No abstract

While the classical view of protein folding kinetics relies on phenomenological models, and regards folding intermediates in a structural way, the new view emphasizes the ensemble nature of protein conformations. Although folding has sometimes been regarded as a linear sequence of events, the new view sees folding as parallel microscopic multi-pathway diffusion-like processes. While the classical view invoked pathways to solve the problem of searching for the needle in the haystack, the pathway idea was then seen as conflicting with Anfinsen's experiments showing that folding is pathway-independent (Levinthal's paradox). In contrast, the new view sees no inherent paradox because it eliminates the pathway idea: folding can funnel to a single stable state by multiple routes in conformational space. The general energy landscape picture provides a conceptual framework for understanding both two-state and multi-state folding kinetics. Better tests of these ideas will come when new experiments become available for measuring not just averages of structural observables, but also correlations among their fluctuations. At that point we hope to learn much more about the real shapes of protein folding landscapes.

The protein-folding problem was first posed about one half-century ago. The term refers to three broad questions: (i) What is the physical code by which an amino acid sequence dictates a protein's native structure? (ii) How can proteins fold so fast? (iii) Can we devise a computer algorithm to predict protein structures from their sequences? We review progress on these problems. In a few cases, computer simulations of the physical forces in chemically detailed models have now achieved the accurate folding of small proteins. We have learned that proteins fold rapidly because random thermal motions cause conformational changes leading energetically downhill toward the native structure, a principle that is captured in funnel-shaped energy landscapes. And thanks in part to the large Protein Data Bank of known structures, predicting protein structures is now far more successful than was thought possible in the early days. What began as three questions of basic science one half-century ago has now grown into the full-fledged research field of protein physical science.

Using lattice statistical mechanics, we develop theory to account for the folding of a heteropolymer molecule such as a protein to the globular and soluble state. Folding is assumed to be driven by the association of solvophobic monomers to avoid solvent and opposed by the chain configurational entropy. Theory predicts a phase transition as a function of temperature or solvent character. Molecules that are too short or too long or that have too few solvophobic residues are predicted not to fold. Globular molecules should have a largely solvophobic core, but there is an entropic tendency for some residues to be "out of place", particularly in small molecules. For long chains, molecules comprised of globular domains are predicted to be thermodynamically more stable than spherical molecules. The number of accessible conformations in the globular state is calculated to be an exceedingly small fraction of the number available to the random coil. Previous estimates of this number, which have motivated kinetic theories of folding, err by many tens of orders of magnitude.

To meet the challenge of modeling the conformational dynamics of biological macromolecules over long time scales, much recent effort has been devoted to constructing stochastic kinetic models, often in the form of discrete-state Markov models, from short molecular dynamics simulations. To construct useful models that faithfully represent dynamics at the time scales of interest, it is necessary to decompose configuration space into a set of kinetically metastable states. Previous attempts to define these states have relied upon either prior knowledge of the slow degrees of freedom or on the application of conformational clustering techniques which assume that conformationally distinct clusters are also kinetically distinct. Here, we present a first version of an automatic algorithm for the discovery of kinetically metastable states that is generally applicable to solvated macromolecules. Given molecular dynamics trajectories initiated from a well-defined starting distribution, the algorithm discovers long lived, kinetically metastable states through successive iterations of partitioning and aggregating conformation space into kinetically related regions. The authors apply this method to three peptides in explicit solvent-terminally blocked alanine, the 21-residue helical F(s) peptide, and the engineered 12-residue beta-hairpin trpzip2-to assess its ability to generate physically meaningful states and faithful kinetic models.