Automated NMR determination of protein backbone dihedral angles from cross-correlated spin relaxation

The simultaneous interpretation of a suite of dipole-dipole and dipole-CSA cross-correlation rates involving the backbone nuclei ¹³C, ¹H,¹³CO, ¹⁵N and ¹H^N can be used to resolve the ambiguities associated with each individual cross-correlation rate. The method is based on the transformation of experimental cross-correlation rates via calculated values based on standard peptide plane geometry and solid-state ¹³CO CSA parameters into a dihedral angle probability surface. Triple resonance NMR experiments with improved sensitivity have been devised for the quantification of relaxation interference between ¹H(i)-¹³C(i)/¹⁵N(i)-¹H^N(i) and ¹H(i–1)-¹³C(i–1)/¹⁵N(i)-¹H^N(i) dipole-dipole mechanisms in ¹⁵N,¹³C-labeled proteins. The approach is illustrated with an application to ¹³C,¹⁵N-labeled ubiquitin.     

Calculations of protein circular dichroism from first principles

Understanding the relationship between the amino acid sequence of a protein and its unique, compact 3D structure is one of the grand challenges in molecular biophysics. One particularly exciting approach is time-resolved electronic circular dichroism (CD) spectroscopy, which offers resolution on a nanosecond (or faster) time scale, although it does not provide the spatial resolution of techniques like X-ray crystallography or NMR. The thrust of our work is to underpin fast time scale spectroscopic studies of protein folding with a stronger theoretical foundation. Ultimately, we seek to use molecular dynamics simulations to study the influence of conformational dynamics and conformational transitions on the electronic CD spectra of proteins. We discuss how improved quantum chemical models of individual chromophores, including aromatic sidechains, can be incorporated into calculations of the electronic structure of proteins and their CD.     

Comparison of protein secondary structures based on backbone dihedral angles

In this article, we propose a relatively similar measure to compare protein secondary structures. We first transform a protein secondary structure into a special sequence representation (angle sequence) based on a partition of the backbone φ,ψ-space. Then, pairwise sequence distance is evaluated on the basis of a symbolic sequence complexity. To illustrate our approach, we construct the similarity tree of 24 proteins from PDB.     

Understanding hierarchical protein evolution from first principles.

We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time-scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time-scales: at short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a "profile" solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.     

TALI: local alignment of protein structures using backbone torsion angles

Torsion angle alignment (TALI) is a novel approach to local structural motif alignment, based on backbone torsion angles (phi, psi) rather than the more traditional atomic distance matrices. Representation of a protein structure in the form of a sequence of torsion angles enables easy integration of sequence and structural information, and adopts mature techniques in sequence alignment to improve performance and alignment quality. We show that TALI is able to match local structural motifs as well as identify global structural similarity. TALI is also compared to other structure alignment methods such as DALI, CE, and SSM, as well as sequence alignment based on PSI-BLAST; TALI is shown to be equally successful as, or more successful than, these other methods when applied to challenging structural alignments. The inference of the evolutionary tree of class II aminoacyl-tRNA synthetase shows the potential for TALI in estimating protein structural evolution and in identifying structural divergence among homologous structures. Availability: http://redcat.cse.sc.edu/index.php/Project:TALI/.     

Prediction of backbone dihedral angles and protein secondary structure using support vector machines

Background  

The prediction of the secondary structure of a protein is a critical step in the prediction of its tertiary structure and, potentially, its function. Moreover, the backbone dihedral angles, highly correlated with secondary structures, provide crucial information about the local three-dimensional structure.     

Relaxation of backbone bond geometry improves protein energy landscape modeling

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine‐grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse‐grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large‐scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non‐native structures. We also find that incorporating bonded geometry flexibility improves low resolution X‐ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.     

