Abstract

The development of new spectral analysis methods in bio thin-film detection has generated intense interest in terahertz (THz) spectroscopy and its application in a wide range of fields. In this paper, it is the first time that machine learning methods are applied to the quantitative characterization of bovine serum albumin (BSA) deposited thin-films detected by terahertz time-domain spectroscopy. The spectra data of BSA thin-films prepared by solutions with concentrations ranging from 0.5 to 35 mg/ml are analyzed using the support vector regression method to learn the underlying model of the frequency against the target concentration. The learned mode successfully predicts the concentrations of the unknown test samples with a coefficient of determination R2 = 0.97932. Furthermore, aiming to identify the relevance of each frequency to the concentration, the maximal information coefficient statistical analysis is used and the three most discriminating frequencies in THz frequency are identified at 1.2, 1.1 and 0.5 THz respectively, which means a good prediction for BSA concentration can be achieved by using the top three relevant frequencies. Moreover, the top discriminating frequencies are in good agreement with the frequencies predicted by a long-wavelength elastic vibration model for BSA protein.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (5)

B. S. Kalanoor, M. Ronen, Z. Oren, D. Gerber, and Y. R. Tischler, “New Method to Study the Vibrational Modes of Biomolecules in the Terahertz Range Based on a Single-Stage Raman Spectrometer,” ACS Omega 2(3), 1232–1240 (2017).
[Crossref] [PubMed]

J. Song, L. C. Chen, and B. J. Li, “Super-sensitive optical biosensor with a spectrometer on a chip,” IEEE Biotechnology & Biotechnological Equipment 27(4), 4040–4043 (2017).
[Crossref]

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quant. 23(4), 8501112 (2017).
[Crossref]

A. Sanchez-Gonzalez, P. Micaelli, C. Olivier, T. R. Barillot, M. Ilchen, A. A. Lutman, A. Marinelli, T. Maxwell, A. Achner, M. Agåker, N. Berrah, C. Bostedt, J. D. Bozek, J. Buck, P. H. Bucksbaum, S. C. Montero, B. Cooper, J. P. Cryan, M. Dong, R. Feifel, L. J. Frasinski, H. Fukuzawa, A. Galler, G. Hartmann, N. Hartmann, W. Helml, A. S. Johnson, A. Knie, A. O. Lindahl, J. Liu, K. Motomura, M. Mucke, C. O’Grady, J. E. Rubensson, E. R. Simpson, R. J. Squibb, C. Såthe, K. Ueda, M. Vacher, D. J. Walke, V. Zhaunerchyk, R. N. Coffee, and J. P. Marangos, “Accurate prediction of X-ray pulse properties from a free-electron laser using machine learning,” Nat. Commun. 8, 15461 (2017).
[Crossref] [PubMed]

S. Ubaru, A. Międlar, Y. Saad, and J. R. Chelikowsky, “Formation enthalpies for transition metal alloys using machine learning,” Phys. Rev. B 95(21), 214102 (2017).
[Crossref]

2016 (4)

M. Hofmann, M. Winzer, C. Weber, and H. Gieseler, “Prediction of protein aggregation in high concentration protein solutions utilizing protein-protein interactions determined by low volume static light scattering,” J. Pharm. Sci. 105(6), 1819–1828 (2016).
[Crossref] [PubMed]

Y. Ren, P. N. Suganthan, and N. Srikanth, “A novel empirical mode decomposition with support vector regression for wind speed forecasting,” IEEE Trans. Neural Netw. Learn. Syst. 27(8), 1793–1798 (2016).
[Crossref] [PubMed]

M. Gocic, D. Petkovic, S. Shamshirband, and A. Kamsin, “Comparative analysis of reference evapotranspiration equations modelling by extreme learning machine,” Comput. Electron. Age. 127, 56–63 (2016).
[Crossref]

H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
[Crossref]

2015 (3)

