Correlations Between Amino Acids at Different Sites in Local Sequences of Protein Fragments with Given Structural Patterns

Ample evidence suggests that the local structures of peptide fragments in native proteins are to some extent encoded by their local sequences. Detecting such local correlations is important but it is still an open question what would be the most appropriate method. This is partly because conventional sequence analyses treat amino acid preferences at each site of a protein sequence independently, while it is often the inter-site interactions that bring about local sequence-structure correlations. Here a new scheme is introduced to capture the correlation between amino acid preferences at different sites for different local structure types. A library of nine-residue fragments is constructed, and the fragments are divided into clusters based on their local structures. For each local structure cluster or type, chi-square tests are used to identify correlated preferences of amino acid combinations at pairs of sites. A score function is constructed including both the single site amino acid preferences and the dual-site amino acid combination preferences, which can be used to identify whether a sequence fragment would have a strong tendency to form a particular local structure in native proteins. The results show that, given a local structure pattern, dual-site amino acid combinations contain different information from single site amino acid preferences. Representative examples show that many of the statistically identified correlations agree with previously-proposed heuristic rules about local sequence-structure correlations, or are consistent with physical-chemical interactions required to stabilize particular local structures. Results also show that such dual-site correlations in the score function significantly improves the Z-score matching a sequence fragment to its native local structure relative to nonnative local structures, and certain local structure types are highly predictable from the local sequence alone if inter-site correlations are considered.     

蛋白质结构的“限域下最低能量结构片段”假说与蛋白质进化的“石器时代”

蛋白质折叠问题被称为第二遗传密码,至今未破译;蛋白质序列的天书仍然是"句读之不知,惑之不解"。在最近工作的基础上,我们提出了蛋白质结构的"限域下最低能量结构片段"假说。这一假说指出,蛋白质中存在一些关键的长程强相互作用位点,这些位点相当于标点符号,将蛋白质序列的天书变成可读的句子(多肽片段)。这些片段的天然结构是在这些强长程相互作用位点限域下的能量最低状态。完整的蛋白质结构由这些"限域下最低能量结构片段"拼合而成,而蛋白质整体结构并不一定是全局性的能量最低状态。在蛋白质折叠过程中,局部片段的天然结构倾向性为强长程相互作用的形成提供主要基于焓效应的驱动力,而天然强长程相互作用的形成为局部片段的天然结构提供主要基于熵效应的稳定性。在蛋白质进化早期,可能存在一个"石器时代",即依附不同界面(比如岩石)的限域作用而稳定的多肽片段先进化出来,后由这些片段逐步进化(包括拼合)而成蛋白质。     

Importance of native-state topology for determining the folding rate of two-state proteins

Understanding the relationship between amino acid sequences and folding rate of proteins is a challenging task similar to protein folding problem. In this work, we have analyzed the relative importance of protein sequence and structure for predicting the protein folding rates in terms of amino acid properties and contact distances, respectively. We found that the parameters derived with protein sequence (physical-chemical, energetic, and conformational properties of amino acid residues) show very weak correlation (|r| < 0.39) with folding rates of 28 two-state proteins, indicating that the sequence information alone is not sufficient to understand the folding rates of two-state proteins. However, the maximum positive correlation obtained for the properties, number of medium-range contacts, and alpha-helical tendency reveals the importance of local interactions to initiate protein folding. On the other hand, a remarkable correlation (r varies from -0.74 to -0.88) has been obtained between structural parameters (contact order, long-range order, and total contact distance) and protein folding rates. Further, we found that the secondary structure content and solvent accessibility play a marginal role in determining the folding rates of two-state proteins. Multiple regression analysis carried out with the combination of three properties, beta-strand tendency, enthalpy change, and total contact distance improved the correlation to 0.92 with protein folding rates. The relative importance of existing methods along with multiple-regression model proposed in this work will be discussed. Our results demonstrate that the native-state topology is the major determinant for the folding rates of two-state proteins.     

