Optimal control of gene regulatory networks for morphogen-driven tissue patterning
Open accessPublished version of a preprint
Abstract
The generation of distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. Often, this is directed by spatially graded chemical signals-known as morphogens. In the "French Flag model," morphogen concentration instructs cells to acquire specific fates. How this mechanism produces timely and organized cell-fate decisions, despite the presence of changing morphogen levels, molecular noise, and individual variability, is unclear. Moreover, feedback is present at various levels in developing tissues, breaking the link between morphogen concentration, signaling activity, and position. Here, we develop an alternative framework using optimal control theory to tackle the problem of morphogen-driven patterning: intracellular signaling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signaling levels and time. This approach recovers experimentally observed properties of patterning strategies and offers insight into design principles that produce timely, precise, and reproducible morphogen patterning.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A cFFL consists of a fast direct pathway and a slow indirect pathway, which filters out short-lived and spurious signals by integrating these inputs.
“A cFFL consists of a fast direct pathway and a slow indirect pathway, which filters out short-lived and spurious signals by integrating these inputs.”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [43]
Cites
Human-level control through deep reinforcement learning
Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidjeland, A. K., Ostrovski, G., et al. (2015) · Nature · doi:10.1038/nature14236 · Cited by 30,357 · see citing works
Continuous control with deep reinforcement learning
Lillicrap, T. P., Hunt, J. J., Pritzel, A., Heess, N., Erez, T., Tassa, Y., Silver, D., & Wierstra, D. (2015) · arXiv · doi:10.48550/arxiv.1509.02971 · Cited by 10,782 · see citing works
(1995) · Cited by 10,558 · see citing works
Stochastic Processes in Physics and Chemistry
(2007) · Elsevier eBooks · doi:10.1016/b978-0-444-52965-7.x5000-4 · Cited by 9,070 · see citing works
Speech recognition with deep recurrent neural networks
Graves, A., Mohamed, A.-R., & Hinton, G. (2013) · 2013 IEEE International Conference on Acoustics, Speech and Signal Processing · doi:10.1109/icassp.2013.6638947 · Cited by 8,893 · see citing works
Reinforcement Learning: An Introduction
Johnson, J. D., Li, J., & Chen, Z. (2000) · Neurocomputing · doi:10.1016/s0925-2312(00)00324-6 · Cited by 8,821 · see citing works
Bryson, A. E., & Ho, Y. (2018) · Routledge eBooks · doi:10.1201/9781315137667 · Cited by 6,031 · see citing works
Soft actor-critic Off-policy maximum entropy deep reinforcement learning with a stochastic actor
Haarnoja, T., Zhou, A., Abbeel, P., & Levine, S. (2018) · arXiv · doi:10.48550/arxiv.1801.01290 · Cited by 5,594 · see citing works
Barlow, H. B. (1983) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(83)90030-5 · Cited by 5,502 · see citing works
More Is Different: Broken symmetry and the nature of the hierarchical structure of science.
