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Engineering morphogenesis of cell clusters with differentiable programming

Nature Computational Science volume 5, pages 875–883 (2025)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Understanding the fundamental rules of organismal development is a central, unsolved problem in biology. These rules dictate how individual cellular actions coordinate over macroscopic numbers of cells to grow complex structures with exquisite functionality. We use recent advances in automatic differentiation to discover local interaction rules and genetic networks that yield emergent, systems-level characteristics in a model of development. We consider a growing tissue with cellular interactions mediated by morphogen diffusion, cell adhesion and mechanical stress. Each cell has an internal genetic network that is used to make decisions based on the cell’s local environment. Here we show that one can learn the parameters governing cell interactions in the form of interpretable genetic networks for complex developmental scenarios. When combined with recent experimental advances measuring spatio-temporal dynamics and gene expression of cells in a growing tissue, the methodology outlined here offers a promising path to unraveling the cellular bases of development.

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Fig. 1: Modeling and optimization framework.
Fig. 2: Chemical control of directional proliferation.
Fig. 3: Chemical regulation of homeostasis.
Fig. 4: Mechano-chemical regulation of homogeneous growth.

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Data availability

No further data are needed to reproduce this study. Source data are provided with this manuscript.

Code availability

The Jax-Morph library is available at https://github.com/fmottes/jax-morph (ref. 49). Code, as well as the instructions to reproduce the results from this work, are available from the ‘paper-natcompsci-2025’ branch of the GitHub repository49, and on Zenodo30.

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Acknowledgements

This work is dedicated to the memory of Alma Dal Co. We thank the members of the Brenner Group, as well as the members of the former Dal Co Group for insightful discussions. We thank B. Shraiman and D. Cislo for insightful discussions. R.D. thanks H. Turlier for helpful discussions. This work was supported by the Office of Naval Research through grant nos. ONR N00014-17-1-3029, ONR N00014-23-1-2654 and the NSF AI Institute of Dynamic Systems (2112085).

Author information

Author notes

  1. These authors contributed equally: Ramya Deshpande, Francesco Mottes.

Authors and Affiliations

  1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Ramya Deshpande, Francesco Mottes, Ariana-Dalia Vlad & Michael P. Brenner

  2. Department of Computational Biology, University of Lausanne, Lausanne, Switzerland

    Francesco Mottes & Alma Dal Co

Authors
  1. Ramya Deshpande
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  2. Francesco Mottes
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  3. Ariana-Dalia Vlad
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  4. Michael P. Brenner
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  5. Alma Dal Co
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Contributions

A.D.C., M.P.B., F.M. and R.D. designed the research. F.M. and R.D. developed the code and performed the research. R.D., F.M. and A.-D.V. performed computational experiments. F.M. and R.D. produced and interpreted the results. A.D.C. and M.P.B. supervised the research. R.D., F.M. and M.P.B. wrote the paper.

Corresponding authors

Correspondence to Ramya Deshpande, Francesco Mottes or Michael P. Brenner.

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M.P.B. is an employee of Google Research.

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Nature Computational Science thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Ananya Rastogi, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

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Deshpande, R., Mottes, F., Vlad, AD. et al. Engineering morphogenesis of cell clusters with differentiable programming. Nat Comput Sci 5, 875–883 (2025). https://doi.org/10.1038/s43588-025-00851-4

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