Charge sequence coding in statistical modeling of unfolded proteins

Unfolded proteins recently attracted attention due to accumulation of experimental evidences for their significant role in different life processes. Modeling of electrostatic interactions (EI) in unfolded state of proteins is becoming increasingly important as well. In this paper, we stress on the importance of how the sequence of charged residues of a given protein is incorporated into the models for calculation of EI in the unfolded state. On the basis of the distributions of distances between titratable sites of charged residues calculated for polypeptide chains of various compositions, it was found that the distance distribution for a pair of residues, located close to each other along the sequence of a protein, depends on what residues constitute the pair in question. It was concluded that the consideration of these residue-specific distributions is essential for a statistical model to be accurate from the physical point of view. It was suggested that use of distance intervals in the spherical model of unfolded proteins accounts better for the charge sequence than the set of single distance values. This was illustrated by comparison of the pK values of the titratable groups of the unfolded N-terminal SH3 domain of the Drosophila protein drk to the available experimental data.     

Patterns in ionizable side chain interactions in protein structures

In a selected set of 44 high-resolution, non-homologous protein structures, the intramolecular hydrogen bonds or salt bridges formed by ionizable amino acid side chains were identified and analyzed. The analysis was based on the investigation of several properties of the involved residues such as their solvent exposure, their belonging to a certain secondary structural element, and their position relative to the N- and C-termini of their respective structural element. It was observed that two-thirds of the interactions made by basic or acidic side chains are hydrogen bonds to polar uncharged groups. In particular, the majority (78%) of the hydrogen bonds between ionizable side chains and main chain polar groups (sch:mch bonds) involved at least one buried atom, and in 42% of the cases both interacting atoms were buried. In α-helices, the sch:mch bonds observed in the proximity of the C- and N-termini show a clear preference for acidic and basic side chains, respectively. This appears to be due to the partial charges of peptide group atoms at the termini of α-helices, which establish energetically favorable electrostatic interactions with side chain carrying opposite charge, at distances even greater than 4.5 Å. The sch:mch interactions involving ionizable side chains that belong either to β-strands or to the central part of α-helices are based almost exclusively on basic residues. This results from the presence of main chain carbonyl oxygen atoms in the protein core which have unsatisfied hydrogen bonding capabilities.     

Sequence-specific 1H NMR assignments and solution structure of bovine pancreatic polypeptide.

Sequence-specific 1H NMR assignments for the 36 residue bovine pancreatic polypeptide (bPP) have been completed. The secondary and tertiary structure of bPP in solution has been determined from experimental NMR data. It is shown that bPP has a very well-defined C-terminal alpha-helix involving residues 15-32. Although regular secondary structure cannot be clearly defined in the N-terminal region, residues 4-8 maintain a rather ordered conformation in solution. This is attributed primarily to the hydrophobic interactions between this region and the C-terminal helix. The two segments of the structure are joined by a turn which is poorly defined. The four end residues both at the N-terminus and the C-terminus are highly disordered in solution. The overall fold of the bPP molecule is very closely similar to that found in the crystal structure of avian pancreatic polypeptide (aPP). The RMS deviation for backbone atoms of residues 4-8 and 15-32 between the bPP mean structure and the aPP crystal structure is 0.65 A, although there is only 39% identity of the residues. Furthermore, the average conformations of some (mostly from the alpha-helix) side chains of bPP in solution are closely similar to those of aPP in the crystal structure. A large number of side chains of bPP, however, show significant conformational averaging in solution.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

Disorder and order in unfolded and disordered peptides and proteins: A view derived from tripeptide conformational analysis. I. Tripeptides with long and predominantly hydrophobic side chains

