Activity Landscapes, Information Theory, and Structure - Activity Relationships.

Activity landscapes provide a comprehensive description of structure-activity relationships (SARs). An information theoretic assessment of their features, namely, activity cliffs, similarity cliffs, smooth-SAR, and featureless regions, is presented based on the probability of occurrence of these features. It is shown that activity cliffs provide highly informative SARs compared to smooth-SAR regions, although the latter are the basis for most QSAR studies. This follows since small structural changes in the former are coupled with relatively large changes in activity, thus pinpointing specific structural features associated with the changes in activity. In contrast, Smooth-SAR regions are typically associated with relatively small changes in both structure and activity. Surprisingly, similarity cliffs, which occur when both compounds in a compound-pair have approximately equal activities but significantly different structures, are the most prevalent feature of activity landscapes. Hence, from an information theoretic point of view, they are the least informative landscape feature. Nevertheless, similarity cliffs do provide SAR information on potentially new active compound classes, and in that sense they are quite useful in drug discovery programs since they provide alternative possibilities should ADMET or other issues arise during the discovery and earlier preclinical development phases of drug research.

Comparing protein structures: a Gaussian-based approach to the three-dimensional structural similarity of proteins.

This study describes a new method for comparing three-dimensional protein structures based on an optimal alignment of their steric fields. The method is based upon the use of spherical Gaussian functions located on individual atoms. This representation generates a flexible description of the underlying fold geometry of proteins that can be adjusted by changing the 'width' of the Gaussians. Reducing the width sharpens the representation and leads to a more 'atomlike' description; increasing the width creates a fuzzier representation that preserves the general shape features of the chain fold but with a consequent loss in atomic resolution. The width used in this study is based upon the features of individual atoms and provides a representation that is quite robust with respect to the variety of geometric features typically encountered in the alignment process. In addition, a post-alignment analysis is performed that generates sequence alignments from the corresponding structure alignments. An example, based on five mammalian and fungal matrix metalloproteinase crystal structures (human fibroblast collagenase, neutrophil collagenase, stromelysin, astacin, and adamalysin), illustrates a number of features of the Gaussian-based approach.

A molecular-field-based similarity study of non-nucleoside HIV-1 reverse transcriptase inhibitors. 2. The relationship between alignment solutions obtained from conformationally rigid and flexible matching.

An analysis of the relationship among alignment solutions obtained from field-based matching of a representative set of rigid conformers of three non-nucleoside HIV-1 reverse transcriptase inhibitors and solutions obtained from flexible matching of the same conformers is presented. In some cases, different alignment solutions obtained from rigid matching converge to the same solution when conformational rigidity is relaxed, indicating that a reduced set of conformers per molecule may be sufficient in many field-based similarity studies. Furthermore, the results also indicate the importance of going beyond the pairwise similarity level to obtain consistent solutions in flexible-matching studies. In this respect, the best conformationally flexible multi-molecule alignment obtained is found to be in good agreement with the relative binding geometry and orientation found experimentally from protein-ligand crystal structures. The rms separation between corresponding atoms in computed and 'experimental' sets of three inhibitor structures is 0.94 A.

Field-based similarity forcing in energy minimization and molecular matching.

A new field-based similarity forcing procedure for matching conformationally-flexible molecules is presented. The method extends earlier work on similarity matching of molecules based upon the program MIMIC, by directly coupling a similarity function to a molecular mechanics force field. In this way conformational energetics are fully accounted for in the similarity matching process. Simultaneous similarity/conformational searches can then be undertaken within a Monte Carlo or molecular dynamics framework. Here, a Monte Carlo approach is used to provide a simple example of two HIV-1 reverse transcriptase inhibitors, nevirapine and alpha APA, that illustrates the basic characteristics of the method and suggests areas for further investigation.

A molecular-field-based similarity study of non-nucleoside HIV-1 reverse transcriptase inhibitors.

