Coarse-Grained Model of Coil-to-Helix Kinetics Demonstrates the Importance of Multiple Nucleation Sites in Helix Folding

Coarse-grained models of the proteins backbone conformational dynamics

Coarse-grained models are more and more frequently used in the studies of the proteins structural and dynamic properties, since the reduced number of degrees of freedom allows to enhance the conformational space exploration. This chapter attempts to provide an overview of the various coarse-grained models that were applied to study the functional conformational changes of the polypeptides main chain around their native state. It will more specifically discuss the methods used to represent the protein backbone flexibility and to account for the physico-chemical interactions that stabilize the secondary structure elements.

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56 Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.

Conformational dynamics of human IAPP monomers

We study the conformational dynamics of the human Islet Amyloid Polypeptide (hIAPP) molecule - a 37 residue-long peptide associated to type 2 diabetes - using molecular dynamics (MD) simulations. We identify partially structured conformational states of the hIAPP monomer, categorized by both end-to-end distance and secondary structure, as suggested by previous experimental and computational studies. The MD trajectories of hIAPP are analyzed using data-driven methods, in particular principal component analysis, in order to identify preferred conformational states of the amylin monomer and to discuss their relative stability as compared to corresponding states in the amylin dimer. These potential hIAPP conformational states could be further tested and described experimentally, or in conjunction with modern computational analysis tools such as Markov state-based methods for extracting kinetics and thermodynamics from atomistic MD trajectories.

Are Peptides Good Two-State Folders?

The folding kinetics of proteins is frequently single-exponential, as basins of folded and unfolded conformations are well separated by a high barrier. However, for relatively short peptides, a two-state character of folding is rather the exception than the rule. In this work, we use a Zwanzig-type model of protein conformational dynamics to study the dependence of folding kinetics on the protein chain length, M. The analysis is focused on the gap in the eigenvalue spectrum of the rate matrix that describes the protein's conformational dynamics. When there is a large gap between the two smallest in magnitude nonzero eigenvalues, the corresponding relaxation times have qualitatively different physical interpretations. The longest of these two times characterizes the interbasin equilibration (i.e., folding), whereas the second time characterizes the intrabasin relaxation. We derive approximate analytical solutions for the two eigenvalues that show how they depend on M. From these solutions, we infer that there is a large gap between the two, and thus, the kinetics is essentially single-exponential when M is large enough such that 2(M+1) is much larger than M(2).

Roles of non-native hydrogen-bonding interaction in helix-coil transition of a single polypeptide as revealed by comparison between Gō-like and non-Gō models

To explore the role of non-native interactions in the helix-coil transition, a detailed comparison between a Gō-like model and a non-Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō-like model, and the non-native ones with sequence interval more than 4 is also included into the non-Gō model. Some significant differences between the results from those two models have been found. The non-native hydrogen bonds were found most populated at temperature around the helix-coil transition. The rearrangement of non-native hydrogen bonds into native ones in the formation of alpha-helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non-Gō model for a non-short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non-native hydrogen bonds have complicated the temperature-dependence of Zimm-Bragg nucleation constant. The increase of relative probability of non-native hydrogen bonding for long polypeptide chains leads to non-monotonous chain length effect on the transition temperature.

Coarse-grained protein model with residue orientation energies derived from atomic force fields

Coarse-grained models for protein simulations can potentially access longer time scales in larger protein systems than atomic-level models. Here, a coarse-grained residue pair potential, with distance and orientation dependency, is derived from equilibrium ensembles of residue pairs generated by molecular dynamics (MD). In particular, the Boltzmann inversion method is used to determine the energies. The residue pair potential is combined with local dihedral angle potentials for the backbone and side chains and used in the folding simulations of six small proteins, (28-67 residues) containing a variety of secondary structures. For the proteins tested, folding simulations by Monte Carlo methods generate structures similar to the native ones. However, these native-like structures were among the lowest in energy for alpha helical proteins but not for proteins containing extended beta structures. It is also found that a careful balance between local and nonlocal interactions is essential. Possibilities for improving coarse-grained models derived from atomic force fields are discussed.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

The effect of charge-charge interactions on the kinetics of alpha-helix formation