H. Zhan, Q. Li, K. Zhao, L. Zhang, Z. Zhang, C. Zhang, and L. Xiao, “Evaluating PM2.5 at a construction site using terahertz radiation,” IEEE T. THZ Sci. Techn. 5(6), 1028–1034 (2015).
[Crossref]

O. Sushko, R. Dubrovka, and R. S. Donnan, “Sub-terahertz spectroscopy reveals that proteins influence the properties of water at greater distances than previously detected,” J. Chem. Phys. 142(5), 055101 (2015).
[Crossref] [PubMed]

Y. Sun, J. Zhong, C. Zhang, J. Zuo, and E. Pickwell-MacPherson, “Label-free detection and characterization of the binding of hemagglutinin protein and broadly neutralizing monoclonal antibodies using terahertz spectroscopy,” J. Biomed. Opt. 20(3), 037006 (2015).
[Crossref] [PubMed]

2014 (2)

W. Withayachumnankul, J. F. O’Hara, W. Cao, I. Al-Naib, and W. Zhang, “Limitation in thin-film sensing with transmission-mode terahertz time-domain spectroscopy,” Opt. Express 22(1), 972–986 (2014).
[Crossref] [PubMed]

J. El Haddad, F. de Miollis, J. Bou Sleiman, L. Canioni, P. Mounaix, and B. Bousquet, “Chemometrics applied to quantitative analysis of ternary mixtures by terahertz spectroscopy,” Anal. Chem. 86(10), 4927–4933 (2014).
[Crossref] [PubMed]

2013 (4)

S. Perticaroli, J. D. Nickels, G. Ehlers, H. O’Neill, Q. Zhang, and A. P. Sokolov, “Secondary structure and rigidity in model proteins,” Soft Matter 9(40), 9548–9556 (2013).
[Crossref] [PubMed]

L. Q. Hou, S. L. Yang, and Z. Q. Chen, “The use of data mining techniques and support vector regression for financial forecasting,” Int. J. Database Theory Appl. 6(4), 145–156 (2013).

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the Thickness of a Thin Paint Film by Applying a Modified Partial-Least-Squares-1 Method to Data Obtained in Terahertz Reflectometry,” J. Infrared Milli. Terahz. Waves 34(10), 646–659 (2013).
[Crossref]

A. Kazem, E. Sharifi, F. K. Hussain, M. Saberi, and O. K. Hussain, “Support vector regression with chaos-based firefly algorithm for stock market price forecasting,” Appl. Soft Comput. 13(2), 947–958 (2013).
[Crossref]

2012 (3)

Y. Sun, Z. Zhu, S. Chen, J. Balakrishnan, D. Abbott, A. T. Ahuja, and E. Pickwell-Macpherson, “Observing the temperature dependent transition of the GP2 peptide using terahertz spectroscopy,” PLoS One 7(11), e50306 (2012).
[Crossref] [PubMed]

J. F. O’Hara, W. Withayachumnankul, and I. Al-Naib, “A review on thin-film sensing with terahertz waves,” J. Infrared Millim. Te. 33(3), 245–291 (2012).
[Crossref]

L. K. Gifford, L. G. Carter, M. J. Gabanyi, H. M. Berman, and P. D. Adams, “The Protein Structure Initiative Structural Biology Knowledgebase Technology Portal: A Structural Biology Web Resource,” J. Struct. Funct. Genomics 13(2), 57–62 (2012).
[Crossref] [PubMed]

2011 (3)

Y. Sun, Y. Zhang, and E. Pickwell-Macpherson, “Investigating antibody interactions with a polar liquid using terahertz pulsed spectroscopy,” Biophys. J. 100(1), 225–231 (2011).
[Crossref] [PubMed]

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” ACM T. Intel. Syst. Tec. 2(3), 27 (2011).

