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The roles of stability and contact order in determining protein folding rates

Nature Structural Biology volume 8, pages 21–22 (2001)Cite this article

The mechanism by which a protein folds, like any reaction, is determined by the underlying free energy surface1. A large separation in energy between the native state and the structurally dissimilar states (an 'energy gap') has been shown to be a thermodynamic and kinetic requirement for folding in both analytical theories2,3 and simulations of lattice models4,5. The ability of a sequence to fold rapidly correlates strongly with measures of the stability of its native (ground) state (such as the Z-score or the gap between the ground and first excited compact states). The relationship between the kinetics and the thermodynamics arises from the fact that the transition state involves a subset of the native interactions1,6. Thus, lowering the (free) energy of the native state also tends to stabilize the transition state. This behavior is consistent with the Hammond effect (the movement of a transition state along a reaction coordinate away from a reactant, intermediate or product state that is stabilized), which has been observed experimentally to hold for certain proteins7.

We use a more sophisticated statistical analysis of the folding data to show that, in fact, both contact order and stability play important roles in determining the folding rate. Specifically, artificial neural networks are trained to reproduce and predict log kf from c and ΔG. Care is taken to crossvalidate the results with an appropriate partitioning scheme; each group of structurally related proteins is left out during the training in turn and then used to test the network. This procedure yields true predictions (denoted 'cv') in contrast to fits of the data, in which all the proteins are included during the training (denoted 'trn'). The latter tend to yield inflated statistics, but we describe them here as well for comparison with earlier studies8,9,19,20, which failed to crossvalidate or otherwise to test their results.

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Figure 1: Correlation between the observed values of log kf and the crossvalidated predictions.
Figure 2: Dependence of the calculated log kf on c and ΔG.

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Acknowledgements

We thank S.-S. So for providing the HIPPO program used to fit the data. A.R.D. is a Burroughs Wellcome Fund Hitchings-Elion Postdoctoral Fellow, and M.K. was the Eastman Visiting Professor at the Oxford Centre for Molecular Sciences. We wish to acknowledge W.G. Richards and C.M. Dobson for the hospitality that has been extended to us during our time in Oxford. This work was supported in part by a grant from the National Science Foundation.

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Authors and Affiliations

  1. New Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QT, UK

    Aaron R. Dinner & Martin Karplus

  2. Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, 02138, MA, USA

    Martin Karplus

  3. Laboratoire de Chimie Biophysique, Institut le Bel Université Louis Pasteur, 4 Rue Blaise Pascal, 67000, Strasbourg, France

    Martin Karplus

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  1. Aaron R. Dinner
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Correspondence to Martin Karplus.

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Dinner, A., Karplus, M. The roles of stability and contact order in determining protein folding rates. Nat Struct Mol Biol 8, 21–22 (2001). https://doi.org/10.1038/83003

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