Neural networks to study invariant features of protein folding

Protein secondary structures result both from short-range and long-range interactions. Here neural networks are used to implement a procedure to detect regions of the protein backbone where local interactions have an overwhelming effect in determining the formation of stretches in α-helical conformation. Within the framework of a modular view of protein folding we have argued that these structures correspond to the initiation sites of folding. The hypothesis to be tested in this paper is that sequence identity beside ensuring similarity of the three-dimensional conformation also entails similar folding mechanisms. In particular, we compare the location and sequence variability of the initiation sites extracted from a set of proteins homologous to horse heart cytochrome c. We present evidence that the initiation sites conserve their position in the aligned sequences and exhibit a more reduced variability in the residue composition than the rest of the protein. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

A statistical analytical approach to predict the secondary structure of proteins from amino acid sequence information

A statistical analytical approach has been used to analyze the secondary structure (SS) of amino acids as a function of the sequence of amino acid residues. We have used 306 non-homologous best-resolved protein structures from the Protein Data Bank for the analysis. A sequence region of 32 amino acids on either side of the residue is considered in order to calculate single amino acid propensities, di-amino acid potentials and tri-amino acid potentials. A weighted sum of predictions obtained using these properties is used to suggest a final prediction method. Our method is as good as the best-known SS prediction methods, is the simplest of all the methods, and uses no homologous sequence/family alignment data, yet gives 72% SS prediction accuracy. Since the method did not use many other factors that may increase the prediction accuracy there is scope to achieve greater accuracy using this approach. Received: 4 May 1998 / Accepted: 17 September 1998 / Published online: 10 December 1998     

SeqFold – fully automated fold recognition and modeling software – evaluation and application

SeqFold is a fold recognition program based on sequence-similarity detection aided by predicted secondary structure [1–3]. Critical validation and evaluation of SeqFold fold recognition performance based on the latest Critical Assessment of protein Structure Prediction (CASP2) targets has been performed. It has revealed that four out of seven CASP2 threading targets were assigned a correct fold using this method. SeqFold has also been applied to the problem of fold recognition for leptin. Mice with a defective leptin gene are extremely obese and diabetic. Leptin does not exhibit clear sequence homology to any protein with known structure. SeqFold predicts that leptin belongs to the class of short-chain four-helical cytokines. The structure of leptin, which has recently been solved by X-ray crystallography, reveals that leptin is a long-chain four-helical cytokine. The 3D model of leptin demonstrates that SeqFold alignment-based homology modeling captures essential features of the leptin structure. Received: 25 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Prediction of stability changes upon single-site mutations using database-derived potentials

One of the purposes of studying protein stability changes upon mutations is to get information about the dominating interactions that drive folding and stabilise the native structure. With this in mind, we present a method that predicts folding free-energy variations caused by point mutations using combinations of two types of database-derived potentials, i.e. backbone torsion-angle potentials and distance potentials, describing local and non-local interactions along the chain, respectively. The method is applied to evaluate the folding free-energy changes of 344 single-site mutations introduced in six different proteins and a synthetic peptide. We found that the relative importance of local versus non-local interactions along the chain is essentially a function of the solvent accessibility of the mutated residues. For the subset of totally buried residues, the optimal potential is the sum of a distance potential and a torsion potential weighted by a factor of 0.4. This combination yields a correlation coefficient between measured and computed changes in folding free energy of 0.80. For mutations of partially buried residues, the best potential is the sum of a torsion potential and a distance potential weighted by 0.7. For fully accessible residues, the torsion potentials taken alone perform best, reaching correlation coefficients of 0.87 on all but 10 mutations; the excluded mutations seem to modify the backbone structure or to involve interactions that are atypical for the surface. These results show that the relative weight of non-local interactions along the sequence decreases as the solvent accessibility of the mutated residue increases, and vanishes at the protein surface. On the contrary, the weight of local interactions increases with solvent accessibility. The latter interactions are nevertheless never negligible, even for the most buried residues. Received: 20 May 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

Towards an order-N DFT method

One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential. Received: 30 March 1998 / Accepted: 6 July 1998 / Published online: 15 September 1998     

Superposition of nonorthogonal Slater determinants towards electron correlation problems

We propose variational and nonvariational methods based on the superposition of nonorthogonal Slater determinants. Properties of the reference functions are discussed. In the nonorthogonal configuration interaction method, all the excited configurations of multiple determinants are integrated into a variational space. An efficient way to manipulate matrix elements over determinants of distinct vacuums is presented by introducing similarity transformed operator and bracket transformations. The method enables us to map a matrix multiplication in the nonorthogonal problem to an orthogonal one, and thus maintains a fundamental scaling property along with the amount of data processed in the corresponding orthogonal configuration interaction method. Furthermore, we discuss a coupled-cluster theory employing a vacuum-dependent wave operator, which is entirely size consistent as well as core extensive. These methods are applied to H₂O + nHe(n = 0−2) and a single-bond dissociation of the HF molecule, compared with conventional methods including full and multireference configuration interaction methods. Received: 7 July 1997 / Accepted: 12 September 1997     