3D-Epitope-Explorer (3DEX): localization of conformational epitopes within three-dimensional structures of proteins

Neutralizing antibodies often recognize conformational, discontinuous epitopes. Linear peptides mimicking such conformational epitopes can be selected from phage display peptide libraries by screening with the respective antibodies. However, it is difficult to localize these "mimotopes" within the three-dimensional (3D) structures of the target proteins. Knowledge of conformational epitopes of neutralizing antibodies would help to design antigens able to elicit protective immune responses. Therefore, we provide here a software that allows to localize linear peptide sequences within 3D structures of proteins. The 3D-Epitope-Explorer (3DEX) software allows to map conformational epitopes in 3D protein structures based on an algorithm that takes into account the physicochemical neighborhood of C(alpha)- or C(beta)-atoms of individual amino acids. A given amino acid of a peptide sequence is localized within the protein and the software searches within predefined distances for the amino acids neighboring that amino acid in the peptide. Surface exposure of the amino acids can also be taken into consideration. The procedure is then repeated for the remaining amino acids of the peptide. The introduction of a joker function allows to map peptide mimotopes, which do not necessarily have 100% sequence homology to the protein. Using this software we were able to localize mimotopes selected from phage displayed peptide libraries with polyclonal antibodies from HIV-positive patient plasma within the 3D structure of gp120, the exterior glycoprotein of HIV-1. We also analyzed two recently published peptide sequences corresponding to known conformational epitopes to further confirm the integrity of 3DEX.     

Statistical mechanical treatment of protein conformation. I. Conformational properties of amino acids in proteins.

A statistical mechanical (one-dimensional Ising model) treatment, based on the dominance of short-range interactions, is developed in this series of papers; it is intended as an improvement over empirical prediction schemes for obtaining approximate initial conformations of proteins (to be used to try to deduce the native conformation by subsequent energy minimization). In the present paper, the statistical weights for a two-state model (alpha-helical and other conformations) and for a three-state model (alpha-helical, extended, and other conformations) are evaluated from x-ray data on 16 native proteins. The method for evaluating the statistical weights is presented. Asymmetric alpha-helical nucleation parameters are also evaluated for the 20 naturally occurring amino acids. On the basis of these statistical weights, the conformational properties of the twenty naturally occurring amino acids are discussed. The statistical weights evaluated from x-ray data are also discussed in comparison with experimental results on the helix--coil transition in polyamino acids in solution. The predominant role of short-range interactions, and some possible long-range effects in determining the statistical weights, are discussed in conjunction with the mechanism of protein folding.     

Effects of guanidinium ions on the conformational structure of glucose oxidase studied by electrochemistry, spectroscopy, and theoretical calculations: towards developing a chemical-induced protein conformation assay

Understanding conformation transitions of proteins in the presence of a chemical denaturant is a topic of great interest because the rich information contained in chemical unfolding is of fundamental importance for proteomic and pharmaceutical research. In this work, the conformational structure changes of glucose oxidase (GOx) induced by guanidinium ions (Gdm(+)) were studied in detail by a combination of electrochemical methods, various spectroscopic techniques including ultraviolet-visible (UV-vis) absorption, fluorescence, Fourier transform infrared (FTIR), and circular dichroism (CD) spectroscopy, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations with the purpose of revealing the mechanism of chemical unfolding of proteins. The results indicated that GOx underwent substantial conformational changes both at the secondary and tertiary structure levels after interacting with Gdm(+) ions. The interaction of GOx with the chemical denaturant resulted in a disturbance of the structure of the flavin prosthetic group (FAD moiety) that induced the moiety to become less exposed to solvent than that in the native protein molecule. The calculation from quantitative second-derivative infrared and CD spectra showed that Gdm(+) ions induced the conversion of α-helix to β-sheet structures. MD simulations and DFT calculations revealed that Gdm(+) ions could enter the active pocket of the GOx molecule and interact with the FAD group, leading to a significant alteration in the structural characteristics and hydrogen bond networks formed between FAD and the surrounding amino acid residues. These alterations in the conformational structure of GOx resulted in a significant decrease in the catalytic activity of the enzyme to glucose oxidation. The study essentially provides an effective way for investigating the mechanism of chemical denaturant-induced protein unfolding, and this approach can be used for assessing the effect of drug molecules on proteins.     

Noncovalent cross-links in context with other structural and functional elements of proteins

Proteins are heteropolymers with evolutionary selected native sequences of residues. These native sequences code for unique and stable 3D structures indispensable for biochemical activity and for proteolysis resistance, the latter which guarantees an appropriate lifetime for the protein in the protease rich cellular environment. Cross-links between residues close in space but far in the primary structure are required to maintain the folded structure of proteins. Some of these cross-links are covalent, most frequently disulfide bonds, but the majority of the cross-links are sets of cooperative noncovalent long-range interactions. In this paper we focus on special clusters of noncovalent long-range interactions: the Stabilization Centers (SCs). The relation between the SCs and secondary structural elements as well as the relation between SCs and functionally important regions of proteins are presented to show a detailed picture of these clusters, which are believed to be primarily responsible for major aspects of protein stability.     

