Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism Alan R. Fersht* Cambridge University Chemical Laboratory and Cambridge Centre for Protein Engineering, Lensfield Road, Cambridge CB2 1EW, United Kingdom Contributed by Alan Fersht, December 9, 1999 I attempt to reconcile apparently conflicting factors and mecha- an important factor in the rate of folding. The questions are why nisms that have been proposed to determine the rate constant for and what does it tell us? two-state folding of small proteins, on the basis of general features The structure of the rate-determining transition state in of the structures of transition states. ⌽-Value analysis implies a protein folding can be derived by ⌽-value analysis (2, 3). This transition state for folding that resembles an expanded and dis- procedure uses protein engineering to make suitable mutants of torted native structure, which is built around an extended nucleus. the protein, and changes in the free energy of activation (⌬⌬G‡) The nucleus is composed predominantly of elements of partly or and equilibrium (⌬⌬G) on mutation are measured. ⌽ is defined well-formed native secondary structure that are stabilized by local by ⌬⌬G‡͞⌬⌬G. A value of ⌽ for folding of 0 means that the and long-range tertiary interactions. These long-range interactions interaction measured is as poorly formed in the transition state give rise to connecting loops, frequently containing the native as it is in the denatured state. A value of one means that it is as loops that are poorly structured. I derive an equation that relates well formed in the transition state as in the native structure. differences in the contact order of a protein to changes in the Exactly the same approach had been used previously (4, 5) to length of linking loops, which, in turn, is directly related to the understand changes in enzyme-substrate reactions during bind- unfavorable free energy of the loops in the transition state. Kinetic ing and catalysis, and the analogous equation was used to define data on loop extension mutants of CI2 and ␣-spectrin SH3 domain the equivalent of ⌽ (5). fit the equation qualitatively. The rate of folding depends primarily Very recently, ⌽-value analysis has been applied to three on the interactions that directly stabilize the nucleus, especially proteins to support the contact order theory and the role of those in native-like secondary structure and those resulting from topology (6–8). But, in apparent contradiction, it has been found the entropy loss from the connecting loops, which vary with that three members of a family of the same topology fold with contact order. This partitioning of energy accounts for the success rate constants that correlate with stability and not contact order of some algorithms that predict folding rates, because they use (9). There is strong evidence that many proteins fold by a these principles either explicitly or implicitly. The extended nucleus nucleation mechanism, whereas arguments have been made in model thus unifies the observations of rate depending on both favor of hierarchical (framework) mechanisms in which pre- stability and topology. formed elements of secondary structure associate (10, 11). I wish now to present arguments that there are no real conflicts among ͉ ͉ ͉ ͉ nucleation-condensation diffusion-collision SH3 CI2 loops these proposals, and that each of these mechanisms is accom- modated in existing schemes that invoke general features of BIOCHEMISTRY o understand pathways of protein folding, experimentalists transition states for folding determined by ⌽-value analysis. Tand theoreticians have, over the past decade, focused their efforts on analyzing small proteins. Many of these fold very Nature of Transition State for Protein Folding. ⌽-Value analysis of rapidly with simple two-state kinetics. The structures of the CI2 (12, 13) shows that: rate-determining transition states have been analyzed in increas- (i) The protein folds around an extended nucleus that is ing numbers at atomic resolution by protein engineering and composed of a contiguous region of structure (for CI2, an ⌽-values and by various types of computer simulation. A recent ␣-helix) and long-range native interactions with groups distant in development has been to correlate rate constants of folding (k) sequence. of the two-state proteins with their topology by using the gross (ii) The transition state for folding is a distorted form of the parameter of the contact order (CO) defined by: native structure, which appears to be more distorted and weak- ened the further away from the nucleus. There is a gradation of N 1 ⌽-values, the ones in the nucleus tending to be 0.5–0.7 and the CO ϭ ͸ ⌬Z , [1] LN i, j more distal ones, from 0.1 to 