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Second derivative and Fourier self-deconvolution (FSD) are two commonly used techniques to resolve the overlapped component peaks from the often featureless amide I band in Fourier transform infrared (FTIR) curve-fitting approach for protein secondary structural analysis. Yet, the reliability of these two techniques is greatly affected by the omnipresent water vapor in the atmosphere. Several criteria are currently in use as quality controls to ensure the protein absorption spectrum is negligibly affected by water vapor interference. In this study, through a second derivative study of liquid water, we first argue that the previously established criteria cannot guarantee a reliable evaluation of water vapor interference due to a phenomenon that we refer to as sample’s absorbance-dependent water vapor interference. Then, through a comparative study of protein and liquid water, we show that a protein absorption spectrum can still be significantly affected by water vapor interference even though it satisfies the established criteria. At last, we propose to use the comparison between the second derivative spectra of protein and liquid water as a new criterion to better evaluate water vapor interference for more reliable second derivative and FSD treatments on the protein amide I band.

Curve-fitting of the Fourier transform infrared (FTIR) spectrum of a protein in the 1700–1600 cm^{−1} amide I region is widely used in the quantitative analysis of protein secondary structures [

The elimination of water vapor interference from protein absorption spectrum can be done in several ways. These methods include purging with dry air or nitrogen during spectral acquisition, subtraction of reference water vapor absorption spectrum from protein absorption spectrum, using sample shuttle to achieve complete atmospheric compensation during spectral acquisition, and using the combined approach of purging and spectral subtraction. Regardless of the actual method that one would choose to eliminate water vapor interference, the success of such elimination must be carefully evaluated by some trusted criteria. For this purpose, when the pioneers had developed the FTIR curve-fitting approach, they had also developed several criteria as quality-controls to ensure that the protein spectrum in the amide I region is negligibly affected by water vapor interference [^{−1}. In practice, these criteria are implemented through the practitioner’s visual inspection. Protein absorption spectrum satisfying these criteria will be considered as being negligibly affected by water vapor interference and ready for second derivative and FSD treatments. The above mentioned criteria are widely used in protein secondary structural analysis by FTIR spectroscopy in the past three decades. However, in this study, we demonstrate that these widely adopted criteria in fact cannot guarantee the reliable evaluation of water vapor interference and a protein spectrum satisfying these established criteria can still be significantly affected by water vapor interference. We provide mathematical reasoning to argue why these established criteria are not reliable and introduce a concept called, “sample’s absorbance-dependent water vapor interference” for our reasoning. We suggest a new criterion that we refer to as a “whole-spectrum” criterion to better evaluate the extent of water vapor interference in the FTIR spectrum to ensure more reliable second derivative or FSD treatment on the protein amide I band during curve-fitting analysis.

We first argue why the previously established criteria for the successful elimination of water vapor interference is not reliable using a simple example, liquid H_{2}O. The bending mode of liquid H_{2}O is located in the amide I region around 1645 cm^{−1}. From a spectroscopic viewpoint, we can consider liquid H_{2}O as some protein mimic which has only one secondary structure. _{2}O bending mode and its corresponding second derivative as well as the absorption spectrum of water vapor in the 2200–1500 cm^{−1} spectral region. _{2}O bending mode and its corresponding second derivative as well as the absorption spectrum of water vapor in the 1300–1100 cm^{−1} spectral region. The comparison between the two figures offers a nice illustration of how water vapor interference affects the outcome of second derivative treatment. As shown in _{2}O only gives one resolved peak located at 1207 cm^{−1}. By contrast, the second derivative spectrum of liquid H_{2}O in ^{−1} bending mode region. Since the only difference between the two cases is that there are water vapor absorptions in the H_{2}O bending mode region and no water vapor absorption in the D_{2}O bending mode region, it is obvious that the resolved peaks in the second derivative spectrum of H_{2}O in _{2}O in _{2}O should have looked like if there was no water vapor interference in the H_{2}O bending mode region. This dashed line was obtained by first over-smoothing the absorption spectrum of liquid H_{2}O for three times using a 25-point window and then performing the second derivative treatment using a 25-point window. Obviously, without knowing the significant impact of water vapor interference on the outcome of second derivative treatment, one may falsely take the resolved artifact peaks in

The absorption spectrum of liquid H_{2}O in _{2}O is still terribly affected by water vapor interference. In the following, we provide a qualitative interpretation as well as a mathematical reasoning for this surprising observation.