Anderson, P. W. (1972) · Science · doi:10.1126/science.177.4047.393 · Cited by 4,018 · see citing works
Addressing Function Approximation Error in Actor-Critic Methods
Fujimoto, S., van Hoof, H., & Meger, D. (2018) · arXiv · doi:10.48550/arxiv.1802.09477 · Cited by 3,650 · see citing works
Positional information and the spatial pattern of cellular differentiation
Wolpert, L. (1969) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(69)80016-0 · Cited by 3,091 · see citing works
Lasry, J., & Lions, P. (2007) · Japanese journal of mathematics · doi:10.1007/s11537-007-0657-8 · Cited by 2,639 · see citing works
Intrinsic and extrinsic contributions to stochasticity in gene expression
Swain, P. S., Elowitz, M. B., & Siggia, E. D. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.162041399 · Cited by 1,661 · see citing works
The chemical Langevin equation
Gillespie, D. T. (2000) · The Journal of Chemical Physics · doi:10.1063/1.481811 · Cited by 1,475 · see citing works
Simberloff, D., Levins, R., & Lewontin, R. C. (1987) · Ornithological Applications · doi:10.2307/1368785 · Cited by 1,398 · see citing works
Deep Recurrent Q-Learning for Partially Observable MDPsPreprint
Hausknecht, M., & Stone, P. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1507.06527 · Cited by 1,224 · see citing works
Stochastic Methods: A Handbook for the Natural and Social Sciences
Gardiner, C. W. (2009) · Cited by 1,097 · see citing works
On the theory of dynamic programming
Bellman, R. (1952) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.38.8.716 · Cited by 998 · see citing works
Probing the Limits to Positional Information
Gregor, T., Tank, D. W., Wieschaus, E. F., & Bialek, W. (2007) · Cell · doi:10.1016/j.cell.2007.05.025 · Cited by 681 · see citing works
Interpretation of the sonic hedgehog morphogen gradient by a temporal adaptation mechanism
Dessaud, É., Yang, L. L., Hill, K., Cox, B., Ulloa, F., Ribeiro, A., Mynett, A., Novitch, B. G., & Briscoe, J. (2007) · Nature · doi:10.1038/nature06347 · Cited by 613 · see citing works
Self-citationFrom Understanding Computation to Understanding Neural Circuitry
Marr, D., & Poggio, T. (1976) · Defense Technical Information Center (DTIC) · Cited by 612 · see citing works
Specification of neuronal fates in the ventral neural tube
Briscoe, J., & Ericson, J. (2001) · Current Opinion in Neurobiology · doi:10.1016/s0959-4388(00)00172-0 · Cited by 548 · see citing works
Self-citationStochastic thermodynamics: principles and perspectives
Seifert, U. (2008) · The European Physical Journal B · doi:10.1140/epjb/e2008-00001-9 · Cited by 497 · see citing works
Morphogen rules: design principles of gradient-mediated embryo patterning
Briscoe, J., & Small, S. (2015) · Development · doi:10.1242/dev.129452 · Cited by 483 · see citing works
Self-citationBalaskas, N., Ribeiro, A., Panovska, J., Dessaud, E., Sasai, N., Page, K., Briscoe, J., & Ribes, V. (2012) · Cell · doi:10.1016/j.cell.2011.10.047 · Cited by 468 · see citing works
Self-citationPositional information and reaction-diffusion: two big ideas in developmental biology combine
Green, J. B. A., & Sharpe, J. A. (2015) · Development · doi:10.1242/dev.114991 · Cited by 430 · see citing works
Efficient computation of optimal actions
Todorov, E. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0710743106 · Cited by 417 · see citing works
Multi-Agent Reinforcement Learning: A Review of Challenges and Applications
Canese, L., Cardarilli, G. C., Nunzio, L. D., Fazzolari, R., Giardino, D., Re, M., & Spanò, S. (2021) · Applied Sciences · doi:10.3390/app11114948 · Cited by 408 · see citing works
Transcriptional regulation by the numbers: applications
Bintu, L., Buchler, N. E. G., García, H. G., Gerland, U., Terence Hwa, B., Kondev, J., Kuhlman, T. E., & Phillips, R. (2005) · Current Opinion in Genetics & Development · doi:10.1016/j.gde.2005.02.006 · Cited by 403 · see citing works
Machine Learning Proceedings 1993
(1993) · Elsevier eBooks · doi:10.1016/c2009-0-27798-1 · Cited by 359 · see citing works
Canalization of Gene Expression in the Drosophila Blastoderm by Gap Gene Cross Regulation
