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Microfluidic Mixers for Studying Protein Folding
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Ultrametricity in Protein Folding Dynamics.

Riccardo Scalco1, Amedeo Caflisch1

  • 1Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.

Journal of Chemical Theory and Computation
|November 24, 2015
PubMed
Summary

The free energy of a transition state (TS) in Markov state models (MSMs) is an ultrametric distance. This property simplifies MSMs and defines rate constants, revealing parallels with transition state theory.

Area of Science:

  • Computational chemistry
  • Statistical mechanics
  • Complex systems analysis

Background:

  • Markov state models (MSMs) are crucial for analyzing molecular dynamics.
  • The free energy of transition states (TS) is often calculated using minimum cut methods.
  • Understanding the structure of MSMs is key to predicting system dynamics.

Purpose of the Study:

  • To demonstrate that the free energy of the TS in an ergodic MSM is an ultrametric distance.
  • To introduce a simplified approach for MSM analysis using the ultrametric property.
  • To define a new cut-based free energy profile (cbFEP) for identifying metastable states.

Main Methods:

  • Analysis of the free energy landscape of transition states in ergodic Markov state models.
  • Application of minimum cut (maximum flow) algorithms to identify separating sets of edges.

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  • Derivation of the ultrametric property for transition state free energy.

    • Main Results:

    • The free energy of the transition state (TS) in an ergodic Markov state model (MSM) is proven to be an ultrametric distance.
    • The ultrametric property allows for the simplification of MSMs into fewer states, enabling the definition of meaningful rate constants (free energy barriers).
    • A novel cut-based free energy profile (cbFEP) is introduced to detect states with rapid equilibration relative to escape times.

    Conclusions:

    • The ultrametric nature of TS free energy offers a powerful simplification for complex MSMs.
    • The cbFEP provides a new tool for characterizing metastable states within dynamical systems.
    • A clear parallelism is established between minimum cut calculations and established theories like transition state theory (TST) and Kramers' theory.