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Digital Immunoassays for Sensitive Quantification of Blood Biomarkers Using Solid-State Nanopores.

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The authors' code

C · 265 lines · 9.6 KB · GPL-3.0

  1. /*
  2. bessel.c is a C port of select functions from the
  3. python library bessel filter implementation, scipy.signal.bessel.
  4. Copyright (c) 2001, 2002 Enthought, Inc.
  5. All rights reserved.
  6. Copyright (c) 2003-2016 SciPy Developers.
  7. All rights reserved.
  8. Redistribution and use in source and binary forms, with or without
  9. modification, are permitted provided that the following conditions are met:
  10. a. Redistributions of source code must retain the above copyright notice,
  11. this list of conditions and the following disclaimer.
  12. b. Redistributions in binary form must reproduce the above copyright
  13. notice, this list of conditions and the following disclaimer in the
  14. documentation and/or other materials provided with the distribution.
  15. c. Neither the name of Enthought nor the names of the SciPy Developers
  16. may be used to endorse or promote products derived from this software
  17. without specific prior written permission.
  18. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  19. AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20. IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21. ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS
  22. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
  23. OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  24. SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  25. INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  26. CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  27. ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
  28. THE POSSIBILITY OF SUCH DAMAGE.
  29. */
  30. #include"bessel.h"
  31. void filter_signal(double *signal, double *paddedsignal, bessel *lpfilter, int64_t length)
  32. {
  33. int64_t i;
  34. int64_t p;
  35. int64_t end;
  36. int64_t order = lpfilter->order;
  37. int64_t padding = lpfilter->padding;
  38. double *temp = lpfilter->temp;
  39. double *dcof = lpfilter->dcof;
  40. double *ccof = lpfilter->ccof;
  41. end = length+2*(order+padding);
  42. int64_t imax = order+padding;
  43. double start_padval = signal_average(signal,padding);
  44. double end_padval = signal_average(&signal[length - padding], padding);
  45. for (i=0; i<imax; i++)
  46. {
  47. temp[i] = start_padval;
  48. paddedsignal[i] = start_padval;
  49. paddedsignal[end-1-i] = end_padval;
  50. temp[end-1-i] = end_padval;
  51. }
  52. for (i=order; i<end; i++)
  53. {
  54. temp[i] = ccof[0]*paddedsignal[i];
  55. for (p=1; p<=order; p++)
  56. {
  57. temp[i] += ccof[p]*paddedsignal[i-p] - dcof[p]*temp[i-p];
  58. }
  59. }
  60. start_padval = signal_average(&temp[order],padding);
  61. end_padval = signal_average(&temp[length+imax],padding);
  62. for (i=0; i<imax; i++)
  63. {
  64. paddedsignal[end-1-i] = end_padval;
  65. paddedsignal[i] = start_padval;
  66. }
  67. for (i=order; i<end; i++)
  68. {
  69. paddedsignal[end-1-i] = ccof[0]*temp[end-1-i];
  70. for (p=1; p<=order; p++)
  71. {
  72. paddedsignal[end-1-i] += ccof[p]*temp[end-1-i+p] - dcof[p]*paddedsignal[end-1-i+p];
  73. }
  74. }
  75. }
  76. void besselap(int64_t N, double complex *poles, double complex *zeros)
  77. {
  78. switch(N)
  79. {
  80. case 2:
  81. poles[0] = -.8660254037844386467637229 + .4999999999999999999999996 * I;
  82. poles[1] = -.8660254037844386467637229 - .4999999999999999999999996 * I;
  83. zeros[0] = -1.0 + 0*I;
  84. zeros[1] = -1.0 + 0*I;
  85. break;
  86. case 4:
  87. poles[0] = -.6572111716718829545787781 - .8301614350048733772399715 * I;
  88. poles[1] = -.6572111716718829545787788 + .8301614350048733772399715 * I;
  89. poles[2] = -.9047587967882449459642637 - .2709187330038746636700923 * I;
  90. poles[3] = -.9047587967882449459642624 + .2709187330038746636700926 * I;
  91. zeros[0] = -1.0 + 0*I;
  92. zeros[1] = -1.0 + 0*I;
  93. zeros[2] = -1.0 + 0*I;
  94. zeros[3] = -1.0 + 0*I;
  95. break;
  96. case 6:
  97. poles[0] = -.9093906830472271808050953 - .1856964396793046769246397 * I;
  98. poles[1] = -.9093906830472271808050953 + .1856964396793046769246397 * I;
  99. poles[2] = -.7996541858328288520243325 - .5621717346937317988594118 * I;
  100. poles[3] = -.7996541858328288520243325 + .5621717346937317988594118 * I;
  101. poles[4] = -.5385526816693109683073792 - .9616876881954277199245657 * I;
  102. poles[5] = -.5385526816693109683073792 + .9616876881954277199245657 * I;
  103. zeros[0] = -1.0 + 0*I;
  104. zeros[1] = -1.0 + 0*I;
  105. zeros[2] = -1.0 + 0*I;
  106. zeros[3] = -1.0 + 0*I;
  107. zeros[4] = -1.0 + 0*I;
  108. zeros[5] = -1.0 + 0*I;
  109. break;
  110. case 8:
  111. poles[0] = -.9096831546652910216327629 - .1412437976671422927888150 * I;