We performed a conformational analysis of the central residues of three tripeptides glycyl‐L ‐isoleucyl‐glycine (GIG), glycyl‐L ‐tyrosyl‐glycine (GYG) and glycyl‐L ‐arginyl‐glycine (GRG) in aqueous solution, based on a global analysis of amide I′ band profiles and NMR J‐coupling constants. The results are compared with recently reported distributions of GVG, GFG and GEG. For GIG and GYG, we found that even though the polyproline II (pPII) fraction is below 0.5, it is still the most populated conformation, whereas GVG and GFG show both a larger β‐strand fraction. For GRG, we observed a clear dominance of pPII over β‐strand, reminiscent of observations for GEG and GKG. This finding indicates that terminal charges on otherwise hydrophobic residue side chains stabilize pPII over β‐strand conformations. For all peptides investigated we found that a variety of compact and turn‐like conformations constitute nearly 20 percent of their conformational distributions. Attempts to analyze our data with a simple two‐state pPII??β model therefore do not yield any satisfactory reproduction of experimental results. A comparison of the obtained GxG ensembles with conformational distributions of GxG segments in truncated coil libraries (helices and sheets omitted) revealed a much larger fraction of type II β_i+2 and type III β like conformations for the latter. Thus, a comparison of conformational distributions of unfolded peptide segments in solution and in coil libraries reveal interesting information on how the interplay between intrinsic propensities of amino acid residues and non‐local interactions in polypeptide chains determine the conformations of loop segments in proteins. Proteins 2013; © 2012 Wiley Periodicals, Inc.     

Protein contacts, inter-residue interactions and side-chain modelling

Three-dimensional structures of proteins are the support of their biological functions. Their folds are stabilized by contacts between residues. Inner protein contacts are generally described through direct atomic contacts, i.e. interactions between side-chain atoms, while contact prediction methods mainly used inter-Calpha distances. In this paper, we have analyzed the protein contacts on a recent high quality non-redundant databank using different criteria. First, we have studied the average number of contacts depending on the distance threshold to define a contact. Preferential contacts between types of amino acids have been highlighted. Detailed analyses have been done concerning the proximity of contacts in the sequence, the size of the proteins and fold classes. The strongest differences have been extracted, highlighting important residues. Then, we studied the influence of five different side-chain conformation prediction methods (SCWRL, IRECS, SCAP, SCATD and SCCOMP) on the distribution of contacts. The prediction rates of these different methods are quite similar. However, using a distance criterion between side chains, the results are quite different, e.g. SCAP predicts 50% more contacts than observed, unlike other methods that predict fewer contacts than observed. Contacts deduced are quite distinct from one method to another with at most 75% contacts in common. Moreover, distributions of amino acid preferential contacts present unexpected behaviours distinct from previously observed in the X-ray structures, especially at the surface of proteins. For instance, the interactions involving Tryptophan greatly decrease.     

Horse heart metmyoglobin. A 2.8-A resolution three-dimensional structure determination

The structure of horse heart metmyoglobin has been determined with a molecular replacement approach and subsequently refined using rigid body and restrained-parameter least squares methods to a conventional crystallographic R-factor of 0.16 for all observed reflections in the 6.0-2.8-A resolution range. The polypeptide chain of this protein is found to be organized into eight helical regions (labeled A-H) which collectively form a hydrophobic pocket in which the heme prosthetic group is bound. Our results show that the overall thermal motions of individual residues of horse heart metmyoglobin are correlated with their mean distances from the heme group. In comparisons with the structure of sperm whale metmyoglobin it has been found that horse heart metmyoglobin has unique polypeptide chain conformations in four regions. These include residues in the immediate vicinity of the amino and carboxyl termini, residues about Lys-16, and residues 117-124 which are in the interhelical region between helices G and H. Many of these conformational changes appear to occur as a consequence of a different pattern of salt-bridging interactions between charged residues on the surface of horse heart metmyoglobin. The overall average positional deviation observed between corresponding alpha-carbons in the polypeptide chains of horse heart and sperm whale metmyoglobin is 0.50 A. This value for atoms of the porphyrin core of the central heme group is 0.39 A. A total of 12 well defined water molecules and 1 sulfate ion are included in the current structural model of horse heart metmyoglobin. One of these water molecules is found to be coordinated to the heme iron atom and hydrogen bonded to the side chain of His-64. The sulfate ion is hydrogen bonded to amide groups at the amino-terminal end of the E-helix and, as well, forms similar interactions with the amino-terminal end of the D-helix of an adjacent protein molecule in the crystalline lattice.     

