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Signal Amplification in the HPT Axis-Evidence for Its Existence, Location, Significance, and Molecular Mechanisms.

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The authors' code

MATLAB · 342 lines · 7.7 KB · no license

  1. clear all
  2. clc
  3. % Time unit: hour
  5. tspan = [0:10:10000];
  7. color_TRH = [75/255, 186/255, 253/255];
  8. color_TSH = [126/255, 210/255, 134/255];
  9. color_TH = [255/255, 153/255, 203/255];
  11. %% Initial condition
  12. init.TRH = 1;
  13. init.TSH = 1;
  14. init.TH = 15;
  15. init_default = init;
  18. %% -------------------------- DESIGN A run to steady state-----------------------------------------------%%
  19. % Load parameters
  20. load('Default_param_A.mat');
  21. param = param_default;
  23. % Run simulation
  24. y0 = [init.TRH, init.TSH, init.TH];
  25. [t,y] = ode15s('HPT_ode',tspan, y0, [], param); %Note: use @HPT_ode does not work for passing argument
  27. % Plot time-course
  28. figure(1)
  29. hold on
  30. plot(t,y(:,1))
  31. xlabel('Time (h)')
  32. ylabel('TRH)')
  34. figure(2)
  35. hold on
  36. plot(t,y(:,2))
  37. xlabel('Time (h)')
  38. ylabel('TSH (mIU/L)')
  40. figure(3)
  41. hold on
  42. plot(t,y(:,3))
  43. xlabel('Time (h)')
  44. ylabel('TH (pM)')
  46. % Obtain steady-state values
  47. TRHss = y(end,1);
  48. TSHss = y(end,2);
  49. THss = y(end,3);
  52. %% -------------------------- DESIGN A Sensitivity Analysis -----------------------------------------------%%
  54. param_cell = struct2cell(param_default);
  56. param_names = fieldnames(param_default);
  58. percent_change = 0.1; % for parameter change
  61. % Increasing parameter values
  62. SC_TRH_increase = [];
  63. SC_TSH_increase = [];
  64. SC_TH_increase = [];
  66. for i = 1:1:length(param_cell)
  67. param = param_default;
  68. eval(strcat('param.', param_names{i}, '=', num2str(param_cell{i}), '*(1 + percent_change);'));
  69. y0 = [init.TRH, init.TSH, init.TH];
  70. [t,y] = ode15s('HPT_ode',tspan, y0, [], param);
  72. % Plot time-course
  73. figure(1)
  74. hold on
  75. plot(t,y(:,1))
  76. xlabel('Time (h)')
  77. ylabel('TRH)')
  79. figure(2)
  80. hold on
  81. plot(t,y(:,2))
  82. xlabel('Time (h)')
  83. ylabel('TSH (mIU/L)')
  85. figure(3)
  86. hold on
  87. plot(t,y(:,3))
  88. xlabel('Time (h)')
  89. ylabel('TH (pM)')
  91. % Obtain steady-state values
  92. TRHss_increase = y(end,1);
  93. TSHss_increase = y(end,2);
  94. THss_increase = y(end,3);
  96. %Calculate sensitivity coefficient (SC)
  97. SC_TRH_increase = [SC_TRH_increase, (TRHss_increase - TRHss)/TRHss/percent_change];
  98. SC_TSH_increase = [SC_TSH_increase, (TSHss_increase - TSHss)/TSHss/percent_change];
  99. SC_TH_increase = [SC_TH_increase, (THss_increase - THss)/THss/percent_change];
  101. end
  103. % Decreasing parameter values
  104. SC_TRH_decrease = [];
  105. SC_TSH_decrease = [];
  106. SC_TH_decrease = [];
  108. for i = 1:1:length(param_cell)
  109. param = param_default;
  110. eval(strcat('param.', param_names{i}, '=', num2str(param_cell{i}), '*(1 - percent_change);'));
  111. y0 = [init.TRH, init.TSH, init.TH];
  112. [t,y] = ode15s('HPT_ode',tspan, y0, [], param);
  114. % Plot time-course
  115. figure(1)
  116. hold on
  117. plot(t,y(:,1))
  118. xlabel('Time (h)')
  119. ylabel('TRH)')
  121. figure(2)
  122. hold on
  123. plot(t,y(:,2))
  124. xlabel('Time (h)')
  125. ylabel('TSH (mIU/L)')
  127. figure(3)
  128. hold on
  129. plot(t,y(:,3))
  130. xlabel('Time (h)')
  131. ylabel('TH (pM)')
  133. % Obtain steady-state values
  134. TRHss_decrease = y(end,1);
  135. TSHss_decrease = y(end,2);
  136. THss_decrease = y(end,3);
  138. %Calculate sensitivity coefficient (SC)
  139. SC_TRH_decrease = [SC_TRH_decrease, -(TRHss_decrease - TRHss)/TRHss/percent_change];
  140. SC_TSH_decrease = [SC_TSH_decrease, -(TSHss_decrease - TSHss)/TSHss/percent_change];
  141. SC_TH_decrease = [SC_TH_decrease, -(THss_decrease - THss)/THss/percent_change];
  143. end
  145. % Averaging SC
  146. SC_TRH = (SC_TRH_increase + SC_TRH_decrease) / 2;
  147. SC_TSH = (SC_TSH_increase + SC_TSH_decrease) / 2;
  148. SC_TH = (SC_TH_increase + SC_TH_decrease) / 2;
  151. %Plot TRH SC
  152. figure(4)
  153. bar(SC_TRH, 'FaceColor', color_TRH);
  154. ylabel('SC (TRH)');
  155. xticklabels(param_names);
  156. pbaspect([3.6 1 1])
  157. ylim([-1.3,1.2]);
  158. yticks([-1 -0.5 0 0.5 1])
  159. set(gca,'Fontsize', 14);
  161. %Plot TSH SC
  162. figure(5)
  163. bar(SC_TSH, 'FaceColor', color_TSH);
  164. ylabel('SC (TSH)');
  165. xticklabels(param_names);
  166. pbaspect([3.6 1 1])
  167. ylim([-1.2,2]);
  168. yticks([-1 -0.5 0 0.5 1 2])