“Topohydrophobic positions” as key markers of globular protein folds

The positions of a given fold always occupied by strong hydrophobic amino acids (V, I, L, F, M, Y, W), which we call “topohydrophobic positions”, were detected and their properties demonstrated within 153 non-redundant families of homologous domains, through 3D structural alignments. Sets of divergent sequences possessing at least four to five members appear to be as informative as larger sets, provided that their mean pairwise sequence identity is low. Amino acids in topohydrophobic positions exhibit several interesting features: they are much more buried than their equivalents in non-topohydrophobic positions, their side chains are far less dispersed; and they often constitute a lattice of close contacts in the inner core of globular domains. In most cases, each regular secondary structure possesses one to three topohydrophobic positions, which cluster in the domain core. Moreover, using sensitive alignment processes such as hydrophobic cluster analysis (HCA), it is possible to identify topohydrophobic positions from only a small set of divergent sequences. Amino acids in topohydrophobic positions, which can be identified directly from sequences, constitute key markers of protein folds, define long-range structural constraints, which, together with secondary structure predictions, limit the number of possible conformations for a given fold. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

A new “hydrophobic template” method detects segments forming transmembrane α-helical bundles in ion channels

We present a “hydrophobic template” method enabling recognition of α-helix bundles in membrane channels from sequence analysis. Inspection of hydrophobic properties of pore-forming helices in proteins with known structure (A-B₅ toxins) permits delineation of a common polarity motif: two hydrophobic surface stretches separated by polar areas. The bundles are stabilized by nonpolar interhelical contacts. A number of transmembrane segments were checked for presence of this motif, and it was detected for pore-forming helices of several ion transporters (segments M2 of acetylcholine and GABA_A receptors, α5 peptide of δ-endotoxin), which reveal five α-helix bundle architecture. Applications of the method to modeling of membrane channels are discussed. Received: 24 April 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

Excited states of acetylene: a CASPT2 study

Valence and low-lying Rydberg states of acetylene (C₂H₂) are reexamined in the singlet as well as in the triplet manifold. The major goal of this work is a better understanding of the valence states that contribute to the low-energy electron-energy-loss spectrum recorded under conditions where transitions to triplet states are enhanced. An appropriate theoretical treatment of these states has to include the low-lying Rydberg states because of their energetic proximity to some of the valence states. The CASSCF/CASPT2 method provides a suitable framework for such a task. For some important states the geometry was optimized at the CASPT2 level to allow a comparison with the results of other highly accurate methods that have been applied to acetylene in the past. Received: 11 June 1998 /Accepted: 30 July 1998 / Published online: 19 October 1998     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

Molecular modeling study of an abasic DNA undecamer duplex: d(GCGTGOGTGCG) · d(CGCACTCACGC)

Molecular mechanics calculations were performed with the JUMNA program on d(GCGTGOGTGCG) · d(CGCACTCACGC) where “O” is a modified abasic site: 3-hydroxy-2-(hydroxymethyl)tetrahydrofuran. From energy minimizations, for intrahelical or extrahelical positions of the unpaired thymine, various structures with different curvatures were obtained. Dynamical properties of this abasic sequence were also investigated through the controlled studies of DNA bending. Poisson-Boltzmann calculations were used to mimic the electrostatic effect of solvent on this sequence. The lowest energy structures show an acceptable agreement with experimental data. Received: 1 June 1998 / Accepted: 17 September 1998 / Published online: 10 December 1998     

How possible is the detection of correlated mutations?

The remarkable conservation of protein structure, compared to that of sequences, suggests that, in the course of evolution, residue substitutions which tend to destabilise a particular structure must be compensated by other substitutions that confer greater stability on that structure. Given the compactness of proteins, spatially close residues are expected to undergo the compensatory process. Surprisingly, approaches designed to detect such correlated changes have led, until now, only to limited success in detecting pairs of residues adjacent in the three-dimensional structures. We have undertaken, by simulating the evolution of DNA sequences including sites mutating in a correlated manner, to analyse whether such poor results can be attributed to the detection methods or if this failure could result from a compensatory process more complex than that implicitly underlying the different approaches. Present results show that only methods taking into account the phylogenetic reconstruction can lead to correct detection. Received: 24 April 1998 / Accepted: 8 August 1998 / Published online: 11 November 1998     

