Ming-Jing Hwang

Derivation of class II force fields. I: methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross‐term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments.

Derivation of class II force fields: V. Quantum force field for amides, peptides, and related compounds

As the field of biomolecular structure advances, there is an ever‐growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever‐increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm−1 was achieved with the coupled anharmonic force field, as compared to 105 cm−1 with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides.  © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical “observables.” The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures.

Alternative alignments from comparison of protein structures

Comparison of two protein structures often results in not only a global alignment but also a number of distinct local alignments; the latter, referred to as alternative alignments, are however usually ignored in existing protein structure comparison analyses. Here, we used a novel method of protein structure comparison to extensively identify and characterize the alternative alignments obtained for structure pairs of a fold classification database. We showed that all alternative alignments can be classified into one of just a few types, and with which illustrated the potential of using alternative alignments to identify recurring protein substructures, including the internal structural repeats of a protein. Furthermore, we showed that among the alternative alignments obtained, permuted alignments, which included both circular and scrambled permutations, are as prevalent as topological alignments. These results demonstrated that the so far largely unattended alternative alignments of protein structures have implications and applications for research of protein classification and evolution. Proteins 2004.

A network perspective on the topological importance of enzymes and their phylogenetic conservation

BackgroundA metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.ResultsEnzyme phylogenetic profile correlates best with betweenness centrality and also quite closely with degree, but poorly with closeness centrality. Both betweenness and closeness centralities are non-local measures of topological importance and it is intriguing that they have contrasting power of predicting phylogenetic profile in bacterial species. We speculate that redundancy in an enzyme network may be reflected by betweenness centrality but not by closeness centrality. We also discuss factors influencing the correlation between phylogenetic profile and topological importance.ConclusionOur analysis falsifies the hypothesis that phylogenetic profile of enzymes is independent of enzyme network importance. Our results show that phylogenetic profile correlates better with degree and betweenness centrality, but less so with closeness centrality. Enzymes that occur in many bacterial species tend to be those that have high network importance. We speculate that this phenomenon originates in mechanisms driving network evolution. Closeness centrality reflects phylogenetic profile poorly. This is because metabolic networks often consist of distinct functional modules and some are not in the centre of the network. Enzymes in these peripheral parts of a network might be important for cell survival and should therefore occur in many bacterial species. They are, however, distant from other enzymes in the same network.

Topological and organizational properties of the products of house-keeping and tissue-specific genes in protein-protein interaction networks

BackgroundHuman cells of various tissue types differ greatly in morphology despite having the same set of genetic information. Some genes are expressed in all cell types to perform house-keeping functions, while some are selectively expressed to perform tissue-specific functions. In this study, we wished to elucidate how proteins encoded by human house-keeping genes and tissue-specific genes are organized in human protein-protein interaction networks. We constructed protein-protein interaction networks for different tissue types using two gene expression datasets and one protein-protein interaction database. We then calculated three network indices of topological importance, the degree, closeness, and betweenness centralities, to measure the network position of proteins encoded by house-keeping and tissue-specific genes, and quantified their local connectivity structure.ResultsCompared to a random selection of proteins, house-keeping gene-encoded proteins tended to have a greater number of directly interacting neighbors and occupy network positions in several shortest paths of interaction between protein pairs, whereas tissue-specific gene-encoded proteins did not. In addition, house-keeping gene-encoded proteins tended to connect with other house-keeping gene-encoded proteins in all tissue types, whereas tissue-specific gene-encoded proteins also tended to connect with other tissue-specific gene-encoded proteins, but only in approximately half of the tissue types examined.ConclusionOur analysis showed that house-keeping gene-encoded proteins tend to occupy important network positions, while those encoded by tissue-specific genes do not. The biological implications of our findings were discussed and we proposed a hypothesis regarding how cells organize their protein tools in protein-protein interaction networks. Our results led us to speculate that house-keeping gene-encoded proteins might form a core in human protein-protein interaction networks, while clusters of tissue-specific gene-encoded proteins are attached to the core at more peripheral positions of the networks.