  169. set(gca,'Fontsize', 14);
  171. %Plot TH SC
  172. figure(6)
  173. bar(SC_TH, 'FaceColor', color_TH);
  174. ylabel('SC (TH)');
  175. xticklabels(param_names);
  176. pbaspect([3.6 1 1])
  177. ylim([-1.2,1.2]);
  178. yticks([-1 -0.5 0 0.5 1])
  179. set(gca,'Fontsize', 14);
  180. %
  184. %% -------------------------- DESIGN B run to steady state-----------------------------------------------%%
  185. % Load parameters
  186. load('Default_param_B.mat');
  187. param = param_default;
  189. % Run simulation
  190. y0 = [init.TRH, init.TSH, init.TH];
  191. [t,y] = ode15s('HPT_ode',tspan, y0, [], param); %Note: use @HPT_ode does not work for passing argument
  193. % Plot time-course
  194. figure(10)
  195. plot(t,y(:,1))
  196. xlabel('Time (h)')
  197. ylabel('TRH)')
  199. figure(20)
  200. plot(t,y(:,2))
  201. xlabel('Time (h)')
  202. ylabel('TSH (mIU/L)')
  204. figure(30)
  205. plot(t,y(:,3))
  206. xlabel('Time (h)')
  207. ylabel('TH (pM)')
  209. % Obtain steady-state values
  210. TRHss = y(end,1);
  211. TSHss = y(end,2);
  212. THss = y(end,3);
  215. %% -------------------------- DESIGN B Sensitivity Analysis -----------------------------------------------%%
  216. param_cell = struct2cell(param_default);
  218. param_names = fieldnames(param_default);
  220. percent_change = 0.1; % for parameter change
  223. % Increasing parameter values
  224. SC_TRH_increase = [];
  225. SC_TSH_increase = [];
  226. SC_TH_increase = [];
  228. for i = 1:1:length(param_cell)
  229. param = param_default;
  230. eval(strcat('param.', param_names{i}, '=', num2str(param_cell{i}), '*(1 + percent_change);'));
  231. y0 = [init.TRH, init.TSH, init.TH];
  232. [t,y] = ode15s('HPT_ode',tspan, y0, [], param);
  234. % Plot time-course
  235. figure(10)
  236. hold on
  237. plot(t,y(:,1))
  238. xlabel('Time (h)')
  239. ylabel('TRH)')
  241. figure(20)
  242. hold on
  243. plot(t,y(:,2))
  244. xlabel('Time (h)')
  245. ylabel('TSH (mIU/L)')
  247. figure(30)
  248. hold on
  249. plot(t,y(:,3))
  250. xlabel('Time (h)')
  251. ylabel('TH (pM)')
  253. % Obtain steady-state values
  254. TRHss_increase = y(end,1);
  255. TSHss_increase = y(end,2);
  256. THss_increase = y(end,3);
  258. %Calculate sensitivity coefficient (SC)
  259. SC_TRH_increase = [SC_TRH_increase, (TRHss_increase - TRHss)/TRHss/percent_change];
  260. SC_TSH_increase = [SC_TSH_increase, (TSHss_increase - TSHss)/TSHss/percent_change];
  261. SC_TH_increase = [SC_TH_increase, (THss_increase - THss)/THss/percent_change];
  263. end
  265. % Decreasing parameter values
  266. SC_TRH_decrease = [];
  267. SC_TSH_decrease = [];
  268. SC_TH_decrease = [];
  270. for i = 1:1:length(param_cell)
  271. param = param_default;
  272. eval(strcat('param.', param_names{i}, '=', num2str(param_cell{i}), '*(1 - percent_change);'));
  273. y0 = [init.TRH, init.TSH, init.TH];
  274. [t,y] = ode15s('HPT_ode',tspan, y0, [], param);
  276. % Plot time-course
  277. figure(10)
  278. hold on
  279. plot(t,y(:,1))
  280. xlabel('Time (h)')
  281. ylabel('TRH)')
  283. figure(20)
  284. hold on
  285. plot(t,y(:,2))
  286. xlabel('Time (h)')
  287. ylabel('TSH (mIU/L)')
  289. figure(30)
  290. hold on
  291. plot(t,y(:,3))
  292. xlabel('Time (h)')
  293. ylabel('TH (pM)')
  295. % Obtain steady-state values
  296. TRHss_decrease = y(end,1);
  297. TSHss_decrease = y(end,2);
  298. THss_decrease = y(end,3);
  300. %Calculate sensitivity coefficient (SC)
  301. SC_TRH_decrease = [SC_TRH_decrease, -(TRHss_decrease - TRHss)/TRHss/percent_change];
  302. SC_TSH_decrease = [SC_TSH_decrease, -(TSHss_decrease - TSHss)/TSHss/percent_change];
  303. SC_TH_decrease = [SC_TH_decrease, -(THss_decrease - THss)/THss/percent_change];
  305. end
  307. % Averaging SC
  308. SC_TRH = (SC_TRH_increase + SC_TRH_decrease) / 2;
  309. SC_TSH = (SC_TSH_increase + SC_TSH_decrease) / 2;
  310. SC_TH = (SC_TH_increase + SC_TH_decrease) / 2;
  313. %Plot TRH SC
  314. figure(40)
  315. bar(SC_TRH, 'FaceColor', color_TRH);
  316. ylabel('SC (TRH)');
  317. xticklabels(param_names);
  318. pbaspect([3.6 1 1])
  319. ylim([-1.3,1.2]);
  320. yticks([-1 -0.5 0 0.5 1])
  321. set(gca,'Fontsize', 14);
  323. %Plot TSH SC
  324. figure(50)
  325. bar(SC_TSH, 'FaceColor', color_TSH);
  326. ylabel('SC (TSH)');
  327. xticklabels(param_names);
  328. pbaspect([3.6 1 1])
  329. ylim([-1.2,1.2]);
  330. yticks([-1 -0.5 0 0.5 1])
  331. set(gca,'Fontsize', 14);
  333. %Plot TH SC
  334. figure(60)
  335. bar(SC_TH, 'FaceColor', color_TH);
  336. ylabel('SC (TH)');
  337. xticklabels(param_names);
  338. pbaspect([3.6 1 1])
  339. ylim([-1.2,1.2]);
  340. yticks([-1 -0.5 0 0.5 1])
  341. set(gca,'Fontsize', 14);
  342. %

