlabeled targets are insufficiently specific for miRNA targets in heterogeneous samples. Plasmonic detection is also very compatible with FRET probes whose donor dye offers small light sources to excite fluorescently labelled targets upon hybridization.7, 10A particular family of FRET reporters does offer label-free sensing: hairpin oligo probes whose end-tagged fluorophores are quenched by the Au NP to which they are functionalized.11 The fluorescent signal is only detected when the hairpin is broken by the hybridizing target nucleic acid or protein (for an aptamer probe), and the more rigid paired segment separates the end fluorophore from the quenching surface to produce a fluorescent signal. It is often hoped that plasmonics on the metal surface will enhance the intensity to overcome the quenching effect, if the linearized hairpin is within the NP plasmonic penetration length. However, since fluorescent quenching decays slowly (linearly) with fluorophore-metal spacing10 whereas the plasmonic intensity decays exponentially from a flat surface, careful experimentation shows that quenching dominates and the hairpin probe actually produces a larger intensity on non-metallic surfaces,10 on which it can not function as a label-free probe. Hence, only μM limit-of-detection (LOD) has been achieved with this technique on single NPs or on flat metal surfaces,12 with expensive laser excitation and confocal detection.Plamonic hot spots formed between metal nanostructures and sharp nanocones can further amplify the plasmonic field.13, 14 The hot spot intensity decays algebraically with respect to the separation or cone tip distance and hence should dominate the linear decay of the metal quenching effect at some optimum separation.15 It is hence possible that plasmonic hot spots may allow much lower LOD with inexpensive optical instruments—ideally light-emitting diode light source and miniature camera. However, the dimension of the gaps, cones, and wedges needs to be at nanoscale, and the cost is now transferred to fabrication of such hot-spot substrates like bow-ties, double crescents, bull-eyes, etc.16 Low-cost wet-etching techniques for addressable nanocones that sustain converging plasmonic hot spots17 have been reported but the fabricated nanocones are often too non-uniform to allow precise quantification. NP monolayers have been shown to exhibit plasmonic hot spots and fluorescence enhancement.18, 19 However, the enhancement only occurs within a range of spacing between aggregated NPs, which is difficult to control and the location or even the existence of the hotspots are not known a priori.Higher sensitivity is expected if a minimum number of NPs are used in an assembly at a known location and if the NP assembly can produce crystal-like aggregates with controllable NP spacing. Induced DC and AC NP dipoles (related to dielectrophoresis) have been used to assemble NP crystals by embedded micro-electrodes to provide the requisite high field.20, 21 The resulting NP crystals are ideal for plasmonic hot spots, since the spacing of the regimented NP crystal can be controlled by the applied voltage. Conic nanocapillaries22, 23 will be used here for such field-induced NP assembly because the submicron-tip can focus the electric field into sufficient high intensity for NP assembly without embedded-electrodes. Because the field is highest at the tip due to field focusing, the micron-sized crystal would be confined to a small volume, which will be shown to be less than typical confocal volumes, at a known location. So long as the hotspots are regimented, the quantification of target molecules is determined by the total fluorescent intensity and is hence insensitive to the exact geometry of the nanocapillary.Fluorescent microscope equipped with tungsten lamp light source and normal CCD camera from Q Imaging were used for simultaneous optical and ion current measurements, as shown in Fig. Fig.1a.1a. The nanocapillaries were pulled from commercial glass capillaries using laser-assisted capillary puller. SEM image of a typical pulled glass nanocapillary in Fig. Fig.1b1b shows an inner diameter of 111 nm and cone angle of 7.3°. The capillary was inserted into a Polydimethylsiloxane chip with two reservoirs. The 20 nm Au NPs, functionalized with fluorescently labelled dsDNA, were injected into the base reservoir. With SEM imaging (Fig. S3 in the supplementary material24), the functionalized DNA is found to prevent NP aggregation even in high ionic-strength Phosphate buffered saline buffer. The NP solution is then driven into the capillary through the tip by applying a positive voltage. Fig. Fig.1c1c shows the ion current evolution over 2 h at +1 V packing voltage. The ion current increases rapidly in the first 10 min, then at a much slower rate. The rise of current indicates assembly of conductive Au NP assembly at the tip. This was confirmed by the strong fluorescence signal at the tip region during the packing process (inset of Fig. Fig.1c).1c). The one-micron region (corresponding to roughly an aggregate volume of one attoliter) near the capillary tip shows a fluorescence signal after 1 min and also appeared as a dark spot in the transmission image (supplementary material, Fig. S124). This spot darkens with longer packing time but does not grow in size, consistent with the monotonically increasing ion current with increased