Manu, Surkova, S. Y., Spirov, A. V., Gursky, V. V., Janssens, H., Kim, A.-R., Radulescu, O., Vanario‐Alonso, C. E., Sharp, D. H., Samsonova, M. G., et al. (2009) · PLoS Biology · doi:10.1371/journal.pbio.1000049 · Cited by 280 · see citing works
Ribes, V., & Briscoe, J. (2009) · Cold Spring Harbor Perspectives in Biology · doi:10.1101/cshperspect.a002014 · Cited by 232 · see citing works
Self-citationRayon, T., Stamataki, D., Pérez-Carrasco, R., Garcia-Perez, L., Barrington, C., Melchionda, M., Exelby, K., Lázaro, J., Tybulewicz, V., Fisher, E., et al. (2020) · Science · doi:10.1126/science.aba7667 · Cited by 230 · see citing works
Self-citationJeong, J., & McMahon, A. P. (2004) · Development · doi:10.1242/dev.01566 · Cited by 223 · see citing works
Manu, Surkova, S. Y., Spirov, A. V., Gursky, V. V., Janssens, H., Kim, A.-R., Radulescu, O., Vanario‐Alonso, C. E., Sharp, D. H., Samsonova, M. G., et al. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000303 · Cited by 211 · see citing works
Decoding of position in the developing neural tube from antiparallel morphogen gradients
Zagórski, M., Tabata, Y., Brandenberg, N., Lütolf, M. P., Tkačik, G., Bollenbach, T., Briscoe, J., & Kicheva, A. (2017) · Science · doi:10.1126/science.aam5887 · Cited by 184 · see citing works
Self-citationOptimal decoding of cellular identities in a genetic network
Petkova, M. D., Tkačik, G., Bialek, W., Wieschaus, E. F., & Gregor, T. (2019) · Cell · doi:10.1016/j.cell.2019.01.007 · Cited by 178 · see citing works
Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms
Cohen, M., Kicheva, A., Ribeiro, A., Blassberg, R. A., Page, K. M., Barnes, C. P., & Briscoe, J. (2015) · Nature Communications · doi:10.1038/ncomms7709 · Cited by 153 · see citing works
Self-citationUnsupervised Predictive Memory in a Goal-Directed AgentPreprint
Wayne, G., Hung, C.-C., Amos, D., Mirza, M., Ahuja, A., Grabska‐Barwińska, A., Rae, J. W., Mirowski, P., Leibo, J. Z., Santoro, A., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1803.10760 · Cited by 137 · see citing works
Generation of extracellular morphogen gradients: the case for diffusion
Stapornwongkul, K. S., & Vincent, J. (2021) · Nature Reviews Genetics · doi:10.1038/s41576-021-00342-y · Cited by 129 · see citing works
Sáez, M., Blassberg, R. A., Camacho-Aguilar, E., Siggia, E. D., Rand, D. A. J., & Briscoe, J. (2021) · Cell Systems · doi:10.1016/j.cels.2021.08.013 · Cited by 125 · see citing works
Self-citationGeometry, epistasis, and developmental patterning
Corson, F., & Siggia, E. D. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201505109 · Cited by 118 · see citing works
Lander, A. D. (2013) · Science · doi:10.1126/science.1224186 · Cited by 110 · see citing works
Lek, M., Dias, J. M., Marklund, U., Uhde, C. W., Kurdija, S., Lei, Q., Sussel, L., Rubenstein, J., Matise, M., Arnold, H., et al. (2010) · Development · doi:10.1242/dev.054288 · Cited by 90 · see citing works
Noise distorts the epigenetic landscape and shapes cell-fate decisions
Coomer, M. A., Ham, L., & Stumpf, M. P. H. (2021) · Cell Systems · doi:10.1016/j.cels.2021.09.002 · Cited by 88 · see citing works
Tkačik, G., Dubuis, J., Petkova, M. D., et al. (2014) · Genetics · doi:10.1534/genetics.114.171850 · Cited by 85 · see citing works
Multiple-scale stochastic processes: Decimation, averaging and beyond
Bo, S., & Celani, A. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.12.003 · Cited by 81 · see citing works
A theoretical framework for the regulation of Shh morphogen-controlled gene expression
Cohen, M., Page, K. M., Perez‐Carrasco, R., Barnes, C. P., & Briscoe, J. (2014) · Development · doi:10.1242/dev.112573 · Cited by 79 · see citing works
Self-citationEntropy Production in Stochastic Systems with Fast and Slow Time-Scales
Bo, S., & Celani, A. (2014) · Journal of Statistical Physics · doi:10.1007/s10955-014-0922-1 · Cited by 75 · see citing works
Memory, modelling and Marr: a commentary on Marr (1971) ‘Simple memory: a theory of archicortex’
Willshaw, D. J., Dayan, P., & Morris, R. (2015) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2014.0383 · Cited by 75 · see citing works