Computer simulation of polypeptides in a confinement

A coarse-grained model of polypeptide chains confined in a slit formed by two parallel impenetrable surfaces was studied. The chains were flexible heteropolymers (polypeptides) built of two kinds of united atoms—hydrophobic and hydrophilic. The positions of the united atoms were restricted to the vertices of a [310] lattice. The force field consisted of a rigorous excluded volume, a long-distance potential between a pair of amino-acid residues and a local preference for forming secondary structure (helices). The properties of the chains were studied at a wide range of temperatures from good to bad solvent conditions. Monte-Carlo simulations were carried out using the algorithm based on the chain’s local changes of conformation and employing the Replica Exchange technique. The influence of the chain length, the distances between the confining surfaces, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that the presence of the confinement chain complicates the process of the chain collapse to low-temperature structures. For some conditions, one can find a rapid decrease of chain size and a second transition indicated by the rapid decrease of the total energy of the system. Figure A scheme of a polypeptide chain built on a [310] lattice and confined to a slit formed by a pair of parallel impenetrable surfaces Proceedings of “Modeling Interactions in Biomolecules II,” Prague, September 5th–9th, 2005.     

Three-dimensional structure of the neurotoxin ATX Ia from Anemonia sulcata in aqueous solution determined by nuclear magnetic resonance spectroscopy

With the aid of 1H nuclear magnetic resonance (NMR) spectroscopy, the three-dimensional structure in aqueous solution was determined for ATX Ia, which is a 46 residue polypeptide neurotoxin of the sea anemone Anemonia sulcata. The input for the structure calculations consisted of 263 distance constraints from nuclear Overhauser effects (NOE) and 76 vicinal coupling constants. For the structure calculation several new or ammended programs were used in a revised strategy consisting of five successive computational steps. First, the program HABAS was used for a complete search of all backbone and chi 1 conformations that are compatible with the intraresidual and sequential NMR constraints. Second, using the program DISMAN, we extended this approach to pentapeptides by extensive sampling of all conformations that are consistent with the local and medium-range NMR constraints. Both steps resulted in the definition of additional dihedral angle constraints and in stereospecific assignments for a number of beta-methylene groups. In the next two steps DISMAN was used to obtain a group of eight conformers that contain no significant residual violations of the NMR constraints or van der Waals contacts. Finally, these structures were subjected to restrained energy refinement with a modified version of the molecular mechanics module of AMBER, which in addition to the energy force field includes potentials for the NOE distance constraints and the dihedral angle constraints. The average of the pairwise minimal RMS distances between the resulting refined conformers calculated for the well defined molecular core, which contains the backbone atoms of 35 residues and 20 interior side chains, is 1.5 +/- 0.3 A. This core is formed by a four-stranded beta-sheet connected by two well-defined loops, and there is an additional flexible loop consisting of the eleven residues 8-18. The core of the protein is stabilized by three disulfide bridges, which are surrounded by hydrophobic residues and shielded on one side by hydrophilic residues.     

The importance of secondary structure in determining CO2-protein binding patterns

One potential means to decrease the level of atmospheric carbon dioxide is through the utilization of protein-CO(2) interactions. A recent bioinformatics analysis [Cundari TR et al. (2009) J Chem Inf Model 49:2111-2115] of these interactions revealed a marked disparity in CO(2) affinity between α-helices and β-sheets. In order to understand this difference, a series of molecular dynamics simulations was performed on polypeptide model systems. Numerous factors that may influence CO(2) affinity were systematically investigated, including the specific location of the amino acids within the secondary structural elements (SSEs), the partial charges on CO(2), chemical modifications made to the protein backbone, the inclusion of singly, doubly, and many functionalized residues, and the effect of solvent water. The differing abilities of the secondary structure types to participate in hydrogen bonding along the backbone were identified as being a crucial influence on CO(2) affinity; the lesser role of polypeptide-CO(2) electrostatic interactions was also noted. The effect of incorporating functionalized amino acid side chains, such as those possessed by Arg and His, on the affinity differs between the two structure types, and also strongly depends on the number included and the distance between them. The inclusion of explicit water molecules was found to attenuate all interactions, but did not change the overall trends in CO(2) affinity. Collectively, these results highlight the role of the backbone atoms in binding the CO(2) ligand, which will have important implications for efforts to ameliorate atmospheric carbon dioxide through the use of natural, designed, and modified proteins.     

