A Spectrum of Free Energy Landscape Topologies Encodes Chromatin Polymorphism and Phase Separation

Chromatin exhibits structural polymorphism, yet how such substantial structural heterogeneity is encoded in its underlying free-energy landscape remains unknown. Here we map the folding landscapes of tetra-nucleosome arrays using adaptive Markov state models constructed from near-atomistic coarse-grained simulations. We find that chromatin is not governed by a single folding funnel analogous to those of many globular proteins. Instead, it spans a continuum of free-energy landscape topologies, ranging from funnelled to rugged to flat. Remarkably, phase separation reshapes chromatins free-energy landscape by stabilising conformations that maximise intermolecular connectivity, demonstrating that the landscape is determined not only by intrinsic molecular parameters but also by the environment and intermolecular interactions. Linker DNA geometry selects among landscape regimes through geometric frustration of zig-zag nucleosome stacking. At short and intermediate linker lengths, canonical 10N bp linkers produce funnelled landscapes dominated by compact zig-zag structures, whereas 10N +5 bp linkers generate rugged landscapes with multiple competing minima. Long linkers relieve frustration and flatten the landscape into a broad entropic basin. This control operates with single-base-pair precision, such that changing linker length by one base pair is sufficient to reorganise both the thermodynamics and kinetics of chromatin folding. DNA sequence provides a second level of control by modulating linker deformability, but only when zig-zag geometric frustration is present. These results establish free-energy landscapes as a framework for understanding the physical origin of chromatin polymorphism and its coupling to phase separation.