  112. poles[1] = -.9096831546652910216327629 + .1412437976671422927888150 * I;
  113. poles[2] = -.8473250802359334320103023 - .4259017538272934994996429 * I;
  114. poles[3] = -.8473250802359334320103023 + .4259017538272934994996429 * I;
  115. poles[4] = -.7111381808485399250796172 - .7186517314108401705762571 * I;
  116. poles[5] = -.7111381808485399250796172 + .7186517314108401705762571 * I;
  117. poles[6] = -.4621740412532122027072175 - 1.034388681126901058116589 * I;
  118. poles[7] = -.4621740412532122027072175 + 1.034388681126901058116589 * I;
  119. zeros[0] = -1.0 + 0*I;
  120. zeros[1] = -1.0 + 0*I;
  121. zeros[2] = -1.0 + 0*I;
  122. zeros[3] = -1.0 + 0*I;
  123. zeros[4] = -1.0 + 0*I;
  124. zeros[5] = -1.0 + 0*I;
  125. zeros[6] = -1.0 + 0*I;
  126. zeros[7] = -1.0 + 0*I;
  127. break;
  128. case 10:
  129. poles[0] = -.9091347320900502436826431 - .1139583137335511169927714 * I;
  130. poles[1] = -.9091347320900502436826431 + .1139583137335511169927714 * I;
  131. poles[2] = -.8688459641284764527921864 - .3430008233766309973110589 * I;
  132. poles[3] = -.8688459641284764527921864 + .3430008233766309973110589 * I;
  133. poles[4] = -.7837694413101441082655890 - .5759147538499947070009852 * I;
  134. poles[5] = -.7837694413101441082655890 + .5759147538499947070009852 * I;
  135. poles[6] = -.6417513866988316136190854 - .8175836167191017226233947 * I;
  136. poles[7] = -.6417513866988316136190854 + .8175836167191017226233947 * I;
  137. poles[8] = -.4083220732868861566219785 - 1.081274842819124562037210 * I;
  138. poles[9] = -.4083220732868861566219785 + 1.081274842819124562037210 * I;
  139. zeros[0] = -1.0 + 0*I;
  140. zeros[1] = -1.0 + 0*I;
  141. zeros[2] = -1.0 + 0*I;
  142. zeros[3] = -1.0 + 0*I;
  143. zeros[4] = -1.0 + 0*I;
  144. zeros[5] = -1.0 + 0*I;
  145. zeros[6] = -1.0 + 0*I;
  146. zeros[7] = -1.0 + 0*I;
  147. zeros[8] = -1.0 + 0*I;
  148. zeros[9] = -1.0 + 0*I;
  149. break;
  150. }
  151. }
  152. void polymult(double complex *roots, int64_t N, double *rcoefs)
  153. {
  154. int64_t i, j;
  155. double complex *polycoefs;
  156. polycoefs = calloc_and_check(N+1, sizeof(double complex),"Cannot allocate polynomial coefficients");
  157. polycoefs[N]=1.0;
  158. for (i=0; i<N; i++)
  159. {
  160. for (j=0; j<N+1; j++)
  161. {
  162. polycoefs[j] = -roots[i]*polycoefs[j] + (j == N ? 0 : polycoefs[j+1]);
  163. }
  164. }
  165. for (i=0; i<N+1; i++)
  166. {
  167. rcoefs[i] = creal(polycoefs[i]);
  168. }
  169. free(polycoefs);
  170. }
  171. double scale_filter(double complex *poles, int64_t N, double warped, double scale)
  172. {
  173. int64_t i;
  174. for (i=0; i<N; i++)
  175. {
  176. poles[i] *= warped;
  177. }
  178. return scale * pow(warped, (double) N);
  179. }
  180. double bilinear(double complex *poles, int64_t N, double scale, double fs)
  181. {
  182. double fs2 = 2.0 * fs;
  183. double complex poleprod = 1;
  184. int64_t i;
  185. for (i=0; i<N; i++)
  186. {
  187. poleprod *= fs2 - poles[i];
  188. poles[i] = (fs2 + poles[i])/(fs2-poles[i]);
  189. }
  190. return scale * creal(1.0 / poleprod);
  191. }
  192. void transform_filter(double complex *poles, double complex *zeros, int64_t N, double scale, double *b, double *a)
  193. {
  194. int64_t i;
  195. polymult(zeros, N, b);
  196. polymult(poles, N, a);
  197. for (i=0; i<N+1; i++)
  198. {
  199. b[i] *= scale;
  200. }
  201. }
  202. bessel *initialize_filter(int usefilter, int eventfilter, int64_t order, double cutoff, int64_t length)
  203. {
  204. if (usefilter || eventfilter)
  205. {
  206. bessel *lpfilter;
  207. lpfilter = calloc_and_check(1,sizeof(bessel),"cannot allocate filter struct");
  208. lpfilter->order = order;
  209. lpfilter->cutoff = cutoff;
  210. lpfilter->padding = 100 * 2.0 / cutoff;;
  211. double complex *poles;
  212. double complex *zeros;
  213. poles = calloc_and_check(order,sizeof(double complex),"Cannot allocate Bessel poles");
  214. zeros = calloc_and_check(order,sizeof(double complex),"Cannot allocate Bessel zeros");
  215. lpfilter->ccof = calloc_and_check(order+1,sizeof(double complex),"Cannot allocate ccof");
  216. lpfilter->dcof = calloc_and_check(order+1,sizeof(double complex),"Cannot allocate dcof");
  217. double fs = 2.0;
  218. double warped = 2.0 * fs * tan(M_PI * cutoff / fs);
  219. double scale = 1;
  220. besselap(order, poles, zeros);
  221. scale = scale_filter(poles,order, warped, scale);
  222. scale = bilinear(poles, order, scale, fs);
  223. transform_filter(poles, zeros, order, scale, lpfilter->ccof, lpfilter->dcof);
  224. lpfilter->temp = NULL;
  225. lpfilter->temp = calloc_and_check(length+2*(order+lpfilter->padding), sizeof(double),"Cannot allocate filter temp");
  226. free(poles);
  227. free(zeros);
  228. return lpfilter;
  229. }
  230. return NULL;
  231. }
  232. void free_filter(bessel *lpfilter)
  233. {
  234. free(lpfilter->dcof);
  235. free(lpfilter->ccof);
  236. free(lpfilter->temp);
  237. free(lpfilter);
  238. }