(_{2}O and the absorption spectrum of water vapor (C: blue). Dashed line: theoretical second derivative spectrum of liquid H_{2}O; (_{2}O and the absorption spectrum of water vapor (C: blue); (_{2}O (C: blue). Second derivative spectrum is displayed with its resolved peaks pointing downwards. The absorbance of water vapor is in arbitrary unit. Spectral resolution: 4 cm^{−1}.

100% transmittance spectrum. This spectrum was taken with an empty optical path and with closed sample compartment. The optical bench of our FTIR spectrometer is a sealed design. This spectrum can be repeatedly obtained with ease under our lab conditions. Spectral resolution: 4 cm^{−1}.

In _{2}O in the two regions are quite different. In principle, the two second derivative spectra of liquid H_{2}O in the paired spectral regions should be affected by water vapor interference to a similar extent upon atmospheric perturbation as the absorbance of water vapor in the two regions are similar. However, we can easily tell from the four marked regions that this is not the case by using the “oscillating” magnitude of the original second derivative signal relative to the reference (_{2}O, we can deduce that the extent of water vapor interference at each frequency must highly depend on the absorbance of liquid H_{2}O at that frequency; and larger absorbance of liquid H_{2}O apparently results in more pronounced water vapor interference in the second derivative spectrum. We here introduce a concept that we refer to as “sample’s absorbance-dependent water vapor interference” to describe the above observation. We should keep in mind that sample’s absorbance means liquid H_{2}O’s absorbance, not water vapor’s absorbance. We can further illustrate our discovery in an alternative way by performing the following experiment. Since the sample’s absorbance can abnormally magnify water vapor interference in second derivative spectrum, if we take the FTIR spectrum of some sample which has no absorption in a spectral region, we should see the disappearance of the sample’s absorbance-dependent water vapor interference phenomenon in the second derivative spectrum in that spectral region. ^{−1} spectral region. The second derivative spectrum of liquid H_{2}O was re-shown here for comparison at the same scale. The absorption spectrum of 2,2,4-trimethylpentane was taken under the same condition as liquid H_{2}O, ^{−1} spectral region is basically a flat line and sample’s absorbance-dependent water vapor interference is negligible.

The sample’s absorbance-dependent water vapor interference is a new phenomenon that has never been reported before. First, this phenomenon is not simply due to the deviation from Beer’s law of the measured absorbance of liquid H_{2}O. A deviation from Beer’s law can result in the situation where water vapor interference can depend on sample’s absorbance as different regions of the sample’s absorption band deviate from Beer’s law to different extents. However, the absorption maxima of liquid H_{2}O in _{2}O such as the regions above 1700 cm^{−1} and below 1600 cm^{−1} in ^{−1}) does not follow Beer’s law. This means that the spectral subtraction between two different water vapor absorption spectra with one universal subtraction factor can never result in complete atmospheric compensation within the entire sample’s absorption band. However, in our study, we keep the concentration of water vapor constant with sample shuttle during spectral acquisition (as evidenced in