0.3. (iii) It was reasoned that the mechanism did not involve the ⌬ where N is the total number of contacts in the protein, Zi.j is association of preformed elements of secondary structure, but the number of residues separating contacts i and j, and L is the that the secondary and tertiary interactions are formed in number of residues in the protein. In a protein with low contact parallel because the ⌽-values in the nucleus were significantly order, residues interact, on average, with others that are close in less than 1. A mechanism was proposed, nucleation-condensa- sequence. A high contact order implies that there is a large tion (or nucleation-collapse), that involves the simultaneous number of long-range interactions (1). That is, residues interact frequently with partners that are far apart in sequence. There is *To whom reprint requests should be addressed. E-mail: [email protected]. a statistically significant correlation between lnk and CO, The publication costs of this article were defrayed in part by page charge payment. This whereby the rate constant of folding decreases with increasing article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. contact order (Fig. 1). This correlation points to topology being §1734 solely to indicate this fact. PNAS ͉ February 15, 2000 ͉ vol. 97 ͉ no. 4 ͉ 1525–1529 Downloaded by guest on October 2, 2021 Fig. 1. Plot of logk vs. 100 ϫ CO for two-state folding proteins listed in Table 18.1 of ref. 3 and unpublished data from this laboratory. Fig. 2. Cartoon of the extended (specific) nucleus mechanism of the nucle- ation-condensation mechanism. This is for the extreme case of the connecting collapse or condensation of the tertiary structure around the loops being unstructured. The filled circles represent native-like elements of extended nucleus as it is formed. secondary structure that interact mainly by native tertiary interactions. The shaded part of the loop illustrates an insertion of length l. (iv) Mutations, especially in the folding nucleus, affect the folding rate, and there is a relation between folding rate and ⅐ stability [a Brønsted plot (14)]. by l NA/B, because each of the NA/B interactions is displaced by The rate-determining transition state in the multistep pathway l residues in sequence. Thus: for the folding of barnase is more polar (15). Many of the ⌽ N -values are very close to 0 or 1, and so the rate-determining step 1 is the docking of preformed structural domains. Mutations in the ϭ ͩ͸ ⌬ ϩ ⅐ ͪ CO ͑ ϩ ͒ Zi, j l NA/B . [2] regions of barnase that are unstructured in the transition state L l N have folding rates that are insensitive to mutation. The transition Thus, contact order increases with increasing loop size. state structures of many small proteins may be classified into The loss of configurational entropy of closing an unstructured ‘‘CI2’’ (a gradation of ⌽-values) or ‘‘barnase’’ (polarized, with a ϩ ⌽ loop of nl l residues relative to one of nl residues is calculated significant number of -values close to 0 or 1) and are listed in from standard polymer theory to be: ref. 3, Table 19.2. Nucleation-condensation appears to be a widespread mechanism. Indeed, lattice simulations indepen- 3 l ⌬⌬S ϭ Ϫ R lnͩ1 ϩ ͪ. [3] dently showed that a specific nucleus is an optimal mechanism 2 n for folding model proteins (16). l Eqs. 2 and 3 show that changes in contact order and configu- Implications of a Native-Like Transition State. The transition state rational entropy are directly related. The relationship becomes ϽϽ resembles native-like structural elements with the connecting simpler when l nl. Then loops tending to be poorly structured (some structured loops are ⅐ formed in the rate-determining transition state for barnase). A l NA/B ⌬CO Ϸ [4] consequence of the extended nucleus is that the overall topology LN of the transition state must resemble that of the native structure. The correlation between folding rate constant, which depends on and transition state structure, and contact order of the native state 3 l for a large number of proteins (Fig. 1) implies that the topology ⌬⌬S Ϸ Ϫ R . [5] of the transition state resembles the topology of the native chain 2 nl in general. To a first approximation: Relationship of Contact Order to Loop Length and Configurational 3RLN Entropy. It has been speculated that the dependence of rate ⌬⌬S Ϸ Ϫ ⌬CO [6] constant on contact order may be a consequence of the relative 2NA/Bnl importance of short-range and long-range interactions, or it or might somehow relate to the length of the connecting loops in ⌬⌬ proteins (17). To resolve this, I derive a simple equation relating 2NA/Bnl S ⌬CO Ϸ Ϫ ϫ . [7] contact order and loop length for a specific case and then apply 3LN R this to kinetic data.