packing density of the NP assembly. As contrast, a strong fluorescence appeared after only 1 min of packing, but the signal became weaker after 15 min (supplementary material, Fig. S124). This reduction in fluorescence is not due to bleaching of fluorophores because we took 2 images in 15 min at 5 s exposure each and control experiments show significant bleaching only beyond an exposure time of 100 s (see supplementary material).24 Instead, the non-monotonic dependence of the fluorescence intensity with respect to time is because of the optimal hotspot spacing for highest plasmonic intensity at about 5–20 nm,25, 26, 27 which is reached at about 10 min.Open in a separate windowFigure 1Plasmonic hotspots generated at the tip of a nano-capillary. (a) Schematic of the experimental set up. (b) SEM image of glass nanocapillary shows opening at the tip with a diameter of 111 nm. (c) Current evolution during packing of fluorescently labeled gold particles at +1 V. Inset shows strong fluorescence only after 1 min of packing.The FRET probe is designed to exploit the plasmonic hotspot.24 We first electrophoretically drove the target molecules in the tip side reservoir into the nano-capillary by applying a negative voltage of −1 V. During this process, the targets are trapped within the capillary and hybridize with the hairpin probes on the Au NP in the nanocapillary. Fluorescence of the unquenched hybridized probes is too weak to be detected by our detector as shown in Fig. Fig.2b.2b. A reverse positive voltage of +1 V was then applied to the capillary to pack the Au NPs to the tip. Due to plasmonic hot spots of aggregated gold nanoparticles, the fluorescence signal is significantly enhanced at the tip and can be detected by our CCD camera, as shown in Fig. Fig.2c2c.Open in a separate windowFigure 2(a) Schematics of designed hairpin probe on gold particle. (b) Before packing gold particles, probe fluorescence signal was too weak to be detect. (c) After packing for 3 minutes, a strong fluorescence signal appears at the NP aggregate. (d) Normalized intensity (average of all pixels above a threshold (15 au) normalized with respect to the average over all pixels (with 0-250 au)) as a function of packing voltage for different samples. Black, 1 nM target ; blue, 10 pM target; purple, 10 nM 2-mismatch non-target. (e) Intensity dependence on target concentration. Measured normalized intensity before packing (black) and after packing (red), for three independent experiments with different nano-capillaries at each concentration. NT stands for non-target at 10 nM as a reference.For the same packing time, the fluorescence intensity increases initially but saturates after 10 min time of trapping (supplementary material, Fig. S2(a)24). Over 10 min of trapping with a negative voltage, we found the fluorescence intensity exhibits a maximum at a packing time of 3 min (supplementary material, Fig. S2(b)24). In later experiments, we used 10 min trapping time and 3 min packing time as standards.Fig. Fig.2d2d shows the fluorescence intensity is sensitive to the positive packing voltage at different concentration of target and non-target molecules. For target samples (1 nM and 10pM), the optimal voltage is about 1 V. We suspect that with larger voltage, the NPs are packed too tightly such that the NP spacing is smaller than the optimal distance for plasmonic hotspots. The fluorescence intensity for a nontarget with two mismatches is 7 times lower than the target even with a 10 times higher concentration (10 nM). Moreover, the optimal voltage for the non-target miRNA is reduced to 0.5 V instead 1 V for the target miRNA. Strong shear during electrophoretic packing has probably endowed this high selectivity.20Using the protocol above, the LOD and dynamic range of the target was determined (Fig. (Fig.2e).2e). The intensity at each concentration is measured with three independent experiments with different nanocapillaries to verify insensitivity with respect to the nanocapillary. The intensity increases monotonically with respect to the concentration from 1fM to 1pM. Beyond 1pM, the fluorescence signal saturates, presumably because all hairpin probes at the tip have been hybridized. At 1 fM, the fluorescent intensity is still well above the background measured from the non-target sample. Note both auto-fluorescence of gold nanoparticles and free diffusing non-target DNA molecules contribute to the background. Given the volume of tip side reservoir (∼50 μl), there are about 30 000 target molecules in the reservoir at 1 fM. However, with a short 10 min trapping time, we estimate only a small fraction of these molecules, less than 100, have been transferred from the tip reservoir into the nanocapillary. 相似文献
10.
An n-port gyrator, terminated by s1-type capacitors in m1-ports, by s2-type capacitors in the next m2-ports and by resistors in the remaining (n-m1-m2)-ports is considered. The determinant of the admittance matrix of the network can be made to yield VSHP (a two-variable Hurwitz polynomial without non-essential singularities of the second kind) under certain conditions involving the sub-determinants of the gyrator matrix. With the gyrator constants as variables and the above conditions as constraints, some 2-D stable low-pass filters have been designed using a suitable optimization procedure. The method is illustrated by examples. 相似文献
11.
