Hydrophobic forces and the length limit of foldable protein domains
To find the native conformation (fold), proteins sample a subspace that is typically hundreds of orders of magnitude smaller than their full conformational space. Whether such fast folding is intrinsic or the result of natural selection, and what is the longest foldable protein, are open questions. Here, we derive the average conformational degeneracy of a lattice polypeptide chain in water and quantitatively show that the constraints associated with hydrophobic forces are themselves sufficient to reduce the effective conformational space to a size compatible with the folding of proteins up to approximately 200 amino acids long within a biologically reasonable amount of time. This size range is in general agreement with the experimental protein domain length distribution obtained from approximately 1,200 proteins. Molecular dynamics simulations of the Trp-cage protein confirm this picture on the free energy landscape. Our analytical and computational results are consistent with a model in which the length and time scales of protein folding, as well as the modular nature of large proteins, are dictated primarily by inherent physical forces, whereas natural selection determines the native state.
Additional Information© 2012 National Academy of Sciences. Contributed by Ahmed H. Zewail, May 2, 2012 (sent for review March 28, 2012). Published online before print June 4, 2012. We thank Dr. David Shaw for thoroughly going over the entire manuscript; we value his comments, which added to the clarity of the work presented. We also appreciate the helpful feedback on the preliminary manuscript from Prof. Thomas Miller III, Prof. Rob Phillips, Prof. Eugene Shakhnovich, Prof. Kenneth Dill, Prof. Peter Wolynes, and Prof. Vijay Pande. We are grateful to the National Science Foundation for funding of this research at Caltech. M.M.L. acknowledges financial support from the Krell Institute and the US Department of Energy for a DoE CSGF graduate fellowship (Grant DE-FG02-97ER25308) at Caltech. Author contributions: M.M.L. and A.H.Z. performed research and wrote the paper. The authors declare no conflict of interest.
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