Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge-based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer-range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Moller-Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree-Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre-calculated values in side chain placement simulations. Energies were calculated for over 35,000 different conformations of leucine, isoleucine and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests

Protein imperfections: separating intrinsic from extrinsic variation of torsion angles

In this paper, the variation of the values of dihedral angles in proteins is divided into two categories by analyzing distributions in a database of structures determined at a resolution of 1.8 A or better [Lovell et al. (2003), Proteins Struct. Funct. Genet. 50, 437-450]. The first analysis uses the torsion angle for the Calpha-Cbeta bond (chi1) of all Gln, Glu, Arg and Lys residues ('unbranched set'). Plateaued values at low B values imply a root-mean-square deviation (RMSD) of just 9 degrees for chi1 related to intrinsic structural differences between proteins. Extrapolation to high resolution gives a value of 11 degrees , while over the entire database the RMSD is 13.4 degrees . The assumption that the deviations arise from independent intrinsic and extrinsic sources gives approximately 10 degrees as the RMSD for chi1 of these unbranched side chains arising from all disorder and error over the entire set. It is also found that the decrease in chi1 deviation that is correlated with higher resolution structures is almost entirely a consequence of the higher percentage of low-B-value side chains in those structures and furthermore that the crystal temperature at which diffraction data are collected has a negligible effect on intrinsic deviation. Those intrinsic aspects of the distributions not related to statistical or other errors, data incompleteness or disorder correlate with energies of model compounds computed with high-level quantum mechanics. Mean side-chain torsion angles for specific rotamers correlate well with local energy minima of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme. Intrinsic RMSD values in examples with B < or = 20 A2 correlate inversely with calculated values for the relevant rotational energy barriers: from a low of 6.5 degrees for chi1 of some rotamers of Ile to a high of 14 degrees for some Met chi3 for fully tetrahedral angles and much higher for chi angles around bonds that are tetrahedral at one end and planar at the other (e.g. 30 degrees for chi2 of the gauche- rotamer of Phe). For the lower barrier Met chi3 rotations there are relatively more well validated cases near eclipsed values and calculated torques from the rest of the protein structure either confine or force the Cepsilon atom into the strained position. These results can be used to evaluate the variability and accuracy of chi angles in crystal structures and also to decide whether to restrain side-chain angles in refinement as a function of the resolution and atomic B values, depending on whether one aims for a realistic distribution of values or a spread that is statistically suitable to the probable data-set errors

Tryptophanyl-tRNA Synthetase Urzyme: A MODEL TO RECAPITULATE MOLECULAR EVOLUTION AND INVESTIGATE INTRAMOLECULAR COMPLEMENTATION

We substantiate our preliminary description of the class I tryptophanyl-tRNA synthetase minimal catalytic domain with details of its construction, structure, and steady-state kinetic parameters. Generating that active fragment involved deleting 65% of the contemporary enzyme, including the anticodon-binding domain and connecting peptide 1, CP1, a 74-residue internal segment from within the Rossmann fold. We used protein design (Rosetta), rather than phylogenetic sequence alignments, to identify mutations to compensate for the severe loss of modularity, thus restoring stability, as evidenced by renaturation described previously and by 70-ns molecular dynamics simulations. Sufficient solubility to enable biochemical studies was achieved by expressing the redesigned Urzyme as a maltose-binding protein fusion. Michaelis-Menten kinetic parameters from amino acid activation assays showed that, compared with the native full-length enzyme, TrpRS Urzyme binds ATP with similar affinity. This suggests that neither of the two deleted structural modules has a strong influence on ground-state ATP binding. However, tryptophan has 103 lower affinity, and the Urzyme has comparably reduced specificity relative to the related amino acid, tyrosine. Molecular dynamics simulations revealed how CP1 may contribute significantly to cognate amino acid specificity. As class Ia editing domains are nested within the CP1, this finding suggests that this module enhanced amino acid specificity continuously, throughout their evolution. We call this type of reconstructed protein catalyst an Urzyme (Ur prefix indicates original, primitive, or earliest). It establishes a model for recapitulating very early steps in molecular evolution in which fitness may have been enhanced by accumulating entire modules, rather than by discrete amino acid sequence changes

