Distance-constraint approach to protein folding. I. Statistical analysis of protein conformations in terms of distances between residues

Kinematic Reconstruction of Cyclic Peptides and Protein Backbones from Partial Data

We present an algorithm, QBKR (Quaternary Backbone Kinematic Reconstruction), a fast analytical method for an all-atom backbone reconstruction of proteins and linear or cyclic peptide chains from C_α coordinate traces. Unlike previous analytical methods for deriving all-atom representations from coarse-grained models that rely on canonical geometry with planar peptides in the trans conformation, our de novo kinematic model incorporates noncanonical, cis-trans, geometry naturally. Perturbations to this geometry can be effected with ease in our formulation, for example, to account for a continuous change from cis to trans geometry. A simple optimization of a spring-based objective function is employed for C_α-C_α distance variations that extend beyond the cis-trans limit. The kinematic construction produces a linked chain of peptide units, C_α-C-N-C_α, hinged at the C_α atoms spanning all possible planar and nonplanar peptide conformations. We have combined our method with a ring closure algorithm for the case of ring peptides and missing loops in a protein structure. Here, the reconstruction proceeding from both the N and C termini of the protein backbone (or in both directions from a starting position for rings) requires freedom in the position of one C_α atom (a capstone) to achieve a successful loop or ring closure. A salient feature of our reconstruction method is the ability to enrich conformational ensembles to produce alternative feasible conformations in which H-bond forming C-O or N-H pairs in the backbone can reverse orientations, thus addressing a well-known shortcoming in C_α-based RMSD structure comparison, wherein very close structures may lead to significantly different overall H-bond behavior. We apply the fixed C_α-based design to the reverse reconstruction from noisy Cryo-EM data, a posteriori to the optimization. Our method can be applied to speed up the process of an all-atom description from voluminous experimental data or subpar electron density maps.

My 65 years in protein chemistry

This is a tour of a physical chemist through 65 years of protein chemistry from the time when emphasis was placed on the determination of the size and shape of the protein molecule as a colloidal particle, with an early breakthrough by James Sumner, followed by Linus Pauling and Fred Sanger, that a protein was a real molecule, albeit a macromolecule. It deals with the recognition of the nature and importance of hydrogen bonds and hydrophobic interactions in determining the structure, properties, and biological function of proteins until the present acquisition of an understanding of the structure, thermodynamics, and folding pathways from a linear array of amino acids to a biological entity. Along the way, with a combination of experiment and theoretical interpretation, a mechanism was elucidated for the thrombin-induced conversion of fibrinogen to a fibrin blood clot and for the oxidative-folding pathways of ribonuclease A. Before the atomic structure of a protein molecule was determined by x-ray diffraction or nuclear magnetic resonance spectroscopy, experimental studies of the fundamental interactions underlying protein structure led to several distance constraints which motivated the theoretical approach to determine protein structure, and culminated in the Empirical Conformational Energy Program for Peptides (ECEPP), an all-atom force field, with which the structures of fibrous collagen-like proteins and the 46-residue globular staphylococcal protein A were determined. To undertake the study of larger globular proteins, a physics-based coarse-grained UNited-RESidue (UNRES) force field was developed, and applied to the protein-folding problem in terms of structure, thermodynamics, dynamics, and folding pathways. Initially, single-chain and, ultimately, multiple-chain proteins were examined, and the methodology was extended to protein-protein interactions and to nucleic acids and to protein-nucleic acid interactions. The ultimate results led to an understanding of a variety of biological processes underlying natural and disease phenomena.

Relationship between protein structure and geometrical constraints

We evaluate to what extent the structure of proteins can be deduced from incomplete knowledge of disulfide bridges, surface assignments, secondary structure assignments, and additional distance constraints. A cost function taking such constraints into account was used to obtain protein structures using a simple minimization algorithm. For small proteins, the approximate structure could be obtained using one additional distance constraint for each amino acid in the protein. We also studied the effect of using predicted secondary structure and surface assignments. The constraints used in this approach typically may be obtained from low-resolution experimental data. When using a cost function based on distances, half of the resulting structures will be mirrored, because the resulting structure and its mirror image will have the same cost. The secondary structure assignments were therefore divided into chirality constraints and distance constraints. Here we report that the problem of mirrored structures, in some cases, can be solved by using a chirality term in the cost function.

Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C alpha atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the alpha-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these alpha-helical and beta-sheet structures. Application to the alpha-carbon trace of the backbone of the crystallographic 5PTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C alpha-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of 5PTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.

A geometrical constraint approach for reproducing the native backbone conformation of a protein

It is known that the backbone conformation of a protein can be reproduced with precision once a correct contact map (two-dimensional representation showing residue pairs in contact) is given as geometrical constraints. There is, however, no way to infer the correct contact map for a protein of unknown structure. We started with one-dimensional constraints using the quantity N14 (the number of neighboring residues within the radius of 14 A). Since the plot of N14 along a chain shows a good correlation with the corresponding amino acid sequence, the N14 profile obtained from the X-ray structure is predictable from the sequence. Construction of backbone conformations under a given N14 profile was carried out in the following two steps: (1) a contact map from the N14 profile was produced by taking the product of N14 values of every two residues; (2) backbone conformations were generated by applying the distance geometry technique to distance constraints given by the contact map. If present, disulfide bonds in a protein, as well as the secondary structure, were treated as additional constraints, and both cases with or without the additional information were examined. The method was tested for 11 proteins of known structure, and the results indicated that the reproduced conformation was fairly good, using an X-ray structure for comparison, for small proteins of less than 80 residues long. The basic assumption and effectiveness of the present method were compared with those of previous studies employing the geometrical constraint approach.(ABSTRACT TRUNCATED AT 250 WORDS)

Pair distribution functions in small systems: implications for protein structure analysis

A general formula is derived for the relation between the pair correlation function and the histogram of interparticle distances in small nonuniform systems. The formula is applied to random packings of spheres in a spherical container, which are generated by a Monte Carlo method. When measured properly, the resultant correlation functions are very similar to ones in bulk systems with the same volume fraction of particles. In contrast, the density is very nonuniform as a function of distance from the center of the container. The variation is an order of magnitude for the number density of particle centers, or severalfold for the occupied volume fraction. It is described how these results can be used to analyze the forces that determine protein structure.

Distance-constraint approach to higher-order structures of globular proteins with empirically determined distances between amino acid residues

An analysis of higher-order structures of globular proteins by means of a distance-constraint approach is presented. Conformations are generated for each of 21 test proteins of small and medium sizes by optimizing an objective function f = sigma sigma wij(dij - (dij]2, where dij is a distance between residues i and j in a calculated conformation, (dij) is an assigned distance to the (ij) pair of residues which is determined based on the statistics of known three-dimensional structures of 14 proteins in the earlier study, and wij is a weighting factor. (dij) involves information about hydrophobicity and hydrophilicity of each amino acid residue and about connectivity of a polypeptide chain. In these calculations, only the amino acid sequence is used as input data specific to a calculated protein. With respect to higher-order structures regenerated in the optimized conformations, the following properties are analyzed: (a) N14 of a residue, defined as the number of residues surrounding the residue located within a sphere of radius of 14 A; (b) root-mean-square differences of the global and local conformations from the corresponding X-ray conformations; (c) distance profiles in the short and medium ranges; and (d) distance maps. The effects of supplementary information about locations of secondary structures and disulfide bonds are also examined to discuss the potential ability of this methodology to predict the three-dimensional structures of globular proteins.

Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation [i-j[ in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.