bessel.c at commit 8bab778, under GPL-3.0 · at the source

Overview

Authors: Liqun He1, Breeana Elliott1, Philipp Mensing1, Kyle Briggs1, Michel Godin1, Jonathan Flax2, James McGrath3, Vincent Tabard-Cossa1
  1. Department of Physics, University of Ottawa, Ottawa K1N 6N5, Canada
  2. Department of Urology, University of Rochester Medical Center, Rochester, New York 14620, United States
  3. Department of Biomedical Engineering, University of Rochester, Rochester, New York 14627, United States
Institutions: University of Ottawa (Canada); University of Rochester Medicine (United States); University of Rochester (United States)
Journal: ACS nano, volume 20, issue 13, pages 10308-10319
Dates: received 26 September 2025; accepted 16 March 2026; published online 24 March 2026; in print April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1021/acsnano.5c16690 · PMID 41873753 · PMCID PMC13063814 · OpenAlex W7140165637
Open access: hybrid, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: other (modality), human (organism), traumatic brain injury (population)
Keywords: solid-state nanopores, digital immunoassay, DNA nanotechnology, single-molecule counting, traumatic brain injury, neurodegenerative disease, glial fibrillary acidic protein
MeSH: Glial Fibrillary Acidic Protein*, Nanopores*, Biomarkers, DNA, Gold, Humans, Immunoassay, Metal Nanoparticles (* major topic)
Topic: Nanopore and Nanochannel Transport Studies (Biomedical Engineering, Engineering), according to OpenAlex
Funding: National Institute of Biomedical Imaging and Bioengineering (5R01EB031581-04); NIBIB NIH HHS (R01 EB031581)
Citations: cited by 1 paper (Europe PMC); 95 references in the paper

Abstract

Digital immunoassays enable highly sensitive detection of biomolecules, offering absolute quantification rather than relying on bulk signal intensity. We adapt a digital immunoassay scheme for a nanopore sensor, a versatile platform for single-molecule counting. Current nanopore sensors have demonstrated great progress when counting nucleic acids but struggle with proteins due to variability in translocation behavior and limited recognition strategies. While recent advancements have highlighted the promise of nanopore platforms for protein studies, precise quantification remains a challenge. Here, building on previous work, we present a nanopore-based digital immunoassay that employs gold nanoparticle-mediated molecular amplification with a single-molecule readout. This approach translates protein recognition into quantifiable DNA, enabling a precise digital assay. This assay employs a DNA NanoLock probe combined with a paramagnetic bead-based immunocapture, where the target proteins trigger a structural transformation of the NanoLock, converting their presence into a binary DNA-based signal. By incorporating AuNPs carrying hundreds of DNA proxy reporters, we effectively amplify the detectable signal by 2 orders of magnitude, significantly improving sensitivity. We validate the performance of this system by detecting the glial fibrillary acidic protein, a biomarker for traumatic brain injury and neurodegenerative diseases, in plasma samples and demonstrate high femtomolar-level sensitivity (∼40 pg/mL). Using the NanoLock probe, we further mitigate previous challenges, with reduced assay times (hours) and extended dynamic range (3-log). The self-calibrating nature of this digital approach offers robust, reproducible measurements across different nanopores, eliminating interdevice variability.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above.