Perez‐Carrasco, R., Guerrero, P., Briscoe, J., & Page, K. M. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005154 · Cited by 74 · see citing works
Self-citationPrecision of tissue patterning is controlled by dynamical properties of gene regulatory networks
Exelby, K., Herrera-Delgado, E., Garcia-Perez, L., Perez‐Carrasco, R., Sagner, A., Metzis, V., Peter Sollich, A., & Briscoe, J. (2021) · Development · doi:10.1242/dev.197566 · Cited by 67 · see citing works
Self-citationGene-free methodology for cell fate dynamics during development
Corson, F., & Siggia, E. D. (2017) · eLife · doi:10.7554/elife.30743 · Cited by 65 · see citing works
A direct fate exclusion mechanism by Sonic hedgehog-regulated transcriptional repressors
Nishi, Y., Zhang, X., Jeong, J., Peterson, K. A., Vedenko, A., Bulyk, M. L., Hide, W. A., & McMahon, A. P. (2015) · Development · doi:10.1242/dev.124636 · Cited by 53 · see citing works
Marr, D. (1975) · Science · doi:10.1126/science.190.4217.875 · Cited by 48 · see citing works
A Predictive Model of Bifunctional Transcription Factor Signaling during Embryonic Tissue Patterning
Junker, J. P., Peterson, K. A., Nishi, Y., Mao, J., McMahon, A. P., & van Oudenaarden, A. (2014) · Developmental Cell · doi:10.1016/j.devcel.2014.10.017 · Cited by 32 · see citing works
Causality and Chance in Modern Physics
Kibble, T. W. B. (1984) · Physics Bulletin · doi:10.1088/0031-9112/35/10/034 · Cited by 31 · see citing works
Spontaneous symmetry breaking and pattern formation of organoids
Ishihara, K., & Tanaka, E. M. (2018) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2018.06.002 · Cited by 26 · see citing works
Variational Regret Bounds for Reinforcement LearningPreprint
Gajane, P., Ortner, R., & Auer, P. L. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.05857 · Cited by 26 · see citing works
Collins, Z. M., Cha, A., Qin, A., et al. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/469239 · Cited by 25 · see citing works
Spontaneous symmetry breaking and pattern formation of organoids
Ishihara, K., & Tanaka, E. M. (2018) · MPG.PuRe (Max Planck Society) · Cited by 24 · see citing works
Chemotaxis emerges as the optimal solution to cooperative search games
Pezzotta, A., Adorisio, M., & Celani, A. (2018) · Physical Review E · doi:10.1103/physreve.98.042401 · Cited by 17 · see citing works
Self-citationMaximum principle for control problems with uncertain horizon and variable discount rate
Sorger, G. (1991) · Journal of Optimization Theory and Applications · doi:10.1007/bf00941305 · Cited by 8 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies
Tottori, T., & Kobayashi, T. J. (2026) · Physical Review Letters · doi:10.1103/5ynb-7k4v
- Authors
- Pezzotta, A., & Briscoe, J.
- Affiliations
- The Francis Crick Institute (GB)
- Corresponding author
- Pezzotta, Alberto
- Briscoe, James
- Venue
- Cell Systems
- Publisher
- Elsevier BV
- Published
- 2023-11
- Volume
- 14
- Issue
- 11
- Pages
- 940-952.e11
- ISSN
- 2405-4712 (ISSN-L)
- OpenAlex
- W4388696149
- Cited by
- 34
- References
- 64
- Citations by year
- 2026: 16 · 2025: 9 · 2024: 5 · 2023: 4
- FWCI
- 3.02
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Cell Systems (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion, cc-by)
- Figshare (submittedVersion, cc-by)
- The Francis Crick Institute (cc-by)
- Funders
- Wellcome Trust (FC001051)
- European Research Council (742138)
- Francis Crick Institute
- Horizon 2020
- Medical Research Council
- European Molecular Biology Organization (ALTF 860-2019)
- European Commission
- Cancer Research UK (CC001051)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Developmental Biology and Gene Regulation
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Keywords
- tissue patterning, gene regulatory networks, optimal control, cell fate specification, intracellular signaling, morphogen gradients, feedback, molecular noise, developmental robustness
- MeSH terms
- Cell Differentiation, Signal Transduction, Gene Regulatory Networks
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review