Protein fold similarity estimated by a probabilistic approach based on C(alpha)-C(alpha) distance comparison.

The distribution of the C(alpha)-C(alpha) distances between residues separated by three to 30 amino acid residues is highly characteristic of protein folds and makes it possible to identify them from a straightforward comparison of the distance histograms. The comparison is carried out by contingency table analysis and yields a probability of identity (PRIDE score), with values between zero and 1. For closely related structures, PRIDE is highly correlated with the root-mean-square distance between C(alpha) atoms, but it provides a correct classification even for unrelated structures for which a structural alignment is not meaningful. For example, an analysis of the CATH database of fold structures showed that 98.8% of the folds fall into the correct CATH homologous superfamily category, based on the highest PRIDE score obtained. Structural alignment and secondary-structure assignment are not necessary for the calculation of PRIDE, which is fast enough to allow the scanning of large databases.     

Energetics of charge-charge interactions between residues adjacent in sequence

Statistical analysis of the residue separation between a pair of ionizable side chains within 4 ? of each other was performed on a set of 1560 non-homologous PDB structures. We found that the frequency of pairs of like charges (i.e., pairs consisting of acidic residues Asp and Glu or pairs consisting of basic residues Arg and Lys) is two orders of magnitude lower than the pairs of oppositely charged residues (salt-bridges). We also found that for pairs of like charges the distribution is skewed dramatically towards short residue separation (<3). On the basis of these observations, we hypothesize that at short residue separation the repulsion between charges does not contribute much to the protein stability and the effects are largely dominated by the long range charge-charge interactions with other ionizable groups in the protein molecule. To test this hypothesis, we incorporated various pairs of charged residues at position 63 and 64 of ubiquitin and compared the stabilities of these variants. We also performed calculations of the expected changes in the charge-charge interactions. A very good correlation between experimental changes in the stability of ubiquitin variants, and changes in the energy of charge-charge interactions provides support for the hypothesis that a pair of ionizable residues next to each other in sequence modulates protein stability via long range charge-charge interactions with the rest of the protein.     

Combined use of proton-proton Overhauser enhancements and a distance geometry algorithm for determination of polypeptide conformations. Application to micelle-bound glucagon

In a new approach for the determination of polypeptide conformation, experimental data on intramolecular distances between pairs of hydrogen atoms obtained from nuclear Overhauser enhancement studies are used as input for a distance geometry algorithm. The algorithm determines the limits of the conformation space occupied by the polypeptide chain. The experimental data are used in such a way that the real conformation should in all cases be within these limits. Two important features of the method are that the results do not depend critically on the accuracy of the distance measurements by nuclear Overhauser enhancement studies and that internal mobility of the polypeptide conformation is explicitly taken into consideration. The use of this new procedure is illustrated with a structural study of the region 19-27 of glucagon bound to perdeuterated dodecylphosphocholine micelles.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the C_α-only elastic network models, which assume elastic interactions between pairs of residues whose C_α atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between C_α atoms or heavy atoms derived from a large set of protein crystal structures.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

Determination of three-dimensional structures of proteins from interproton distance data by hybrid distance geometry-dynamical simulated annealing calculations

