Abstract

Fluorescence readout is an important technique for detecting biomolecules. In this paper, we present a multiplexed fluorescence readout method using time varied fluorescence signals. To generate the fluorescence signals, coded strands and a set of universal molecular beacons are introduced. Each coded strand represents the existence of an assigned target molecule. The coded strands have coded sequences to generate temporary fluorescence signals through binding to the molecular beacons. The signal generating processes are modeled based on the reaction kinetics between the coded strands and molecular beacons. The model is used to decode the detected fluorescence signals using maximum likelihood estimation. Multiplexed fluorescence readout was experimentally demonstrated with three molecular beacons. Numerical analysis showed that the readout accuracy was enhanced by the use of time-varied fluorescence signals.

© 2016 Optical Society of America

Full Article  |  PDF Article
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2015 (1)

K. Komiya and Y. Yamamura, “Cascading DNA Generation Reaction for Controlling DNA Nanomachines at a Physiological Temperature,” New Generat. Comput. 33, 213–229 (2015).
[Crossref]

2014 (3)

T. Nishimura, Y. Ogura, K. Yamada, Y Ohno, and J. Tanida, “Biomolecule-to-fluorescent-color encoder: modulation of fluorescence emission via DNA structural changes,” Biomed. Opt. Express 7, 2082–2090 (2014).
[Crossref]

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

2013 (3)

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

2012 (3)

Y. N. Teo and E. T. Kool, “DNA-Multichromophore Systems,” Chem. Rev. 1124221–4245 (2012).
[Crossref] [PubMed]

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

M. B. Baker, G. Bao, and C. D. Searles, “In vitro quantification of specific microRNA using molecular beacons,” Nucl. Acids Res. 40, 1–12 (2012).
[Crossref]

2011 (3)

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

2007 (1)

Q. Huang, Q. Hu, and Q. Li, “Identification of 8 Foodborne Pathogens by Multicolor Combinational Probe Coding Technology in a Single Real-Time PCR,” Clinical Chemistry 53, 1741–1748 (2007).
[Crossref] [PubMed]

2006 (1)

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Li, Y. T. H. Cu, and D. Luo, “Multiplexed detection of pathogen DNA with DNA-based fluorescence nanobar-codes,” Nat. Biotechnol. 23, 885–889 (2005).
[Crossref] [PubMed]

2004 (3)

R. M. Dirks and N. A. Pierce, “Triggered amplification by hybridization chain reaction,” Proc. Natl. Acad. Sci. USA 101, 15275–15278 (2004).
[Crossref] [PubMed]

R. G. Rutledge, “Sigmoidal curve-fitting redefines quantitative real-time PCR with the prospective of developing automated high-throughput applications,” Nucl. Acids Res. 32, e178 (2004).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

2003 (1)

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

2001 (1)

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

1999 (1)

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

1998 (1)

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Alland, D.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Allen, K. E.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Alonso-Betanzos, A.

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

Atochin, I.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Baker, M. B.

M. B. Baker, G. Bao, and C. D. Searles, “In vitro quantification of specific microRNA using molecular beacons,” Nucl. Acids Res. 40, 1–12 (2012).
[Crossref]

Bao, G.

M. B. Baker, G. Bao, and C. D. Searles, “In vitro quantification of specific microRNA using molecular beacons,” Nucl. Acids Res. 40, 1–12 (2012).
[Crossref]

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

Behlke, M. A.

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

Benhaim, L.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Bentez, J.M.

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

Blons, H.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Boln-Canedo, V.

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

Bouch, O.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Chen, C.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Church, G. M.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Corre, D. L.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Cu, Y. T. H.

Y. Li, Y. T. H. Cu, and D. Luo, “Multiplexed detection of pathogen DNA with DNA-based fluorescence nanobar-codes,” Nat. Biotechnol. 23, 885–889 (2005).
[Crossref] [PubMed]

Dirks, R. M.

R. M. Dirks and N. A. Pierce, “Triggered amplification by hybridization chain reaction,” Proc. Natl. Acad. Sci. USA 101, 15275–15278 (2004).
[Crossref] [PubMed]

Foss, K. M.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Franco, E.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Gao, X.

