Properties of integral membrane protein structures: derivation of an implicit membrane potential

Distributions of each amino acid in the trans-membrane domain were calculated as a function of the membrane normal using all currently available alpha-helical membrane protein structures with resolutions better than 4 A. The results were compared with previous sequence- and structure-based analyses. Calculation of the average hydrophobicity along the membrane normal demonstrated that the protein surface in the membrane domain is in fact much more hydrophobic than the protein core. While hydrophobic residues dominate the membrane domain, the interfacial regions of membrane proteins were found to be abundant in the small residues glycine, alanine, and serine, consistent with previous studies on membrane protein packing. Charged residues displayed nonsymmetric distributions with a preference for the intracellular interface. This effect was more prominent for Arg and Lys resulting in a direct confirmation of the positive inside rule. Potentials of mean force along the membrane normal were derived for each amino acid by fitting Gaussian functions to the residue distributions. The individual potentials agree well with experimental and theoretical considerations. The resulting implicit membrane potential was tested on various membrane proteins as well as single trans-membrane alpha-helices. All membrane proteins were found to be at an energy minimum when correctly inserted into the membrane. For alpha-helices both interfacial (i.e. surface bound) and inserted configurations were found to correspond to energy minima. The results demonstrate that the use of trans-membrane amino acid distributions to derive an implicit membrane representation yields meaningful residue potentials.     

Prediction of secondary structural content of proteins from their amino acid composition alone. I. New analytic vector decomposition methods

The predictive limits of the amino acid composition for the secondary structural content (percentage of residues in the secondary structural states helix, sheet, and coil) in proteins are assessed quantitatively. For the first time, techniques for prediction of secondary structural content are presented which rely on the amino acid composition as the only information on the query protein. In our first method, the amino acid composition of an unknown protein is represented by the best (in a least square sense) linear combination of the characteristic amino acid compositions of the three secondary structural types computed from a learning set of tertiary structures. The second technique is a generalization of the first one and takes into account also possible compositional couplings between any two sorts of amino acids. Its mathematical formulation results in an eigenvalue/eigenvector problem of the second moment matrix describing the amino acid compositional fluctuations of secondary structural types in various proteins of a learning set. Possible correlations of the principal directions of the eigenspaces with physical properties of the amino acids were also checked. For example, the first two eigenvectors of the helical eigenspace correlate with the size and hydrophobicity of the residue types respectively. As learning and test sets of tertiary structures, we utilized representative, automatically generated subsets of Protein Data Bank (PDB) consisting of non-homologous protein structures at the resolution thresholds ≤1.8Å, ≤2.0Å, ≤2.5Å, and ≤3.0Å. We show that the consideration of compositional couplings improves prediction accuracy, albeit not dramatically. Whereas in the self-consistency test (learning with the protein to be predicted), a clear decrease of prediction accuracy with worsening resolution is observed, the jackknife test (leave the predicted protein out) yielded best results for the largest dataset (≤3.0 Å, almost no difference to the self-consistency test!), i.e., only this set, with more than 400 proteins, is sufficient for stable computation of the parameters in the prediction function of the second method. The average absolute error in predicting the fraction of helix, sheet, and coil from amino acid composition of the query protein are 13.7, 12.6, and 11.4%, respectively with r.m.s. deviations in the range of 8.6 ÷ 11.8% for the 3.0 Å dataset in a jackknife test. The absolute precision of the average absolute errors is in the range of 1 ÷ 3% as measured for other representative subsets of the PDB. Secondary structural content prediction methods found in the literature have been clustered in accordance with their prediction accuracies. To our surprise, much more complex secondary structure prediction methods utilized for the same purpose of secondary structural content prediction achieve prediction accuracies very similar to those of the present analytic techniques, implying that all the information beyond the amino acid composition is, in fact, mainly utilized for positioning the secondary structural state in the sequence but not for determination of the overall number of residues in a secondary structural type. This result implies that higher prediction accuracies cannot be achieved relying solely on the amino acid composition of an unknown query protein as prediction input. Our prediction program SSCP has been made available as a World Wide Web and E-mail service. © 1996 Wiley-Liss, Inc.     

How do potentials derived from structural databases relate to “true” potentials?

Knowledge-based potentials are used widely in protein folding and inverse folding algorithms. Two kinds of derivation methods are used. (1) The interactions in a database of known protein structures are assumed to obey a Boltzmann distribution. (2) The stability of the native folds relative to a manifold of misfolded structures is optimized. Here, a set of previously derived contact and secondary structure propensity potentials, taken as the \"true\" potentials, are employed to construct an artificial protein structural database from protein fragments. Then, new sets of potentials are derived to see how they are related to the true potentials. Using the Boltzmann distribution method, when the stability of the structures in the database lies within a certain range, both contact potentials and secondary structure propensities can be derived separately with remarkable accuracy. In general, the optimization method was found to be less accurate due to errors in the \"excess energy\" contribution. When the excess energy terms are kept as a constraint, the true potentials are recovered exactly.     

Fold recognition and ab initio structure predictions using hidden markov models and β-strand pair potentials

Protein structure predictions were submitted for 9 of the target sequences in the competition that ran during 1994. Targets sequences were selected that had no known homology with any sequence of known structure and were members of a reasonably sized family of related but divergent sequences. The objective was either to recognize a compatible fold for the target sequence in the database of known structures or to predict ab initio its rough 3D topology. The main tools used were Hidden Markov models (HMM) for fold recognition, a β- strand pair potential to predict β-sheet topology, and the PHD server for secondary structure prediction. Compatible folds were correctly identified in a number of cases and the β-strand pair potential was shown to be a useful tool for ab initio topology prediction. © 1995 Wiley-Liss, Inc.