Different Kinds of Protein Folding Identified with a Coarse-Grained Heteropolymer Model (original) (raw)
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The Journal of Chemical Physics, 2007
Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.
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.
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.
Folding simulations of a three-stranded antiparallel β-sheet peptide
Proceedings of the National Academy of Sciences, 2000
Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 μs provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel β-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2–3 β-hairpin. The folding mechanism presented here, formation of a β-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic t...
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.
The Journal of Physical Chemistry B, 2000
The folding of an R-helix and a-hairpin was studied by 862 molecular dynamics simulations with an implicit solvation model that allowed sampling of a total of 4 µs. The average effective energy is rather flat for conformations having less than about 50% of the folded state contacts formed, except for the R-helix at very high temperatures. For both peptides there is a smooth decrease of the effective energy close to the folded state. The free energy landscape shows that the helix-coil transition is not first order, while the-hairpin has one or two minima, depending on the temperature. At low temperature (T < 1.1T m) there is an increase in the folding rate with increasing temperature as expected from an activation energy limited process. At higher temperatures the rate decreases for both peptides which is consistent with an activation entropy dominated process. The unfolding rate, by contrast, shows an Arrhenius-like behavior; i.e., it increases monotonously with temperature. The-hairpin peptide folds about 30 times slower than the R-helix peptide at 300 K. Multiple folding pathways are present for the R-helix, whereas the-hairpin initiates folding mainly at the-turn.