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

Graham, R.J.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Griffiths, A. D.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Hamada, S.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Han, M.

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

Han, W.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Hartman, M. R.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Herrera, F.

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

Homyk, A.

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

Hu, Q.

Q. Huang, Q. Hu, and Q. Li, “Identification of 8 Foodborne Pathogens by Multicolor Combinational Probe Coding Technology in a Single Real-Time PCR,” Clinical Chemistry 53, 1741–1748 (2007).
[Crossref] [PubMed]

Huang, J.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Huang, Q.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Q. Huang, Q. Hu, and Q. Li, “Identification of 8 Foodborne Pathogens by Multicolor Combinational Probe Coding Technology in a Single Real-Time PCR,” Clinical Chemistry 53, 1741–1748 (2007).
[Crossref] [PubMed]

Hutchison, J. B.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Jia, H.

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

Jungmann, R.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Kapsner, K.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Kartalov, E.

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

Kim, J.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Komiya, K.

K. Komiya and Y. Yamamura, “Cascading DNA Generation Reaction for Controlling DNA Nanomachines at a Physiological Temperature,” New Generat. Comput. 33, 213–229 (2015).
[Crossref]

Kool, E. T.

Y. N. Teo and E. T. Kool, “DNA-Multichromophore Systems,” Chem. Rev. 1124221–4245 (2012).
[Crossref] [PubMed]

Kotsopoulos, S. K.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Kramer, F. R.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Landi, B.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Lao, K.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Laurent-Puig, P.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Lee, L.G.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Leifer, A. M.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Levner, D.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Li, C.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

Li, Q.

Q. Huang, Q. Hu, and Q. Li, “Identification of 8 Foodborne Pathogens by Multicolor Combinational Probe Coding Technology in a Single Real-Time PCR,” Clinical Chemistry 53, 1741–1748 (2007).
[Crossref] [PubMed]

Li, X.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Li, Y.

Y. Li, Y. T. H. Cu, and D. Luo, “Multiplexed detection of pathogen DNA with DNA-based fluorescence nanobar-codes,” Nat. Biotechnol. 23, 885–889 (2005).
[Crossref] [PubMed]

Li, Z.

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

Lin, C.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Link, D. R.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Livak, K. J.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Livak, K.J.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Luo, D.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Y. Li, Y. T. H. Cu, and D. Luo, “Multiplexed detection of pathogen DNA with DNA-based fluorescence nanobar-codes,” Nat. Biotechnol. 23, 885–889 (2005).
[Crossref] [PubMed]

Miller, L. P.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Mullah, B.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Neri, M.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Nie, S.

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

Nishimura, T.

Ogura, Y.

Ohno, Y

Pallier, K.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Pekin, D.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Piatek, A. S.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Pierce, N. A.

R. M. Dirks and N. A. Pierce, “Triggered amplification by hybridization chain reaction,” Proc. Natl. Acad. Sci. USA 101, 15275–15278 (2004).
[Crossref] [PubMed]

Pol, A. C.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Rajagopal, A.

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

Rose, S. D.

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

Ruiz, R. C. H.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Rutledge, R. G.

R. G. Rutledge, “Sigmoidal curve-fitting redefines quantitative real-time PCR with the prospective of developing automated high-throughput applications,” Nucl. Acids Res. 32, e178 (2004).
[Crossref] [PubMed]

Scherer, A.

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

Searles, C. D.

M. B. Baker, G. Bao, and C. D. Searles, “In vitro quantification of specific microRNA using molecular beacons,” Nucl. Acids Res. 40, 1–12 (2012).
[Crossref]

Shih, W. M.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Sima, C.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Simmel, F. C.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Snchez-Maroo, N.

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

Straus, N. A.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Su, J. Z.

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

Taly, V.

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Tanida, J.

Telentii, A.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Teo, Y. N.

Y. N. Teo and E. T. Kool, “DNA-Multichromophore Systems,” Chem. Rev. 1124221–4245 (2012).
[Crossref] [PubMed]

Tsourkas, A.

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

Tyagi, S.

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Ugolini, D.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Vinayak, R.S.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Weiss, G. J.