To better understand this new phenomenon, we provide the following mathematical reasoning. As we know, the negative logarithm of the ratio of sample’s single-beam spectrum to reference’s single-beam spectrum gives an FTIR absorption spectrum. If we take the liquid H_{2}O spectrum in _{2}O taken under atmospheric conditions can in principle be expressed according to Equation (1). In Equation (1), _{H2O}(_{2}O’s absorbance; _{H2O}(_{2}O’s absorbance; the second term, log_{0} is the energy of infrared (IR) radiation from the IR source; _{caF2} is the transmittance of CaF_{2} window and is assumed to be identical for both sample scanning and reference scanning; _{2}O, _{H2O}(_{H2O}(_{2}O will be free from water vapor interference. However, any spectral measurement is accompanied by noise. Therefore, in practice, the measured absorbance of liquid H_{2}O, _{H2O}(^{s′}^{R}^{s′}^{R}_{H2O}(_{H2O}(_{2}O in the optical path actually behaves like an optical filter that attenuates the energy of IR radiation from the IR source. As spectral noise level depends on the energy of IR radiation [^{s′}^{R}_{2}O will contain the contributions from uncompensated water vapor absorptions even if _{2}O at each frequency, the water vapor interference term of log^{s}_{2}O, the greater the water vapor interference. In this mathematical reasoning, we use noise as the origin of the additive term in Equation (2). Whether there is an alternative cause for the additive term is an open question and deserves future investigation.

We here take liquid H_{2}O as an example for our reasoning, the sample’s absorbance-dependent water vapor interference phenomenon is apparently an issue inherent to any FTIR measurement including in the case of measuring protein FTIR spectrum whenever the measurement is taken under atmospheric conditions. By nature, the sample’s absorbance-dependent water vapor interference can be considered as a unique type of deviation from Beer’s law, but it is different from the deviation from Beer’s law in quantitative analysis in our conventional wisdom because the measured sample’s absorbance still follows Beer’s law. It is the second derivative spectrum that is significantly “deviated” from its true spectrum.

An immediate implication from the sample’s absorbance-dependent water vapor interference phenomenon is that the successful elimination of water vapor interference at several selected frequencies in the amide I region or from the 1850–1720 cm^{−1} window region cannot guarantee the successful elimination of water vapor interference from the entire amide I region because the extent of water vapor interference varies with protein’s absorbance at each frequency. Therefore, the above mathematical reasoning provides the theoretical basis for us to challenge the reliability of the established “single-point” criterion and “window-region” criterion.

We now provide several examples to further question the reliability of the established “single-point” and “window-region” criteria. ^{−1} window regions in both of the original spectrum and the second derivative spectrum in _{2}O in _{2}O very well. In

FTIR absorption (a) and second derivative (b) spectra of HEWL in D_{2}O and second derivative spectrum of liquid H_{2}O (c). Second derivative spectrum is displayed with its resolved peaks pointing downwards and is in arbitrary unit (a.u.). The negative _{2}O subtraction. This has no effect on water vapor compensation between sample scanning and reference scanning [^{−1}.

Frequencies of the resolved peaks in the second derivative spectra of HEWL and liquid H_{2}O and frequencies of the absorption peaks of water vapor in the amide I region.

Spectrum | Peak Frequency (cm^{−1}) |
|||||||
---|---|---|---|---|---|---|---|---|

HEWL (second derivative) | 1682 | 1674 | 1667 | 1660 | 1651 | 1638 | 1630 | 1618 |

Liquid H_{2}O (second derivative) |
1682 | 1674 | 1667 | 1660 | 1651 | 1638 | 1630 | 1618 |

Water Vapor (absorption) | 1684 | 1670 | 1663 | 1653 | 1647 | 1636 | 1623 | 1616 |

In _{2}O under different conditions, ^{−1} spectral resolution to collect the absorption spectrum of HEWL and using smoothing to pretreat the absorption spectrum of HEWL before second derivative treatment. ^{−1} resolution and its second derivative; _{2}O that are subjected to the same acquisition condition and spectral treatment are shown for comparison. The two HEWL absorption spectra apparently satisfy both the “single-point” criterion and the “window-region” criterion. This is as expected because low spectral resolution and smoothing are known to be able to further suppress water vapor interference. Yet, the perfect match in frequency between the second derivative spectra of HEWL and liquid H_{2}O as illustrated by the vertical lines in _{2}O in _{2}O. These observations again support our argument that the established criteria cannot offer reliable evaluation of water vapor interference in the protein amide I band.

FTIR absorption (a) and second derivative (b) spectra of HEWL in D_{2}O and second derivative spectrum of liquid H_{2}O (c). Second derivative spectrum is displayed with its resolved peaks pointing downwards and is in arbitrary unit (a.u.). Spectral resolution: 8 cm^{−1}.

