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Subdiffusion from competition between multi-exponential friction memory and energy barriers.

Anton Klimek1, Benjamin A Dalton1, Roland R Netz2

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Summary
This summary is machine-generated.

Subdiffusion, common in complex systems, arises from memory effects or energy barriers. This study provides tools to distinguish these origins, showing memory dominates for low energy barriers, relevant to protein folding.

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Area of Science:

  • Physics
  • Biophysics
  • Physical Chemistry

Background:

  • Subdiffusion is prevalent in complex systems like protein folding and transport in viscoelastic media.
  • The precise mechanisms driving subdiffusion, whether memory-dependent friction or energy barriers, are still debated.
  • Understanding these origins is crucial for diverse fields from biophysics to polymer science.

Purpose of the Study:

  • To differentiate the contributions of memory-dependent friction and energy barriers to subdiffusion.
  • To develop an analytical framework connecting subdiffusion to multi-scale memory effects in the generalized Langevin equation (GLE).
  • To identify characteristic timescales that define dynamical regimes dominated by memory or energy barriers.

Main Methods:

  • Analysis of both Markovian and non-Markovian dynamics, with and without energy barriers.
  • Development of an analytical framework for the mean squared displacement (MSD) based on the generalized Langevin equation (GLE).
  • Derivation of subdiffusive scaling behavior for multi-exponential memory kernels.
  • Comparison of analytical predictions with simulation data.

Main Results:

  • An analytical framework linking subdiffusion to multi-scale memory effects in the GLE was established.
  • Subdiffusive scaling behavior of the MSD was derived for systems with multi-exponential memory kernels.
  • Persistence and relaxation timescales were identified to distinguish between memory-driven and barrier-driven subdiffusion.
  • Simulations confirmed that memory effects dominate overdamped dynamics for energy barriers up to approximately 2 kBT, relevant for fast-folding proteins.

Conclusions:

  • The study successfully disentangles the roles of memory and energy barriers in subdiffusion.
  • Memory effects are shown to be the dominant driver of subdiffusion in systems with low energy barriers.
  • The developed theoretical framework and identified timescales offer practical tools for analyzing anomalous diffusion in various complex systems.