Hydrophobic, hydrophilic, and charged amino acid networks within protein

The native three-dimensional structure of a single protein is determined by the physicochemical nature of its constituent amino acids. The 20 different types of amino acids, depending on their physicochemical properties, can be grouped into three major classes: hydrophobic, hydrophilic, and charged. The anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic, and charged residues separately for a large number of proteins were studied. Results showed that the average degree of the hydrophobic networks has a significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of the charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network, whereas that of hydrophilic networks has a smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in a charged network increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the "small-world" property. Our results further indicate that the all-amino-acids networks and hydrophobic networks are of assortative type. Although most of the hydrophilic and charged networks are of the assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all-amino-acids networks and hydrophobic networks bear the signature of hierarchy, whereas the hydrophilic and charged networks do not have any hierarchical signature.     

Gene coexpression network alignment and conservation of gene modules between two grass species: maize and rice

One major objective for plant biology is the discovery of molecular subsystems underlying complex traits. The use of genetic and genomic resources combined in a systems genetics approach offers a means for approaching this goal. This study describes a maize (Zea mays) gene coexpression network built from publicly available expression arrays. The maize network consisted of 2,071 loci that were divided into 34 distinct modules that contained 1,928 enriched functional annotation terms and 35 cofunctional gene clusters. Of note, 391 maize genes of unknown function were found to be coexpressed within modules along with genes of known function. A global network alignment was made between this maize network and a previously described rice (Oryza sativa) coexpression network. The IsoRankN tool was used, which incorporates both gene homology and network topology for the alignment. A total of 1,173 aligned loci were detected between the two grass networks, which condensed into 154 conserved subgraphs that preserved 4,758 coexpression edges in rice and 6,105 coexpression edges in maize. This study provides an early view into maize coexpression space and provides an initial network-based framework for the translation of functional genomic and genetic information between these two vital agricultural species.     

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

Background  

A 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.     

不同类型氨基酸网络参量与蛋白质折叠的关系

理论和实验研究表明,蛋白质天然拓扑结构对其折叠过程具有重要的影响．采用复杂网络的方法分析蛋白质天然结构的拓扑特征,并探索蛋白质结构特征与折叠速率之间的内在联系．分别构建了蛋白质氨基酸网络、疏水网、亲水网、亲水-疏水网以及相应的长程网络,研究了这些网络的匹配系数(assortativity coefficient)和聚集系数(clustering coefficient)的统计特性．结果表明,除了亲水-疏水网,上述各网络的匹配系数均为正值,并且氨基酸网和疏水网的匹配系数与折叠速率表现出明显的线性正相关,揭示了疏水残基间相互作用的协同性有助于蛋白质的快速折叠．同时,研究发现疏水网的聚集系数与折叠速率有明显的线性负相关关系,这表明疏水残基间三角结构(triangle construction)的形成不利于蛋白质快速折叠．还进一步构建了相应的长程网络,发现序列上间距较远的残基接触对的形成将使蛋白质折叠进程变慢．     

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.     

Distribution and complementarity of hydropathy in multisubunit proteins

A survey of 40 multisubunit proteins and 2 protein-protein complexes was performed to assay quantitatively the distribution of hydropathy among the exterior surface, interior, contact surface, and noncontact exterior surface of the isolated subunits. We suggest a useful way to present this distribution by using a "hydropathy level diagram." Additionally, we have devised a function called "hydropathy complementarity" to quantitate the degree to which interacting surfaces have matching hydropathy distributions. Our survey revealed the following patterns: (1) The difference in hydropathy between the interior and exterior of subunits is a fairly invariant quantity. (2) On average, the hydropathy of the contact surface is higher than that of the exterior surface, but is not greater than that of the protein as a whole. There was variation, however, among the proteins. In some instances, the contact surface was more hydrophilic than the noncontact exterior, and in a few cases the contact surface was as hydrophobic as the protein interior. (3) The average interface manifests significant hydropathy complementarity, signifying that proteins interact by placing hydrophobic centers of one surface against hydrophobic centers of the other surface, and by similarly matching hydrophilic centers. As a measure of recognition and specificity, hydropathy complementarity could be a useful tool for predicting correct docking of interacting proteins. We suggest that high hydropathy complementarity is associated with static inflexible interactions. (4) We have found that some subunits that bind predominantly through hydrophilic forces, such as hydrogen bonds, ionic pairs, and water and metal bridges, are involved in dynamic quaternary organization and allostery.     