shadowk29/CUSUM

License: GPL-3.0
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 8bab778137a3caed2feedc28b213738d7028caa5, 24 June 2020
Languages: C (7), C/C++ (7)
Size: 19 files, 14 scripts
Software Heritage: not archived
Found in: “Data Availability Statement”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
16 files

Zenodo 595675

License: other-open
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: the references
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
16 files
At the source:

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 28 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability Statement

The raw data included this study are available from the corresponding author upon reasonable request. Liqun He, Breeana Elliott, Philipp Mensing, Kyle Briggs, Michel Godin, Jonathan Flax, James McGrath and Vincent Tabard-Cossa. Digital Immunoassay for Sensitive Quantification of Blood Biomarkers using Solid-State Nanopores. 2025, ChemRxiv Preprint, DOI: 10.26434/chemrxiv-2025-zth1z (https://doi.org/10.26434/chemrxiv-2025-zth1z) (accessed March 14, 2026). Code Availability Nanopore data analysis was done using in-house program available at https://www.github.com/shadowk29/CUSUM.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 8 authors, 7 keywords, 8 MeSH terms, 2 funders, 90 references.

Cite

This paper

He, L., Elliott, B., Mensing, P., Briggs, K., Godin, M., Flax, J., McGrath, J., & Tabard-Cossa, V. (2026). Digital Immunoassays for Sensitive Quantification of Blood Biomarkers Using Solid-State Nanopores. ACS nano, 20(13), 10308-10319. https://doi.org/10.1021/acsnano.5c16690

BibTeX

@article{he2026digital,
author = {He, Liqun and Elliott, Breeana and Mensing, Philipp and Briggs, Kyle and Godin, Michel and Flax, Jonathan and McGrath, James and Tabard-Cossa, Vincent},
title = {{Digital Immunoassays for Sensitive Quantification of Blood Biomarkers Using Solid-State Nanopores}},
journal = {ACS nano},
year = {2026},
month = mar,
volume = {20},
number = {13},
pages = {10308--10319},
publisher = {American Chemical Society},
issn = {1936-0851},
doi = {10.1021/acsnano.5c16690},
url = {https://doi.org/10.1021/acsnano.5c16690},
pmid = {41873753},
pmcid = {PMC13063814}
}

RIS

TY - JOUR
AU - He, Liqun
AU - Elliott, Breeana
AU - Mensing, Philipp
AU - Briggs, Kyle
AU - Godin, Michel
AU - Flax, Jonathan
AU - McGrath, James
AU - Tabard-Cossa, Vincent
TI - Digital Immunoassays for Sensitive Quantification of Blood Biomarkers Using Solid-State Nanopores
T2 - ACS nano
J2 - ACS Nano
PY - 2026
DA - 2026/03/24
VL - 20
IS - 13
SP - 10308
EP - 10319
SN - 1936-0851
PB - American Chemical Society
DO - 10.1021/acsnano.5c16690
UR - https://doi.org/10.1021/acsnano.5c16690
LA - en
ER -

CSL-JSON

{
"id": "10.1021/acsnano.5c16690",
"type": "article-journal",
"title": "Digital Immunoassays for Sensitive Quantification of Blood Biomarkers Using Solid-State Nanopores",
"container-title": "ACS nano",
"author": [
{
"family": "He",
"given": "Liqun"
},
{
"family": "Elliott",
"given": "Breeana"
},
{
"family": "Mensing",
"given": "Philipp"
},
{
"family": "Briggs",
"given": "Kyle"
},
{
"family": "Godin",
"given": "Michel"
},
{
"family": "Flax",
"given": "Jonathan"
},
{
"family": "McGrath",
"given": "James"
},
{
"family": "Tabard-Cossa",
"given": "Vincent"
}
],
"container-title-short": "ACS Nano",
"volume": "20",
"issue": "13",
"page": "10308-10319",
"DOI": "10.1021/acsnano.5c16690",
"PMID": "41873753",
"PMCID": "PMC13063814",
"ISSN": "1936-0851",
"publisher": "American Chemical Society",
"URL": "https://doi.org/10.1021/acsnano.5c16690",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
24
]
]
}
}

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