Performance of protein-structure predictions with the physics-based UNRES force field in CASP11.

Participating as the Cornell-Gdansk group, we have used our physics-based coarse-grained UNited RESidue (UNRES) force field to predict protein structure in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11). Our methodology involved extensive multiplexed replica exchange simulations of the target proteins with a recently improved UNRES force field to provide better reproductions of the local structures of polypeptide chains. All simulations were started from fully extended polypeptide chains, and no external information was included in the simulation process except for weak restraints on secondary structure to enable us to finish each prediction within the allowed 3-week time window. Because of simplified UNRES representation of polypeptide chains, use of enhanced sampling methods, code optimization and parallelization and sufficient computational resources, we were able to treat, for the first time, all 55 human prediction targets with sizes from 44 to 595 amino acid residues, the average size being 251 residues. Complete structures of six single-domain proteins were predicted accurately, with the highest accuracy being attained for the T0769, for which the CαRMSD was 3.8 Å for 97 residues of the experimental structure. Correct structures were also predicted for 13 domains of multi-domain proteins with accuracy comparable to that of the best template-based modeling methods. With further improvements of the UNRES force field that are now underway, our physics-based coarse-grained approach to protein-structure prediction will eventually reach global prediction capacity and, consequently, reliability in simulating protein structure and dynamics that are important in biochemical processes. AVAILABILITY AND IMPLEMENTATION: Freely available on the web at http://www.unres.pl/ CONTACT: has5@cornell.edu.

Lessons from application of the UNRES force field to predictions of structures of CASP10 targets.

The performance of the physics-based protocol, whose main component is the United Residue (UNRES) physics-based coarse-grained force field, developed in our laboratory for the prediction of protein structure from amino acid sequence, is illustrated. Candidate models are selected, based on probabilities of the conformational families determined by multiplexed replica-exchange simulations, from the 10th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP10). For target T0663, classified as a new fold, which consists of two domains homologous to those of known proteins, UNRES predicted the correct symmetry of packing, in which the domains are rotated with respect to each other by 180° in the experimental structure. By contrast, models obtained by knowledge-based methods, in which each domain is modeled very accurately but not rotated, resulted in incorrect packing. Two UNRES models of this target were featured by the assessors. Correct domain packing was also predicted by UNRES for the homologous target T0644, which has a similar structure to that of T0663, except that the two domains are not rotated. Predictions for two other targets, T0668 and T0684_D2, are among the best ones by global distance test score. These results suggest that our physics-based method has substantial predictive power. In particular, it has the ability to predict domain-domain orientations, which is a significant advance in the state of the art.

A Maximum-Likelihood Approach to Force-Field Calibration.