Development of novel statistical potentials describing cation-pi interactions in proteins and comparison with semiempirical and quantum chemistry approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation-pi and amino-pi interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation-pi and amino-pi systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree-Fock level (HF) and at the second order of the M?ller-Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation-pi statistical potentials suggests their utility in protein structure and stability prediction and in protein design.     

Determination of an empirical energy function for protein conformational analysis by energy embedding

It is quite easy to propose an empirical potential for conformational analysis such that given crystal structures lie near local minima. What is much more difficult, is to devise a function such that the native structure lies near a relatively deep local minimum, at least in some neighborhood of the native in conformation space. An algorithm is presented for finding such a potential acting on proteins where each amino acid residue is represented by a single point. When the given structure is either an α-helical, β-strand, or hairpin bend segment of pancreatic trypsin inhibitor, the resulting potential function in each case possesses a deep minimum within 0.10 Å of the native conformation. The improved energy embedding algorithm locates a marginally better minimum in each case only 0.1–1.3 Å away from the respective native state. In other words, this potential function guides a conformational search toward structures very close to the native over a wide range of conformation space.     

Absolute free energies of biomolecules from unperturbed ensembles

Computing the absolute free energy of a macromolecule's structural state, F, is a challenging problem of high relevance. This study presents a method that computes F using only information from an unperturbed simulation of the macromolecule in the relevant conformational state, ensemble, and environment. Absolute free energies produced by this method, dubbed V aluation of L ocal C onfiguration I ntegral with D ynamics (VALOCIDY), enable comparison of alternative states. For example, comparing explicitly solvated and vaporous states of amino acid side‐chain analogs produces solvation free energies in good agreement with experiments. Also, comparisons between alternative conformational states of model heptapeptides (including the unfolded state) produce free energy differences in agreement with data from μs molecular‐dynamics simulations and experimental propensities. The potential of using VALOCIDY in computational protein design is explored via a small design problem of stabilizing a β‐turn structure. When VALOCIDY‐based estimation of folding free energy is used as the design metric, the resulting sequence folds into the desired structure within the atomistic force field used in design. The VALOCIDY‐based approach also recognizes the distinct status of the native sequence regardless of minor details of the starting template structure, in stark contrast with a traditional fixed‐backbone approach. © 2013 Wiley Periodicals, Inc.     

A preference for edgewise interactions between aromatic rings and carboxylate anions: the biological relevance of anion-quadrupole interactions

Noncovalent interactions are quite important in biological structure-function relationships. To study the pairwise interaction of aromatic amino acids (phenylalanine, tyrosine, tryptophan) with anionic amino acids (aspartic and glutamic acids), small molecule mimics (benzene, phenol or indole interacting with formate) were used at the MP2 level of theory. The overall energy associated with an anion-quadrupole interaction is substantial (-9.5 kcal/mol for a benzene-formate planar dimer at van der Waals contact distance), indicating the electropositive ring edge of an aromatic group can interact with an anion. Deconvolution of the long-range coplanar interaction energy into fractional contributions from charge-quadrupole interactions, higher-order electrostatic interactions, and polarization terms was achieved. The charge-quadrupole term contributes between 30 to 45% of the total MP2 benzene-formate interaction; most of the rest of the interaction arises from polarization contributions. Additional studies of the Protein Data Bank (PDB Select) show that nearly planar aromatic-anionic amino acid pairs occur more often than expected from a random angular distribution, while axial aromatic-anionic pairs occur less often than expected; this demonstrates the biological relevance of the anion-quadrupole interaction. While water may mitigate the strength of these interactions, they may be numerous in a typical protein structure, so their cumulative effect could be substantial.     

A statistical model for predicting protein folding rates from amino acid sequence with structural class information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.     

Effect of small molecule surfactants on molecular parameters and thermodynamic properties of legumin in a bulk and at the air–water interface depending on a protein structure in an aqueous medium