FTIR absorption (a) and second derivative (b) spectra of HEWL in D_{2}O and second derivative spectrum of liquid H_{2}O (c). Second derivative spectrum is displayed with its resolved peaks pointing downwards and is in arbitrary unit (a.u.). Both of the spectra of HEWL and liquid H_{2}O were subjected to 17-point smoothing. Spectral resolution: 4 cm^{−1}.

Besides second derivative, FSD is another widely used resolution-enhancement technique in protein secondary structural analysis. To see whether the FSD result also supports the argument that a protein spectrum satisfying the established criteria for successful water vapor absorption elimination can still be significantly affected by water vapor interference, we performed a comparative FSD study of HEWL and liquid H_{2}O, as shown in ^{−1} and noise suppression factor of 0.3. FSD is a subjective technique and there is no consensus in the literature on what should be the most appropriate values for bandwidth and noise suppression factor in FSD for protein secondary structure analysis. The two parameters for _{2}O very well. Therefore, the FSD study also supports our argument that the previously established criteria for successful elimination of water vapor interference are not reliable.

FSD spectrum of HEWL in D_{2}O (a) and its corresponding second derivative (b) and second derivative spectrum of liquid H_{2}O (c). Second derivative spectrum is displayed with its resolved peaks pointing downwards and is in arbitrary unit (a.u.). Spectral resolution: 4 cm^{−1}.

Since the above mathematical reasoning demonstrates that both the “single-point” and “window-region” criteria are problematic, it is thus desirable to develop some type of “whole-spectrum” criterion to better evaluate the extent of water vapor interference. In fact, the comparative second derivative study of protein and liquid H_{2}O has provided us a solution. We can employ such comparison as a new criterion to more reliably evaluate water vapor interference. This new criterion can be implemented in the following way. First, we take the absorption spectra of a protein sample and liquid H_{2}O under identical acquisition conditions and then make them subject to the same data processing such as smoothing and spectral subtraction. Second, we perform a comparison between the second derivative spectra of protein and liquid H_{2}O. There are two possible situations that one would face. If we do have a perfect elimination of water vapor interference, the second derivative spectrum of liquid H_{2}O will be like that of liquid D_{2}O, showing only one component peak. Then under this situation, the resolved peaks from the second derivative spectrum of protein should be identified to be the true component peaks due to protein secondary structures. If we do not have a perfect elimination of water vapor interference, we will search for the matched peaks between the second derivative spectra of protein and liquid H_{2}O like what we have done in _{2}O in frequency should be considered as artifacts due to water vapor interference (or at least suspected as coincidence does exist occasionally). Besides frequency matching, the similarity in shape between the two matched peaks is another piece of strong evidence for us to confirm the identity of the artifact peak due to water vapor interference.

Before we conclude, there are two additional issues that we would like to address particularly with respect to the implications of our work for the FTIR analysis of protein secondary structures. First, we want to emphasize that though we proposed a new criterion in this study and also questioned the reliability of the established criteria, we have no intent to say that the previously established criteria should be abandoned. In practice, the previously established criteria and the newly proposed criterion can work together to ensure a more reliable second derivative or FSD treatment on protein absorption spectrum. Second, we would like to state that water vapor interference needs not to be a serious concern in every FTIR analysis of protein secondary structure. As we know, there are three types of FTIR approaches in protein secondary structural analysis. The first one is the FTIR curve-fitting approach with the aid of second derivative and FSD. With this approach, the initial guess about the frequencies and the number of the component peaks are based on the results from second derivative or FSD treatment. The actual curve-fitting can be performed on the original spectrum, the inverted second derivative spectrum, or the FSD spectrum. This type of approach is the one that we have been discussing in this study and it is the widely used one compared to the latter two. The second approach is through the curve-fitting of the original absorption spectrum without the aid of second derivative or FSD [

Hen egg white lysozyme (catalog number, L6876) was obtained from Sigma-Aldrich (St. Louis, MO, USA). Deionized water with a resistivity of 18.2 MΩ·cm was obtained from a Millipore system (Billerica, MA, USA). Deuterium oxide (D_{2}O) with a purity of >99.8% was obtained from J&K Chemical (Beijing, China). 2,2,4-Trimethylpentane with a purity of 99% was obtained from Sigma-Aldrich.

