Pathway diversity and concertedness in protein folding: an ab-initio approach

Minimalist representations and the importance of nearest neighbor effects in protein folding simulations

In order to investigate the level of representation required to simulate folding and predict structure, we test the ability of a variety of reduced representations to identify native states in decoy libraries and to recover the native structure given the advanced knowledge of the very broad native Ramachandran basin assignments. Simplifications include the removal of the entire side-chain or the retention of only the Cbeta atoms. Scoring functions are derived from an all-atom statistical potential that distinguishes between atoms and different residue types. Structures are obtained by minimizing the scoring function with a computationally rapid simulated annealing algorithm. Results are compared for simulations in which backbone conformations are sampled from a Protein Data Bank-based backbone rotamer library generated by either ignoring or including a dependence on the identity and conformation of the neighboring residues. Only when the Cbeta atoms and nearest neighbor effects are included do the lowest energy structures generally fall within 4 A of the native backbone root-mean square deviation (RMSD), despite the initial configuration being highly expanded with an average RMSD > or = 10 A. The side-chains are reinserted into the Cbeta models with minimal steric clash. Therefore, the detailed, all-atom information lost in descending to a Cbeta-level representation is recaptured to a large measure using backbone dihedral angle sampling that includes nearest neighbor effects and an appropriate scoring function.

Prediction of protein structure by simulating coarse-grained folding pathways: a preliminary report

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local phi-psi energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 A backbone rmsd for fragments of about 60-70 residues of alpha-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of beta-sheet structures are briefly described.

The folding pathway of ubiquitin from all-atom molecular dynamics simulations

The folding (unfolding) pathway of ubiquitin is probed using all-atom molecular dynamics simulations. We dissect the folding pathway using two techniques: first, we probe the folding pathway of ubiquitin by calculating the evolution of structural properties over time and second, we identify the rate determining transition state for folding. The structural properties that we look at are hydrophobic solvent accessible surface area (SASA) and Calpha-root-mean-square deviation (rmsd). These properties on their own tell us relatively little about the folding pathway of ubiquitin; however, when plotted against each other, they become powerful tools for dissecting ubiquitin's folding mechanism. Plots of Calpha-rmsd against SASA serve as a phase space trajectories for the folding of ubiquitin. In this study, these plots show that ubiquitin folds to the native state via the population of an intermediate state. This is shown by an initial hydrophobic collapse phase followed by a second phase of secondary structure arrangement. Analysis of the structure of the intermediate state shows that it is a collapsed species with very little secondary structure. In reconciling these observations with recent experimental data, the transition that we observe in our simulations from the unfolded state (U) to the intermediate state (I) most likely occurs in the dead-time of the stopped flow instrument. The folding pathway of ubiquitin is probed further by identification of the rate-determining transition state for folding. The method used for this is essential dynamics, which utilizes a principal component analysis (PCA) on the atomic fluctuations throughout the simulation. The five transition state structures identified in silico are in good agreement with the experimentally determined transition state. The calculation of phi-values from the structures generated in the simulations is also carried out and it shows a good correlation with the experimentally measured values. An initial analysis of the denatured state shows that it is compact with fluctuating regions of nonnative secondary structure. It is found that the compactness in the denatured state is due to the burial of some hydrophobic residues. We conclude by looking at a correlation between folding kinetics and residual structure in the denatured state. A hierarchical folding mechanism is then proposed for ubiquitin.

Investigations into sequence and conformational dependence of backbone entropy, inter-basin dynamics and the Flory isolated-pair hypothesis for peptides

The populations and transitions between Ramachandran basins are studied for combinations of the standard 20 amino acids in monomers, dimers and trimers using an implicit solvent Langevin dynamics algorithm and employing seven commonly used force-fields. Both the basin populations and inter-conversion rates are influenced by the nearest neighbor's conformation and identity, contrary to the Flory isolated-pair hypothesis. This conclusion is robust to the choice of force-field, even though the use of different force-fields produces large variations in the populations and inter-conversion rates between the dominant helical, extended beta, and polyproline II basins. The computed variation of conformational and dynamical properties with different force-fields exceeds the difference between explicit and implicit solvent calculations using the same force-field. For all force-fields, the inter-basin transitions exhibit a directional dependence, with most transitions going through extended beta conformation, even when it is the least populated basin. The implications of these results are discussed in the context of estimates for the backbone entropy of single residues, and for the ability of all-atom simulations to reproduce experimental protein folding data.

Dynamics of hydrogen bond desolvation in protein folding

As proteins fold, a progressive structuring, immobilization and eventual exclusion of water surrounding backbone hydrogen bonds takes place. This process turns hydrogen bonds into major determinants of the folding pathway and compensates for the penalty of desolvation of the backbone polar groups. Taken as an average over all hydrogen bonds in a native fold, this extent of protection is found to be nearly ubiquitous. It is dynamically crucial, determining a constraint in the long-time limit behavior of coarse-grained ab initio simulations. Furthermore, an examination of one of the longest available (1micros) all-atom simulations with explicit solvent reveals that this average extent of protection is a constant of motion for the folding trajectory. We propose how such a stabilization is best achieved by clustering five hydrophobes around the backbone hydrogen bonds, an arrangement that yields the optimal stabilization. Our results support and clarify the view that hydrophobic surface burial should be commensurate with hydrogen-bond formation and enable us to define a basic desolvation motif inherent to structure and folding dynamics.