The burial of hydrophobic amino acids in the protein core is a driving force in protein folding. The extent to which an amino acid interacts with the solvent and the protein core is naturally proportional to the surface area exposed to these environments. However, an accurate calculation of the solvent-accessible surface area (SASA), a geometric measure of this exposure, is numerically demanding as it is not pair-wise decomposable. Furthermore, it depends on a full-atom representation of the molecule. This manuscript introduces a series of four SASA approximations of increasing computational complexity and accuracy as well as knowledge-based environment free energy potentials based on these SASA approximations. Their ability to distinguish correctly from incorrectly folded protein models is assessed to balance speed and accuracy for protein structure prediction. We find the newly developed “Neighbor Vector” algorithm provides the most optimal balance of accurate yet rapid exposure measures.

Clustering algorithms are used as data analysis tools in a wide variety of applications in Biology. Clustering has become especially important in protein structure prediction and virtual high throughput screening methods. In protein structure prediction, clustering is used to structure the conformational space of thousands of protein models. In virtual high throughput screening, databases with millions of drug-like molecules are organized by structural similarity, e.g. common scaffolds. The tree-like dendrogram structure obtained from hierarchical clustering can provide a qualitative overview of the results, which is important for focusing detailed analysis. However, in practice it is difficult to relate specific components of the dendrogram directly back to the objects of which it is comprised and to display all desired information within the two dimensions of the dendrogram. The current work presents a hierarchical agglomerative clustering method termed bcl::Cluster. bcl::Cluster utilizes the Pymol Molecular Graphics System to graphically depict dendrograms in three dimensions. This allows simultaneous display of relevant biological molecules as well as additional information about the clusters and the members comprising them.

The topology of most experimentally determined protein domains is defined by the relative arrangement of secondary structure elements, i.e. α-helices and β-strands, which make up 50–70% of the sequence. Pairing of β-strands defines the topology of β-sheets. The packing of side chains between α-helices and β-sheets defines the majority of the protein core. Often, limited experimental datasets restrain the position of secondary structure elements while lacking detail with respect to loop or side chain conformation. At the same time the regular structure and reduced flexibility of secondary structure elements make these interactions more predictable when compared to flexible loops and side chains. To determine the topology of the protein in such settings, we introduce a tailored knowledge-based energy function that evaluates arrangement of secondary structure elements only. Based on the amino acid Cβ atom coordinates within secondary structure elements, potentials for amino acid pair distance, amino acid environment, secondary structure element packing, β-strand pairing, loop length, radius of gyration, contact order and secondary structure prediction agreement are defined. Separate penalty functions exclude conformations with clashes between amino acids or secondary structure elements and loops that cannot be closed. Each individual term discriminates for native-like protein structures. The composite potential significantly enriches for native-like models in three different databases of 10,000–12,000 protein models in 80–94% of the cases. The corresponding application, “BCL::ScoreProtein,” is available at www.meilerlab.org.

Computational de novo protein structure prediction is limited to small proteins of simple topology. The present work explores an approach to extend beyond the current limitations through assembling protein topologies from idealized α-helices and β-strands. The algorithm performs a Monte Carlo Metropolis simulated annealing folding simulation. It optimizes a knowledge-based potential that analyzes radius of gyration, β-strand pairing, secondary structure element (SSE) packing, amino acid pair distance, amino acid environment, contact order, secondary structure prediction agreement and loop closure. Discontinuation of the protein chain favors sampling of non-local contacts and thereby creation of complex protein topologies. The folding simulation is accelerated through exclusion of flexible loop regions further reducing the size of the conformational search space. The algorithm is benchmarked on 66 proteins with lengths between 83 and 293 amino acids. For 61 out of these proteins, the best SSE-only models obtained have an RMSD100 below 8.0 Å and recover more than 20% of the native contacts. The algorithm assembles protein topologies with up to 215 residues and a relative contact order of 0.46. The method is tailored to be used in conjunction with low-resolution or sparse experimental data sets which often provide restraints for regions of defined secondary structure.