Mathematical modeling and optimization of cellulase protein production using Trichoderma reesei RL-P37

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.     

Self-complementarity within proteins: bridging the gap between binding and folding

Complementarity, in terms of both shape and electrostatic potential, has been quantitatively estimated at protein-protein interfaces and used extensively to predict the specific geometry of association between interacting proteins. In this work, we attempted to place both binding and folding on a common conceptual platform based on complementarity. To that end, we estimated (for the first time to our knowledge) electrostatic complementarity (Em) for residues buried within proteins. Em measures the correlation of surface electrostatic potential at protein interiors. The results show fairly uniform and significant values for all amino acids. Interestingly, hydrophobic side chains also attain appreciable complementarity primarily due to the trajectory of the main chain. Previous work from our laboratory characterized the surface (or shape) complementarity (Sm) of interior residues, and both of these measures have now been combined to derive two scoring functions to identify the native fold amid a set of decoys. These scoring functions are somewhat similar to functions that discriminate among multiple solutions in a protein-protein docking exercise. The performances of both of these functions on state-of-the-art databases were comparable if not better than most currently available scoring functions. Thus, analogously to interfacial residues of protein chains associated (docked) with specific geometry, amino acids found in the native interior have to satisfy fairly stringent constraints in terms of both Sm and Em. The functions were also found to be useful for correctly identifying the same fold for two sequences with low sequence identity. Finally, inspired by the Ramachandran plot, we developed a plot of Sm versus Em (referred to as the complementarity plot) that identifies residues with suboptimal packing and electrostatics which appear to be correlated to coordinate errors.     

Use of Data-Biased Random Walks on Graphs for the Retrieval of Context-Specific Networks from Genomic Data

Extracting network-based functional relationships within genomic datasets is an important challenge in the computational analysis of large-scale data. Although many methods, both public and commercial, have been developed, the problem of identifying networks of interactions that are most relevant to the given input data still remains an open issue. Here, we have leveraged the method of random walks on graphs as a powerful platform for scoring network components based on simultaneous assessment of the experimental data as well as local network connectivity. Using this method, NetWalk, we can calculate distribution of Edge Flux values associated with each interaction in the network, which reflects the relevance of interactions based on the experimental data. We show that network-based analyses of genomic data are simpler and more accurate using NetWalk than with some of the currently employed methods. We also present NetWalk analysis of microarray gene expression data from MCF7 cells exposed to different doses of doxorubicin, which reveals a switch-like pattern in the p53 regulated network in cell cycle arrest and apoptosis. Our analyses demonstrate the use of NetWalk as a valuable tool in generating high-confidence hypotheses from high-content genomic data.     

Detecting network communities: an application to phylogenetic analysis

This paper proposes a new method to identify communities in generally weighted complex networks and apply it to phylogenetic analysis. In this case, weights correspond to the similarity indexes among protein sequences, which can be used for network construction so that the network structure can be analyzed to recover phylogenetically useful information from its properties. The analyses discussed here are mainly based on the modular character of protein similarity networks, explored through the Newman-Girvan algorithm, with the help of the neighborhood matrix . The most relevant networks are found when the network topology changes abruptly revealing distinct modules related to the sets of organisms to which the proteins belong. Sound biological information can be retrieved by the computational routines used in the network approach, without using biological assumptions other than those incorporated by BLAST. Usually, all the main bacterial phyla and, in some cases, also some bacterial classes corresponded totally (100%) or to a great extent (>70%) to the modules. We checked for internal consistency in the obtained results, and we scored close to 84% of matches for community pertinence when comparisons between the results were performed. To illustrate how to use the network-based method, we employed data for enzymes involved in the chitin metabolic pathway that are present in more than 100 organisms from an original data set containing 1,695 organisms, downloaded from GenBank on May 19, 2007. A preliminary comparison between the outcomes of the network-based method and the results of methods based on Bayesian, distance, likelihood, and parsimony criteria suggests that the former is as reliable as these commonly used methods. We conclude that the network-based method can be used as a powerful tool for retrieving modularity information from weighted networks, which is useful for phylogenetic analysis.     

