A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition (original) (raw)
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Biopolymers, 1987
The nature of the equilibrium conformational transition from the denatured state to a four-member a-helical bundle was studied er.iploying a dynamic Monte Carlo algorithm in which the model protein chain was confined to a tetrahedral lattice. The model chain was allowed to hunt over all phase space, the target native state was not assumed a priori, and no sitespecific interactions were introduced, The exterior vs the interior part of the protein is distinguished by the pattern of hydrophilic and hydrophobic interactions encoded into the primary sequence. The importance of a statistical preference for forming bends, as a function of bend location in the primary sequence, and helical wheel type cooperative interactions were examined, and the necessary conditions for collapse of the chain to the unique native structure were investigated. It was found that an amphipathic pattern of hydrophobic/hydrophilic interactions along with a statistical preference of the central residues for bend formation are sufficient to obtain the four-helix bundle. The transition to the native state has an all-or-none character.
Folding & design, 1996
The role of intermediates in protein folding has been a matter of great controversy. Although it was widely believed that intermediates play a key role in minimizing the search problem associated with the Levinthal paradox, experimental evidence has been accumulating that small proteins fold fast without any detectable intermediates. We study the thermodynamics and kinetics of folding using a simple lattice model. Two folding sequences obtained by the design procedure exhibit different folding scenarios. The first sequence folds fast to the native state and does not exhibit any populated intermediates during folding. In contrast, the second sequence folds much slower, often being trapped in misfolded low-energy conformations. However, a small fraction of folding molecules for the second sequence fold on a fast track avoiding misfolded traps. In equilibrium at the same temperature the second sequence has a highly populated intermediate with structure similar to that of the kinetics i...
Parallel Computing, 2000
Studies are performed using an early proposed, but relatively little investigated, model that eciently emulates a hydrophobic funneling eect in protein folding. Its simple form, introduced as a further interaction term going as the square of the separation distance, is suitable for initial searches of conformational space by parallel computation and special processors which use polynomial representation of pair-wise interactions. Use of such a term implies calculation of the square of the Lagrange radius of gyration, but weighted by hydrophobicity rather than the masses of the constituent particles. The unusual choice is justi®ed by the observation that experimental protein structures have forms consistent with this Lagrange formalism for hydrophobic residues, and so compact model structures have appropriate density. However, since the long-range and square-power form strains open structures and leads to rapid generation of compact structures, such that for most of the simulation chain the movements result in intra-chain clashes, a rapid rejection algorithm is employed that prunes out similar but high energy structures. The studies also explore the choice of the simplest possible models which might be used to explore folding. Hence pancreatic trypsin inhibitor is modeled as a Ôstring-of-beadsÕ, where the beads represent residues of diering hydrophobicity. This model has only limited success, and because there are no identi®able common centers of interaction between the Ôstring-of-beadsÕ model and all-atom protein representations, it encounters the diculties: (a) of comparing such highly simpli®ed models with observed structures, and (b) of using such models as a starting point for conversion to all-atom models. The conclusion is that this solvent treatment is best applied to all-atom simulations from the outset. Nonetheless, low energy predictions obtained in this simple study can be considered as having promising features, and provide interesting insight into protein folding and the funneling contribution. Ó (B. Robson). 0167-8191/00/$ -see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -8 1 9 1 ( 0 0 ) 0 0 0 2 2 -3
Physical Review E, 2001
We show that a nonspecific hydrophobic energy function can produce proteinlike folding behavior of a three-dimensional protein model of 40 monomers in the cubic lattice when the native conformation is chosen judiciously. We confirm that monomer inside/outside segregation is a powerful criterion for the selection of appropriate structures, an idea that was recently proposed with basis on a general theoretical analysis and simulations of much simpler two-dimensional models.
Local Interactions Dominate Folding in a Simple Protein Model
Journal of Molecular Biology, 1996
between low-energy states of the model) is a necessary and sufficient condition to ensure folding of a sequence to its lowest-energy 2 Center for Advanced conformation. Here, we show that this conclusion strongly depends on the Research in Biotechnology particular temperature scheme selected to govern the simulations. On the University of Maryland other hand, we show that there is a dominant factor determining if a Biotechnology Institute, 9600 sequence is foldable. That is, the strength of possible interactions between Gudelsky Drive, Rockville residues close in the sequence. We show that sequences with many MD 20850, USA possible strong local interactions (either favorable or, more surprisingly, a mixture of strong favorable and unfavorable ones) are easy to fold. Progressively increasing the strength of such local interactions makes sequences easier and easier to fold. These results support the idea that initial formation of local substructures is important to the foldability of real proteins.
The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein
Journal of Molecular Biology, 2009
Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Gō model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by non-native contacts, typically imagined as a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences, and a concomitantly diverse set of folding pathways. Enabled by a novel means of fingerprinting folding trajectories, our study reveals a profound insensitivity of the order in which native contacts accumulate to the omission of non-native interactions. Contrary to conventional thinking, this robustness does not arise from topological restrictions and does not depend on folding rate. We find instead that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies. Our results challenge conventional thinking on the relationship between sequence design and free energy landscapes for protein folding, and help justify the widespread use of Gō-like models to scrutinize detailed folding mechanisms of real proteins.
Biophysical Journal, 2011
Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.
Principles of protein folding - A perspective from simple exact models
Protein Science, 2008
General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics —fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating “foldable” chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.