The concept of hydrophobicity is critical to our understanding of the principles of membrane protein folding, structure, and function. In the last decades several groups have derived hydrophobicity scales using both experimental and statistical methods that are optimized to mimic certain natural phenomena as closely as possible. The present work adds to this toolset the first knowledge-based scale that unifies the characteristics of both, α-helical and β-barrel multi-span membrane proteins. This Unified Hydrophobicity Scale (UHS) distinguishes between amino acid preference for solution, transition, and trans-membrane states. The scale represents average hydrophobicity values of amino acids in folded proteins, irrespective of their secondary structure type. We furthermore present the first knowledge-based hydrophobicity scale for mammalian α-helical MPs (Mammalian Hydrophobicity Scale -MHS). Both scales are particularly useful for computational protein structure elucidation, for example as input for machine learning techniques, such as secondary structure or trans-membrane span prediction, or as reference energies for protein structure prediction or protein design. The knowledge-based UHS shows a striking similarity to a recent experimental hydrophobicity scale introduced by Hessa and co-workers. Convergence of two very different approaches onto similar hydrophobicity values consolidates the major differences between experimental and knowledge-based scales observed in earlier studies. Moreover, the UHS scale represents an accurate absolute free energy measure for folded, multispan membrane proteins -a feature that is absent from many existing scales. The utility of the UHS was demonstrated by analyzing a series of diverse MPs. It is further shown that the UHS outperforms nine established hydrophobicity scales in predicting trans-membrane spans along the protein sequence. The accuracy of the present hydrophobicity scale profits from the doubling of the number of integral membrane proteins in the PDB over the past years. The UHS paves the way for an increased accuracy in the prediction of trans-membrane spans.

Prediction of transmembrane spans and secondary structure from the protein sequence is generally the first step in the structural characterization of (membrane) proteins. Preference of a stretch of amino acids in a protein to form secondary structure and being placed in the membrane are correlated. Nevertheless, current methods predict either secondary structure or individual transmembrane states. We introduce a method that simultaneously predicts the secondary structure and transmembrane spans from the protein sequence. This approach not only eliminates the necessity to create a consensus prediction from possibly contradicting outputs of several predictors but bears the potential to predict conformational switches, i.e., sequence regions that have a high probability to change for example from a coil conformation in solution to an α-helical transmembrane state. An artificial neural network was trained on databases of 177 membrane proteins and 6048 soluble proteins. The output is a 3 × 3 dimensional probability matrix for each residue in the sequence that combines three secondary structure types (helix, strand, coil) and three environment types (membrane core, interface, solution). The prediction accuracies are 70.3% for nine possible states, 73.2% for three-state secondary structure prediction, and 94.8% for three-state transmembrane span prediction. These accuracies are comparable to state-of-the-art predictors of secondary structure (e.g., Psipred) or transmembrane placement (e.g., OCTOPUS). The method is available as web server and for download at www.meilerlab.org.

Summary Membrane protein structure determination remains a challenging endeavor. Computational methods that predict membrane protein structure from sequence can potentially aid structure determination for such difficult target proteins. The de novo protein structure prediction method, BCL::Fold, rapidly assembles secondary structure elements into 3-dimensional models. Here we describe modifications to the algorithm, named BCL::MP-Fold, in order to simulate membrane protein folding. Models are built into a static membrane object and are evaluated using a knowledge-based energy potential, which has been modified to account for the membrane environment. Additionally, a new symmetry folding mode allows for the prediction of obligate homomultimers, a common property amongst membrane proteins. In a benchmark test of 40 proteins of known structure, the method samples the correct topology in 34 cases. This demonstrates that the algorithm can accurately predict protein topology without the need for large multiple sequence alignments, homologous template structures, or experimental restraints.

For many membrane proteins, the determination of their topology remains a challenge for methods like X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. Electron paramagnetic resonance (EPR) spectroscopy has evolved as an alternative technique to study structure and dynamics of membrane proteins. The present study demonstrates the feasibility of membrane protein topology determination using limited EPR distance and accessibility measurements. The BCL::MP-Fold algorithm assembles secondary structure elements (SSEs) in the membrane using a Monte Carlo Metropolis (MCM) approach. Sampled models are evaluated using knowledge-based potential functions and agreement with the EPR data and a knowledge-based energy function. Twenty-nine membrane proteins of up to 696 residues are used to test the algorithm. The protein-size-normalized root-mean-square-deviation (RMSD100) value of the most accurate model is better than 8 Å for twenty-seven, better than 6 Å for twenty-two, and better than 4 Å for fifteen out of twenty-nine proteins, demonstrating the algorithm’s ability to sample the native topology. The average enrichment could be improved from 1.3 to 2.5, showing the improved discrimination power by using EPR data.