HPT_cmd.m at commit 8b982f4, no license · at the source

Overview

Authors: Li Jing1, Sarahna A Moyd2, Qiang Zhang2
  1. Department of Toxicology and Hygienic Chemistry, School of Public Health, Capital Medical University, Beijing, China
  2. Gangarosa Department of Environmental Health, Rollins School of Public Health, Emory University, Atlanta, Georgia, USA
Institutions: Capital Medical University (China); Emory University (United States)
Journal: Acta physiologica (Oxford, England), volume 242, issue 4, article e70202
Dates: received 4 September 2025; accepted 28 January 2026; published online 20 March 2026; in print April 2026
Type: Review · Language: English
License: CC BY
Identifiers: DOI 10.1111/apha.70202 · PMID 41862191 · PMCID PMC13004654 · OpenAlex W7139944415
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), cellular / molecular (subfield)
Methods: Complexity, Smoothing, state filtering, decompositions, Spectral & time-frequency, Statistics
Keywords: negative feedback, signal amplification, thyroid hormone, TRH, TSH, ultrasensitivity
MeSH: Hypothalamo-Hypophyseal System*, Signal Transduction*, Thyroid Gland*, Thyroid Hormones*, Animals, Feedback, Physiological, Humans (* major topic)
Topic: Thyroid Disorders and Treatments (Endocrinology, Diabetes and Metabolism, Medicine), according to OpenAlex
Funding: NIEHS NIH HHS (P42ES004911, P42 ES004911); National Institute of Environmental Health Sciences (P42ES004911)
Citations: not cited yet (Europe PMC); 320 references in the paper

