Geometry derived Hamiltonian organization distinguishes recurrent biological Fe S architectures

Iron-sulfur (Fe-S) clusters are among the most ancient biological cofactors, yet the physical properties associated with the recurrent biological utilization of specific Fe-S architectures remain unclear. Here, we analyzed 2,404 experimentally resolved Fe-S clusters using an integrated framework combining structural geometry, geometry-derived effective-coupling network robustness, and coarse-grained open-system quantum transport simulations. We show that 4Fe-4S clusters occupy a compact and partially distinct region of structural-descriptor space characterized by low geometric distortion, elevated geometry-derived network robustness, and broad taxonomic representation within the available structural dataset. Geometry-derived coarse-grained effective Hamiltonian reconstruction and Lindblad simulations further showed architecture-dependent differences in Hamiltonian organization and simulated transport behavior under a common set of model assumptions. Together, these findings establish a hierarchical comparative framework linking Fe-S geometry, effective Hamiltonian organization, simulated open-system transport, and broad taxonomic recurrence, and suggest that geometry-derived transport organization may represent one physical property contributing to the recurrent biological utilization of Fe-S architectures.