Interactions between an alpha-helix and a beta-sheet. Energetics of alpha/beta packing in proteins

Conformational energy computations have been carried out to determine the favorable ways of packing a right-handed alpha-helix on a right-twisted antiparallel or parallel beta-sheet. Co-ordinate transformations have been developed to relate the position and orientation of the alpha-helix to the beta-sheet. The packing was investigated for a CH3CO-(L-Ala)16-NHCH3 alpha-helix interacting with five-stranded beta-sheets composed of CH3CO-(L-Val)6-NHCH3 chains. All internal and external variables for both the alpha-helix and the beta-sheet were allowed to change during energy minimization. Four distinct classes of low-energy packing arrangements were found for the alpha-helix interacting with both the parallel and the anti-parallel beta-sheet. The classes differ in the orientation of the axis of the alpha-helix relative to the direction of the strands of the right-twisted beta-sheet. In the class with the most favorable arrangement, the alpha-helix is oriented along the strands of the beta-sheet, as a result of attractive non-bonded side-chain-side-chain interactions along the entire length of the alpha-helix. A class with nearly perpendicular orientation of the helix axis to the strands is also of low energy, because it allows similarly extensive attractive interactions. In the other two classes, the helix is oriented diagonally relative to the strands of the beta-sheet. In one of them, it interacts with the convex surface near the middle of the saddle-shaped twisted beta-sheet. In the other, it is oriented along the concave diagonal of the beta-sheet and, therefore, it interacts only with the corner regions of the sheet, so that this packing is energetically less favorable. The packing arrangements involving an antiparallel and a parallel beta-sheet are generally similar, although the antiparallel beta-sheet has been found to be more flexible. The major features of 163 observed alpha/beta packing arrangements in 37 proteins are accounted for in terms of the computed structural preferences. The energetically most favored packing arrangement is similar to the right-handed beta alpha beta crossover structure that is observed in proteins; thus, the preference for this connectivity arises in large measure from this energetically favorable interaction.

Conformation of glucagon in a lipid-water interphase by 1H nuclear magnetic resonance

A determination of the spatial structure of the polypeptide hormone glucagon bound to perdeuterated dodecylphosphocholine micelles is described. A map of distance constraints between individually assigned hydrogen atoms of the polypeptide chain was obtained from two-dimensional nuclear Overhauser enhancement spectroscopy. These data were used as the input for a distance geometry algorithm for computing conformations that would be compatible with the experiments. In the region from residues 5 to 29 the mobility of the polypeptide backbone and most of the amino acid side-chains was found to be essentially restricted to the overall rotational tumbling of the micelles. The secondary structure in this region includes three turns of irregular alpha-helix in the segment of residues 17 to 29 near the C terminus, a stretch of extended polypeptide chain from residues 14 to 17, an alpha-helix-like turn formed by the residues 10 to 14 and another extended region from residues 5 to 10. In the N-terminal tetrapeptide H-His-Ser-Gln-Gly- the two terminal residues are highly mobile, indicating that they extend into the aqueous phase, and the mobility of the residues Gln3 and Gly4 appears to be only partially restricted by the binding to the micelle. The absence of long range nuclear Overhauser effects between the peptide segments 5-9 and 11-29, and between 5-16 and 19-29 shows that the polypeptide chain does not fold back on itself and hence that micelle-bound glucagon does not adopt a globular tertiary structure. Previously it was shown that the polypeptide backbone of glucagon is located close to and runs roughly parallel to the micelle surface. Combination of these observations suggests that the overall spatial arrangement of the glucagon polypeptide chain in a lipid-water interphase is largely determined by the topology of the lipid support, in the present case the curvature of the dodecylphosphocholine micelles. The tertiary structure is further characterized by the formation of two hydrophobic patches by the side-chains of Phe6, Tyr10 and Leu14, and the side-chains of Ala19, Phe22, Val23, Trp25 and Leu26, respectively.

[Dynamics of protein structures]

This review presents a survey of experimental and theoretical methods capable of providing a many-parameter characterization of internal mobility of protein molecules. Special emphasis is on applications of high-resolution nuclear magnetic resonance for studies of non-crystalline proteins and discussions of possible correlations between protein dynamics and biological functions of proteins.