Abstract

Thyroid hormones (THs) are under negative feedback regulation via the hypothalamic–pituitary‐thyroid (HPT) axis. How this axis operates to keep the circulating THs within a narrow physiological range is not well understood quantitatively. Led by the design principle of robust homeostatic feedback control, here we review and synthesize the literature under a unifying theme of signal amplification in the HPT axis, providing evidence for its existence, location, functional significance, and potential molecular mechanisms. Drawing on human studies of the circulating TSH‐T4 relationship, we assert that a signal amplifier exists in the brain, where the TH feedback signal is amplified to inhibit TRH and TSH. With mathematical models we illustrate that placing the signal amplifier of the HPT feedback loop in the brain, not in the thyroid, provides an evolutionary advantage, which minimizes the disruption of operating TH levels by possible perturbations. We review the molecular neuroendocrine literature to reveal how signal amplification (ultrasensitivity) is likely achieved mechanically in the hypothalamus and anterior pituitary. We identify multiple signaling pathways in the TRH neurons, β2‐tanycytes, and thyrotropes that mediate the feedback action of THs, including transcriptional and posttranslational regulations of the synthesis, maturation, degradation, and release of TRH and TSH. Collectively, these multistep regulations amplify T3 signal, providing a high feedback loop gain for robust TH homeostatic control. The nature's design principle revealed here enhances our cross‐scale understanding of the systems biology of the HPT axis as a dynamical control system, which can promote precision thyroid medicine and risk assessment of thyroid‐disrupting chemicals.

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

Repository

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

pulsatility/2025-signal-amplification-in-HPT-axis

License: none: the authors keep all their rights
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: 8b982f43da213fa431b0a702c1571c82b2abdce9, 14 January 2026
Languages: MATLAB (2)
Size: 6 files, 2 scripts
Software Heritage: not archived
Found in: the text, “Functional Significance of Central Location of S”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
3 files
At the source: github.com/pulsatility/2025-signal-amplification-in-HPT-axis

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.

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 2 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

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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 2, 28 September 2026

  • Publisher: n/a → Wiley

Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 6 keywords, 7 MeSH terms, 2 funders, 313 references.

Cite

This paper

Jing, L., Moyd, S. A., & Zhang, Q. (2026). Signal Amplification in the HPT Axis-Evidence for Its Existence, Location, Significance, and Molecular Mechanisms. Acta physiologica (Oxford, England), 242(4), e70202. https://doi.org/10.1111/apha.70202

BibTeX

@article{jing2026signal,
author = {Jing, Li and Moyd, Sarahna A and Zhang, Qiang},
title = {{Signal Amplification in the HPT Axis-Evidence for Its Existence, Location, Significance, and Molecular Mechanisms}},
journal = {Acta physiologica (Oxford, England)},
year = {2026},
month = apr,
volume = {242},
number = {4},
pages = {e70202},
publisher = {Wiley},
issn = {1748-1708},
doi = {10.1111/apha.70202},
url = {https://doi.org/10.1111/apha.70202},
pmid = {41862191},
pmcid = {PMC13004654}
}

RIS

TY - JOUR
AU - Jing, Li
AU - Moyd, Sarahna A
AU - Zhang, Qiang
TI - Signal Amplification in the HPT Axis-Evidence for Its Existence, Location, Significance, and Molecular Mechanisms
T2 - Acta physiologica (Oxford, England)
J2 - Acta Physiol (Oxf)
PY - 2026
DA - 2026/04/01
VL - 242
IS - 4
SP - e70202
SN - 1748-1708
PB - Wiley
DO - 10.1111/apha.70202
UR - https://doi.org/10.1111/apha.70202
LA - en
ER -

CSL-JSON

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"family": "Jing",
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"container-title-short": "Acta Physiol (Oxf)",
"volume": "242",
"issue": "4",
"page": "e70202",
"DOI": "10.1111/apha.70202",
"PMID": "41862191",
"PMCID": "PMC13004654",
"ISSN": "1748-1708",
"publisher": "Wiley",
"URL": "https://doi.org/10.1111/apha.70202",
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