Hydrophobic patches on the surfaces of protein structures

A survey of hydrophobic patches on the surface of 112 soluble, monomeric proteins is presented. The largest patch on each individual protein averages around 400 Ų but can range from 200 to 1,200 Ų. These areas are not correlated to the sizes of the proteins and only weakly to their apolar surface fraction. Ala, Lys, and Pro have dominating contributions to the apolar surface for smaller patches, while those of the hydrophobic amino acids become more important as the patch size Increases. The hydrophilic amino acids expose an approximately constant fraction of their apolar area independent of patch size; the hydrophobic residue types reach similar exposure only in the larger patches. Though the mobility of residues on the surface is generally higher, it decreases for hydrophilic residues with Increasing patch size. Several characteristics of hydrophobic patches catalogued here should prove useful in the design and engineering of proteins. © 1996 Wiley-Liss, Inc.     

Discovery of similar regions on protein surfaces.

Discovery of a similar region on two protein surfaces can lead to important inference about the functional role or molecular interaction of this region for one of the proteins if such information is available for the other. We propose a new characterization of protein surfaces based on a spin-image representation of the surfaces that facilitates the simultaneous search of the entire surface of each of two proteins for a matching region. For a surface point, we introduce spin-image profiles that are related to the degree of exposure of the point to identify structurally equivalent surface regions in two proteins. Unlike some related methods, we do not assume that a known fixed region of one of the protein surfaces is to be matched on the other protein surface. Rather, we search for the largest similar regions on each of the two surfaces. In spite of the fact that this approach is entirely geometric and no use is made of physicochemical properties of the protein surfaces or fold information, it is effective in identifying similar regions on both surfaces even when the region corresponds to a binding site on one of the proteins. The discovery of similar regions on two or more proteins also has implications for drug design and pharmacophore identification. We present experimental results from datasets of more than 50 protein surfaces.     

Hydrophobic folding units derived from dissimilar monomer structures and their interactions.

We have designed an automated procedure to cut a protein into compact hydrophobic folding units. The hydrophobic units are large enough to contain tertiary non-local interactions, reflecting potential nucleation sites during protein folding. The quality of a hydrophobic folding unit is evaluated by four criteria. The first two correspond to visual characterization of a structural domain, namely, compactness and extent of isolation. We use the definition of Zehfus and Rose (Zehfus MH, Rose GD, 1986, Biochemistry 25:35-340) to calculate the compactness of a cut protein unit. The isolation of a unit is based on the solvent accessible surface area (ASA) originally buried in the interior and exposed to the solvent after cutting. The third quantity is the hydrophobicity, equivalent to the fraction of the buried non-polar ASA with respect to the total non-polar ASA. The last criterion in the evaluation of a folding unit is the number of segments it includes. To conform with the rationale of obtaining hydrophobic units, which may relate to early folding events, the hydrophobic interactions are implicitly and explicitly applied in their generation and assessment. We follow Holm and Sander (Holm L, Sander C, 1994, Proteins 19:256-268) to reduce the multiple cutting-point problem to a one-dimensional search for all reasonable trial cuts. However, as here we focus on the hydrophobic cores, the contact matrix used to obtain the first non-trivial eigenvector contains only hydrophobic contracts, rather than all, hydrophobic and hydrophilic, interactions. This dataset of hydrophobic folding units, derived from structurally dissimilar single chain monomers, is particularly useful for investigations of the mechanism of protein folding. For cases where there are kinetic data, the one or more hydrophobic folding units generated for a protein correlate with the two or with the three-state folding process observed. We carry out extensive amino acid sequence order independent structural comparisons to generate a structurally non-redundant set of hydrophobic folding units for fold recognition and for statistical purposes.     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

Derivation of antibody distribution from experimental binding data.

It can be demonstrated that antibody populations cannot be suitably described in terms of a Sips distribution. Use of the Stieltjes transform allows instead derivation, from experimental binding data, of the most probable distribution of the association constants. From graphical interpolation of the experimental data four parameters can be obtained, which characterize a satisfactory bimodal distribution. By this procedure, analysis of data taken at different times of a humoral immune response, indicates that the relative abundance of the two sub-populations, rather than their mean association constant, is mainly affected by time or by variations of antigen dose. By use of the same procedure it is also possible to show that, at least as far as haptens are concerned, the slope of the 50% antigen-binding plot, often taken as a measure of the “avidity” of antibodies, is instead a function of the relative weight of the two sub-populations and of the spread of each of them.     

