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  Estimating ruggedness of free-energy landscapes of small globular proteins from principal component analysis of molecular dynamics trajectories

Volkhardt, A., & Grubmüller, H. (2022). Estimating ruggedness of free-energy landscapes of small globular proteins from principal component analysis of molecular dynamics trajectories. Physical Review E, 105: 044404. doi:10.1103/PhysRevE.105.044404.

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Volkhardt, A.1, Author           
Grubmüller, H.1, Author           
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1Department of Theoretical and Computational Biophysics, Max Planck Institute for Multidisciplinary Sciences, Max Planck Society, ou_3350132              

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 Abstract: The internal dynamics of biomolecules, and hence their function, is governed by the structure of their free- energy landscape. Early flash-photolysis experiments on myoglobin suggested that the free-energy landscapes of proteins are hierarchically structured, with a characteristic distribution of free-energy barriers which gives rise to anomalous diffusion. Analytical results have been derived for one-dimensional or high-dimensional hierar- chical free-energy landscapes. Recent improvements in methods and computer performance enable generating sufficiently long molecular dynamics (MD) trajectories to extract dynamics information covering many orders of magnitude, such that the broad distributions of energy barriers of proteins become accessible to quantitative studies of intermediate dimensions. In this work, we present a nonequilibrium method to estimate barrier height distributions from microsecond-long MD simulations. It infers barrier height distributions from anomalous diffusion exponents derived from principal component analysis and by comparison to simple hierarchical lattice models. These models are d-dimensional lattices of states separated by free-energy barriers, the heights of which are distributed as p(AG) = 1/γ exp(−AG/γ ). The parameter γ quantifies the “ruggedness” of the free-energy landscape in such models. We show that both parameters, i.e., ruggedness and effective dimensionality d, can be inferred from anomalous diffusion exponents. Assuming a similar dependency of anomalous diffusion exponents on γ and d for proteins, we estimate the ruggedness of the free-energy landscapes of 500 small, single-domain globular proteins between 15 and 20 kT per dimension with an estimated accuracy of 4.2 kT and dimensionality between 40 and 60 with an estimated accuracy of 10 dimensions. Remarkably, neither effective dimensionality nor the ruggedness correlates with protein size and both ruggedness and effective dimensionality are much smaller than the scatter of protein sizes. From this finding, we conclude that these two properties of the free-energy landscape of a protein are rather adapted to the particular function of each single protein and that, quite generally, are functionally relevant for globular proteins.

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Language(s): eng - English
 Dates: 2021-08-182022-02-282022-04-15
 Publication Status: Published online
 Pages: 12
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevE.105.044404
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: - Volume / Issue: 105 Sequence Number: 044404 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012