This article describes a molecular-field-based similarity method for aligning molecules by matching their steric and electrostatic fields and an application of the method to the alignment of three structurally diverse non-nucleoside HIV-1 reverse transcriptase inhibitors. A brief description of the method, as implemented in the program MIMIC, is presented, including a discussion of pairwise and multi-molecule similarity-based matching. The application provides an example that illustrates how relative binding orientations of molecules can be determined in the absence of detailed structural information on their target protein. In the particular system studied here, availability of the X-ray crystal structures of the respective ligand-protein complexes provides a means for constructing an 'experimental model' of the relative binding orientations of the three inhibitors. The experimental model is derived by using MIMIC to align the steric fields of the three protein P66 subunit main chains, producing an overlay with a 1.41 A average rms distance between the corresponding C alpha's in the three chains. The inter-chain residue similarities for the backbone structures show that the main-chain conformations are conserved in the region of the inhibitor-binding site, with the major deviations located primarily in the 'finger' and RNase H regions. The resulting inhibitor structure overlay provides an experimental-based model that can be used to evaluate the quality of the direct a priori inhibitor alignment obtained using MIMIC. It is found that the 'best' pairwise alignments do not always correspond to the experimental model alignments. Therefore, simply combining the best pairwise alignments will not necessarily produce the optimal multi-molecule alignment. However, the best simultaneous three-molecule alignment was found to reproduce the experimental inhibitor alignment model. A pairwise consistency index has been derived which gauges the quality of combining the pairwise alignments and aids in efficiently forming the optimal multi-molecule alignment analysis. Two post-alignment procedures are described that provide information on feature-based and field-based pharmacophoric patterns. The former corresponds to traditional pharmacophore models and is derived from the contribution of individual atoms to the total similarity. The latter is based on molecular regions rather than atoms and is constructed by computing the percent contribution to the similarity of individual points in a regular lattice surrounding the molecules, which when contoured and colored visually depict regions of highly conserved similarity. A discussion of how the information provided by each of the procedures is useful in drug design is also presented.

Domain structural class prediction.

The structural class of a protein domain can be approximately predicted according to its amino acid composition. However, can the prediction quality be improved by taking into account the coupling effect among different amino acid components? This question has evoked much controversy because completely different conclusions have been obtained by different investigators. To resolve such a perplexing problem, predictions by means of various algorithms were performed based on the SCOP database (Murzin et aL, 1995), which is more natural and reliable for the study of structural classes because it is based on evolutionary relationships and on the principles that govern their three-dimensional structure. The results obtained using both resubstitution and jackknife tests indicated that the overall rates of correct prediction by an algorithm incorporating the coupling effect among different amino acid components were significantly higher than those by the algorithms that did not include such an effect. A completely consistent conclusion was also obtained when tests were performed on two large independent testing datasets classified into four and seven structural classes, respectively. It is revealed through an analysis that the reasons for reaching the opposite conclusion are mainly due to (1) misclassifying structural classes according to a conceptually incorrect rule, (2) misapplying the component-coupled algorithm by ignoring some important factors and (3) misrepresenting structural classes with statistically insignificant training subsets. Clarification of these problems would be instructive for effectively using the prediction algorithm and correctly interpreting the results.

Prediction and classification of domain structural classes.

Can the coupling effect among different amino acid components be used to improve the prediction of protein structural classes? The answer is yes according to the study by Chou and Zhang (Crit. Rev. Biochem. Mol. Biol. 30:275-349, 1995), but a completely opposite conclusion was drawn by Eisenhaber et al. when using a different dataset constructed by themselves (Proteins 25:169-179, 1996). To resolve such a perplexing problem, predictions were performed by various approaches for the datasets from an objective database, the SCOP database (Murzin, Brenner, Hubbard, and Chothia. J. Mol. Biol. 247:536-540, 1995). According to SCOP, the classification of structural classes for protein domains is based on the evolutionary relationship and on the principles that govern the 3D structure of proteins, and hence is more natural and reliable. The results from both resubstitution tests and jackknife tests indicate that the overall rates of correct prediction by the algorithm incorporated with the coupling effect among different amino acid components are significantly higher than those by the algorithms without using such an effect. It is elucidated through an analysis that the main reasons for Eisenhaber et al. to have reached an opposite conclusion are the result of (1) misusing the component-coupled algorithm, and (2) using a conceptually incorrect rule to classify protein structural classes. The formulation and analysis presented in this article are conducive to clarify these problems, helping correctly to apply the prediction algorithm and interpret the results.

