A coarse-grained protein model in a water-like solvent (original) (raw)
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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
Simulations of the role of water in the protein-folding mechanism
Proceedings of the National Academy of Sciences, 2004
There are many unresolved questions regarding the role of water in protein folding. Does water merely induce hydrophobic forces, or does the discrete nature of water play a structural role in folding? Are the nonadditive aspects of water important in determining the folding mechanism? To help to address these questions, we have performed simulations of the folding of a model protein (BBA5) in explicit solvent. Starting 10,000 independent trajectories from a fully unfolded conformation, we have observed numerous folding events, making this work a comprehensive study of the kinetics of protein folding starting from the unfolded state and reaching the folded state and with an explicit solvation model and experimentally validated rates. Indeed, both the raw TIP3P folding rate (4.5 ؎ 2.5 s) and the diffusion-constant corrected rate (7.5 ؎ 4.2 s) are in strong agreement with the experimentally observed rate of 7.5 ؎ 3.5 s. To address the role of water in folding, the mechanism is compared with that predicted from implicit solvation simulations. An examination of solvent density near hydrophobic groups during folding suggests that in the case of BBA5, there are water-induced effects not captured by implicit solvation models, including signs of a ''concurrent mechanism'' of core collapse and desolvation.
Physica A: Statistical Mechanics and its Applications, 2018
We assume that the protein folding process follows two autonomous steps: the conformational search for the native, mainly ruled by the hydrophobic effect; and, the final adjustment stage, which eventually gives stability to the native. Our main tool of investigation is a 3D lattice model provided with a ten-letter alphabet, the stereochemical model. This model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. In order to characterize the folding characteristic time (τ) by two distinct sampling methods, first we present two sets of 10 3 MC simulations for a fast protein-like sequence. For these sets of folding times, τ and τ q were obtained with the application of the standard Metropolis algorithm (MA), and a modified algorithm (M q A). The results for τ q reveal two things: i) the hydrophobic chain-solvent interactions plus a set of inter-residues steric constraints are enough to emulate the first stage of the process: for each one of the 10 3 MC performed simulations, the native is always found without exception, ii) the ratio τ q /τ≅1/3 suggests that the effect of local thermal fluctuations, encompassed by the Tsallis weight, provides an innate efficiency to the chain escapes from energetic and steric traps. A physical insight is provided. Our second result was obtained through a set of 600 independent MC simulations performed with the M q A method applied to a set of 200 representative targets (native structures). The results show how structural patterns modulate τ q , which cover four orders of magnitude in the temporal scale. The third, and last result, was obtained from a special kind of simulation for those same 200 targets, we simulated their stability. We obtained a strong correlation (R=0.85) between the hydrophobic component of protein stability and the folding rate: the faster is the protein to find the native, larger is the hydrophobic component of its stability. This final result suggests that the hydrophobic interactions could not be a general stabilizing factor for proteins.
Journal of Molecular Liquids
Proteins work only if folded in their native state, but changes in temperature T and pressure P induce their unfolding. Therefore for each protein there is a stability region (SR) in the T-P thermodynamic plane outside which the biomolecule is denaturated. It is known that the extension and shape of the SR depend on i) the specific protein residue-residue interactions in the native state of the amino acids sequence and ii) the water properties at the hydration interface. Here we analyze by Monte Carlo simulations of different coarse-grained protein models in explicit water how changes in i) and ii) affect the SR. We show that the solvent properties ii) are essential to rationalize the SR shape at low T and high P and that our finding are robust with respect to parameter changes and with respect to different protein models. These results can help in developing new strategies for the design of novel synthetic biopolymers.
The water factor in the protein-folding problem
Brazilian Journal of Physics, 2004
Globular proteins are produced as a linear chain of aminoacids in water solution in the cell and, in the same aqueous environment, fold into their respective unique and functional native structures. In spite of this, many theoretical studies have tried to explain the folding process in vacuum, but in this paper we adopt an alternative point of view: the folding problem of heteropolymers is analyzed from the solvent perspective. The thermodynamics of the folding process is discussed for a non homogeneous system composed by the chain and solvent together; hydrophobic effects, modulated by the polar/nonpolar attributes of the residue sequence and by its corresponding steric specificities, are proposed as basic ingredients for the mechanisms of the folding process. These ideas are incorporated in both lattice and off-lattice models and treated by Monte Carlo simulations. Configurational and thermodynamical results are compared with properties of real proteins. The results suggest that the folding problem of small globular protein can be considered as a process in which the mechanism to reach the native structure and the requirements for the globule stability are uncoupled.
Hydrophobic models of protein folding and the thermodynamics of chain-boundary interactions
Brazilian Journal of Physics, 2003
We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past.
Advances in Colloid and Interface Science, 2010
Previously, we presented a review of our kinetic models for the nucleation mechanism of protein folding and for the protein thermal denaturation in a barrierless way. A protein was treated as a random heteropolymer consisting of hydrophobic, hydrophilic, and neutral beads. As a crucial idea of the model, an overall potential around the cluster of native residues wherein a residue performs a chaotic motion was considered as the combination of the average dihedral, effective pairwise, and confining potentials. The overall potential as a function of the distance from the cluster has a double well shape. This allowed one to develop kinetic models for the nucleation mechanism of protein folding (NMPF) and barrierless protein denaturation (BPD) by using the mean first passage time analysis. In the original models, however, hydrogen bonding effects were taken into account only indirectly which affected the accuracy of the models because hydrogen bonding does play a crucial role in the folding, stability, and denaturation of proteins. To improve the NMPF and BPD models and explicitly take into account the hydrogen bonding "water-water" and "water-protein residue", we have developed a probabilistic hydrogen bond (PHB) model for the effect of hydrogen bond networks of water molecules around two solute particles (immersed in water) on their interaction, and have then combined the PHB model with the NMPF and BPD models. In this paper, that can be regarded as sequel of our previous review, we analyze the modified NMPF and BPD models that explicitly take into account the effect of water-water hydrogen bonding on these processes. As expected, the application of the modified models to the folding/unfolding of two model proteins (one short, consisting of 124 residues and the other large, consisting of 2500 residues) demonstrate that the hydrogen bond networks play a very important role in the protein folding/unfolding phenomena.
Heteropolymer Collapse Theory for Protein Folding in the Pressure-Temperature Plane
Biophysical Journal, 2006
We revisit a heteropolymer collapse theory originally introduced to explore how the balance between hydrophobic interactions and configurational entropy determines the thermal stability of globular proteins at ambient pressure. We generalize the theory by introducing a basic statistical mechanical treatment for how pressure impacts the solvent-mediated interactions between hydrophobic amino-acid residues. In particular, we estimate the strength of the hydrophobic interactions using a molecular thermodynamic model for the interfacial free energy between liquid water and a curved hydrophobic solute. The model, which also reproduces many of the distinctive thermodynamic properties of aqueous solutions in bulk and interfacial environments, predicts that the water-solute interfacial free energy is significantly reduced by the application of high hydrostatic pressures. This allows water to penetrate into folded heteropolymers at high pressure and break apart their hydrophobic cores, a scenario suggested earlier by information theory calculations. As a result, folded heteropolymers are predicted to display the kind of closed region of stability in the pressure-temperature plane exhibited by native proteins. We compare predictions of the collapse theory with experimental data for several proteins.