Leslie A. Kuhn

Dimensionality reduction using genetic algorithms

Pattern recognition generally requires that objects be described in terms of a set of measurable features. The selection and quality of the features representing each pattern affect the success of subsequent classification. Feature extraction is the process of deriving new features from original features to reduce the cost of feature measurement, increase classifier efficiency, and allow higher accuracy. Many feature extraction techniques involve linear transformations of the original pattern vectors to new vectors of lower dimensionality. While this is useful for data visualization and classification efficiency, it does not necessarily reduce the number of features to be measured since each new feature may be a linear combination of all of the features in the original pattern vector. Here, we present a new approach to feature extraction in which feature selection and extraction and classifier training are performed simultaneously using a genetic algorithm. The genetic algorithm optimizes a feature weight vector used to scale the individual features in the original pattern vectors. A masking vector is also employed for simultaneous selection of a feature subset. We employ this technique in combination with the k nearest neighbor classification rule, and compare the results with classical feature selection and extraction techniques, including sequential floating forward feature selection, and linear discriminant analysis. We also present results for the identification of favorable water-binding sites on protein surfaces.

Protein flexibility predictions using graph theory

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond‐rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side‐chains from analysis of a single, static three‐dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase. Proteins 2001;44:150–165.

Transferrin receptor internalization sequence YXRF implicates a tight turn as the structural recognition motif for endocytosis

Using detailed functional studies on 24 human transferrin receptor mutants, we identified YXRF as the internalization sequence. Provided that at least 7 residues separate this tetrapeptide from the transmembrane region, changing the tetrapeptide position within the TR cytoplasmic domain does not reduce internalization activity. Thus, any conformational determinant for internalization must be localized to the YXRF sequence. Twenty-eight tetrapeptide analogs of YXRF, found by an unbiased search of all known three-dimensional protein structures, significantly favored tight turns similar to a type I turn. Of the ten tetrapeptides most closely related to YXRF, eight were surface exposed and had tight-turn conformations, as were four of five tetrapeptides with sequences related to the low density lipoprotein receptor internalization motif, NPXY. The internalization sequences of both receptors contain aromatic residues with intervening hydrogen-bonding residues. Thus, two distinct internalization sequences favor a common structural chemistry and implicate an exposed tight turn as the recognition motif for high efficiency endocytosis.

Target Flexibility: An Emerging Consideration in Drug Discovery and Design†

Department of General and Inorganic Chemistry, UniVersity of Parma, Via G.P. Usberti 17/A 43100, Parma, Italy, National Institute for Biosystems and Biostructures, Rome, Italy, Department of Medicinal Chemistry and Institute for Structural Biology & Drug DiscoVery, Virginia Commonwealth UniVersity, Richmond, Virginia 23298-0540, Department of Pharmaceutics, UniVersity of Parma, Via GP Usberti 27/A, 43100 Parma, Italy, High Performance Systems, CINECA Supercomputing Centre, Casalecchio di Reno, Bologna, Italy, Dulbecco Telethon Institute, Department of Chemistry, UniVersity of Modena and Reggio Emilia, Via Campi 183, 41100 Modena, Italy, Department of Mathematics and Natural Sciences, Pharmaceutical Institute, Christian-Albrechts-UniVersity, Gutenbergstrasse 76, 24118 Kiel, Germany, Departments of Biochemistry & Molecular Biology, Computer Science & Engineering, and Physics & Astronomy, Michigan State UniVersity, East Lansing, Michigan 48824-1319, Department of Molecular Biology, MB-5, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037-1000, Molecular Modeling and Bioinformatics Unit, Institute of Biomedical Research, Scientific Park of Barcelona, Department of Biochemistry and Molecular Biology, UniVersity of Barcelona, Josep Samitier 1-5, Barcelona 08028, Spain, Department of Experimental Medicine, UniVersity of Parma, Via Volturno, 39, 43100, Parma, Italy, Department of Chemical, Food, Pharmaceutical and Pharmacological Sciences, UniVersity of Piemonte Orientale “Amedeo AVogadro”, Via BoVio 6, 28100 NoVara, Italy, Institute of Pharmacy and Food Chemistry, UniVersity of Wurzburg, Am Hubland, D-97074 Wurzburg, Germany

Protein unfolding: Rigidity lost

We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of 〈r〉 = 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway.

Side-chain flexibility in protein–ligand binding: The minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side‐chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein–ligand complexes. Following analysis of protein side‐chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side‐chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side‐chain rotations to those experimentally observed. None of these proteins undergoes major main‐chain conformational change upon ligand binding, ensuring that side‐chain flexibility modeling is not required to compensate for main‐chain motions. Although more frugal in the number of side‐chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein–ligand interactions for the 20 proteins analyzed.