The FTIR spectrum of HEWL in solution was measured in D_{2}O. Deuteration of HEWL was performed according to a literature protocol [^{−1} confirms full H/D exchange.

The FTIR spectra were obtained with a Bruker Vertex 70 FTIR spectrometer (Bruker, Karlsruhe, Germany). The spectrometer is equipped with a DTGS detector. The interferometer is a cube corner design. A Bruker-made sample shuttle (Model: A508/Q) is installed inside the sample compartment. The sample shuttle is an FTIR sampling accessory, which can provide interleaved sample and reference single-beam scanning in transmission mode without the need of opening sample compartment for sample change which could cause atmospheric perturbation. Sample shuttle can ensure constant water vapor concentration level during spectral acquisition thus result in complete atmospheric compensation. As shown in

To obtain a FTIR spectrum of a liquid sample, demountable CaF_{2} liquid cells are used. In particular, to obtain the absorption spectrum of HEWL in D_{2}O, the sample cell contains protein solution in D_{2}O and the reference cell contains solvent D_{2}O. Fifty micrometers spacer is used for both sample cell and reference cell. To obtain the absorption spectrum of liquid H_{2}O or D_{2}O, the sample cell contains H_{2}O or D_{2}O and the reference cell is empty cell. No spacer is used due to the strong absorption of water bending mode. To obtain the absorption spectrum of 2,2,4-trimethylpentane, the sample cell contains 2,2,4-trimethylpentane and the reference cell is empty. A 50 µm spacer is used for sample cell. The absorption spectrum of water vapor was obtained by introducing some atmospheric fluctuation between sample scanning and reference scanning of the empty optical path.

Spectral processing such as second derivative and FSD was performed using Bruker’s OPUS software (Version 7.2). The default window size in Savitzky-Golay algorithm for second derivative treatment is 9-point in OPUS software. Savitzky-Golay algorithm is also used for smoothing. All FTIR measurements were performed under ambient conditions. Typical acquisition parameters are listed below: spectral resolution, 4 cm^{−1}; scan number, 32; zero-filling factor, 4; apodization function, Blackman-Harris 3-Term; phase resolution, 16; phase correction mode, Mertz; aperture, 6 mm; scan speed, 10 kHz; acquisition mode, double-sided, forward-backward. The FTIR spectra presented here were all taken under the above acquisition condition unless otherwise mentioned. Besides the typical condition, we have run our experiments under other acquisition conditions such as using different scan number (

In this study, we challenged the reliability of the established criteria for the evaluation of water vapor interference in protein secondary structural analysis by FTIR spectroscopy through a comparative study of protein and liquid water. We explained why the established criteria are not reliable using mathematical reasoning and introduced a new concept called sample’s absorbance-dependent water vapor interference to support our argument. We then proposed a new criterion based on the comparison between the second derivative spectra of protein and liquid water to better evaluate water vapor interference. We suggest that people use this newly proposed criterion to evaluate the extent of water vapor interference in their FTIR spectra to ensure more reliable second derivative or FSD treatment on the protein amide I band during FTIR curve-fitting analysis.

Supplementary Information (PDF, 220 KB)

We gratefully acknowledge the financial supports from the National Natural Science Foundation of China (No. 21075027), the Natural Science Foundation of Hebei Province (No. B2011201082), Juren Plan of Hebei Province, the Key Project of Chinese Ministry of Education (No. 211014), and Research Fund for the Doctoral Program of Higher Education of China (20121301110003). G. Ma acknowledges Y. Sun for English editing.

Y. Zou conducted the experiment; Y. Zou and G. Ma performed the data analysis; G. Ma wrote the manuscript.

The authors declare no conflict of interest.

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