D. N. Reshef, Y. A. Reshef, H. K. Finucane, S. R. Grossman, G. McVean, P. J. Turnbaugh, E. S. Lander, M. Mitzenmacher, and P. C. Sabeti, “Detecting novel associations in large data sets,” Science 334(6062), 1518–1524 (2011).
[Crossref] [PubMed]

2008 (1)

H. Yoneyama, M. Yamashita, S. Kasai, K. Kawase, R. Ueno, H. Ito, and T. Ouchi, “Terahertz spectroscopy of native-conformation and thermally denatured bovine serum albumin (BSA),” Phys. Med. Biol. 53(13), 3543–3549 (2008).
[Crossref] [PubMed]

2007 (3)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

E. Mylonas and D. I. Svergun, “Accuracy of molecular mass determination of proteins in solution by small-angle X-ray scattering,” J. Appl. Cryst. 40(s1), s245–s249 (2007).
[Crossref]

T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paint meters by multiple-regression analysis,” Appl. Opt. 46(30), 7518–7526 (2007).
[Crossref] [PubMed]

2006 (1)

J. Xu, K. W. Plaxco, and S. J. Allen, “Probing the collective vibrational dynamics of a protein in liquid water by terahertz absorption spectroscopy,” Protein Sci. 15(5), 1175–1181 (2006).
[Crossref] [PubMed]

2005 (1)

C. Mircean, I. Shmulevich, D. Cogdell, W. Choi, Y. Jia, I. Tabus, S. R. Hamilton, and W. Zhang, “Robust estimation of protein expression ratios with lysate microarray technology,” Bioinformatics 21(9), 1935–1942 (2005).
[Crossref] [PubMed]

2004 (2)

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385(1–2), 45–51 (2004).
[Crossref]

A. J. Smola and B. Scholkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
[Crossref]

2003 (2)

M. R. Kutteruf, C. M. Brown, L. K. Iwaki, M. B. Campbell, T. M. Korter, and E. J. Heilweil, “Terahertz spectroscopy of short-chain polypeptides,” Chem. Phys. Lett. 375(3–4), 337–343 (2003).
[Crossref]

H. J. Willison, K. Townson, J. Veitch, J. Boffey, N. Isaacs, S. M. Andersen, P. Zhang, C. C. Ling, and D. R. Bundle, “Synthetic disialylgalactose immunoadsorbents deplete anti-GQ1b antibodies from autoimmune neuropathy sera,” Brain 127(3), 680–691 (2003).
[Crossref] [PubMed]

2002 (1)

Y. Y. Studentsov, M. Schiffman, H. D. Strickler, G. Y. Ho, Y. Y. Pang, J. Schiller, R. Herrero, and R. D. Burk, “Enhanced enzyme-linked immunosorbent assay for detection of antibodies to virus-like particles of human papillomavirus,” J. Clin. Microbiol. 40(5), 1755–1760 (2002).
[Crossref] [PubMed]

2000 (1)

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320(1-2), 42–48 (2000).
[Crossref]

1996 (1)

J. I. Boye, I. Alli, and A. A. Ismail, “Interactions involved in the gelation of bovine serum albumin,” J. Agric. Food Chem. 44(4), 996–1004 (1996).
[Crossref]

1994 (1)

S. I. Bastrukov, “Low-frequency elastic response of a spherical particle,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 3166–3170 (1994).
[Crossref] [PubMed]

1948 (1)

J. D. Ferry, “Protein gels,” Adv. Protein Chem. 4, 1–78 (1948).
[Crossref] [PubMed]

Abbott, D.

Y. Sun, Z. Zhu, S. Chen, J. Balakrishnan, D. Abbott, A. T. Ahuja, and E. Pickwell-Macpherson, “Observing the temperature dependent transition of the GP2 peptide using terahertz spectroscopy,” PLoS One 7(11), e50306 (2012).
[Crossref] [PubMed]

Achner, A.