Virtual screening with solvation and ligand-induced complementarity

We present our database-screening tool SLIDE, which is capable of screening large data sets of organic compounds for potential ligands to a given binding site of a target protein. Its main feature is the modeling of induced complementarity by making adjustments in the protein side chains and ligand upon binding. Mean-field theory is used to balance the conformational changes in both molecules in order to generate a shape-complementary inter-face. Solvation is considered by prediction of water molecules likely to be conserved from the crystal structure of the ligand-free protein, and allowing them to mediate ligand interactions, if possible, or including a desolvation penalty when they are displaced by ligand atoms that do not replace the lost hydrogen bonds. A data set of over 175 000 organic molecules was screened for potential ligands to the progesterone receptor, dihydrofolate reductase, and a DNA-repair enzyme. In all cases the screening time was less than a day on a Pentium II processor, and known ligands as well as highly complementary new potential ligands were found.

The interdependence of protein surface topography and bound water molecules revealed by surface accessibility and fractal density measures

To characterize water binding to proteins, which is fundamental to protein folding, stability and activity, the relationships of 10,837 bound water positions to protein surface shape and residue type were analyzed in 56 high-resolution crystallographic structures. Fractal atomic density and accessibility algorithms provided an objective characterization of deep grooves in solvent-accessible protein surfaces. These deep grooves consistently had approximately the diameter of one water molecule, suggesting that deep grooves are formed by the interactions between protein atoms and bound water molecules. Protein surface topography dominates the chemistry and extent of water binding. Protein surface area within grooves bound three times as many water molecules as non-groove surface; grooves accounted for one-quarter of the total surface area yet bound half the water molecules. Moreover, only within grooves did bound water molecules discriminate between different side-chains. In grooves, main-chain surface was as hydrated as that of the most hydrophilic side-chains, Asp and Glu, whereas outside grooves all main and side-chains bound water to a similar, and much decreased, extent. This identification of the interdependence of protein surface shape and hydration has general implications for modelling and prediction of protein surface shape, recognition, local folding and solvent binding.

Protein flexibility and dynamics using constraint theory.

A new approach is presented for determining the rigid regions in proteins and the flexible joints between them. The short-range forces in proteins are modeled as constraints and we use a recently developed formalism from graph theory to analyze flexibility in the bond network. Forces included in the analysis are the covalent bond-stretching and bond-bending forces, salt bridges, and hydrogen bonds. We use a local function to associate an energy with individual hydrogen bonds, which then can be included or excluded depending on the bond strength. Colored maps of the rigid and flexible regions provide a direct visualization of where the motion of the protein can take place, consistent with these distance constraints. We also define a flexibility index that quantifies the local density of flexible or floppy modes, in terms of the dihedral angles that remain free to rotate in each flexible region. A negative flexibility index provides a measure of the density of redundant bonds in rigid regions. A new application of this approach is to simulate the maximal range of possible motions of the flexible regions by introducing Monte Carlo changes in the free dihedral angles, subject to the distance constraints. This is done using a method that maintains closure of the rings formed by covalent and hydrogen bonds in the flexible parts of the protein, and van der Waals overlaps between atoms are avoided. We use the locus of the possible motions of HIV protease as an example: movies of its motion can be seen at http://www.pa.msu.edu/~lei.

Identifying protein folding cores from the evolution of flexible regions during unfolding

The unfolding of a protein can be described as a transition from a predominantly rigid, folded structure to an ensemble of denatured states. During unfolding, the hydrogen bonds and salt bridges break, destabilizing the secondary and tertiary structure. Our previous work shows that the network of covalent bonds, salt bridges, hydrogen bonds, and hydrophobic interactions forms constraints that define which regions of the native protein are flexible or rigid (structurally stable). Here, we test the hypothesis that information about the folding pathway is encoded in the energetic hierarchy of non-covalent interactions in the native-state structure. The incremental thermal denaturation of protein structures is simulated by diluting the network of salt bridges and hydrogen bonds, breaking them one by one, from weakest to strongest. The structurally stable and flexible regions are identified at each step, providing information about the evolution of flexible regions during denaturation. The folding core, or center of structure formation during folding, is predicted as the region formed by two or more secondary structures having the greatest stability against denaturation. For 10 proteins with different architectures, we show that the predicted folding cores from this flexibility/stability analysis are in good agreement with those identified by native-state hydrogen-deuterium exchange experiments.