Analytical Chemistry Chemical Cytometry Quantitates Superoxide

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Figure 4. With limited sampling, PCA can have problems to distinguish small components in the spectra. An example is shown here with a mixture of 80 and 20 nM of CV and NB, respectively. In (a) we show the average (over 400 spectra), with arrows showing the positions where the fingerprint modes of NB at 590 cm -1 and 1645 cm -1 should appear. The signal is dominated by CV throughout the entire spectral range, with many overlap regions. In (b) we show a PCA analysis of the ∼1630 cm -1 region, where both the 1620 and 1645 cm -1 peaks of CV and NB are expected, respectively. But with a difference of factor of ∼20 between the intensities of CV and NB in this range, fluctuations larger than ∼5% in the CV signal have a larger weight for the covariance matrix than the induced (electrochemical) variations of NB. With limited sampling, PCA cannot clearly distinguish the NB signal. We show here the first four PCA eigenvectors as an example. The limited sampling problem can be partially compensated by a prefiltering of the data with a FFT-transform, filtered at the appropriate electrochemical modulation frequency (see Figure 5). by the intensity fluctuations of the much larger CV peak, whereas the second one has the typical characteristic of an eigenvector accounting for frequency shifts of the CV peak. 40 From the third eigenvector onward, the covariance matrix in PCA is trying to find “correlations in the noise”. With enough sampling, these correlations will be zero and the peak of NB will appear as a third eigenvector. But in this case, the limited sampling establishes a competition between the random fluctuations of the much larger peak and the signal we are trying to observe (from NB). It is in situations like this one that a prefiltering of the data can help. The basic idea of Fourier prefiltering is explained in full in the SI with further examples, but here we shall give a brief version of it. From a FFT-transform of the total integrated intensity as a function of time we can easily reveal the main modulation frequency in the FFT-spectrum, as can be seen in Figure 5(a). This comes primarily from the modulation of the CV signal, but that is irrelevant at this stage: the FFT-transform of the total integrated intensity is used to identify the modulation in FFTfrequency units. 48-50 We can now perform a wavelength-bywavelength (i.e., pixel-by-pixel) FFT filtering of the data at this 6924 Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 Figure 5. (a) A FFT of the total integrated intensity of the spectra (which varies mainly here due to the electrochemical modulation of CV), reveals clearly the main frequency of the modulation (i.e., scan rate of 50 mV. sec -1 ). We can filter each pixel (wavelength) at this frequency and then transformed back the spectra into the time domain. The average of the filtered data (at the electrochemical modulation frequency) is shown in (b). Now the signal of NB is more clearly visible in the average and its relative intensity with respect to the CV peak is larger (because only the part of the CV signal that is modulated survives the filtering). A PCA analysis of the prefiltered signal shows a first eigenvector representing the CV intensity, and a second eigenvector which now contains the NB peak at ∼1645 cm -1 , and a small fraction of frequency shifts of the CV peak. The vertical intensity scale for both curves in (c) is the same. Green lines are guides to the eye. particular frequency. This is simply done by an FFT-transform to the time evolution of each pixel, multiplication by an appropriate filter centered at the spikes of Figure 5(a), and followed by an inverse FFT-transform to go back to the time domain. In these data, therefore, we have enhanced the importance of only those fluctuations that happen at the known electrochemical modulation frequency, with respect to any other random fluctuation. Figure 5(b) and (c) show the resulting PCA analysis after FFTfiltering. It is worth noting that the average of the filtered signal has now a much better ratio of intensities between the CV and NB signals; this is because only the fraction of the CV signal that is being modulated survives the filtering. Accordingly, this puts (48) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing; Cambridge University Press: Cambridge, 1989. (49) Kreyszig, E. Advanced Engineering Mathematics, 9th ed.; John Wiley & Sons: New York, 2006. (50) Kauppinen, J.; Partanen, J. Fourier Transforms in Spectroscopy; Wiley-VCH Verlag: Berlin, 2001.