A. Sanchez-Gonzalez, P. Micaelli, C. Olivier, T. R. Barillot, M. Ilchen, A. A. Lutman, A. Marinelli, T. Maxwell, A. Achner, M. Agåker, N. Berrah, C. Bostedt, J. D. Bozek, J. Buck, P. H. Bucksbaum, S. C. Montero, B. Cooper, J. P. Cryan, M. Dong, R. Feifel, L. J. Frasinski, H. Fukuzawa, A. Galler, G. Hartmann, N. Hartmann, W. Helml, A. S. Johnson, A. Knie, A. O. Lindahl, J. Liu, K. Motomura, M. Mucke, C. O’Grady, J. E. Rubensson, E. R. Simpson, R. J. Squibb, C. Såthe, K. Ueda, M. Vacher, D. J. Walke, V. Zhaunerchyk, R. N. Coffee, and J. P. Marangos, “Accurate prediction of X-ray pulse properties from a free-electron laser using machine learning,” Nat. Commun. 8, 15461 (2017).
[Crossref] [PubMed]

Adams, P. D.

L. K. Gifford, L. G. Carter, M. J. Gabanyi, H. M. Berman, and P. D. Adams, “The Protein Structure Initiative Structural Biology Knowledgebase Technology Portal: A Structural Biology Web Resource,” J. Struct. Funct. Genomics 13(2), 57–62 (2012).
[Crossref] [PubMed]

Agåker, M.

A. Sanchez-Gonzalez, P. Micaelli, C. Olivier, T. R. Barillot, M. Ilchen, A. A. Lutman, A. Marinelli, T. Maxwell, A. Achner, M. Agåker, N. Berrah, C. Bostedt, J. D. Bozek, J. Buck, P. H. Bucksbaum, S. C. Montero, B. Cooper, J. P. Cryan, M. Dong, R. Feifel, L. J. Frasinski, H. Fukuzawa, A. Galler, G. Hartmann, N. Hartmann, W. Helml, A. S. Johnson, A. Knie, A. O. Lindahl, J. Liu, K. Motomura, M. Mucke, C. O’Grady, J. E. Rubensson, E. R. Simpson, R. J. Squibb, C. Såthe, K. Ueda, M. Vacher, D. J. Walke, V. Zhaunerchyk, R. N. Coffee, and J. P. Marangos, “Accurate prediction of X-ray pulse properties from a free-electron laser using machine learning,” Nat. Commun. 8, 15461 (2017).
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Y. Ren, P. N. Suganthan, and N. Srikanth, “A novel empirical mode decomposition with support vector regression for wind speed forecasting,” IEEE Trans. Neural Netw. Learn. Syst. 27(8), 1793–1798 (2016).
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S. Ubaru, A. Międlar, Y. Saad, and J. R. Chelikowsky, “Formation enthalpies for transition metal alloys using machine learning,” Phys. Rev. B 95(21), 214102 (2017).
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[Crossref] [PubMed]

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W. Withayachumnankul, J. F. O’Hara, W. Cao, I. Al-Naib, and W. Zhang, “Limitation in thin-film sensing with transmission-mode terahertz time-domain spectroscopy,” Opt. Express 22(1), 972–986 (2014).
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[Crossref]

Xiao, L.

H. Zhan, Q. Li, K. Zhao, L. Zhang, Z. Zhang, C. Zhang, and L. Xiao, “Evaluating PM2.5 at a construction site using terahertz radiation,” IEEE T. THZ Sci. Techn. 5(6), 1028–1034 (2015).
[Crossref]

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H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
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[Crossref] [PubMed]

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L. Q. Hou, S. L. Yang, and Z. Q. Chen, “The use of data mining techniques and support vector regression for financial forecasting,” Int. J. Database Theory Appl. 6(4), 145–156 (2013).

Yasuda, T.