Incorporation of crystallographic temperature factors in the statistical analysis of protein tertiary structures

A method to identify statistically significant differences between equivalent atoms in two closely related protein X-ray crystallographic structures is described. This method uses the linear relationship found between the logarithm of the distance between equivalent atoms and their mean temperature factor to determine, by linear regression, the expected difference and variance.     

AlphaCutter: Efficient removal of non-globular regions from predicted protein structures

A huge number of high-quality predicted protein structures are now publicly available. However, many of these structures contain non-globular regions, which diminish the performance of downstream structural bioinformatic applications. In this study, we develop AlphaCutter for the removal of non-globular regions from predicted protein structures. A large-scale cleaning of 542,380 predicted SwissProt structures highlights that AlphaCutter is able to (1) remove non-globular regions that are undetectable using pLDDT scores and (2) preserve high integrity of the cleaned domain regions. As useful applications, AlphaCutter improved the folding energy scores and sequence recovery rates in the re-design of domain regions. On average, AlphaCutter takes less than 3 s to clean a protein structure, enabling efficient cleaning of the exploding number of predicted protein structures. AlphaCutter is available at https://github.com/johnnytam100/AlphaCutter . AlphaCutter-cleaned SwissProt structures are available for download at https://doi.org/10.5281/zenodo.7944483 .     

Accuracy of functional surfaces on comparatively modeled protein structures

Identification and characterization of protein functional surfaces are important for predicting protein function, understanding enzyme mechanism, and docking small compounds to proteins. As the rapid speed of accumulation of protein sequence information far exceeds that of structures, constructing accurate models of protein functional surfaces and identify their key elements become increasingly important. A promising approach is to build comparative models from sequences using known structural templates such as those obtained from structural genome projects. Here we assess how well this approach works in modeling binding surfaces. By systematically building three-dimensional comparative models of proteins using Modeller, we determine how well functional surfaces can be accurately reproduced. We use an alpha shape based pocket algorithm to compute all pockets on the modeled structures, and conduct a large-scale computation of similarity measurements (pocket RMSD and fraction of functional atoms captured) for 26,590 modeled enzyme protein structures. Overall, we find that when the sequence fragment of the binding surfaces has more than 45% identity to that of the template protein, the modeled surfaces have on average an RMSD of 0.5 Å, and contain 48% or more of the binding surface atoms, with nearly all of the important atoms in the signatures of binding pockets captured.     

Analysis of temperature factor distribution in high-resolution protein structures.

The temperature factors obtained from X-ray refinement of proteins at high resolution show large variations from one structure to another. However, the B-values expressed in units of standard deviation about their mean value (B'-factor) at the C alpha atoms show remarkably characteristic frequency distribution. In all of the 110 proteins examined in this study, the frequency distribution exhibited a bimodal distribution. The peaks in the B'-factor frequency distribution occur at -1.1 and 0.4 for a bin size of 0.5. The peak at lower temperature factor corresponds largely to buried residues, whereas the peak at larger value corresponds to exposed residues. The distribution could be accurately described as a superposition of two Gaussian functions. The parameters describing the distribution are therefore characteristic of protein structures. The frequency distribution for a given amino acid over all the proteins also shows a similar bimodal distribution, although the areas under the two Gaussians differ from one amino acid to another. The area under the frequency distribution curve for any interval in B'-factor represents the propensity of the amino acid to occur in that interval. This propensity is related both to the hydrophilicity/hydrophobicity of the residue and the tendency of the residue to impose a different degree of rigidity on the polypeptide chain. The frequency distribution of stretches of high B'-factors departs appreciably from that expected for a random distribution. The correlation in the B-values of sequentially proximal residues is probably responsible for the bimodal distribution.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

X-ray crystallographic structures of the Escherichia coli periplasmic protein FhuD bound to hydroxamate-type siderophores and the antibiotic albomycin.

