Analytical Chemistry Chemical Cytometry Quantitates Superoxide

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The zone diagram built from eq 12 or 13 is reported in Figure 3B. Thus, three curves (curves 2-4) delineate a new domain corresponding to a mixed regime between the limiting ones previously identified (Figure 3A). In particular, the transitions from hemispherical diffusion to convection (i.e., vertical displacement on the diagram) and from hemispherical diffusion to planar diffusion (i.e., horizontal displacement) are relatively broad since they occur approximately over 2 orders of magnitude on the r0/ δconv and r0/(πDt) 1/2 scales, respectively. Only the transition from planar diffusion to convection is very sharp. Indeed, as soon as δplanar ≈ δconv, the diffusion layer reaches its steadystate limit and mass transport is fully controlled by convection. In contrast, when the condition δz ≈ δconv is met for hemispherical-type diffusion, the layer may still expand laterally along the r axis until reaching its steady-state limit (see Figure 2A-C). This latter condition corresponds to curve 1 in Figure 3B when |δ - δdiff|/δ ) 0.1 or |i - idiff|/|idiff| ) 0.1. It allows delineating the upper zone of the diagram where convection starts to interfere in the mass transport. A chronoamperometric experiment can be represented on the diagram by a horizontal straight line described from the right to the left when the time duration increases. According to the size of the electrode, r0, and thickness, δconv, the nature of the steadystate regime reached at longer time may be different. On the one hand, if log(r0/δconv) > 0.95, a sharp transition from planar diffusion to convection occurs. On the other hand, if log(r0/ δconv) < -0.7, a broad transition with a mixed regime from planar diffusion to quasi-hemispherical diffusion operates without any influence of natural convection. When log(r0/ (πDt) 1/2 ) < -0.75, a steady-state regime is always observed though its nature (diffusional or convective) only depends on the ratio r0/δconv. Under given experimental conditions (i.e., the same position of the electrode in the cell, temperature, viscosity of the electrolyte, environment, etc.), δconv is approximately constant so that the mass transport regime under steady state depends only on the electrode dimension. This was checked experimentally by mapping diffusion layers in the vicinity of electrodes of various radii. Figure 4 shows the concentration profiles along the vertical axis of symmetry of the electrodes for both the reactant and product. δconv was evaluated independently by chronoamperometry at a large electrode 18 and was found to range from 200 to 250 µm. It was thus possible to compare the experimental data with concentration profiles predicted with or without natural convection. A very good agreement was observed in Figure 4 whatever the size of the electrodes between experimental data and predictions issued from the model when natural convection was taken into account. Alterations on the concentration profiles due to convection were apparent as soon as r0 ) 25 µm. The experimental conditions pertaining to each concentration profile in Figure 4 are reported as symbols in the zone diagram of Figure 3B. According to the threshold previously defined with |δ - δhemisph|/δ ) 0.1 or |i - ihemisph|/|ihemisph| ) 0.1, the results show that a hemispherical diffusion regime was reached for r0 ) 12.5 and 25 µm while a mixed regime was achieved for the other radii (r0 ) 62.5-500 µm). These experimental data validate the predictions of the present model, yet they involved only the effect of natural convection along 6938 Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 Figure 5. Comparison between simulated (curves) and experimental (symbols) steady-state concentration profiles at a disk electrode of radius r0 ) 25 µm when the electrode potential is poised onto the oxidation plateau of FeCH2OH. (A) Experimental concentration profiles of the product FcCH2OH + along the vertical axis of symmetry (circles). (B) Experimental concentration profiles of FcCH2OH + along the r axis at various vertical distances z: z ) 6(O), 16 (0), 26 (]), 36 (×), 46 (+), and 56 µm (∆). The black area indicates the extent of the electrode coordinates along the r axis. The concentration profiles are simulated without (dashed curves) and with (solid curves) consideration of the influence of natural convection (δconv ) 200 µm). [FeCH2OH] ) 2 mM in 0.1 KNO3. the axis of symmetry of the electrodes. Conversely, we showed above (see Figure 2) that this effect is also effective along lateral directions due to the compensation of transport between vertical and lateral fluxes. In the following, we investigated this latter issue experimentally by performing 2D imaging. Figure 5 reports the mapping of concentration profiles established in the steady-state regime along the z axis and r axis when r0 ) 25 µm. As in Figure 4, the concentration profiles were compared to the predictions established with and without the influence of convection. Apart from the good agreement obtained between the data and predictions, these results clearly illustrate the fact that convection may still alter the diffusion layers even when quasi-hemispherical diffusion is expected to prevail (Figure 3B). In the present case, the concentration profiles are distorted over distances z equivalent to 10 times the electrode radius, r0. Simultaneously, the relative
Figure 6. Comparison between simulated (curves) and experimental (symbols) thicknesses of the diffusion layer at disk electrodes of various radii: δz/δconf (dashed lines, O) and δ/δconf (solid curve, 0). error in the current obtained by the model is |i - ihemisph|/ |ihemisph| ) 0.07. Finally, variation of δz issued from the mapping of concentration profiles in Figure 4 is reported in Figure 6 as a function of the electrode size and then compared to the predicted one. The diffusion layer thicknesses, δ, estimated from the experimental steady-state currents (through eq 8) are also plotted. As observed, all these data show that the model applies satisfactorily under the steady-state regime to predict the influence of natural convection on current responses or concentration profiles. CONCLUSION The model elaborated in this work predicts within a very good accuracy the relative contributions of diffusion and natural convection to the mass transport at disk