Unifying constraints linking protein folding and native dynamics decoded from AlphaFold

The interplay between protein folding and native dynamics remains a central question in biophysics. Analyzing an extensive set of AlphaFold-predicted structures, we uncover a robust relationship between folding topology (contact order) and native dynamics (fluctuation entropy), showing that long-range contacts that slow folding also restrict conformational flexibility across protein sizes and taxonomic groups. Scaling analysis reveals that this relationship, together with its chain-length dependence, is consistent with power-law-like trends, reflecting common organizing constraints of protein architecture. Across species, increasing organismal complexity is associated with proteome-wide shifts toward lower contact order and higher fluctuation entropy. Together, evidence from folding, stability, and functional dynamics converges on unifying constraints, revealing an intrinsic physical organizing principle captured by AI models.