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T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the Thickness of a Thin Paint Film by Applying a Modified Partial-Least-Squares-1 Method to Data Obtained in Terahertz Reflectometry,” J. Infrared Milli. Terahz. Waves 34(10), 646–659 (2013).
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H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
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H. Zhan, Q. Li, K. Zhao, L. Zhang, Z. Zhang, C. Zhang, and L. Xiao, “Evaluating PM2.5 at a construction site using terahertz radiation,” IEEE T. THZ Sci. Techn. 5(6), 1028–1034 (2015).
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[Crossref] [PubMed]

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H. Zhan, Q. Li, K. Zhao, L. Zhang, Z. Zhang, C. Zhang, and L. Xiao, “Evaluating PM2.5 at a construction site using terahertz radiation,” IEEE T. THZ Sci. Techn. 5(6), 1028–1034 (2015).
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H. Zhan, Q. Li, K. Zhao, L. Zhang, Z. Zhang, C. Zhang, and L. Xiao, “Evaluating PM2.5 at a construction site using terahertz radiation,” IEEE T. THZ Sci. Techn. 5(6), 1028–1034 (2015).
[Crossref]

Zhao, H.

H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
[Crossref]

Zhao, K.

H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
[Crossref]

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[Crossref]

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Y. Sun, J. Zhong, C. Zhang, J. Zuo, and E. Pickwell-MacPherson, “Label-free detection and characterization of the binding of hemagglutinin protein and broadly neutralizing monoclonal antibodies using terahertz spectroscopy,” J. Biomed. Opt. 20(3), 037006 (2015).
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H. L. Zhan, K. Zhao, H. Zhao, Q. Li, S. M. Zhu, and L. Z. Xiao, “The spectral analysis of fuel oils using terahertz radiation and chemometric methods,” J. Phys. D Appl. Phys. 49(39), 395101 (2016).
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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of PCA-based denoising method. The scores plot of the first two principal components of the 7 measurements at the concentration of 6 mg/ml.
Fig. 2
Fig. 2 (a) Time dependence THz intensity spectra of reference and BSA thin-films prepared by the protein aqueous solutions in the concentration range from 0.5 to 35 mg/ml; (b) The transmission spectrum for BSA thin-film prepared by the protein solution of 6 mg/ml from 0.1 to 2.6 THz; (c) illustration of the data matrix with 147 rows (21 concentrations * 7 measurements) and 44 columns (43 frequencies + 1 concentration value).
Fig. 3
Fig. 3 LOOCV-SVR prediction for various concentrations in the range from 0.5 to 35 mg/ml. (a) The distributions of actual and predicted concentrations in LOOCV, the valid value of x axes is from 1 to 135 represents the 135 spectroscopy measurements; (b) The actual concentrations against the predicted concentrations in LOOCV.
Fig. 4
Fig. 4 The prediction results using hold-out validation for various concentrations in the range from 0.5 to 35 mg/ml. (a) The distributions of actual and predicted concentrations in hold-out validation, the valid value of x axes is from 1 to 135 represents the 135 spectroscopy measurements; (b) The actual concentrations against the predicted concentrations in hold-out validation.
Fig. 5
Fig. 5 The curves of R2 with different the number of the input relevant frequencies
Fig. 6
Fig. 6 The distribution of the instances in (a) the 3D-space of the top three relevant frequencies, and in (b)(c)(d) the corresponding 2D projections in the top two frequencies respectively. The units for the x, y, and z axes are normalized units represent the amplitude of the complex transmission coefficient of the samples.

Tables (1)

Tables Icon

Table 1 The top five relevant frequencies based on MIC values

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

f(x)=w·Φ( x )+b
y i f( x i )ε+ ξ i
f( x i ) y i ε+ ξ i *
min w,b,ξ 1 2 | | w | | 2 +C i=1 n ( ξ i + ξ i * )
M ( F,Y ) ( a,b ) = maxI( ( F,Y ) | G ) logmin{ a,b }
MIC( F,Y )= max ab<B( n ) { M ( F,Y ) ( a,b ) }
T s (ω)=abs[ FFT( E s (t)) FFT( E r (t)) ]

Metrics