Identifying the fundamental reaction coordinates that connect a protein’s native structure to its dynamical and evolutionary behavior remains a central challenge in molecular biophysics. Here, we introduce the topological and geometrical descriptors writhe and local topological energy (LTE), which provide powerful means to uncover these connections. By applying these metrics to both present-day and reconstructed ancestral forms of thioredoxin and β-lactamase, we demonstrate that LTE correlates strongly with the Dynamical Flexibility Index (DFI), a widely used measure of conformational dynamics. Strikingly, the distribution of LTE values also recapitulates known evolutionary trajectories, suggesting that the topology of the native state encodes essential information about both dynamical properties and evolutionary pressures. Molecular dynamics simulations reveal that evolutionary changes in these proteins are accompanied by systematic shifts in their topological landscapes, providing a mechanistic explanation for how functional adaptation can proceed through alterations in conformational dynamics. Extending this framework to a dataset of more than 100 structurally diverse proteins, we show that static topological descriptors alone reliably predict dynamical behavior across protein families. Together, these results establish a new conceptual bridge between protein structure, dynamics, and evolution. By demonstrating that simple geometric measures derived from native-state structures capture essential features of conformational landscapes, our work provides a broadly applicable approach for probing protein function, guiding protein engineering, and understanding the evolutionary principles that shape molecular machines.
Ramesh et al. (Sun,) studied this question.