Disposition of amphiphilic helices in heteropolar environments.

It is known that alpha helices in globular proteins usually consist of two types of residues, hydrophobic and hydrophilic, with the number of each type being roughly equal. Except for many transmembrane helices, alpha-helices are generally amphiphilic to some degree. This is not entirely surprising because alpha-helices typically reside in heteropolar environments that arise from the polar aqueous solution that surrounds a protein and the apolar "hydrophobic core" located at its center. The packing of alpha-helices in such heteropolar environments is driven by the minimization of free energy brought about by placing hydrophobic sidechains into apolar environments and hydrophilic sidechains into polar environments. The interface between the two environments can be characterized by an interfacial plane, called the demarcation plane, that optimally separates the two classes of residues. The inclination angle omega between the axis of the helix and the demarcation plane provides a measure of the degree of amphiphilicity of an alpha-helix. For highly amphiphilic helices, omega approximately 0. The inclination angle provides a new measure of amphiphilicity that complements the hydrophobic moments of Eisenberg et al. Based on the simple physical model described above, an algorithm is developed for predicting the helix inclination angle. The calculated results show that the inclination angle for most alpha-helices extracted from globular proteins is less than 25 degrees in magnitude. This suggests that helices found in globular proteins tend to be reasonably amphiphilic with half their face dominated by hydrophobic residues and the other half by hydrophilic residues. A new two-dimensional representation that characterizes the disposition of hydrophobic and hydrophilic residues in alpha-helices, called a "wenxiang diagram," is presented. The wenxiang diagram can also be used as an important element to represent a protein molecule.

A molecular field-based similarity approach to pharmacophoric pattern recognition.

The use of molecular field-based similarity approaches for obtaining quality molecular alignments and for identifying field-based patterns in bioactive molecules is described. In addition to pairwise similarities, computation of multimolecule similarities affords a means for determining consensus multimolecule alignments. These multimolecule alignments constitute the basis for developing models for the relative binding of bioactive molecules to common protein-binding sites and for the graphical portrayal of molecular field similarity surface plots that identify, visually, molecular regions possessing similar molecular field characteristics. The latter information can then be exploited in the design of molecules that mimic appropriate characteristics of these highly similar steric and electrostatic domains. Regions with low steric and electrostatic similarity in suitably aligned sets of bioactive molecules represent tolerant domains where new structural motifs can be incorporated without significant reductions in activity. To illustrate the potential applicability of the actual molecular field-based similarity approaches to the design of bioactive molecules, a study on a set of HIV-1 protease inhibitors is presented.

Predicting protein structural classes from amino acid composition: application of fuzzy clustering.

Most globular proteins can be classified into one of four structural classes--all-alpha, all-beta, alpha + beta and alpha/beta--depending upon the type, amount and arrangement of secondary structures present. In this work a new method, based upon fuzzy clustering, is proposed for predicting the structural class of a protein from its amino acid composition. Here, each of the structural classes is described by a fuzzy cluster and each protein is characterized by its membership degree, a number between zero and one in each of the four clusters, with the constraint that the sum of the membership degrees equals unity. A given protein is then classified as belonging to that structural class corresponding to the fuzzy cluster with maximum membership degree. Calculation of membership degrees is carried out using the fuzzy c-means algorithm on a training set of 64 proteins. Results obtained for the training set show that the fuzzy clustering approach produces results comparable with or better than those obtained by other methods. A test set of 27 proteins also produced comparable results to those obtained with the training set. The success of the present preliminary work on protein structure class prediction suggests that further refinements of method may lead to improved predictions and this is currently being investigated.

A consensus procedure for predicting the location of alpha-helical transmembrane segments in proteins.

