A backbone-based theory of protein folding

Rose et al. 10.1073/pnas.0606843103.

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As discussed in the main text, globular proteins share many common characteristics. These include their ability to fold rapidly and reproducibly into their native state structures; the total number of topologically distinct folds is only of the order of a few thousand; these structures are modular forms made up of simple building blocks, helices of a specific pitch to radius ratio and almost planar sheets assembled from zigzag strands; these structures are flexible accounting for the ability of these proteins to carry out a wide variety of tasks; proteins are able to interact with each other and with other cell products in a very versatile yet robust manner; the same fold is used to often perform different biological functions; proteins are able to act as molecular targets of evolution; and proteins have a tendency to aggregate and form amyloid, which is implicated in human diseases such as Alzheimer's. How does one understand these remarkable similarities? Can one identify a phase of matter that proteins occupy, which is characterized not just by stability (as exemplified by their ability to fold reproducibly) and diversity (as exemplified by the many distinct folds) but also by sensitivity to the right types of perturbations (as needed for their functionality)? Such a phase ought not to depend on the specific amino acid sequence. It has been suggested that simple considerations of symmetry and geometry may shed some light on this question (1-4).

A protein is a chain molecule. Any chain molecule is anisotropic because each of its constituents has a special axis (direction) associated with it defined by the local tangent vector of the chain. A simple caricature of such a molecule is a chain of coins that in a continuum description resembles a tube of nonzero thickness (5) and may be thought of as a coarse-grained description of the protein backbone (3). For a protein, the tube size is comparable to the range of the self-attraction (due to hydrophobicity) that serves to promote compaction of the tube. This is because both length scales are effectively determined by the constituent amino acids, which interact with each other through short-ranged interactions screened by the water. Indeed, the folding of a protein requires that tube segments snap into place nearly simultaneously to avail of the attraction accounting for the cooperative nature of the folding transition (6).

One finds two kinds of structures associated with a compact, short tube at the edge of compaction: a helix with a pitch to radius ratio equal to that observed in protein structures (3) and zigzag strands assembled into an almost planar sheet (2). It recently has been demonstrated that the key ingredients of symmetry (the choice of a coin as the basic constituent of the chain molecule) and geometry (arising from the constraints imposed by sterics and hydrogen bond formation) lead to novel phase behavior of a homopolymer chain (1). The coarse-grained potential depends on very few crucial parameters, such as hydrogen bond energies and an energy reward for cooperativity of hydrogen bonds, an overall pair-wise attraction meant to mimic the hydrophobicity and an energy penalty for tight local turns. On just varying the last two parameters and keeping fixed the hydrogen bond energies, a rich phase diagram for a short homopolymer is obtained. Adjoining the swollen or denatured phase and, thus, sensitive to certain perturbations, one finds a marginally compact phase characterized by a variety of putative native state folds including a single helix, helix bundles, sheets, b-helix and assembled structures of helices and sheets with topologies typical of native states of globular proteins.

This result demonstrates that the free energy landscape of proteins is presculpted by considerations of geometry and symmetry: the role of the sequence of a protein is the selection from this predetermined menu of its native state. A consequence of the fixed menu of possible folds accounts for the fact that many sequences can adopt the same fold. There are only few key details of a given sequence that determine its preferred fold. The remaining freedom has been used by nature, through evolution, to select sequences allowing for efficient interactions among proteins and other cell products (2). There is a new class of "fold" that appears when one considers aggregation of several proteins, these are cross-linked b-structures akin to amyloid (4).

Even though hydrogen bonds and sterics are not related to each other, they are both promoters of helices and sheets. The marginally compact phase of short tubes has helices and sheets as its preferred structures. In order for nature to take advantage of this phase of matter, proteins, which obey physical laws, may have been selected to conform to the tube geometry. Hydrogen bonds serve to enforce the parallelism of nearby tube segments, a feature of both helices and sheets, while sterics emphasizes the nonzero thickness of the tube and serves to position it in the marginally compact phase. These considerations suggest that protein native state folds as well as amyloid aggregates are determined by the overarching features of geometry and symmetry and provide a fixed backdrop for evolution to act in shaping sequences and functionalities.

J.R.B. and A.M. are grateful to Trinh Hoang, Flavio Seno, and Antonio Trovato for insightful discussions.

1. Hoang TX, Trovato A, Seno F, Banavar JR, Maritan A (2004) Proc Natl Acad Sci USA 101:7960-7964.

2. Banavar JR, Hoang TX, Maritan A, Seno F, Trovato A (2004) Phys Rev E Stat Nonlin Soft Matter Phys 70:041905.

3. Maritan A, Micheletti C, Trovato A, Banavar JR (2000) Nature 406:287-290.

4. Hoang TX, Marsella L, Trovato A, Seno F, Banavar JR, Maritan A (2006) Proc Natl Acad Sci USA 103:6883-6888.

5. Marenduzzo D, Flammini A, Trovato A, Banavar JR, Maritan A (2005) J. Polymer Sci B 43:650-679.

6. Banavar JR, Flammini A, Marenduzzo D, Maritan A, Trovato, A (2003) ComPlexUs 1:4-13.

This Article

  1. Published online before print October 30, 2006, doi: 10.1073/pnas.0606843103 PNAS November 7, 2006 vol. 103 no. 45 16623-16633
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