Real-value prediction of backbone torsion angles

The backbone structure of a protein is largely determined by the phi and psi torsion angles. Thus, knowing these angles, even if approximately, will be very useful for protein-structure prediction. However, in a previous work, a sequence-based, real-value prediction of psi angle could only achieve a mean absolute error of 54 degrees (83 degrees, 35 degrees, 33 degrees for coil, strand, and helix residues, respectively) between predicted and actual angles. Moreover, a real-value prediction of phi angle is not yet available. This article employs a neural-network based approach to improve psi prediction by taking advantage of angle periodicity and apply the new method to the prediction to phi angles. The 10-fold-cross-validated mean absolute error for the new method is 38 degrees (58 degrees, 33 degrees, 22 degrees for coil, strand, and helix, respectively) for psi and 25 degrees (35 degrees, 22 degrees, 16 degrees for coil, strand, and helix, respectively) for phi. The accuracy of real-value prediction is comparable to or more accurate than the predictions based on multistate classification of the phi-psi map. More accurate prediction of real-value angles will likely be useful for improving the accuracy of fold recognition and ab initio protein-structure prediction. The Real-SPINE 2.0 server is available on the website http://sparks.informatics.iupui.edu.     

STARS: statistics on inter-atomic distances and torsion angles in protein secondary structures

SUMMARY: A graphics package has been developed for performing statistics on interatomic distances and torsion angles in protein secondary structures (STARS) from a protein crystal structure database. It allows one to obtain both the graphical view and the text format of distributions of the distances and angles for atoms located in 10 types of protein secondary structures. STARS will facilitate assignment of ambiguous NOESY peaks, structure determination by nuclear magnetic resonance, structure validation and comparison of protein folds. AVAILABILITY: All data, documents and execute files are freely downloadable at http://stars.zhengyuhome.com. The software works appropriately on Windows system, without any compilation or installation. CONTACT: dbsydw@nus.edu.sg.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts

NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between ¹³C, ¹⁵N and ¹H chemical shifts and backbone torsion angles ϕ and ψ (Cornilescu et al. J Biomol NMR 13 289–302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted ϕ and ψ angles, equals ±13°. Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Comparing short protein substructures by a method based on backbone torsion angles

An efficient algorithm was characterized that determines the similarity in main chain conformation between short protein substructures. The algorithm computes Δt, the root mean square difference in ? and ψ torsion angles over a small number of amino acids (typically 3–5). Using this algorithm, large number of protein substrates comparisons were feasible. The parameter Δt was sensitive to variations in local protein conformation, and it correlates with Δr, the root mean square deviation in atomic coordinates. Values for Δt were obtained that define similarity thresholds, which determine whether two substructure are considered structurally similar. To set a lower bound on the similarity threshold, we estimated the component of Δt due to measurement noise fromcomparisons of independently refined coordinates of the same protein. A sample distribution of Δt from nonhomologous protein comparisons identified an upper bound on the similarity threshold, one that refrains from incorporating large numbers of nonmatching comparisons large numbers of nonmatching comparisons. Unlike methods based on Cα atoms alone, Δt was sensitive to rotations in the peptide plane, shown to occur in several proteins. Comparisons of homologus proteins by Δt showed that the active site torsion angles are highly conserved. The Δt method was applied to the α-chain of human hemoglobin, where it readily demonstrated the local differences in the structures of different ligation states.     

Psychological essentialism from first principles

Cognitive scientists have documented the existence of “essentialist” intuitions in humans: from a very early age, we assume that things have deep unobserved properties that make them what they are. I provide a sketch of an adaptationist explanation of psychological essentialism, arguing that these intuitions are the unsurprising output of adaptations for inductive inference. Variations on this insight have previously been used mostly as after-the-fact speculations, yet theories of adaptive function should ideally have a primary role in informing psychological research. Here I propose that viewing essentialist intuitions through an adaptationist lens has implications for some widespread assumptions about the phenomenon. Notably, researchers' focus on “higher-level” processes like categorization has led them to assume that essentialism is restricted to a few cognitive processes, but the ubiquity of inductive inference problems in cognition suggests otherwise. Additionally, because essentialist intuitions are the output of mechanisms solving related but distinct inference problems, it is unlikely that a single mechanistic theory can account for them all.     