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Weitz, M.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Wen, H.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Winfree, E.

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

Woudenberg, T.M.

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Xu, C. Y.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Xu, N. L.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Yamada, K.

Yamamura, Y.

K. Komiya and Y. Yamamura, “Cascading DNA Generation Reaction for Controlling DNA Nanomachines at a Physiological Temperature,” New Generat. Comput. 33, 213–229 (2015).
[Crossref]

Yana, J.

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

Yancey, K. G.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Yeung, V.

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Yin, P.

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

Yu, Y.

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Zhang, J.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Zheng, L.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Zhu, Y.

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Anal. Chem. (1)

A. Rajagopal, A. Scherer, A. Homyk, and E. Kartalov, “Supercolor Coding Methods for Large-Scale Multiplexing of Biochemical Assays,” Anal. Chem. 85, 7629–7636 (2013).
[Crossref] [PubMed]

Biochemical and Biophysical Research Communications (1)

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Multiplexing RT-PCR for the detection of multiple miRNA species in small samples,” Biochemical and Biophysical Research Communications 343, 85–89 (2006).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

BioTechniques (1)

L.G. Lee, K.J. Livak, B. Mullah, R.J. Graham, R.S. Vinayak, and T.M. Woudenberg, “Seven-color, homogeneous detection of six PCR products,” BioTechniques 27, 342–349 (1999).
[PubMed]

Chem. Commun. (1)

C. Li, Z. Li, H. Jia, and J. Yana, “One–step ultrasensitive detection of microRNAs with loop-mediated isothermal amplification (LAMP),” Chem. Commun. 47, 2595–2597 (2011).
[Crossref]

Chem. Rev. (1)

Y. N. Teo and E. T. Kool, “DNA-Multichromophore Systems,” Chem. Rev. 1124221–4245 (2012).
[Crossref] [PubMed]

Clin. Chem. (1)

V. Taly, D. Pekin, L. Benhaim, S. K. Kotsopoulos, D. L. Corre, X. Li, I. Atochin, D. R. Link, A. D. Griffiths, K. Pallier, H. Blons, O. Bouch, B. Landi, J. B. Hutchison, and P. Laurent-Puig, “Multiplex picodroplet digital PCR to detect KRAS mutations in circulating DNA from the plasma of colorectal cancer patients,” Clin. Chem. 59, 1722–1731 (2013).
[Crossref] [PubMed]

Clinical Chemistry (1)

Q. Huang, Q. Hu, and Q. Li, “Identification of 8 Foodborne Pathogens by Multicolor Combinational Probe Coding Technology in a Single Real-Time PCR,” Clinical Chemistry 53, 1741–1748 (2007).
[Crossref] [PubMed]

Information Sciences (1)

V. Boln-Canedo, N. Snchez-Maroo, A. Alonso-Betanzos, J.M. Bentez, and F. Herrera, “A review of microarray datasets and applied feature selection methods,” Information Sciences 282, 10141–10154 (2014).

J. Thorac. Oncol. (1)

K. M. Foss, C. Sima, D. Ugolini, M. Neri, K. E. Allen, and G. J. Weiss, “miR-1254 and miR-574-5p: serum-based microRNA biomarkers for early-stage non-small cell lung cancer,” J. Thorac. Oncol. 6, 482–488 (2011).
[Crossref] [PubMed]

Nano Letters (1)

K. Lao, N. L. Xu, V. Yeung, C. Chen, K. J. Livak, and N. A. Straus, “Nanometer-scale Fluorescence Resonance Optical Waveguides,” Nano Letters 4, 1035–1039 (2004).
[Crossref]

Nanoscale (1)

M. R. Hartman, R. C. H. Ruiz, S. Hamada, C. Y. Xu, K. G. Yancey, Y. Yu, W. Han, and D. Luo, Nanoscale, “Point-of-care nucleic acid detection using nanotechnology,” Nanoscale 5, 10141–10154 (2013).
[Crossref] [PubMed]

Nat. Biotechnol. (3)

M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. 19, 631–635 (2001).
[Crossref] [PubMed]