To aid in the development of three-dimensional models of membrane-bound proteins, a consensus procedure for predicting alpha-helical transmembrane segments from amino acid sequence is presented. The algorithm combines the results of six individual prediction methods and some basic properties of membrane-spanning helices to obtain a final consensus prediction. Comparison with experiment and several other recently developed methods shows that the consensus procedure performs quite well in comparison to other recent methods. A FORTRAN program has been developed which takes an input file containing an amino acid sequence in one-letter code and outputs a list of the alpha-helical transmembrane segments predicted by the consensus algorithm.

Solitary wave dynamics as a mechanism for explaining the internal motion during microtubule growth.

Microtubules, which play many diverse and important roles in biological systems, are usually made up of 13 nearly axial protofilaments formed from individual tubulin molecules. In this paper, a nonlinear dynamic model has been developed to elucidate the mechanism of the internal motion occurring during the assembly of microtubules. The results derived from the model indicate that such internal motion is associated with a solitary wave, or kink, excited by the energy released from the hydrolysis of GTP-->GDP in microtubular solutions. As the kink moves forward, the individual tubulin molecules involved in the kink undergo motions that can be likened to the dislocation of atoms within the crystal lattice. Thus, the dynamic instability of microtubules may be characterized by a series of dislocation motions of the tubulin molecules. An energy estimate shows that a kink in the system possesses about 0.36-0.44 eV, which is quite close to but smaller than the 0.49 eV of energy released from the hydrolysis of GTP. Therefore, the relevant energy derived from our model is fully consistent with experimental observations; this finding also suggests that the hydrolysis energy may be responsible for exciting the solitary wave, or kink, leading to tubulin dislocation in microtubules. Our model, and its intrinsic properties, i.e., dynamic nonlinearity, thermodynamic irreversibility, as well as an energy input from a sustained source, implies that the growth of microtubules is a typical dissipative process and that their structure in vivo is typical of dissipative structures.

Role of loop-helix interactions in stabilizing four-helix bundle proteins.

One of the critical issues regarding proteins with a four-helix bundle motif is which interactions play the major role in stabilizing this type of folded structure: the interaction among the four alpha-helices or the interaction between the loop and helix segments. To answer this question, an energetic analysis has been carried out for three proteins with a four-helix bundle--namely, methemerythrin, cytochrome b-562, and cytochrome c'. The structures on which the analysis has been made were derived from their respective crystallographic coordinates. All three proteins have long helices (16-26 residues) and most of their loops are short (3-5 residues). However, it was found in all three proteins that loop-helix interactions were stronger than helix-helix interactions. Moreover, not only the nonbonded component but also the electrostatic component of the interaction energy were dominated by loop-helix interactions rather than by interhelix interactions, although the latter involve favorable helix-dipole interactions due to the antiparallel arrangement of neighboring helices. The results of the energetic analysis indicate that the loop segments, whether they are in a theoretical model or in real proteins, play a significant role in stabilizing proteins with four-helix bundles.

An energy-based approach to packing the 7-helix bundle of bacteriorhodopsin.

Based on the heavy-atom coordinates determined by the electron microscopy for the seven main helical regions of bacteriorhodopsin with the all-trans retinal isomer, energy optimizations were carried out for helix bundles containing the all-trans retinal and 13-cis retinal chromophores, respectively. A combination of simulated annealing and energy minimization was utilized during the process of energy optimization. It was found that the 7-helix bundle containing the all-trans isomer is about 10 kcal/mol lower in conformational energy than that containing the 13-cis isomer. An energetic analysis indicates that such a difference in energy is consistent with the observation that absorption of a 570-nm proton is required for the conversion of a bacteriorhodopsin from its all-trans to 13-cis form. It was also found that the above conversion process is accompanied by a significant conformational perturbation around the chromophore, as reflected by the fact that the beta-ionone ring of retinal moves about 5.6 A along the direction perpendicular to the membrane plane. This is consistent with the observation by Fodor et al. (Fodor, S.P.A., Ames, J.B., Gebhard, R., van der Berg, E.M.M., Stoeckenius, W., Lugtenburg, J., & Mathies, R.A., 1988, Biochemistry 27, 7097-7101). Furthermore, it is interesting to observe that although the retinal chromophore undergoes a significant change in its spatial position, the orientation of its transition dipole changes only slightly, in accord with experimental observations. In other words, even though orientation of the retinal transition dipole is very restricted, there is sufficient room, and degrees of freedom, for the retinal chromophore to readjust its position considerably. This finding provides new insight into the subtle change of the retinal microenvironment, which may be important for revealing the proton-pumping mechanism of bacteriorhodopsin. The importance of electrostatic and nonbonded interactions in stabilizing the 7-helix bundle structure has also been analyzed. Electrostatic interactions favor an antiparallel arrangement among adjacent helices. Nonbonded interactions, however, drive most of the closely packed helices into an arrangement in which the packing angles lie around -160 degrees, a value very near the -154 degrees value computed earlier as the most favorable packing arrangement of two poly(Ala) alpha-helices (Chou, K.-C., Némethy, G., & Scheraga, H.A., 1983, J. Phys. Chem. 87, 2869-2881). The structural features of the 7-helix bundle and their relationship to those found in typical 4-helix bundle proteins are also discussed.(ABSTRACT TRUNCATED AT 400 WORDS)