The triplet code from first principles

Temporal order ("chronology") of appearance of amino acids and their respective codons on evolutionary scene is reconstructed. A consensus chronology of amino acids is built on the basis of 60 different criteria each offering certain temporal order. After several steps of filtering the chronology vectors are averaged resulting in the consensus order: G, A, D, V, P, S, E, (L, T), R, (I, Q, N), H, K, C, F, Y, M, W. It reveals two important features: the amino acids synthesized in imitation experiments of S. Miller appeared first, while the amino acids associated with codon capture events came last. The reconstruction of codon chronology is based on the above consensus temporal order of amino acids, supplemented by the stability and complementarity rules first suggested by M. Eigen and P. Schuster, and on the earlier established processivity rule. At no point in the reconstruction the consensus amino-acid chronology was in conflict with these three rules. The derived genealogy of all 64 codons suggested several important predictions that are confirmed. The reconstruction of the origin and evolutionary history of the triplet code becomes, thus, a powerful research tool for molecular evolution studies, especially in its early stages.     

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the α and β regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.     

Calculation of isotope effects from first principles

Various means of calculating the effect of changing the mass of a given atom upon a chemical process are reviewed. Of particular interest is the deuterium isotope effect comparing the normal protium nucleus with its heavier deuterium congener. The replacement of the bridging protium in a neutral hydrogen bond such as the water dimer by a deuterium strengthens the interaction by a small amount via effects upon the vibrational energy. In an ionic H-bond such as the protonated water dimer, on the other hand, the reverse trend is observed in that replacement of the bridging protium by dimer weakens the interaction. In addition to the stability of a given complex, the rate at which a proton transfers from one group to another is likewise affected by deuterium substitution, viz. kinetic isotope effects (KIEs). The KIE is enlarged as the temperature drops, particularly so if the calculation of KIE includes proton tunneling. The KIE is also sensitive to any angular distortions or stretches present in the H-bond of interest. KIEs can be computed either by the standard transition state theory which is derived via only two points on the potential energy surface, or by more complete formalisms which take account of larger swaths of the surface. While more time intensive, the latter can also be applied to provide insights important in interpretation of experimental data.     

Locally oscillatory motion of RNA helix derived from linear relationships of backbone torsion angles

A linear relationship in each of the torsion angle pairs, α-β, β-?, ?-ζ, and α-γ, has been found by applying a statistical method based on the concept of circular variates to backbone torsion angle data of helical in yeast tTNA^Phe. A series of helical dimer models generated with these relationships have been found to be stereochemically acceptable, and the models also indicate that the backbone unit in the RNA helix is geometrically capable of an oscillatory motion with the distance of about 3.4 Å between adjacent bases. The motion of the backbone unit is analogous to that of a helical spring. The adjacent bases, because of being attached to the backbone, oscillate in a manner similar to the oscillatory dimer model proposed by Davis and Tinoco [Davis, R. C. & Tinoco, I., Jr. (1968) Biopolymers 6 , 223–242]. Here, the oscillation of the backbone unit in the RNA helix is discussed in terms of two geometrical quantities: the torsion (τ) and curvature (κ) of the helix. On these lines, a stereochemical model of RNA strand separation is proposed.     

Pyridoxamine protects protein backbone from oxidative fragmentation

Oxidative damage to proteins is one of the major pathogenic mechanisms in many chronic diseases. Therefore, inhibition of this oxidative damage can be an important part of therapeutic strategies. Pyridoxamine (PM), a prospective drug for treatment of diabetic nephropathy, has been previously shown to inhibit several oxidative and glycoxidative pathways, thus protecting amino acid side chains of the proteins from oxidative damage. Here, we demonstrated that PM can also protect protein backbone from fragmentation induced via different oxidative mechanisms including autoxidation of glucose. This protection was due to hydroxyl radical scavenging by PM and may contribute to PM therapeutic effects shown in clinical trials.