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Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis. (English) Zbl 1460.55007

A protein and the connections within it are modeled by a simplicial complex which incorporates time via the oscillations of perturbed elements of the system. The time evolution of the system as oscillators move to synchronization allows the definition of a real valued function on the complex. Evolutionary homology studies the persistence barcodes of the resulting system. As a major application the ideas can be applied to the study of the flexibility of proteins. The resulting analysis of protein flexibility, which is computationally feasible, is shown to outperform other state of the art methods.

MSC:

55N31 Persistent homology and applications, topological data analysis
62R40 Topological data analysis
37N25 Dynamical systems in biology
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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