A preliminary 3-D model of the tertiary fold of the polymerase domain of HIV-1 reverse transcriptase.

Development of a 3-D model of the reverse transcriptase from type 1 human immunodeficiency virus (HIV-1 RT), a key enzyme in the pathogenesis of the virus, presents a significant challenge. Three-dimensional structural information is not available for any close homolog, the only 3-D structural data being that of the Klenow fragment (KF) of Escherichia coli DNA polymerase I, for which coordinates of only the alpha-carbons are available. A recently published study of the sequences of a large number of polymerases led to the identification of three common sequence patterns, nominally motif A, motif B and motif C, and to the hypothesis that the various DNA and RNA polymerases including E. coli DNA polymerase I and HIV-1 RT share a common structural motif around their respective polymerase active sites. The preliminary results of recent structural studies on two other polymerases also support this hypothesis. Based on the assumption of structural homology in the active site regions of their polymerase domains, the HIV-1 RT and KF sequences were aligned using pattern-based secondary structure predictions as a guide and motifs A, B and C as 'anchor points'. However, as suggested by the results of chemical modification experiments, it was assumed that the order of the motifs in KF, viz. A, B and C, differed from that of the related motifs A, C and B' in HIV-1 RT, a rearrangement that could have been brought about by an exon shuffling type of mechanism.(ABSTRACT TRUNCATED AT 250 WORDS)

Mass-weighted molecular dynamics simulation of cyclic polypeptides.

A modified molecular dynamics (MD) method in which atomic masses are weighted was developed previously for studying the conformational flexibility of neuroregulating tetrapeptide Phe-Met-Arg-Phe-amide (FMRF-amide). The method has now been applied to longer and constrained molecules, namely a disulfide-linked cyclic hexapeptide, c[CYFQNC], and its linear and "pseudo-cyclic" analogues. The sampling of dehedral conformational space of teh linear hexapeptide in mass-weighted MD simulations was found to be improved significantly over conventional MD simulations, as in the case of the shorter FMRF-amide molecule studied previously. In the cyclic hexapeptide, the internal constraint of the molecule due to the intramolecular disulfide bond (hence the absence of free terminals in the molecule) does not adversely affect the significant improvement of conformational sampling in mass-weighted MD simulations over normal MD simulations. The pseudo-cyclic polypeptide is identical to the linear CYFQNC molecule in amino acid sequence (i.e., side chains of the cysteine residues are reduced), but the positions of its two terminal heavy atoms were held fixed in space such that the molecule has a nearly cyclic conformation. For this molecule, the mass-weighted MD simulation generated a wide range of polypeptide backbone conformations covering the internal dihedral degrees of freedom; moreover, the physical space of the pseudo-cyclic structure was also sampled in a complete revolution of the entire molecular fragment about the two fixed termini during the simulation. These characteristics suggest that mass-weighted MD can also be an extremely useful method for conformational analyses of constrained molecules and, in particular, for modeling loops on protein surfaces.

A heuristic approach to predicting the tertiary structure of bovine somatotropin.