This paper presents the effect of fatty acid salts, namely, Na-caprate and Na-palmitate on the legumin (11S globulin of Vicia Faba broad beans) molecular and thermodynamic properties in the bulk aqueous medium and at the air–water interface under different molecular states of the protein. That are the native state of the protein globule (pH 7.2, ionic strength of 0.05 mol dm⁻³), as well as the acidic denatured (pH 3.0, ionic strength of 0.01 mol dm⁻³) and the heat denatured ones (after heating at 90°C for 30 min, pH 7.2, ionic strength of 0.05 mol dm⁻³). In turn, an importance of the state of the small molecule surfactants in a solution in reference to the critical concentrations of micelle formation (CMC), for their effect on the protein properties, was also under our studying. The peculiarities of the legumin structure in the aqueous medium appeared in the different nature of the interactions between the protein and the fatty acid salts, as was indicated by the mixing calorimetry data. So, the hydrophobic contacts provided a basis for interactions between both the native and heat denatured legumin with the fatty acid salts. At the same time, the electrostatic interactions between the oppositely charged functional groups of the fatty acid salts and the acidic denatured protein formed principally a basis of their interactions in an aqueous medium. In response to interactions of the fatty acid salts with legumin the essential changes in the protein conformational stability, depending on both the protein molecular state and concentration of the fatty acid salts, were found using differential scanning calorimetry (DSC). The rather high level of the protein association was observed by light scattering in the bulk aqueous medium in the presence of the fatty acid salts. As this takes place, the surface hydrophilicity of the protein increased under the formation of the associates. The combined data of mixing calorimetry, differential scanning calorimetry and light scattering suggested the complex formation between legumin and the fatty acid salts. The interactions of the fatty acid salts with the protein produced a change in the surface activity for the mixture of the protein with the fatty acid salts. That is a decrease in the protein surface tension at the air–water interface for the mixed solutions in comparison with ones for both the protein and small molecule surfactant alone in the case of Na-caprate, and those are the intermediate values of the surface tension in the case of Na-palmitate. These results were observed independently of the protein state (native or acidic/heat denatured) in an aqueous medium. As this took place, the most dramatic increase in the surface activity was found for the mixtures of the acidic denatured protein with Na-caprate as if the most hydrophobic species were formed in this case. The combined data of mixing calorimetry, DSC, light scattering and tensiometry showed that the effect of the fatty acid salts on the legumin thermodynamic properties in a bulk and at interfaces is governed by a number of the key factors such as: a structure of both the protein and fatty acid salt (a length of the hydrocarbon chain); a degree of the protein association in the bulk aqueous phase (as a result of the interactions with the small molecule surfactants); a change in the protein conformational stability (flexibility) under the influence of the small molecule surfactants; as well as by the nature (hydrophobic, electrostatic) of the protein–small molecule surfactant interactions, determining ultimately the hydrophilic–lipophilic balance of the protein surface.     

STATISTICAL PROPERTIES OF LONG-RANGE CONTACTS IN GLOBULAR PROTEINS

The analysis of residue-residue contacts in protein structures can shed some light on our understanding of the folding and stability of proteins. In this paper, we study the statistical properties of long-range and short-range residue-residue contacts of 91 globular proteins using CSU software and analyze the importance of long-range contacts in globular protein structure. There are many short-range and long-range contacts in globular proteins, and it is found that the average number of long-range contacts per residue is 5.63 and the percentage of residue-residue contacts which are involved in long-range ones is 59.4%. In more detail, the distribution of long-range contacts in different residue intervals is investigated and it is found that the residues occurring in the interval range of 4-10 residues apart in the sequence contribute more long-range contacts to the stability of globular protein. The number of long-range contacts per residue, which is a measure of ability toform residue-residue contacts, is also calculated for 20 different amino acid residues. It is shown that hydrophobic residues (including Leu, Val, Ile, Met, Phe, Tyr, Cys and Trp) having a large number of long-range contacts easily form long-range contacts, while the hydrophilic amino acids (including Ala, Gly, Thr, His, Glu, Gln, Asp, Asn, Lys, Ser, Arg, and Pro) form long-range contacts with more difficulty. The relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of short-range and long-range contacts per residue for 20 amino acid residues is also studied. An approximately linear relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of long-range contacts per residue CL is found and can be expressed as     

Improved greedy algorithm for protein structure reconstruction

This article concerns the development of an improved greedy algorithm for protein structure reconstruction. Our stochastic greedy algorithm, which attempts to locate the ground state of an approximate energy function, exploits the fact that protein structures consist of overlapping structural building blocks that are not independent. Application of this approach to a series of 16 proteins with 50-250 amino acids leads to predicted models deviating from the experimental structures by 0.5 A RMSD using an RMSD-based energy function and within 1.5 to 4.8 A RMSD using a Go-based energy function. The Go-based results are significant because they illustrate the strength of combining structural fragments and stochastic greedy algorithms in capturing the native structures of proteins stabilized by long-range interactions separated by more than 30 amino acids. These results clearly open the door to less computationally demanding solutions to predict structures from sequences.     

Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.