In this section
@article{Kim:2026:10.1073/pnas.2536690123,
author = {Kim, S and Matas-Gil, A and Endres, RG},
doi = {10.1073/pnas.2536690123},
journal = {Proceedings of the National Academy of Sciences},
title = {How nature discovers rare Turing islands: Exploration by common limit cycles},
url = {http://dx.doi.org/10.1073/pnas.2536690123},
volume = {123},
year = {2026}
}
TY - JOUR
AB - <jats:p>Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving biological systems reliably find and exploit such rare conditions? In this work, we propose that common biochemical limit cycles, such as those arising from genetic feedback loops, can act as natural explorers of Turing space. By coupling a reaction–diffusion system to an orbit that modulates some of its parameters, we show that the system can dynamically sweep through Turing-permissive regimes and generate transient spatial patterns. We use an entropy-based measure in Fourier space to quantify pattern formation and demonstrate how cycles enhance the detectability and robustness of Turing islands. We further explore how coupling to positional gradients increases reproducibility, suggesting a route from oscillatory dynamics to stable developmental programs. Our results highlight a powerful mechanism by which nature might bootstrap complex spatial structure from simple temporal motifs.</jats:p>
AU - Kim,S
AU - Matas-Gil,A
AU - Endres,RG
DO - 10.1073/pnas.2536690123
PY - 2026///
SN - 0027-8424
TI - How nature discovers rare Turing islands: Exploration by common limit cycles
T2 - Proceedings of the National Academy of Sciences
UR - http://dx.doi.org/10.1073/pnas.2536690123
UR - https://doi.org/10.1073/pnas.2536690123
VL - 123
ER -
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