The formation of the monomeric alpha-helix represents one of the simplest scenarios in protein folding; however, our current understanding of the folding dynamics of the alpha-helix motif is mainly based on studies of alanine-rich model peptides. To examine the effect of peptide sequence on the folding kinetics of alpha-helices, we studied the relaxation kinetics of a 21-residue helical peptide, Conantokin-T (Con-T), using time-resolved infrared spectroscopy in conjunction with a laser-induced temperature jump technique. Con-T is a neuroactive peptide containing a large number of charged residues that is found in the venom of the piscivorous cone snail Conus tulipa . The temperature-jump relaxation kinetics of Con-T is distinctly slower than that of previously studied alanine-based peptides, suggesting that the folding time of alpha-helices is sequence-dependent. Furthermore, it appears that the slower folding of Con-T can be attributed to the fact that its helical conformation is stabilized by charge-charge interactions or salt bridges. Although this finding contradicts an earlier molecular dynamics simulation, it also has implications for existing models of protein folding.

A Coarse-Grained Protein−Protein Potential Derived from an All-Atom Force Field

In order to study protein-protein nonbonded interactions, we present the development of a new reduced protein model that represents each amino acid residue with one to three coarse grains, whose physical properties are derived in a consistent bottom-up procedure from the higher-resolution all-atom AMBER force field. The resulting potential energy function is pairwise additive and includes distinct van-der-Waals and Coulombic terms. The van-der-Waals effective interactions are deduced from preliminary molecular dynamics simulations of all possible amino acid homodimers. They are best represented by a soft 1/r6 repulsion and a Gaussian attraction, with parameters obeying Lorentz-Berthelot mixing rules. For the Coulombic interaction, coarse grain charges are optimized for each separate protein in order to best represent the all-atom electrostatic potential outside the protein core. This approach leaves the possibility of using any implicit solvent model to describe solvation effects and electrostatic screening. The coarse-grained force field is tested carefully for a small homodimeric complex, the magainin. It is shown to reproduce satisfactorily the specificity of the all-atom underlying potential, in particular within a PB/SA solvation model. The coarse-grained potential is applied to the redocking prediction of three different protein-protein complexes: the magainin dimer, the barnase-barstar, and the trypsin-BPTI complexes. It is shown to provide per se an efficient and discriminating scoring energy function for the protein-protein docking problem that remains pertinent at both the global and refinement stage.

Multiscale modeling of biomolecular systems: in serial and in parallel

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.

UV Raman spatially resolved melting dynamics of isotopically labeled polyalanyl peptide: slow alpha-helix melting follows 3(10)-helices and pi-bulges premelting

We used UV resonance Raman (UVRR) to examine the spatial dependence of the T-jump secondary structure relaxation of an isotopically labeled 21-residue mainly Ala peptide, AdP. The AdP penultimate Ala residues were perdeuterated, leaving the central residues hydrogenated, to allow separate monitoring of melting of the middle versus the end peptide bonds. For 5 to 30 degrees C T-jumps, the central peptide bonds show a approximately 2-fold slower relaxation time (189 +/- 31 ns) than do the exterior peptide bonds (97 +/- 15 ns). In contrast, for a 20 to 40 degrees C T-jump, the central peptide bond relaxation appears to be faster (56 +/- 6 ns) than that of the penultimate peptide bonds (131 +/- 46 ns). We show that, if the data are modeled as a two-state transition, we find that only exterior peptide bonds show anti-Arrhenius folding behavior; the middle peptide bonds show both normal Arrhenius-like folding and unfolding. This anti-Arrhenius behavior results from the involvement of pi-bulges/helices and 3(10)-helix states in the melting. The unusual temperature dependence of the (un)folding rates of the interior and exterior peptide bonds is due to the different relative (un)folding rates of 3(10)-helices, alpha-helices, and pi-bulges/helices. Pure alpha-helix unfolding rates are approximately 12-fold slower (approximately 1 micros) than that of pi-bulges and 3(10)-helices. In addition, we also find that the alpha-helix is most stable at the AdP N-terminus where eight consecutive Ala occur, whereas the three hydrophilic Arg located in the middle and at the C-terminus destabilize the alpha-helix in these regions and induce defects such as pi-bulges and 3(10)-helices.