Computational Design of the Sequence and Structure of a Protein-Binding Peptide

The de novo design of protein-binding peptides is challenging, because it requires identifying both a sequence and a backbone conformation favorable for binding. We used a computational strategy that iterates between structure and sequence optimization to redesign the C-terminal portion of the RGS14 GoLoco motif peptide so that it adopts a new conformation when bound to Gαi1. An X-ray crystal structure of the redesigned complex closely matches the computational model, with a backbone RMSD of 1.1 Å

Computational Design of a PAK1 Binding Protein

We describe a computational protocol, called DDMI, for redesigning scaffold proteins to bind to a specified region on a target protein. The DDMI protocol is implemented within the Rosetta molecular modeling program and uses rigid-body docking, sequence design, and gradient-based minimization of backbone and side chain torsion angles to design low energy interfaces between the scaffold and target protein. Iterative rounds of sequence design and conformational optimization were needed to produce models that have calculated binding energies that are similar to binding energies calculated for native complexes. We also show that additional conformation sampling with molecular dynamics can be iterated with sequence design to further lower the computed energy of the designed complexes. To experimentally test the DDMI protocol we redesigned the human hyperplastic discs protein to bind to the kinase domain of p21-activated kinase 1 (PAK1). Six designs were experimentally characterized. Two of the designs aggregated and were not characterized further. Of the remaining four designs, three bound to the PAK1 with affinities tighter than 350 μM. The tightest binding design, named Spider Roll, bound with an affinity of 100 μM. NMR –based structure prediction of Spider Roll based on backbone and 13Cβ chemical shifts using the program CS-ROSETTA indicated that the architecture of human hyperplastic discs protein is preserved. Mutagenesis studies confirmed that Spider Roll binds the target patch on PAK1. Additionally, Spider Roll binds to full length PAK1 in its activated state, but does not bind PAK1 when it forms an auto-inhibited conformation that blocks the Spider Roll target site. Subsequent NMR characterization of the binding of Spider Roll to PAK1 revealed a comparably small binding `on-rate' constant (<< 105 M−1 s−1). The ability to rationally design the site of novel protein-protein interactions is an important step towards creating new proteins that are useful as therapeutics or molecular probes

Rational Design of Temperature-Sensitive Alleles Using Computational Structure Prediction

Temperature-sensitive (ts) mutations are mutations that exhibit a mutant phenotype at high or low temperatures and a wild-type phenotype at normal temperature. Temperature-sensitive mutants are valuable tools for geneticists, particularly in the study of essential genes. However, finding ts mutations typically relies on generating and screening many thousands of mutations, which is an expensive and labor-intensive process. Here we describe an in silico method that uses Rosetta and machine learning techniques to predict a highly accurate “top 5” list of ts mutations given the structure of a protein of interest. Rosetta is a protein structure prediction and design code, used here to model and score how proteins accommodate point mutations with side-chain and backbone movements. We show that integrating Rosetta relax-derived features with sequence-based features results in accurate temperature-sensitive mutation predictions

Boltzmann-type distribution of side-chain conformation in proteins

We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C–C and C–S torsion angles (χ3) correlates well with the Boltzmann factor of the torsion energy, exp(−βE) of the model compounds C2H5—C2H5 and C2H5—S—CH3. An exponential relation was again found between the relative occurrence of g+, g− and t conformations for Cα—Cβ bonds in long side chains and the energy differences of rotamers of α-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model’s rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the β-conformation, but less clear for backbone α-conformation. In all correlations, the value of the coefficient β corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium

Establishment of atropisomerism in 3-indolyl furanoids: a synthetic, experimental and theoretical perspective

Introduction of axial chirality in bioactive 3-indolyl furanoids has been achieved by systematic alteration of functional groups around the stereogenic axis, keeping in mind that atropisomerically pure analogues may possess different binding affinities and selectivities towards a target protein. The kinetics of racemization of axially chiral 3-indolyl furanoids have been studied through chiral HPLC analysis, electronic circular dichroism (ECD) spectroscopy, and computational modeling. The results identify the configurational parameters for optically pure 3-indolyl furanoids to exist as stable and isolable atropisomeric form