Molecular dynamics simulations of the isolated domain 1 of annexin I

Annexin molecules consist of a symmetrical arrangement of four domains of identical folds but very different sequences. Nuclear magnetic resonance (NMR) experiments on the isolated domains of annexin I in aqueous solution have indicated that domain 1 retains its native structure whereas domain 2 unfolds. Therefore these two domains constitute interesting models for comparative simulations of structural stability using molecular dynamics. Here we present the preliminary results of molecular dynamics simulations of the isolated domain 1 in explicit water at 300 K, using two different simulation protocols. For the first, domain 1 was embedded in a 46 ? cubic box of water. A group-based non-bonded cut-off of 9 ? with a 5–9 ? non-bonded switching function was used and a 2 fs integration step. Bonds containing hydrogens were constrained with the SHAKE algorithm. These conditions led to unfolding of the domain within 400 ps at 300 K. In the second protocol, the domain was embedded in a 62 ? cubic box of water. An atom-based non-bonded cut-off of 8–12 ? using a force switching function for electrostatics and a shifting function for van der Waals interactions were used with a 1 fs integration step. This second protocol led to a native-like conformation of the domain in accord with the NMR data which was stable over the whole trajectory (∼2 ns). A small, but well-defined relaxation of the structure, from that observed for the same domain in the entire protein, was observed. This structural relaxation is described and methodological aspects are discussed. Received: 10 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Covalent imprinted polymer for selective and rapid enrichment of ractopamine by a noncovalent approach

A novel molecularly imprinted polymer (MIP) for the separation and concentration of ractopamine (RAC) was prepared by a covalent imprinting approach and the template was removed successfully by hydrolysis, so that four carboxylic acid groups were left in the cavities and could specifically rebind RAC through noncovalent interaction: hydrogen bonding. The conditions for synthesis of the MIP were optimized during the polymerization process, and a molar ratio of template–functional monomer complexes to cross-linker of 1:3 was confirmed. The adsorption capacity of the MIP was 4.1-fold that of the nonimprinted polymer, and the adsorption reaction reached equilibrium after 25 min at 50 mg L^-1 concentration. The results of the competitive adsorption test showed that the MIPs had specific recognition ability for the analyte RAC. In addition, the important factors affecting the efficiency of the method which was developed using the MIPs as a solid-phase sorbent for separation and determination of RAC combined with high-performance liquid chromatography with fluorescence detection were optimized. Under the optimum experimental conditions, the linear range of the calibration curve in the method was 0.05-5 μg L^-1 (R ² = 0.98) and the limit of detection (signal-to-noise ratio of 3) was 0.01 μg L^-1. The proposed method was applied to determination of RAC in spiked feedstuffs and urine samples, with recoveries ranging from 74.17 to 114.46% and relative standard deviation (n = 3) below 4.55 in all cases.     

Theoretical pKa calculations of proteins; the tyrosine and lysine residues of b-elicitin

Elicitins are small proteins that are secreted by plant pathogenic fungi. In this work we have used a computer program that utilizes the boundary element method for heterogeneous dielectrics with ionic strength to calculate the pK _a of all titrating groups in the 98-residue protein β-cryptogein. Our results are in reasonable agreement with the experimentally determined pK _a values for the Tyr residues in the protein. We find that the functionally important Lys13 residue has a normal pK _a of 10.3. Our work also shows that there is no direct correlation between the exposure of an amino acid sidechain and its pK _a. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

Grid-free DFT implementation of local and gradient-corrected XC functionals

Following an approach to density functional theory calculations based on the matrix representation of operators, we implemented a scheme as an alternative to traditional grid-based methods. These techniques allow integrals over exchange-correlation operators to be evaluated through matrix manipulations. Both local and gradient-corrected functionals can be treated in a similar way. After deriving all the required expressions, selected examples with various functionals are given. Received: 7 March 1998 / Accepted: 21 May 1998 / Published on line: 6 August 1998     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Dynamics of the transmembrane domain of the ErbB-2 receptor

The structure and dynamics of the ErbB-2 transmembrane domain have been examined using molecular dynamics techniques both in vacuum and within an explicit hydrated L-α-dilauroyl-phosphatidyl-ethanolamine environment. In-vacuum simulations show that a highly cooperative structural transition occurs frequently within the α-helical transmembrane domain which converts to local π-helices. We show that the α-helix alteration does not depend upon the force field or initial side-chain conformations but is intimately related to the sequence. The membrane-like environment does not prevent the structural transition in the helix but slows down the peptide dynamics indicating that the appearance of a π-bulge is not an artifact of the vacuum approximation. The consequences of π-helix formation could be very huge for the ErbB-2 receptor which is involved in numerous human cancers and also for other membrane proteins wherein similar local structures are also observed experimentally. Received: 9 May 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Multireference perturbation CI III. Fast evaluation of the one-particle density matrix

Within the frame of multireference perturbation configuration interaction we have developed a fast algorithm, based on diagrammatic techniques, for the calculation of the first-order correction to the one-particle density matrix. As an example of an application we have chosen the evaluation of the dipole moment of the CO molecule, where utilization of the first-order density is shown to corroborate the variational calculation. Received: 4 August 1998 / Accepted: 21 September 1998 / Published online: 16 November 1998