Site-directed mutagenesis evidence for a negatively charged trypsin inhibitory loop in sweet potato sporamin

Sporamin, a sweet potato tuberous storage protein, has trypsin inhibitory activity. Sequence comparison with other plant trypsin inhibitors (TIs) of the Kunitz family reveals that, instead of the conserved Arg or Lys found in other Kunitz TIs, sporamin contains a negatively charged residue (Asp70 or Glu72) at the P1 reactive site. Using site‐directed mutagenesis, six mutants were generated containing substitutions at the reactive site and at one of the disulfide bonds, and the recombinant proteins were assayed for TI activity. Mutants Asp70Val and Glu72Arg were found to have only 2–3% of the wild‐type activity. These results provide the first evidence for a negatively charged trypsin inhibitory loop and a new mechanism of trypsin inhibition in the Kunitz family.

An interaction-motif-based scoring function for protein-ligand docking

BackgroundA good scoring function is essential for molecular docking computations. In conventional scoring functions, energy terms modeling pairwise interactions are cumulatively summed, and the best docking solution is selected. Here, we propose to transform protein-ligand interactions into three-dimensional geometric networks, from which recurring network substructures, or network motifs, are selected and used to provide probability-ranked interaction templates with which to score docking solutions.ResultsA novel scoring function for protein-ligand docking, MotifScore, was developed. It is non-energy-based, and docking is, instead, scored by counting the occurrences of motifs of protein-ligand interaction networks constructed using structures of protein-ligand complexes. MotifScore has been tested on a benchmark set established by others to assess its ability to identify near-native complex conformations among a set of decoys. In this benchmark test, 84% of the highest-scored docking conformations had root-mean-square deviations (rmsds) below 2.0 Å from the native conformation, which is comparable with the best of several energy-based docking scoring functions. Many of the top motifs, which comprise a multitude of chemical groups that interact simultaneously and make a highly significant contribution to MotifScore, capture recurrent interacting patterns beyond pairwise interactions.ConclusionsWhile providing quite good docking scores, MotifScore is quite different from conventional energy-based functions. MotifScore thus represents a new, network-based approach for exploring problems associated with molecular docking.

Protein structure comparison by probability-based matching of secondary structure elements

MOTIVATION Protein structure comparison (PSC) has been used widely in studies of structural and functional genomics. However, PSC is computationally expensive and as a result almost all of the PSC methods currently in use look only for the optimal alignment and ignore many alternative alignments that are statistically significant and that may provide insight into protein evolution or folding. RESULTS We have developed a new PSC method with efficiency to detect potentially viable alternative alignments in all-against-all database comparisons. The efficiency of the new PSC method derives from the ability to directly home in on a limited number of viable and ranked alignment solutions based on intuitively derived SSE (secondary structure element)-matching probabilities.

In silico identification and comparative analysis of differentially expressed genes in human and mouse tissues

BackgroundScreening for differentially expressed genes on the genomic scale and comparative analysis of the expression profiles of orthologous genes between species to study gene function and regulation are becoming increasingly feasible. Expressed sequence tags (ESTs) are an excellent source of data for such studies using bioinformatic approaches because of the rich libraries and tremendous amount of data now available in the public domain. However, any large-scale EST-based bioinformatics analysis must deal with the heterogeneous, and often ambiguous, tissue and organ terms used to describe EST libraries.ResultsTo deal with the issue of tissue source, in this work, we carefully screened and organized more than 8 million human and mouse ESTs into 157 human and 108 mouse tissue/organ categories, to which we applied an established statistic test using different thresholds of the p value to identify genes differentially expressed in different tissues. Further analysis of the tissue distribution and level of expression of human and mouse orthologous genes showed that tissue-specific orthologs tended to have more similar expression patterns than those lacking significant tissue specificity. On the other hand, a number of orthologs were found to have significant disparity in their expression profiles, hinting at novel functions, divergent regulation, or new ortholog relationships.ConclusionComprehensive statistics on the tissue-specific expression of human and mouse genes were obtained in this very large-scale, EST-based analysis. These statistical results have been organized into a database, freely accessible at our website http://gln.ibms.sinica.edu.tw/product/HMDEG/EST/index.php, for easy searching of human and mouse tissue-specific genes and for investigating gene expression profiles in the context of comparative genomics. Comparative analysis showed that, although highly tissue-specific genes tend to exhibit similar expression profiles in human and mouse, there are significant exceptions, indicating that orthologous genes, while sharing basic genomic properties, could result in distinct phenotypes.