A new approach to the calibration of the force fields is proposed, in which the force-field parameters are obtained by maximum-likelihood fitting of the calculated conformational ensembles to the experimental ensembles of training system(s). The maximum-likelihood function is composed of logarithms of the Boltzmann probabilities of the experimental conformations, calculated with the current energy function. Because the theoretical distribution is given in the form of the simulated conformations only, the contributions from all of the simulated conformations, with Gaussian weights in the distances from a given experimental conformation, are added to give the contribution to the target function from this conformation. In contrast to earlier methods for force-field calibration, the approach does not suffer from the arbitrariness of dividing the decoy set into native-like and non-native structures; however, if such a division is made instead of using Gaussian weights, application of the maximum-likelihood method results in the well-known energy-gap maximization. The computational procedure consists of cycles of decoy generation and maximum-likelihood-function optimization, which are iterated until convergence is reached. The method was tested with Gaussian distributions and then applied to the physics-based coarse-grained UNRES force field for proteins. The NMR structures of the tryptophan cage, a small α-helical protein, determined at three temperatures (T = 280, 305, and 313 K) by Halabis et al. ( J. Phys. Chem. B 2012 , 116 , 6898 - 6907 ), were used. Multiplexed replica-exchange molecular dynamics was used to generate the decoys. The iterative procedure exhibited steady convergence. Three variants of optimization were tried: optimization of the energy-term weights alone and use of the experimental ensemble of the folded protein only at T = 280 K (run 1); optimization of the energy-term weights and use of experimental ensembles at all three temperatures (run 2); and optimization of the energy-term weights and the coefficients of the torsional and multibody energy terms and use of experimental ensembles at all three temperatures (run 3). The force fields were subsequently tested with a set of 14 α-helical and two α + ß proteins. Optimization run 1 resulted in better agreement with the experimental ensemble at T = 280 K compared with optimization run 2 and in comparable performance on the test set but poorer agreement of the calculated folding temperature with the experimental folding temperature. Optimization run 3 resulted in the best fit of the calculated ensembles to the experimental ones for the tryptophan cage but in much poorer performance on the training set, suggesting that use of a small α-helical protein for extensive force-field calibration resulted in overfitting of the data for this protein at the expense of transferability. The optimized force field resulting from run 2 was found to fold 13 of the 14 tested α-helical proteins and one small α + ß protein with the correct topologies; the average structures of 10 of them were predicted with accuracies of about 5 Å C(α) root-mean-square deviation or better. Test simulations with an additional set of 12 α-helical proteins demonstrated that this force field performed better on α-helical proteins than the previous parametrizations of UNRES. The proposed approach is applicable to any problem of maximum-likelihood parameter estimation when the contributions to the maximum-likelihood function cannot be evaluated at the experimental points and the dimension of the configurational space is too high to construct histograms of the experimental distributions.

A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions.

A unified coarse-grained model of three major classes of biological molecules--proteins, nucleic acids, and polysaccharides--has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site-site interactions as mean-field dipole-dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo's cluster-cumulant series leads to the appearance of mean-field dipole-dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and ß-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

Ensemble fits of restrained peptides' conformational equilibria to NMR data. Dependence on force fields: AMBER/8 ff03 versus ECEPP/3.

Two variants of NMR-based conformational analyses of flexible peptides are compared using two examples meeting the formula Tyr-D-Daa-Phe-Daa-NH2 (Daa=diamino acid): 1 combining D-Dab² (α,γ-diaminobutyryl) with Lys4, and 2 -D-Dap² (α,ß-diaminopropionyl) with Orn4. The ω-amino groups of D-Daa² and Daa4 are coupled with C=O into the urea, restraining 1 and 2 with 16- and 14-membered rings and leading to potent and impotent µ/δ opioid peptides, respectively. To the current task, we took from an earlier work (Filip et al, J. Pept. Sci. 11 (2005) 347-352) the NMR NOE- and J-data in H2O/D2O; and the selection of the ensembles of 1 and 2, 822 and 788 conformational families, respectively, obtained by using the EDMC/ECEPP3 method. Here, we generated ensembles of 1 and 2 using AMBER molecular dynamics in explicit water to eventually selected 686 and 761 conformers for 1 and 2, respectively. We did numbers of fits for both types of the conformational ensembles of 1 and 2 to their NOE- and J-data using a common method i.e. maximum entropy approach (Groth et al, J. Biomol. NMR 15 (1999) 315-330). Both types of the well structurally diversified ensembles fit to quite different equilibria in regressions to common experimental NOE- and J-restraints using maximum entropy principle, which is a disappointing message. Intriguing is startlingly small standard deviation in J-couplings: σ(JNHαH) ≈ 0.01 Hz for LES-MD/AMBER ensemble, contrary to σ(JNHαH) = 0.8 - 1.1 Hz for the EDMC/ECEPP ensemble, over the wide range of entropy, i.e. relatively insensitive to it. A similar feature is not the case when comparing σ(NOE) in both methods. Hence, at minute entropy contributions, it follows that J does or does not transpose "overfitted" into the final σ(J) in the AMBER or ECEPP ensemble, respectively. Could this be an effect of softness of the AMBER flexible-valence force field compared to ECEPP rigid-geometry, and its effect on ensemble sampling? We do not know an answer.