A combination of a heuristic approach and energy minimization was used to predict the three-dimensional structure of bovine somatotropin (bSt), also known as bovine growth hormone, a protein of 191 amino acids. The starting points for energy minimizations were generated from the following two types of inputs: (a) the amino acid sequence and (b) the heuristic inputs, which were derived according to physical, chemical, and biological principles by piecing together all useful information available. The predicted 3-D structure of the bSt molecule has all the features observed in four-helix bundle proteins. The four alpha-helices in bSt are intimately packed to form an assembly with an approximately square cross section. All the adjacent alpha-helices are antiparallel, with a somewhat tilted angle between each of the adjacent pairs so that the assembly of the four helices looks like a left-handed twisted bundle. There are two disulfide bonds in the bSt structure: one "hooking" the middle of a long loop with helix 4 so as to pull the long loop onto the surface of the helix bundle and the other "hooking" the C-terminal segment with the same helix so as to force the C-terminal segment to bend toward the helix bundle. As a consequence, a considerable part of the surface of the four-helix bundle is closely packed or intimately embraced by the loop segments. The predicted bSt structure has a hydrophobic core and a hydrophilic exterior surface. The energetic analysis of the predicted bSt structure indicates that the interaction between helices and loops plays a dominant role in stabilizing the four-helix bundle structure from the viewpoint of both electrostatic and nonbonded interactions. A technique called FOLD was meanwhile developed, by which one can fold a polypeptide chain into any shape as desired. This tool proved to be very useful during the heuristic model-building process.

Conformational and geometrical properties of idealized beta-barrels in proteins.

An equation for calculating the distances between the atoms involved in forming an idealized hydrogen bond in a parallel or antiparallel beta-barrel has been derived by adjusting the corresponding data given by Pauling and Corey for a beta-sheet. Based on these distances, a geometrical optimization method was developed, by which one can generate various idealized beta-barrels: parallel or antiparallel, tilted or non-tilted, right-tilted or left-tilted. For each type of idealized beta-barrel thus obtained, the corresponding conformation and characteristic geometric parameters as well as their relationship are analyzed and discussed. Since the strand in a tilted beta-barrel traces a curve rather than a straight line on a cylinder-like surface, a regular chain in which the dihedral angles of each residue are the same cannot form a tilted beta-barrel but only a non-tilted beta-barrel. As observed, the strands of a right-tilted beta-barrel possess a very strong right-handed twist. The radii of the idealized tilted parallel and antiparallel beta-barrels are greater than those of the corresponding non-tilted ones by approximately 1 A and approximately 1.5 A, respectively. Consequently, there is relatively more room for a tilted beta-barrel to accommodate the internal side-chains, suggesting that a conformational change from a non-tilted beta-barrel to a tilted one would ease the repulsion among the crowded internal side-chains so as to make the structure more stable. The values of root-mean-square fits indicate that the idealized right-tilted beta-barrels coincide quite well with the observed beta-barrels in both parallel and antiparallel cases.

Topological analysis of hydrogen bonding in protein structure.

A recent study has shown that topological stereoisomers exist for the polypeptide chain in disulfide-containing proteins that are represented by non-planar graphs. This topological stereochemistry is demonstrated in the structure of variant 3 toxin in the venom of the North American scorpion Centruroides sculpturatus Ewing and the structure of toxin II from the North African scorpion Androctonus australis Hector. In this report, we found that a similar topological analysis can be applied to the hydrogen bonding in alpha-helices and beta-sheets within protein molecules, and we described the topological characteristics of chiral properties of protein secondary structure elements. Specifically, a closed right-handed alpha-helix of more than six residues long is shown formally to be non-planar and has the L topology. Antiparallel beta-sheets are planar. Two parallel beta-strands each of at least three residues in length, however, constitute a non-planar structural element and can have either L or D topology. The favored right-handed crossover for parallel beta-sheets has the L form, the same as the right-handed alpha-helix. This topological description of the hydrogen bonding in secondary structures may be extended to higher levels of protein structure and may provide a conceptual framework for studying complex protein architecture in general.