Y. Li, Y. T. H. Cu, and D. Luo, “Multiplexed detection of pathogen DNA with DNA-based fluorescence nanobar-codes,” Nat. Biotechnol. 23, 885–889 (2005).
[Crossref] [PubMed]

A. S. Piatek, S. Tyagi, A. C. Pol, A. Telentii, L. P. Miller, F. R. Kramer, and D. Alland, “Molecular beacon sequence analysis for detecting drug resistance in Mycobacterium tuberculosis, ” Nat. Biotechnol. 16, 359–363 (1998).
[Crossref] [PubMed]

Nat. Chem. (2)

C. Lin, R. Jungmann, A. M. Leifer, C. Li, D. Levner, G. M. Church, W. M. Shih, and P. Yin, “Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA,” Nat. Chem. 4, 832–839 (2012).
[Crossref] [PubMed]

M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F. C. Simmel, “Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator,” Nat. Chem. 6, 295–302 (2014).
[Crossref] [PubMed]

New Generat. Comput. (1)

K. Komiya and Y. Yamamura, “Cascading DNA Generation Reaction for Controlling DNA Nanomachines at a Physiological Temperature,” New Generat. Comput. 33, 213–229 (2015).
[Crossref]

Nucl. Acids Res. (3)

M. B. Baker, G. Bao, and C. D. Searles, “In vitro quantification of specific microRNA using molecular beacons,” Nucl. Acids Res. 40, 1–12 (2012).
[Crossref]

R. G. Rutledge, “Sigmoidal curve-fitting redefines quantitative real-time PCR with the prospective of developing automated high-throughput applications,” Nucl. Acids Res. 32, e178 (2004).
[Crossref] [PubMed]

A. Tsourkas, M. A. Behlke, S. D. Rose, and G. Bao, “Hybridization kinetics and thermodynamics of molecular beacons,” Nucl. Acids Res. 31, 1313–1330 (2003).
[Crossref]

PLoS ONE (1)

Q. Huang, L. Zheng, Y. Zhu, J. Zhang, H. Wen, and J. Huang, “Multicolor Combinatorial Probe Coding for Real-Time PCR, ” PLoS ONE 6, e16033 (2011).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

R. M. Dirks and N. A. Pierce, “Triggered amplification by hybridization chain reaction,” Proc. Natl. Acad. Sci. USA 101, 15275–15278 (2004).
[Crossref] [PubMed]

Other (1)

M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming,” http://cvxr.com/cvx (2013).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of multiplexed fluorescence detection. (b) Implementation of fluorescence conversion of a target molecule with a coded strand and set of molecular beacons.

Fig. 2
Fig. 2

(a) Fluorescence spectra and (b) log-likelihoods for samples 1 to 10.

Fig. 3
Fig. 3

Estimated and measured fluorescence signals for (a) sample A, (b) sample B, and (c) sample C. “Estimated” refers to the intensities calculated taking the minimum likelihood.

Fig. 4
Fig. 4

Correct readout rate to (a) readout noise, (b) reaction speed error, and (c) signal intensity error.

Tables (3)

Tables Icon

Table 1 Sequences used in this study. *1, *2, *3, and *4 represent the positions modified with Alexa555, BHQ-2, Alexa594, and Alexa647, respectively.

Tables Icon

Table 2 Sequences of coded strands.

Tables Icon

Table 3 Measured parameters of fluorescence time variations for coded strands.

Equations (7)

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

y ( t ) = H ( t ) x + z ,
L = t = 1 T i = 1 N λ j = 1 N tar 1 2 π σ exp { [ y i ( t ) h i , j ( t ) x j b ] 2 2 σ 2 } ,
x ^ = arg max x { 0 , 1 } N tar × 1 ( L ) .
h i , j ( t ) = A i , j { 1 exp ( k i , j B 0 t ) } ,
SNR = 20 log I max σ SN ,
SDR = 10 log 10 t = 1 T H ( t ) x 2 2 t = 1 T H ( t ) x y sd ( t ) 2 2 ,
MER = 10 log 10 t = 1 T H ( t ) x 2 2 t = 1 T H ( t ) x y me ( t ) 2 2 ,

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