Wang Zhao Li Zhang Wenwen Jing Sixiu Liu Hiroshi Tachibana Xunjia Cheng Guodong Sui 《Biomicrofluidics》2013,7(1)
A microfluidic device was successfully fabricated for the rapid serodiagnosis of amebiasis. A micro bead-based immunoassay was fabricated within integrated microfluidic chip to detect the antibody to Entamoeba histolytica in serum samples. In this assay, a recombinant fragment of C terminus of intermediate subunit of galactose and N-acetyl-D-galactosamine-inhibitable lectin of Entamoeba histolytica (C-Igl, aa 603-1088) has been utilized instead of the crude antigen. This device was validated with serum samples from patients with amebiasis and showed great sensitivity. The serodiagnosis can be completed within 20 min with 2 μl sample consumption. The device can be applied for the rapid and cheap diagnosis of other infectious disease, especially for the developing countries with very limited medical facilities.Entamoeba histolytica is the causative agent of amebiasis and is globally considered a leading parasitic cause of human mortality.1 It has been estimated that 50 × 106 people develop invasive disease such as amebic dysentery and amebic liver abscess, resulting in 100 000 deaths per annum.2, 3 High sensitive diagnosis method for early stage amebiasis is quite critical to prevent and cure this disease. To date, various serological tests have been used for the immune diagnosis of amebiasis, such as the indirect fluorescent antibody test (IFA) and enzyme-linked immunosorbent assay (ELISA).We have recently identified a 150-kDa surface antigen of E. histolytica as an intermediate subunit (Igl) of galactose and N-acetyl-D-galactosamine-inhibitable lectin.4, 5 In particular, it has been shown that the C-terminus of Igl (C-Igl, aa 603-1088) was an especially useful antigen for the serodiagnosis of amebiasis. ELISA using C-Igl is more specific than the traditional ELISA using crude antigen.6 However, the ELISA process usually takes several hours, which is still labor-intensive and requires experienced operators to perform. More economic and convenient filed diagnosis methods are still in need, especially for the developing countries with limited medical facilities.Among all the bioanalytical techniques, microfluidics has been attracting more and more attention because of its low reagent/power consumption, the rapid analysis speed as well as easy automation.7, 8, 9, 10, 11 Especially with the development of the fabrication technique, microfluidics chip can include valves, mixers, pumps, heating devices, and even micro sensors, so many traditional bioanalytical methods can be performed in the microfluidics. Qualitative and quantitative immune analysis on the microfluidic chip was successfully proved by plenty of research with improved sensitivity, shorten reaction time, and less sample consumption.8, 10, 11, 12, 13, 14, 15, 16, 17 Moreover, with the intervention of other physical, chemical, biology, and electronic technology, microfluidic technique has been successfully utilized in protein crystallization, protein and gene analysis, cell capture and culturing and analysis as well as in the rapid and quantitative detection of microbes.13, 14, 15, 16, 17, 18, 19, 20Herein, we report a new integrated microfluidic device, which is capable of rapid serodiagnosis of amebiasis with little sample consumption. The microfluidic device was fabricated from polydimethysiloxane (PDMS) following standard soft lithography.21, 22 The device was composed of two layers (shown in Figure Figure1)1) including upper fluidic layer (in green and blue) and bottom control layer (in red).Open in a separate windowFigure 1Structure illustration of microfluidic chip.To create the fluidic layer and the control layer, two different molds with different patterns have fabricated by photolithographic processes. The mold to create the fluidic channels was made by positive photoresist (AZ-50 XT), while the control pneumatic mold was made by negative photoresist (SU8 2025). For the chip fabrication, the fluidic layer is made from PDMS (RTV 615 A: B in ratio 5:1), and the pattern was transferred from the respective mold. The control layer is made from PDMS (RTV 615 A:B in ratio 20:1). The two layers were assembled and bonded together accurately, and there is elastic PDMS membrane about 30 μm thick between the fluidic layer channels and control layer.21, 22 The elastic membrane at the intersection can deform to block the fluid inside the fluidic channels, functioning as valves under the pressures introduced though control channels. There are two types of channels in fluidic layer, the rectangular profiled (in green, 200 μm wide, 35 μm thick) channel and round profiled channels (in blue, 200 μm wide, 25 μm center height). Because of the position of the valves on the fluidic channels, two types of valves (Figure (Figure2a)2a) were built, working as a standard valve and a sieve valve. The standard valves (on blue fluidic channels) can totally block the fluid because of the round profile of fluidic channel; the sieve valve can only half