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Behind the Folding Funnel Diagram

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Behind the Folding Funnel Diagram commentary Behind the folding funnel diagram Martin Karplus This Commentary clarifies the meaning of the funnel diagram, which has been widely cited in papers on protein folding. To aid in the analysis of the funnel diagram, this Commentary reviews historical approaches to understanding the mechanism of protein folding. The primary role of free energy in protein folding is discussed, and it is pointed out that the decrease in the configurational entropy as the native state is approached hinders folding, rather than guiding it. Diagrams are introduced that provide a less ambiguous representation of the factors governing the protein folding reaction than the funnel diagram. nderstanding the mechanism fewer) generally fold in times on the order to that shown in Figure 1. It is a schematic by which proteins fold to their of milliseconds to seconds (except in cases representation of how the effective Unative state remains a problem of with special factors that slow the folding, potential energy, implicitly averaged fundamental interest in biology, in spite of such as proline isomerization), there was over solvent interactions (in the vertical the fact that it has been studied for many indeed a paradox. The ultimate statement direction), and the configurational entropy years1. Moreover, now that misfolding has of the paradox was given in the language (in the horizontal direction) of a protein been shown to be the source of a range of of computational complexity5. Many decrease as the native state is approached; diseases, a knowledge of the factors that phenomenological models were proposed picturesque three-dimensional funnels are determine whether a polypeptide chain to show how the conformational space that also being used11. Both the two- and three- will fold to its native state or aggregate has has to be searched is restricted to reduce dimensional diagrams have a funnel-like become all the more important. the folding time to the experimental range. shape because the number of accessible The folding funnel diagram (see Fig. 1), Examples include the nucleation-growth or configurations, which determine the introduced by Wolynes, Onuchic and nucleation-condensation mechanism6,7, the configurational entropy, decreases as the Thirumalai2, is intended to provide diffusion-collision model8 and the jigsaw- energy decreases. Such funnel diagrams a pictorial representation of how the puzzle model9. are very appealing images from which Levinthal paradox3, which had dominated In the late 1980s, the focus of approaches many readers have concluded that folding discussion of protein folding for many to the protein folding problem shifted a protein is like “funneling wine into a © 2011 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2011 years, is resolved. Since the original from phenomenological models to a bottle.” A typical statement of this type publication, funnel diagrams have become consideration of the general characteristics appears in a study of the folding of PDZ a fixture in papers on protein folding, of the energy surface of a polypeptide chain. domains12; in the introduction, it is stated and they are now being introduced in The new focus is eminently reasonable, as that “Free energy landscapes of many discussions of other problems, such as the energy surface is one of the fundamental proteins appear to resemble the shape of ligand binding4. Unfortunately, the funnel determinants of any reaction1, whether a a funnel that guides the folding process diagram has created a misconception in small-molecule reaction or protein folding. toward the native state.” Although Wolynes many readers. The change made explicit a concept that is et al.2 were aware that the occurrence of The concept introduced by Levinthal is implicit in the phenomenological models— that the appropriate point of reference for for any of the models to work, there must protein folding is a random search problem. be energetic factors that bias the folding Configurational entropy Taken literally, as it has been by many process. For example, only if a nucleus is people, this means that all conformations stable, relative to the random coil structures, of the polypeptide chain (except the native can it play a role in folding. In an insightful state) are equally probable, so that the native paper, Zwanzig et al.10 used a simplified state can be found only by an unbiased model to demonstrate that if there is a bias e energy random search. For such a search, the in the potential energy such that it decreases time to find the native state is given by the relatively smoothly toward the native state, Effectiv number of configurations of the polypeptide only a limited number of configurations chain (on the order of 1070 for a 100-residue would be visited in the folding reaction, protein) multiplied by the time required to and the configurational search (Levinthal) find one configuration (say, 10−11 seconds). problem would be solved. Figure 1 | A schematic folding funnel diagram. This leads to an enormously long folding The required energy bias is embodied The effective energy is plotted vertically and the time (say, 1059 seconds or about 1052 years). in the two-dimensional funnel diagram, configurational entropy horizontally. Adapted from Given that small proteins (100 residues or the most widely used of which is similar reference 2. NATURE CHEMICAL BIOLOGY | VOL 7 | JULY 2011 | www.nature.com/naturechemicalbiology 401 commentary a to microseconds and more recently to b 14 −55 nanoseconds . An important result of such studies is the finding that the folding −40 −60 reaction of many small proteins follows an exponential time course. This is interpreted −65 −60 to mean, as in chemical reactions1, that there are only two significantly populated −70 −80 states, the denatured state and the native Average energy −75 state, and that there is a barrier separating −100 the two that is larger than a few kilocalories. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 However, it has so far not been possible to determine experimentally the detailed c d folding trajectories even for a simple −85 protein—that is, a complete description of the conformations that are sampled in going −65 −90 from the multiconfiguration denatured state to a well-defined native state. Consequently, −95 −70 a range of theoretical methods continues to be used to supplement the experimental Free energy −100 data. Models that go beyond the −75 phenomenological approaches mentioned −105 above by focusing on the structural and 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Q Q thermodynamic parameters include lattice models1,13, coarse-grained models15 and Figure 2 | Folding of a lattice polymer. (a–d)The effective energy a( ,b) and free energy (c,d) calculated as atomistic simulations with implicit (see, a function of the fraction of native contacts for the 27-mer lattice polymer: a and c at a low temperature; for example, ref. 16) and explicit (see, and b and d at a high temperature. Adapted with permission from reference 22. for example, ref. 17) representations of the solvent. Also, unfolding simulations in explicit solvent, combined with such “guiding” is a misconception, as can the mechanism, such as those making use experimental data, have been used to be seen from their original paper, they of NMR1 and protein engineering7. Also, propose folding pathways for small proteins have not emphasized this point, and the it has become possible to rapidly trigger (see, for example, ref. 7). misconception concerning the funnel folding and unfolding so that measurements The first concrete demonstration of diagram has continued to proliferate. can be extended from milliseconds down how the Levinthal paradox can be resolved The essence of the misconception is that the decrease in configuration entropy, a b which gives the diagram its funnel-like −100 −100 shape, aids the polypeptide chain in finding 270 K 390 K ) the native state. In fact, exactly the opposite –1 −110 −110 © 2011 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2011 is true; that is, the decrease in the number of available configurations, as the native −120 −120 state is approached, actually tends to slow −130 −130 folding. The difficulty of finding these configurations is essentially the origin of −140 −140 the Levinthal paradox. To understand the Average energy (kcal mol −150 −150 folding process it must be realized that the 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 major determinant of the folding rate is the free-energy surface (often referred to as a c d “landscape”) of the polypeptide chain1,2,7,13, 4 4 rather than the energy shown in the funnel ) diagram. The free energy is the sum of the –1 2 2 potential energy, which decreases as the native state is approached and therefore 0 0 favors folding, and the unfavorable contribution of the decrease in the −2 −2 configuration entropy. The delicate balance Free energy (kcal mol −4 −4 between the two generally leads to a free- 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 energy barrier that results in the two-state Q Q folding behavior observed for most small proteins (see ref. 7 and references therein). Figure 3 | Folding of a designed α-helical peptide. (a–d) The effective energy a( ,b) and free energy (c,d) The developing understanding of protein calculated as a function of the fraction of native hydrogen bonds for a designed α-helical peptide: a and folding has been aided by experiments c at a low temperature (270 K); b and d at a high temperature (390 K).
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