The Flory isolated-pair hypothesis is not valid for polypeptide chains: Implications for protein folding

Abstract

Using an all-atom representation, we exhaustively enumerate all sterically allowed conformations for short polyalanyl chains. Only intrachain interactions are considered, including one adjustable parameter, a favorable backbone energy (e.g., a peptide hydrogen bond). The counting is used to reevaluate Flory's isolated-pair hypothesis, the simplifying assumption that each , pair is sterically independent. This hypothesis is a conceptual linchpin in helix-coil theories and protein folding. Contrary to the hypothesis, we find that systematic local steric effects can extend beyond nearest-chain neighbors and can restrict the size of accessible conformational space significantly. As a result, the entropy price that must be paid to adopt any specific conformation is far less than previously thought. helix-coil theory ͉ Levinthal paradoxWe will have to decide whether the assembly, when left to itself in the way already specified, tends to settle down mainly into one or other of a small preferred group of stationary states, whose properties are or control the equilibrium properties of the assembly; or whether it shows no such discrimination, but wanders apparently or effectively at random over the whole range of stationary states made accessible by the general conditions of the problem (1).T he central thermodynamic question in protein folding is: How can a polypeptide chain overcome conformational entropy and fold to its native state (2)? Typically, the unfolded state is depicted as a rugged energy landscape with an exorbitant number of local minima. Under suitable conditions, the protein negotiates this landscape spontaneously and finds its way to the global minimumthe native state.This view of the unfolded state corresponds to the latter case referred to by Fowler and Guggenheim (1), in which the assembly wanders apparently at random over the whole range of conceivable stationary states. The view was placed on a rigorous foundation by the work of Flory (3), who showed that each , pair in the peptide backbone is sterically insensitive to the values of its neighbors. Flory's simplifying conclusion is known as the isolated-pair hypothesis.The isolated-pair hypothesis has influenced the development of helix-coil (4-6) and protein-folding theories (7). It follows from the hypothesis that local structural transitions are ruled out as a possible origin of cooperativity in protein folding (8); the entropic price is simply too high for short polypeptide backbones to preferentially populate a small set of highly similar conformations.In contrast to these ideas, both experiments (9) and calculations (10) suggest the prevalence of biases in polypeptide chains, which motivated us to reevaluate the isolated-pair hypothesis. We find that the former case referred to by Fowler and Guggenheim-in which a small preferred group of states account for the equilibrium properties of the assembly-better describes the situation for polypeptide chains in both folded and unfolded forms. The validity of the isolated-pair hypothesis has also been ...

UV Resonance Raman Investigation of a 310-Helical Peptide Reveals a Rough Energy Landscape

“…We estimate that at 1°C on average six of the 12 peptide bonds are in folded conformations (predominantly 3 10 -and π-helix), while the other six are in unfolded ( -turn/PPII) conformations. The folded and unfolded populations do not change significantly as the temperature is increased from 1 to 60°C, suggesting a unique energy landscape where the folded and unfolded conformations are essentially degenerate in energy and exhibit identical temperature dependences.An understanding of the mechanisms of protein folding will enable the de novo design of proteins with profound commercial and medical applications (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). Over the past 50 years, significant effort to elucidate protein folding and unfolding mechanisms has been expended.…”

The Levinthal paradox of the interactome

“…8 The Levinthal estimate is based on Flory's simplifying assumption 9 that each /,w-pair is sterically independent of the others. That assumption has been challenged, 10,11 but the search problem persists.…”

Protein folding: Then and now

“…Several theoretical and computational studies [199][200][201][202] have addressed the role of specific interactions in conformational biasing toward the native state in the denatured states. Using a simple force field with only steric and hydrogen bond interactions, Pappu et al [200] demonstrated that denatured protein states have a strong preference for the native structure.…”

“…Using a simple force field with only steric and hydrogen bond interactions, Pappu et al [200] demonstrated that denatured protein states have a strong preference for the native structure. It was suggested [199][200][201][202] that the conformational bias of native structures in the denatured state is a possible explanation of the Levinthal's paradox [3].…”