the NB signal in a much better footing to be identified among the first PCA eigenvectors. Effectively, we can see now in Figure 5(c) that the first eigenvector is still dominated by the CV signal, but the second one contains both the NB signal and some contributions to frequency shifts of the CV peak. What we have achieved by FFT-prefiltering is to put the NB signal at the same level of importance of frequency shifts of the CV peak (according to the covariance matrix) and this therefore “lifts” a very small signal from accidental correlations in the noise. As explained further in the SI, this is nothing but the well established principle of “lock-in” amplification; applied here as a prefiltering for PCA. In general, in any other experimental situation, if we have access to unlimited sampling then time lock-in “amplification” might not be needed; for the signal will always increase linearly with time while the noise increases like the square root of it. Therefore, the signal-to-noise ratio will always improve with integration time and eventually a small signal can be resolved. But we can achieve a much faster result in a shorter time (with less sampling) with a lock-in. Like in the case at hand here, unlimited amount of sampling is sometimes not possible in other experimental situations because the long-term stability of the experiment is compromised or it is simply too long. The situation depicted here is the exact analog of this latter situation but for the problem of spectral deconvolution with PCA. The combination of FFT-prefiltering and PCA might not be necessary in many situations and whenever possible, the simplest analysis should prevail. But the covariance matrix of PCA is basically “blind” to the time sequence of the electrochemical cycle. If we scrambled all the spectra (in time) we would still have the same covariance matrix and the same PCA eigenvectors. However, we do know the frequency (or period) with which we are inducing the electrochemical modulation. What we are doing with FFTprefiltering is, accordingly, to “pick” the appropriate fluctuations that happen at the frequency where we know the real physical effect is happening. In that manner, we bias the PCA analysis toward a physically relevant set of fluctuations, and this helps to improve the ability of PCA to distinguish what is correlated and what is not, in a situation where limited sampling is unavoidable. In the language of lock-in amplification, we have improved the signal-to-noise ratio by discarding all fluctuations except those that happen at the right frequency. The example chosen here is tailormade to show the concept and, as such, we have different options at hand. We could have done, for example, a PCA analysis is a much narrower window around the NB peak (to try to minimize the influence of the CV peak nearby). However, in real applications, we might not even know where to expect the peaks, and considerable spectral overlap is always possible. FFT-prefiltering is one additional tool to consider in these situation, and it could -in many cases- be the difference between being able to isolate a particular spectral feature of the weaker signal or not. CONCLUSIONS We have shown a combination of electrochemical modulation with fluctuation analysis to discriminate and isolate different species in cases where there is spectral congestion and coadsorption of molecules. Needless to say, the technique is not limited to two species, and can be applied to multicomponent systems in general. PCA contains, in principle, all the elements it needs to distinguish all spectral components given enough sampling. The restriction of limited sampling to “lift” small signals from other contributions has also been shown through the addition of FFTprefiltering. Prefiltering is not strange in PCA analysis. The most common type of prefiltering used in the PCA literature is “pre-whitening”. 41,42 In this latter case, this is done for a different purpose: to ensure that the samples are as unbiased as possible before the PCA analysis is carried out. Here we use prefiltering in a different way: to bias the study of correlations in the data that happen at a prescribed frequency, imposed externally by the electrochemical modulation. We believe that techniques to solve spectral congestion of coadsorbed species will be of great interest, as SERS moves into areas (like bioelectrochemistry) where the purity and characteristics of the sample cannot be chosen at will. We hope the concepts developed here in our paper will contribute to that endeavor. ACKNOWLEDGMENT E.C. acknowledges the financial support of UNLP, ANPCyT (Argentina) and the MacDiarmid Institute (New Zealand) for a research/exchange program between Argentina and New Zealand. Thanks are also given to the host institution, Victoria University of Wellington, where the work was carried out. We acknowledge financial support from ANPCyT (Argentina, PICT06-621, PAE 22711, PICT06-01061, PICT-CNPQ 08-019). E.C., A.F., and RCS are also at CONICET. MEV is a member of the research career of CIC BsAs. R.C.S and A.F. are Guggenheim Foundation Fellows. PGE and ECLR are indebted to the Royal Society of New Zealand for additional financial support under a Marsden Grant. SUPPORTING INFORMATION AVAILABLE Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review May 3, 2010. Accepted July 10, 2010. AC101152T Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 6925
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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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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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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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Page 177 and 178: the ×10 objective, to have a large
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for the fill time, and we find that
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nucleotide tails. 3-5 Thus, the amo
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allow the use of higher aptamer con
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quent ligation of the aptamers afte
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Anal. Chem. 2010, 82, 6983-6990 Imp
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Figure 2. Configuration editor wind
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Figure 4. Dependencies between volu
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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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