electrodes. The electrochemical behaviors of the electrodes not only are related to their dimensions but also depend on the time scale of the experiment and thickness of the convection-free layer (i.e., δconv). These results stress once more the futility of trying to propose an absolute definition of ultramicroelectrodes based on the objects themselves. Indeed, the same electrode may behave as a microelectrode or an ultramicroelectrode, depending on these parameters. Our model allowed us to clearly delineate the situations where natural convection alters both the dynamic and steady-state regimes at disk electrodes. The properties of ultramicroelectrodes are mainly achieved when r0/δconv < 0.2. This condition has practical consequences if one needs, for example, to exploit the characteristics of ultramicroelectrodes to detect or measure concentrations in restricted volumes, without any alteration of natural convection on the measurements. ACKNOWLEDGMENT This work has been supported in part by the CNRS (Grant UMR8640), Ecole Normale Superieure, UPMC, and French Ministry of Research. Received for review May 7, 2010. Accepted July 9, 2010. AC101210R Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 6939
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Anal. Chem. 2010, 82, 6745-6750 Let
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purchased from Invitrogen-Molecular
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Figure 3. Electropherograms of TPP-
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Anal. Chem. 2010, 82, 6751-6755 Res
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(pH 8.0) with cysteine and cystamin
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Figure 4. Ion mobility mass spectra
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GOx glucose + O298 gluconic acid +
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coater at 2000 rpm for 20 s, and th
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Figure 5. Comparison of cyclic volt
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in channels with either no grooves
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indicators of atmospheric processin
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Figure 1. GC/MS total ion chromatog
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Table 2. Concentrations and Stable
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on a substrate are preferred. 20-24
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Figure 4. SERS analysis of NAADP co
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Anal. Chem. 2010, 82, 6775-6781 Hig
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tion, 2 µL of proprionaldehyde wer
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Figure 4. Analysis of 2a by HPLC-MS
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eaction of 1a with PBH can be condu
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Numerous references had demonstrate
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Figure 1. TEM images of the prepare
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Figure 4. Schematic representation
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esult in a big SPR signal change wi
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also reduces chemical noise, which
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Table 1. Extraction Yields, Liquid
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scanning of AMPP amides of the anal
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Anal. Chem. 2010, 82, 6797-6806 δ
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Figure 1. Schematic view of the pre
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from the specimen and enclosed in a
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Figure 4. (A) IRMS mass-44 chromato
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Table 3. Ambient Measurement Result
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Anal. Chem. 2010, 82, 6807-6813 Dir
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Polymerase (1 U per sample). Reacti
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of which was constant for all ampli
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analytically useful signals at less
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carbon black and RP-C18 for the ext
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solution in an equal volume, and 1
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Table 2. Concentrations and Ratios
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Anal. Chem. 2010, 82, 6821-6829 Mac
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mg/mL protein, followed by separati
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Figure 2. Productivity of SEQUST an
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Figure 4. High-resolution MS/MS spe
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Figure 6. Characterization of PSMs
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containing T-T mismatches. 23 Based
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Figure 1. Extinction spectra of sol
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Figure 3. (A) The value of Ex650 nm
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Figure 5. Extinction spectra and co
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wished to explore the dehydration o
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constant medium for separation; we
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Figure 2. Standards of (Pi)n, n ) 1
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Figure 5. Quantitative calibration
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Anal. Chem. 2010, 82, 6847-6853 Met
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Figure 1. 226 Ra spectrum by liquid
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Table 1. Counting Properties and De
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Table 3. Analysis of 226 Ra in Sedi
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mercial microarray scanner and fabr
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Figure 2. Optical transmission meas
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Figure 5. Volcano plots detailing t
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data as well. The 41 genes in Table
