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Oscillatory co-expression of HES1 and HES5 enables a hybrid state in a cross-repressive transcription factor regulatory motif.

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The authors' code

MATLAB · 75 lines · 2.2 KB · GPL-3.0

  1. clear, close all, clc
  2. Tend = 900;
  3. % define the dde
  4. % HES1 self-repression + HES5 repressing Hes1
  5. % dp1/dt=ap1*m1(t)-dp1*p1(t);
  6. % dm1/dt=am1*HIll1(p1(t-tau1),p0_1,n1)*Hill51(p5(t-tau51),po_51,n51)-dm1*m1(t);
  7. % HES5 self-repression + HES1 repressing Hes5
  8. % dp5/dt=ap5*m5(t)-dp5*p5(t);
  9. % dm5/dt=am5*Hill(p5(t-tau5),p0_5,n5)*Hill15(p15(t-tau15),p0_15,n15)-dm5*m5(t);
  10. tau = 29;
  11. h1h5_tau=29;
  12. %HES1 parameters
  13. par.ap1=1; % protein production
  14. par.dp1=log(2)/22; % protein degradation
  15. par.am1=1; %mrna production
  16. par.dm1=log(2)/25; %mrna degradation
  17. % hill function params
  18. par.n1=7;
  19. par.p0_1=390;
  20. %HES5 parameters
  21. par.ap5=1; % protein production
  22. par.dp5=log(2)/80; % protein degradation
  23. par.am5=1; %mrna production
  24. par.dm5=log(2)/25; %mrna degradation
  25. % hill function params
  26. par.n5=7;
  27. par.p0_5=390;
  28. % HES1-HES5 parameters
  29. par.n15=5;
  30. par.p0_15=390000;
  31. par.n51=5;
  32. par.p0_51=390000;
  33. %% figure 4A- uncoupled example; cross-rep set to a very high thresh
  34. % solve the DDEs
  35. opt=ddeset('RelTol',1e-5);
  36. sol = dde23(@ddePM_coupled,tau,[0 1 0 1],[0, Tend],opt,par);
  37. t = sol.x'/60;
  38. figure,plot(t,sol.y(1,:),'color','r');
  39. hold on
  40. plot(t,sol.y(3,:),'color','b');
  41. legend('HES1','HES5');
  42. xlabel('Time (h)');
  43. ylabel('Protein Level');
  44. title ('Uncoupled (free-running)');
  45. %% figure 4B- coupled at balanced values of cross-repression
  46. par.p0_15=390;
  47. par.p0_51=390;
  48. sol = dde23(@ddePM_coupled,tau,[0 1 0 1],[0, Tend],opt,par);
  49. t = sol.x'/60;
  50. figure,plot(t,sol.y(1,:),'color','r');
  51. hold on
  52. plot(t,sol.y(3,:),'color','b');
  53. legend('HES1','HES5');
  54. xlabel('Time (h)');
  55. ylabel('Protein Level');
  56. title('Coupled HES1-HES5 (balanced)')
  57. function dydt=ddePM_coupled(t,y,Z,par)
  58. % HES1
  59. ylag1 = Z(1); % delayed protein-HES1
  60. ylag51= Z(3);
  61. inv_hill1=1+(ylag1/par.p0_1).^par.n1;
  62. inv_hill51=1+(ylag51/par.p0_51).^par.n51;
  63. inv_hill_tot1=inv_hill1*inv_hill51;
  64. dydt(1,1) = par.ap1*y(2)-par.dp1*y(1);% protein variation
  65. dydt(2,1)= par.am1/inv_hill_tot1-par.dm1*y(2);%mrna variation
  66. % HES5
  67. ylag5 = Z(3); % delayed protein-HES5
  68. ylag15=Z(1);
  69. inv_hill5=1+(ylag5/par.p0_5).^par.n5;
  70. inv_hill15=1+(ylag15/par.p0_15).^par.n15;
  71. inv_hill_tot2=inv_hill5*inv_hill15;
  72. dydt(3,1) = par.ap5*y(4)-par.dp5*y(3);% protein variation
  73. dydt(4,1)= par.am5/inv_hill_tot2-par.dm5*y(4);%mrna variation
  74. end

hes1hes5Fig4AB.m at commit c9be5fb, under GPL-3.0 · at the source

Overview

Authors: Veronica Biga1, Anzy Miller1, Anoushka Kamath1,2, Robert Lea1, Ying Q P Mak1,3, Antony D Adamson4, Elli Marinopoulou1,5, Paul François6, Nancy Papalopulu1, Cerys S Manning1
ORCID iDs: Veronica Biga, Anzy Miller, Anoushka Kamath, Robert Lea, Ying Q P Mak, Antony D Adamson, Elli Marinopoulou, Paul François, Nancy Papalopulu, Cerys S Manning
  1. Faculty of Biology Medicine and Health, School of Medical Sciences, Division of Developmental Biology and Medicine, The University of Manchester, Manchester M13 9PT, UK
  2. Faculty of Biology Medicine and Health, Division of Cardiovascular Sciences, University of Manchester, Manchester M13 9PT, UK
  3. UK Dementia Research Institute, University College London, London WC1E 6BT, UK
  4. Genome Editing Unit, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PT, UK
  5. Research Development and Innovation, Faculty of Biology Medicine and Health, The University of Manchester, Manchester M13 9PT, UK
  6. Department of Biochemistry and Molecular Medicine, University of Montreal, Montreal, Quebec QC H3T 1J4, Canada
Institutions: University of Manchester (United Kingdom); UK Dementia Research Institute (United Kingdom); University College London (United Kingdom); Université de Montréal (Canada)
Journal: Development (Cambridge, England), volume 153, issue 11, article dev204969
Dates: received 22 May 2025; accepted 25 April 2026; published online 10 June 2026; in print June 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1242/dev.204969 · PMID 42063361 · PMCID PMC13286377 · OpenAlex W7159675690
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: mouse (organism), cellular / molecular (subfield)
Methods: Statistics, Spectral & time-frequency, Machine learning, Preprocessing, Evoked potentials
Keywords: Oscillatory dynamics, Transcription factor regulation, Cross-repressing transcription factors
MeSH: Basic Helix-Loop-Helix Proteins*, Gene Expression Regulation, Developmental*, Homeodomain Proteins*, Repressor Proteins*, Transcription Factors*, Animals, Mice, Neural Stem Cells, Spinal Cord, Transcription Factor HES-1 (* major topic)
Topic: Neurogenesis and neuroplasticity mechanisms (Developmental Neuroscience, Neuroscience), according to OpenAlex
Funding: Wellcome Trust (210912/Z/18/Z, 224394/Z/21/Z, 201380/Z/16/Z); UKRI/Wellcome (EP/T022000/1- PoLNET3a Physics of Life); UK Research and Innovation (EP/T022000/1); The University of Manchester; Medical Research Council (MR/V032534/1)
Citations: cited by 1 paper (Europe PMC); 83 references in the paper