Siderophore-binding proteins play an essential role in the uptake of iron in many Gram-positive and Gram-negative bacteria. FhuD is an ATP-binding cassette-type (ABC-type) binding protein involved in the uptake of hydroxamate-type siderophores in Escherichia coli. Structures of FhuD complexed with the antibiotic albomycin, the fungal siderophore coprogen and the drug Desferal have been determined at high resolution by x-ray crystallography. FhuD has an unusual bilobal structure for a periplasmic ligand binding protein, with two mixed beta/alpha domains connected by a long alpha-helix. The binding site for hydroxamate-type ligands is composed of a shallow pocket that lies between these two domains. Recognition of siderophores primarily occurs through interactions between the iron-hydroxamate centers of each siderophore and the side chains of several key residues in the binding pocket. Rearrangements of side chains within the binding pocket accommodate the unique structural features of each siderophore. The backbones of the siderophores are not involved in any direct interactions with the protein, demonstrating how siderophores with considerable chemical and structural diversity can be bound by FhuD. For albomycin, which consists of an antibiotic group attached to a hydroxamate siderophore, electron density for the antibiotic portion was not observed. Therefore, this study provides a basis for the rational design of novel bacteriostatic agents, in the form of siderophore-antibiotic conjugates that can act as "Trojan horses," using the hydroxamate-type siderophore uptake system to actively deliver antibiotics directly into targeted pathogens.     

The distribution of structures in evolving protein populations

Proteins exhibit a nonuniform distribution of structures. A number of models have been advanced to explain this observation by considering the distribution of designabilities, that is, the fraction of all sequences that could successfully fold into any particular structure. It has been postulated that more designable structures should be more common, although the exact nature of this relationship has not been addressed. We find that the nonuniform distribution of protein structures found in nature can be explained by the interplay of evolution and population dynamics with the designability distribution. The relative frequency of different structures has a greater-than-linear dependence on designability, making the distribution of observed protein structures more uneven than the distribution of designabilities. The distribution of structures is also affected by additional factors such as the topology of the sequence space and the similarity of other structures.     

A novel approach to segregate and identify functional loop regions in protein structures using their Ramachandran maps

The loops which connect or flank helices/sheets in protein structures are known to be functionally important. However, ironically they also belong to the part of protein whose structure is least accurately predicted. Here, a new method to isolate and analyze loop regions in protein structure is proposed using the spatial coordinates of the solved three‐dimensional structure. The extent of dispersion among points of successive amino acid residues in the Ramachandran map of protein region is utilized to calculate the Mean Separation between these points in the Ramachandran Plot (MSRP). Based on analysis of 2935 protein secondary structure regions obtained using DSSP software, spanning a range from 2 to 64 residues, taken from a set of 170 proteins, it is shown that helices (MSRP < 17) and strands (MSRP < 64) stand effectively demarcated from the loop regions (MSRP > 130). Analysis of 43 DNA binding and 98 ligand binding proteins revealed several loop regions with clear change in MSRP subsequent to binding. The population of such loops correlated with the magnitude of backbone displacement in the protein subsequent to binding. Can changes in MSRP quantify the temporal oscillations in dihedral angles among structured/unstructured regions in proteins? Molecular dynamics simulations (10 ns) revealed that deviations in MSRP among different snapshots in the trajectory were at least twofold higher for unstructured proteins in comparison with ordered proteins. The above results validate the use of MSRP parameter as a tool to identify and investigate functionally active loops and unstructured regions in protein structures. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Airway area distribution from the forced expiration maneuver.

The maximal expiratory flow-volume (MEFV) maneuver is a commonly used test of lung function. More detailed interpretation than is currently available might be useful to understand disease better. We propose that a previously published computational model (Lambert RK, Wilson TA, Hyatt RE, and Rodarte JR. J Appl Physiol 52: 44-56, 1982) can be used to deduce, from the MEFV curve, the serial distribution of airway areas in the larger airways. An automated procedure based on the simulated annealing technique was developed. It was tested with model-generated flow data in which airway areas were reduced one generation at a time. The procedure accurately located the constriction and predicted its size within narrow bounds when the constriction was in the six most central generations of airways. More peripheral constrictions were detected but were not precisely located, nor were their sizes accurately evaluated. Airway areas of generations upstream of the constriction were usually overestimated. The procedure was applied to spirometric data obtained from eight volunteers (4 asthmatic and 4 normal subjects) at baseline and after methacholine challenge. The predicted areas show individual differences both in absolute values, and in relative distribution of areas. This result shows that detailed information can be obtained from the MEFV curve through the use of a model. However, this initial model, which lacks airway smooth muscle, needs further refinement.     

Analysis of thermodynamic non-ideality in terms of protein solvation.

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical-mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter delta are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein-protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.