Go-ing for the prediction of protein folding mechanisms.

P folding has been a long-lived problem in biophysics. Much important progress has been made in the 90s by focusing on small single-domain proteins (1). In particular, (i) site-resolved measurement of the folding transition state ensemble, quantified as f-values (2), made it possible to understand folding mechanisms relatively unambiguously, stimulating interaction between experimentalists and theoreticians; (ii) the energy-landscape theory (3) gave us a general framework based on statistical physics; and (iii) the finding of a significant correlation between folding rates and native structure topology (4), which suggested that the native topology is a key determinant of folding mechanisms, all lead us to believe that the underlying physics could be relatively simple. These three ingredients are linked together with an almost one-line free energy equation in three papers (5–7), which appeared in a recent issue of PNAS, as well as some previous work (8, 9). The surprise of the three papers is that apparently one can have both simplicity and fair predictability. Papers by Galzitskaya and Finkelstein (5), Alm and Baker (6), and Muñoz and Eaton (7), which are independent but resemble each other greatly, report that even highly simplified theories based on energy-landscape ideas can predict trends in the folding rates for many fast folding proteins. The calculations of the three papers are easy to summarize. In all three papers, each amino acid (or a few adjacent amino acids grouped) is taken to be either in a native configuration (n) or in a completely random set (r). A reduced protein configuration, or microstate, is represented as a sequence of n and r, such as rrrr-nnnnnnrrrrrr-nnnnnnn. The (globally) native and denatured states correspond to the microstate in which all amino acids are in n and r, respectively. The authors introduce simple free energies for microstates given the native three-dimensional structure. Assuming an elementary step to be a change in one amino acid from r to n, the researchers look for the pathways that connect native and denatured states in the microstate space. On each pathway, there is a maximum along the reaction coordinate number of native-like amino acids. The investigators assign this maximum as a member of transition state ensemble (see Fig. 1). Finally, they compare characteristics of their transition states with those measured experimentally. Galzitskaya and Finkelstein (5) as well as Alm and Baker (6) analyzed the structure of the transition states and compared their estimated f-values with the experimental values. The researchers found significant correlation coefficients (r . 0.4) for several proteins but with some exceptions (r ' 0). Muñoz and Eaton (7), in addition to the f-value test, focus more on the free-energy barrier height at the transition state and the corresponding total folding rate measured in kinetic experiments. In their paper, figure 5 shows the excellent agreement of folding rate coefficients with those measured in experiments. One underlying assumption for these analyses is common to all three papers as well as previous, more elaborate treatments (8, 9): all of these theories take into account only the interactions that are present in the native structure, the socalled native interactions. The theories assume that nonnative interactions do not contribute to the global shape of the folding energy surface. We often call this class of models Go# models, because this type of interaction was first introduced in old lattice simulation work by Go# and coworkers (ref. 10 and references therein). [I also would like to mention that, inspired by Go# ’s work, Miyazawa and Jernigan (11) developed a theory rather parallel to the three papers (5–7). Without good experiments, however, their work received little attention.] The Go# model is one realization of a central idea of the energy landscape theory that the energy landscape resembles a funnel (3). The landscape theory, however, incorporates both the global funnel shape toward the native basin and the ruggedness of the energy landscape which it views as arising from unavoidable frustration upon refolding. While the Go# model captures the first feature, the latter aspect is entirely ignored. The crudeness of the approximation, which is an extreme limiting case of a folding funnel, would lead one to doubt its applicability for quantitatively calculating properties of the ensemble of folding pathways for specific proteins. But, surprisingly enough, the perfect funnel models give reasonable prediction even up to the site-resolved level. If the interactions included are all attractive to the native structure, why does a barrier or transition state exist for folding at all? Upon folding of small singledomain proteins, the solvent averaged free energy of a chain configuration E almost always decreases because most interactions are favorable, whereas acquisition of specific order results in the loss of chain entropy S. At temperature T, the free energy F 5 E 2 TS has a barrier along the reaction coordinate, because chain entropy is lost at a somewhat earlier stage than energetic stability is gained. In all of the above mentioned theories, folding pathways are determined in such a way that the protein gains a given number of native contacts while keeping entropy loss as small as possible. A local contact is more favorable than a nonlocal one in the early stage of folding, because a smaller number of peptides need to be pinned down by a local contact. For the protein as a whole, the ensemble of pathways is controlled by the distribution of native contacts and the latter is determined by the topology of the native structure based on the perfect funnel approximation. It is interesting to compare these papers and related works (5–9) more closely, because there are indeed some differences in formulation that apparently do not perturb agreement with experiments. For interaction energies, all the investigators, except Alm and Baker (6), use paircontact models as major interactions. Shoemaker et al. (8) employ local hydrogen bond interaction, whereas others do not. Alm and Baker (6) employ an accessible surface-area form of interaction without hydrogen bonding. The chainentropy terms in each case consist of an