A new hybrid distance space-real space method for determining three-dimensional structures of proteins on the basis of interproton distance restraints is presented. It involves the following steps: (i) the approximate polypeptide fold is obtained by generating a set of substructures comprising only a small subset of atoms by projection from multi-dimensional distance space into three-dimensional cartesian coordinate space using a procedure known as 'embedding'; (ii) all remaining atoms are then added by best fitting extended amino acids one residue at a time to the substructures; (iii) the resulting structures are used as the starting point for real space dynamical simulated annealing calculations. The latter involve heating the system to a high temperature followed by slow cooling in order to overcome potential barriers along the pathway towards the global minimum region. This is carried out by solving Newton's equations of motion. Unlike conventional restrained molecular dynamics, however, the non-bonded interactions are represented by a simple van der Waals repulsion term. The method is illustrated by calculations on crambin (46 residues) and the globular domain of histone H5 (79 residues). It is shown that the hybrid method is more efficient computationally and samples a larger region of conformational space consistent with the experimental data than full metric matrix distance geometry calculations alone, particularly for large systems.     

Resolution of Two Sub-Populations of Conformers and Their Individual Dynamics by Time Resolved Ensemble Level FRET Measurements

Most active biopolymers are dynamic structures; thus, ensembles of such molecules should be characterized by distributions of intra- or intermolecular distances and their fast fluctuations. A method of choice to determine intramolecular distances is based on Förster resonance energy transfer (FRET) measurements. Major advances in such measurements were achieved by single molecule FRET measurements. Here, we show that by global analysis of the decay of the emission of both the donor and the acceptor it is also possible to resolve two sub-populations in a mixture of two ensembles of biopolymers by time resolved FRET (trFRET) measurements at the ensemble level. We show that two individual intramolecular distance distributions can be determined and characterized in terms of their individual means, full width at half maximum (FWHM), and two corresponding diffusion coefficients which reflect the rates of fast ns fluctuations within each sub-population. An important advantage of the ensemble level trFRET measurements is the ability to use low molecular weight small-sized probes and to determine nanosecond fluctuations of the distance between the probes. The limits of the possible resolution were first tested by simulation and then by preparation of mixtures of two model peptides. The first labeled polypeptide was a relatively rigid Pro₇ and the second polypeptide was a flexible molecule consisting of (Gly-Ser)₇ repeats. The end to end distance distributions and the diffusion coefficients of each peptide were determined. Global analysis of trFRET measurements of a series of mixtures of polypeptides recovered two end-to-end distance distributions and associated intramolecular diffusion coefficients, which were very close to those determined from each of the pure samples. This study is a proof of concept study demonstrating the power of ensemble level trFRET based methods in resolution of subpopulations in ensembles of flexible macromolecules.     

Towards understanding the crosstalk between protein post‐translational modifications: Homo‐ and heterotypic PTM pair distances on protein surfaces are not random

Post‐translational modifications (PTMs) represent an important regulatory layer influencing the structure and function of proteins. With broader availability of experimental information on the occurrences of different PTM types, the investigation of a potential “crosstalk” between different PTM types and combinatorial effects have moved into the research focus. Hypothesizing that relevant interferences between different PTM types and sites may become apparent when investigating their mutual physical distances, we performed a systematic survey of pairwise homo‐ and heterotypic distances of seven frequent PTM types considering their sequence and spatial distances in resolved protein structures. We found that actual PTM site distance distributions differ from random distributions with most PTM type pairs exhibiting larger than expected distances with the exception of homotypic phosphorylation site distances and distances between phosphorylation and ubiquitination sites that were found to be closer than expected by chance. Random reference distributions considering canonical acceptor amino acid residues only were found to be shifted to larger distances compared to distances between any amino acid residue type indicating an underlying tendency of PTM‐amenable residue types to be further apart than randomly expected. Distance distributions based on sequence separations were found largely consistent with their spatial counterparts suggesting a primary role of sequence‐based pairwise PTM‐location encoding rather than folding‐mediated effects. Our analysis provides a systematic and comprehensive overview of the characteristics of pairwise PTM site distances on proteins and reveals that, predominantly, PTM sites tend to avoid close proximity with the potential implication that an independent attachment or removal of PTMs remains possible. Proteins 2016; 85:78–92. © 2016 Wiley Periodicals, Inc.