Abstract

Many cell fate decisions in the developing neural tube are directed by cross-repressive transcription factor (TF) motifs that generate bistability, such that cells express one TF but not both. Hybrid states in which cells express both cross-repressing fate determinants have been observed, but how these arise or persist remains unclear. Here, we focus on HES1 and HES5, which are auto-repressive oscillatory TFs that regulate neural progenitor maintenance and are expressed in adjacent dorsoventral progenitor domains in the developing spinal cord. Knockdown experiments demonstrate that HES1 and HES5 are cross-repressing in mouse spinal cord neural progenitors, and live-cell imaging in vitro shows that they can be co-expressed, defining a hybrid state. In this state, HES proteins co-oscillate in-phase within single cells. Computational modelling indicates that modulation of cross-repression strength or relative TF abundance destabilises this state, driving resolution towards a single oscillatory HES TF. This is consistent with in vivo analysis showing transient HES1 and HES5 co-expression, followed by progressive restriction to a single TF oscillator. Our findings suggest that oscillatory expression enables the co-existence of cross-repressing TFs, allowing hybrid states within a developmental bistable motif.

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

Repository

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

VBiga/BIGA-HES1-HES5-2026

License: GPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: c9be5fb5a52f12d4e5fe8e68ce363ea300bbccae, 7 May 2026
Languages: MATLAB (9)
Size: 13 files, 9 scripts
Software Heritage: not archived
Found in: the text, “Footnotes”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Signal Processing Toolbox (4 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
11 files
At the source: github.com/VBiga/BIGA-HES1-HES5-2026

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Versions

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Version 2, 28 September 2026

  • Publisher: — → The Company of Biologists

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 10 authors, 3 keywords, 10 MeSH terms, 5 funders, 83 references.

Cite

This paper

Biga, V., Miller, A., Kamath, A., Lea, R., Mak, Y. Q. P., Adamson, A. D., Marinopoulou, E., François, P., Papalopulu, N., & Manning, C. S. (2026). Oscillatory co-expression of HES1 and HES5 enables a hybrid state in a cross-repressive transcription factor regulatory motif. Development (Cambridge, England), 153(11), dev204969. https://doi.org/10.1242/dev.204969

BibTeX

@article{biga2026oscillatory,
author = {Biga, Veronica and Miller, Anzy and Kamath, Anoushka and Lea, Robert and Mak, Ying Q P and Adamson, Antony D and Marinopoulou, Elli and François, Paul and Papalopulu, Nancy and Manning, Cerys S},
title = {{Oscillatory co-expression of HES1 and HES5 enables a hybrid state in a cross-repressive transcription factor regulatory motif}},
journal = {Development (Cambridge, England)},
year = {2026},
month = jun,
volume = {153},
number = {11},
pages = {dev204969},
publisher = {The Company of Biologists},
issn = {0950-1991},
doi = {10.1242/dev.204969},
url = {https://doi.org/10.1242/dev.204969},
pmid = {42063361},
pmcid = {PMC13286377}
}

RIS

TY - JOUR
AU - Biga, Veronica
AU - Miller, Anzy
AU - Kamath, Anoushka
AU - Lea, Robert
AU - Mak, Ying Q P
AU - Adamson, Antony D
AU - Marinopoulou, Elli
AU - François, Paul
AU - Papalopulu, Nancy
AU - Manning, Cerys S
TI - Oscillatory co-expression of HES1 and HES5 enables a hybrid state in a cross-repressive transcription factor regulatory motif
T2 - Development (Cambridge, England)
J2 - Development
PY - 2026
DA - 2026/06/10
VL - 153
IS - 11
SP - dev204969
SN - 0950-1991
PB - The Company of Biologists
DO - 10.1242/dev.204969
UR - https://doi.org/10.1242/dev.204969
LA - en
ER -

CSL-JSON

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"type": "article-journal",
"title": "Oscillatory co-expression of HES1 and HES5 enables a hybrid state in a cross-repressive transcription factor regulatory motif",
"container-title": "Development (Cambridge, England)",
"author": [
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"family": "Biga",
"given": "Veronica"
},
{
"family": "Miller",
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{
"family": "Kamath",
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"issue": "11",
"page": "dev204969",
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"PMID": "42063361",
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"publisher": "The Company of Biologists",
"URL": "https://doi.org/10.1242/dev.204969",
"language": "en",
"issued": {
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}

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