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A kinetic ensemble of the Alzheimer’s Aβ peptide

A preprint version of the article is available at bioRxiv.

Abstract

The conformational and thermodynamic properties of disordered proteins are commonly described in terms of structural ensembles and free energy landscapes. To provide information on the transition rates between the different states populated by these proteins, it would be desirable to generalize this description to kinetic ensembles. Approaches based on the theory of stochastic processes can be particularly suitable for this purpose. Here, we develop a Markov state model and apply it to determine a kinetic ensemble of Aβ42, a disordered peptide associated with Alzheimer’s disease. Through the Google Compute Engine, we generated 315-µs all-atom molecular dynamics trajectories. Using a probabilistic-based definition of conformational states in a neural network approach, we found that Aβ42 is characterized by inter-state transitions on the microsecond timescale, exhibiting only fully unfolded or short-lived, partially folded states. Our results illustrate how kinetic ensembles provide effective information about the structure, thermodynamics and kinetics of disordered proteins.

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Fig. 1: Illustration of a kinetic ensemble of a protein and the training methodology.
Fig. 2: Determination of the states in the kinetic ensemble of Aβ42.
Fig. 3: Structural properties of Aβ42 in the kinetic ensemble.
Fig. 4: Populations and mean first-passage times in the kinetic ensemble of Aβ42.

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Data availability

Subsampled trajectory and intermediate data, as well as the trained neural network weights, analysis notebooks and source data, are available from https://zenodo.org/record/424732178. Source data are provided with this paper.

Code availability

Analysis notebooks, code and example data are available from https://github.com/vendruscolo-lab/ab42-kinetic-ensemble and https://zenodo.org/record/424732178.

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Acknowledgements

G.T.H. is supported by the Rosalind Franklin Research Fellowship at Newnham College. We thank S. Kearnes for useful feedback and suggestions for the manuscript and M. Bonomi for useful discussions and suggestions. We also acknowledge support from Google and the Google Accelerated Science team for providing access to the Google Cloud Platform for simulations and analysis.

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Authors

Contributions

T.L., K.K., G.T.H., C.C. and M.V. designed the research plan. T.L. and K.K. performed the simulations. T.L., K.K., G.T.H., C.C. and M.V. analyzed the data. T.L., K.K., G.T.H., C.C. and M.V. wrote the manuscript.

Corresponding author

Correspondence to Michele Vendruscolo.

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The authors declare no competing interests.

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Peer review information Fernando Chirigati was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team. Nature Computational Science thanks Christopher Lockhart, Andreas Mardt and Fanjie Meng for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Relaxation (implied) timescales for conventional discrete-state Markov state models, showing inability to construct a model with converging timescales.

a, Relaxation timescales for a 200-microstate model as a function of model lag time. b-d, Relaxation timescales for hidden Markov state models using 2, 4, and 6 output states respectively, as a function of model lag time. e-f, Relaxation timescales for 4 and 6-state Markov state models built using Perron cluster-cluster analysis (PCCA) from the 200-microstate model as a function of model lag time. The gray shading indicates the timescales for which the Koopman model can no longer resolve the relaxation timescales. Shaded areas indicate 95% confidence intervals of the sample mean of the 20 models.

Source data

Extended Data Fig. 2 Equilibrium distributions of the models.

a, 2, (b) 3, (c) 4, (d) 5, and (e) 6-state model equilibrium distributions. The whiskers, boxes and horizontal lines indicate 95th percentiles, quartiles, and the median values over all 20 models, respectively, the labels show the mean model values.

Source data

Extended Data Fig. 3 Relaxation (implied) timescales as a function of model lag time.

a, 2, (b) 3, (c) 5, and (d) 6-state model timescales. The gray shading indicates the timescales for which the Koopman model can no longer resolve the relaxation timescales. Shaded areas indicate 95th percentiles of the sample mean over 20 models.

Source data

Extended Data Fig. 4 Experimental validation and comparison to an existing ensemble.

a, Root-mean-square deviations between experimentally determined NMR chemical shifts and those back calculated using CamShift49; the deviations are smaller than the intrinsic CamShift errors. b, Comparison of the probability distributions of the radius of gyration computed for the current Markov state model (MSM, green) and the previously performed metadynamic metainference simulations (MI, purple)31.

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Löhr, T., Kohlhoff, K., Heller, G.T. et al. A kinetic ensemble of the Alzheimer’s Aβ peptide. Nat Comput Sci 1, 71–78 (2021). https://doi.org/10.1038/s43588-020-00003-w

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