close because of the rectangular profile. The sieve valve can be used to trap the microspheres (beads) filled inside the green fluidic channels, while letting the fluid pass through. By this sieve valve, a micro column (in green) is constructed, where the entire ELISA reaction happens. The micrograph of the fabricated micro device is shown in Figure Figure2b.2b. The channels were filled with food dyes in different colors to show the relative positions of the channels. The pressures though different control channels are individually controlled by solenoid valves, connected to a computer through relay board. By programming the status (on/off) of various valves at different time periods, all the microfluidic chip operation can be digitally controlled by the computer in manual, semi-automatic, or automatic manner.Open in a separate windowFigure 2(a) Structure illustration of micro column, standard valve and sieve valve; (b) photograph of the microfluidic chip.To validate this device, 12 patient serum samples were collected. Sera from 9 patients (Nos. 1–9) with an amebic liver abscess or amebic colitis were used as symptomatic cases. The diagnosis of these patients was based on their clinical symptoms, ultrasound examination (liver abscess) and endoscopic or microscopic examination (colitis). We also identified the clinical samples using PCR amplification of rRNA genes.24 As negative control, sera obtained from 3 healthy individuals with no known history of amebiasis were mixed into pool sera. The serum was positive for E. histolytica with a titer of 1:64 (borderline positive), as determined by an indirect fluorescent-antibody (IFA) test.23, 24 In our previously study, the sensitivity and specificity of the recombinant C-Igl in the ELISA were 97% and 99%.6, 25 In the current study, the serodiagnosis of amebiasis was also examined by ELISA using C-Igl.26 The cut-off for a positive result was defined as an ELISA value > 3 SD above the mean for healthy negative controls27 (shown in Figure Figure3).3). The seropositivity to C-Igl was 100% in patients with amebiasis.Open in a separate windowFigure 3ELISA reactivity of sera from patients against C-Igl. ELISA plate was coated with 100 ng per well of C-Igl. Serum samples from patients and healthy controls were used at 1:400 dilutions. The dashed line indicates the cut-off value. Data are representative of results from three independent experiments.In the diagnosis process with microfluidic chip, the 4 micro immuno-columns filled with C-Igl-coated microspheres were the key components of the device. The C-Igl was prepared in E. coli as inclusion bodies. After expression, the recombinant protein was purified and analyzed by SDS-PAGE. The apparent molecular mass was 85 kDa.26The immune-reaction mechanism is illustrated in Figure Figure4.4. The anti-His monocolonal antibody was immobilized onto the microspheres (beads, 9 μm diameter) coated with protein A. The C-Igl was then immobilized onto the beads through the binding between the His tag and C-Igl. For the diagnosis, the microspheres immobilized with C-Igl and blocked by 5% BSA were preloaded into the columns for the rapid analysis of the patient serum samples. Generally, serum samples which were diluted 100 times were first loaded into the reaction column and incubated at room temperature for 5 min. After being washed by PBS buffer, FITC-conjugated goat anti-human polyclonal antibody was added into the column for 4 min incubation. The fluorescence image can be collected by the fluorescence microscope after the micro column was washed with PBS buffer. From loading diluted serum samples into column to collecting fluorescence images, the total time to complete the immunoassay is less than 10 min. The final fluorescence results were analyzed by Image Pro Plus 6.0.Open in a separate windowFigure 4Schematic representation of the ELISA in the chip.Different reaction conditions have been investigated to find the optimized ones. For each patient, 2 μl sample is enough for the analysis. The designed microfluidic chip with 4 micro columns is capable for 4 parallel analyses at the same time. More micro columns can be integrated into the device if more parallel tests are needed.Different incubating time for the diagnosis has also been investigated and no significant difference has been found for various time periods. It is enough to incubate the chip for only 5 min. The total diagnosis time for one sample is less than 10 min. The detection result appeared as the fluorescence intensity of the reaction column. As shown in Figure Figure5,5, the negative sample showed relatively low fluorescence intensity, because little FITC-conjugated goat anti-human polyclonal antibody could attach to the surface of microspheres; on the contrast, the positive sample showed much brighter fluorescence. The fluorescence intensity can be transferred to digital data (Table Sample Average scores Standard deviation 1 33 790 368 2 23 269 271 3 39 598 307 4 7784 52 5 21 222 197 6 38 878 290 7 22 437 227 8 36 295 334 9 41 024 396 Negative 200 32