Dominating biological networks

Proteins are essential macromolecules of life that carry out most cellular processes. Since proteins aggregate to perform function, and since protein-protein interaction (PPI) networks model these aggregations, one would expect to uncover new biology from PPI network topology. Hence, using PPI networks to predict protein function and role of protein pathways in disease has received attention. A debate remains open about whether network properties of "biologically central (BC)" genes (i.e., their protein products), such as those involved in aging, cancer, infectious diseases, or signaling and drug-targeted pathways, exhibit some topological centrality compared to the rest of the proteins in the human PPI network.To help resolve this debate, we design new network-based approaches and apply them to get new insight into biological function and disease. We hypothesize that BC genes have a topologically central (TC) role in the human PPI network. We propose two different concepts of topological centrality. We design a new centrality measure to capture complex wirings of proteins in the network that identifies as TC those proteins that reside in dense extended network neighborhoods. Also, we use the notion of domination and find dominating sets (DSs) in the PPI network, i.e., sets of proteins such that every protein is either in the DS or is a neighbor of the DS. Clearly, a DS has a TC role, as it enables efficient communication between different network parts. We find statistically significant enrichment in BC genes of TC nodes and outperform the existing methods indicating that genes involved in key biological processes occupy topologically complex and dense regions of the network and correspond to its "spine" that connects all other network parts and can thus pass cellular signals efficiently throughout the network. To our knowledge, this is the first study that explores domination in the context of PPI networks.     

Ranking differential hubs in gene co-expression networks

Identifying the genes that change their expressions between two conditions (such as normal versus cancer) is a crucial task that can help in understanding the causes of diseases. Differential networking has emerged as a powerful approach to detect the changes in network structures and to identify the differentially connected genes among two networks. However, existing differential network-based methods primarily depend on pairwise comparisons of the genes based on their connectivity. Therefore, these methods cannot capture the essential topological changes in the network structures. In this paper, we propose a novel algorithm, DiffRank, which ranks the genes based on their contribution to the differences between the two networks. To achieve this goal, we define two novel structural scoring measures: a local structure measure (differential connectivity) and a global structure measure (differential betweenness centrality). These measures are optimized by propagating the scores through the network structure and then ranking the genes based on these propagated scores. We demonstrate the effectiveness of DiffRank on synthetic and real datasets. For the synthetic datasets, we developed a simulator for generating synthetic differential scale-free networks, and we compared our method with existing methods. The comparisons show that our algorithm outperforms these existing methods. For the real datasets, we apply the proposed algorithm on several gene expression datasets and demonstrate that the proposed method provides biologically interesting results.     

Scoring docked conformations generated by rigid-body protein-protein docking

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.     

A protein-protein docking algorithm dependent on the type of complexes

An efficient 'soft docking' algorithm is described to assist the prediction of protein-protein association using three-dimensional structures of molecules. The basic tools are the 'simplified protein' model and the docking algorithm of Wodak and Janin. The side chain flexibility of Arg, Lys, Asp, Glu and Met residues at the protein surface is taken into account. The complex type-dependent filtering technique on the basis of the geometric matching, hydrophobicity and electrostatic complementarity is used to select candidate binding modes. Subsequently, we calculate a scoring function which includes electrostatic and desolvation energy terms. In the 44 complexes tested including enzyme-inhibitor, antibody-antigen and other complexes, native-like structures were all found, of which 30 were ranked in the top 20. Thus, our soft docking algorithm has the potential to predict protein-protein recognition.     

Variability in quaternary association of proteins with the same tertiary fold: a case study and rationalization involving legume lectins

Legume lectins constitute a family of proteins in which small alterations arising from sequence variations in essentially the same tertiary structure lead to large changes in quaternary association. All of them are dimers or tetramers made up of dimers. Dimerization involves side-by-side or back-to-back association of the flat six-membered beta-sheets in the protomers. Variations within these modes of dimerization can be satisfactorily described in terms of angles defining the mutual disposition of the two subunits. In all tetrameric lectins, except peanut lectin, oligomerization involves the back-to-back association of side-by-side dimers. An attempt has been made to rationalize the observed modes of oligomerization in terms of hydrophobic surface area buried on association, interaction energy and shape complementarity, by constructing energy minimised models in each of which the subunit of one legume lectin is fitted in the quaternary structure of another. The results indicate that all the three indices favor and, thus, provide a rationale for the observed arrangements. However, the discrimination provided by buried hydrophobic surface area is marginal in a few instances. The same is true, to a lesser extent, about that provided by shape complementarity. The relative values of interaction energy turns out to be a still better discriminator than the other two indices. Variability in the quaternary association of homologous proteins is a widely observed phenomenon and the present study is relevant to the general problem of protein folding.     

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks.