Cislo, Delás, Briscoe & Siggia (2025) fit Waddington's landscape directly to high-dimensional single-cell gene-expression data

Cislo, Delás, Briscoe & Siggia, "Reconstructing Waddington's Landscape from Data" (bioRxiv, posted 2025-08-13; published PNAS 2025, DOI 10.1073/pnas.2521762122, online 2025-12-03), present "a computational geometry framework for fitting dynamical landscapes directly to high-dimensional single-cell data." The load-bearing word is directly: the method models "the time evolution of probability distributions in gene expression space" itself, rather than in a separately chosen, hand-designed low-dimensional coordinate system.

The paper frames this as a departure from a specific prior tradition. Earlier applications of the dynamical-systems landscape formalism — the Morse–Smale "fate space" line, citing C. elegans vulval patterning, Drosophila bristle patterning, and in vitro stem-cell systems — "built landscapes in low-dimensional spaces without explicit reference to gene expression." Cislo et al. skip that hand-built intermediate and fit the potential on a point set sampled from the measured data (see the mechanism in claim-cislo-siggia-2025-landscape-from-discretized-fokker-planck-on-sampled-data-points and the validation in claim-cislo-siggia-2025-validated-on-real-mesc-neural-tube-flow-and-rnaseq-data).

This answers the vault's open question question-siggia-2025-reconstructs-waddington-landscape-single-cell and extends the Waddington-landscape thread from the 2016 Hopfield-network formalization (claim-hopfield-network-formalizes-waddington-epigenetic-landscape, claim-2016-hopfield-landscape-paper-not-first-cell-fate-attractor-model) to a live 2025 single-cell method. Notably, this paper cites the Morse–Smale dynamical-systems lineage, not the Hopfield-network one — the two formalization traditions of Waddington's landscape run in parallel here without meeting.