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BP: Fachverband Biologische Physik

BP 31: Protein Structure and Dynamics

BP 31.9: Talk

Thursday, March 21, 2024, 17:30–17:45, H 0112

Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins — •Emanuel Dorbath, Adnan Gulzar, and Gerhard Stock — Institute of Physics, University of Freiburg, 79104 Freiburg, Germany

The time-dependent relaxation of a dynamical system may follow a power law that is superimposed by log-periodic oscillations. This behavior can by explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Recent time-resolved experiments and molecular dynamics simulations suggest that this also holds for hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur.

An entropy-based timescale analysis and Markov state modeling is applied to a simple one-dimensional hierarchical model and biomolecular simulation data of the achiral peptide helix Aib9, showing that hierarchical systems in fact give rise to logarithmically spaced discrete time scales [arXiv:2311.11839 (2023)]. Introducing a one-dimensional reaction coordinate, the free energy landscape exhibits a characteristic staircase shape with two metastable states, which causes the observed log-periodic time evolution of the system. The period of these oscillations reflects the effective roughness of the energy landscape and can in simple cases be interpreted as the energy barriers of the staircase.

Keywords: Molecular dynamics; Hierarchical dynamics; Data driven analysis; Timescales; Scale invariance