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corresponding compound if its chemi
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Figure 1. Schematic illustration of
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Table 1. Absolute Quantification Re
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ment. Therefore, the long-time drea
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Figure 1. Chemically actuated micro
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Figure 2. Influence of a surfactant
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Figure 5. Device to eject and mix s
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Anal. Chem. 2010, 82, 6877-6886 Imm
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NaCl, phosphate buffer saline (PBS)
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Figure 2. Product ion mass spectra
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-70 °C resolved the problem, givin
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Table 1. Intraday Precision and Acc
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Page 145 and 146: Figure 1. Infrared spectra of (A) u
Page 147 and 148: Figure 3. Cyclic voltammograms obta
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Page 153 and 154: Table 1. Chemical Structure, pKa Va
Page 155 and 156: pH with a tilted baseline (Figure 1
Page 157 and 158: Table 2. Linearity and Detection Li
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Page 161 and 162: the multielement capabilities, the
Page 163 and 164: RESULTS AND DISCUSSION Sulfur Detec
Page 165 and 166: Table 2. Molecular Properties and C
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Page 169 and 170: dilution and hybridization buffer.
Page 171 and 172: solution under appropriate incubati
Page 173 and 174: Figure 4. Standardization curve for
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Page 177 and 178: the ×10 objective, to have a large
Page 179 and 180: Figure 2. With a suitable removal o
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Page 183 and 184: Scheme 1. Reactions of Selenium Rea
Page 185 and 186: Figure 2. (a) ESI-MS spectrum showi
Page 187 and 188: Figure 4. (a) ESI-MS spectrum showi
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Page 191 and 192: trode 28 by a finite element using
Page 193: Figure 4. Comparison between simula
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Page 199 and 200: Figure 2. Normalized product ion ab
Page 201 and 202: Figure 4. EID (a) and IRMPD (b) of
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Page 205 and 206: Figure 1. Schematic flowchart showi
Page 207 and 208: difference, ppm compound Table 1. I
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Page 211 and 212: Figure 5. Extracted ion current ESI
Page 213 and 214: m/z 1172.935 was observed for Ser14
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Page 217 and 218: Scheme 2. Fragmentation Mechanism o
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Page 221 and 222: Figure 3. (A) ESI-LTQ-CID-MS 2 prod
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Page 227 and 228: Figure 3. Equilibrium response as a
Page 229 and 230: Figure 6. The average measured resp
Page 231 and 232: for the fill time, and we find that
Page 233 and 234: nucleotide tails. 3-5 Thus, the amo
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Page 241 and 242: Figure 2. Configuration editor wind
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Since the time for liquid expulsion
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Anal. Chem. 2010, 82, 6991-6999 Int
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Figure 1. Representation of the Car
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Table 2. Capillary Electrophoresis
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Figure 4. (A) Typical raw electroph
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field. DNA profiles were delivered
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Another approach to handle this lim
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(principal components, PCs) in whic
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Figure 5. Relevant score plots and
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CONCLUSIONS In this paper we have i
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electroactive-species loaded liposo
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Figure 2. Qdot-based FLFTS response
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Figure 6. Fluorescence imaging of Q
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Anal. Chem. 2010, 82, 7015-7020 Sel
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Table 1. Effect of 1 D-LC Condition
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Figure 3. Peak-production rate vers
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Anal. Chem. 2010, 82, 7021-7026 Cel
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luciferase (T7 control vector) was
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Figure 3. Inhibitory effects of luc
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Anal. Chem. 2010, 82, 7027-7034 Pat
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Electrochemistry. Electrochemical m
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Figure 2. SEM images of Au substrat
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Table 3. Film Thickness Measurement
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Anal. Chem. 2010, 82, 7035-7043 Qua
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Figure 1. (A) FL spectra of BSPOTPE
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Figure 4. (A) Variation in the FL i
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Figure 6. (A) FL spectra of BSPOTPE
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Scheme 1. Proposed Mechanism for Fl
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one or more drawbacks including poo
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Figure 2. Free fluorophores do not
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Anal. Chem. 2010, 82, 7049-7052 Dev
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Figure 2. Comparative analysis of d
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Analytical Chemistry Chemical Cytometry Quantitates Superoxide

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