Predicting properties of molecules using graph invariants

Topological indices (TIs) have been used to study structure-activity relationships (SAR) with respect to the physical, chemical, and biological properties of congeneric sets of molecules. Since there are many TIs and many are correlated, it is important that we identify redundancies and extract useful information from TIs into a smaller number of parameters. Moreover, it is important to determine if TIs, or parameters derived from TIs, can be used for global SAR models of diverse sets of chemicals. We calculated seventy-one TIs for three groups of molecules of increasing complexity and diversity: (a) 74 alkanes, (b) 29 alkylbenzenes, and (c) 37 polycyclic aromatic hydrocarbons (PAHs). Principal components analysis (PCA) revealed that a few principal components (PCs) could extract most of the information encoded by the seventy-one TIs. The structural basis of the first few PCs could be derived from their pattern of correlation with individual TIs. For the three sets of molecules, viz. alkanes, alkylbenzenes and PAHs, PCs were able to predict the boiling points reasonably well. Also, for the combined set of 140 chemicals consisting of the alkanes, alkylbenzenes and PAHs, the derived PCs were not as effective in predicting properties as in the case of individual classes of compounds.     

Optimal characterization of structure for prediction of properties

Different topological and physicochemical parameters have been used to predict hydrophobicity (logP, octanol-water) of chemicals. We calculated a hydrogen bonding parameter (HB₁) and a large number of molecular connectivity and complexity indices for a diverse set of 382 molecules. It is known from earlier studies that topological indices (TIs) predict properties of congeneric sets reasonably well. Since HB₁ is an approximate quantifier of hydrogen bonding and has integral values, we used HB₁ to classify the diverse set into strongly and weakly hydrogen bonding subsets. In an attempt to examine the utility of Us in predicting properties of relatively similar groups of molecules, we carried out a correlation of logP with TIs for a subset (n = 139) of the original diverse set (n = 382) with a weak hydrogen bonding ability (HB₁ = 0). Results show that TIs give a better predictive model for the more homogeneous subset as compared to the diverse set of molecules.     

GTI-space: the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.     

A Reactive,Rigid GdIII Labeling Tag for In‐Cell EPR Distance Measurements in Proteins

The cellular environment of proteins differs considerably from in vitro conditions under which most studies of protein structures are carried out. Therefore, there is a growing interest in determining dynamics and structures of proteins in the cell. A key factor for in‐cell distance measurements by the double electron–electron resonance (DEER) method in proteins is the nature of the used spin label. Here we present a newly designed Gd^III spin label, a thiol‐specific DOTA‐derivative (DO3MA‐3BrPy), which features chemical stability and kinetic inertness, high efficiency in protein labelling, a short rigid tether, as well as favorable spectroscopic properties, all are particularly suitable for in‐cell distance measurements by the DEER method carried out at W‐band frequencies. The high performance of DO3MA‐3BrPy‐Gd^III is demonstrated on doubly labelled ubiquitin D39C/E64C, both in vitro and in HeLa cells. High‐quality DEER data could be obtained in HeLa cells up to 12 h after protein delivery at in‐cell protein concentrations as low as 5–10 μm .     

Exploring the relationship between hub proteins and drug targets based on GO and intrinsic disorder

Protein–protein interactions (PPIs) play essential roles in many biological processes. In protein–protein interaction networks, hubs involve in numbers of PPIs and may constitute an important source of drug targets. The intrinsic disorder proteins (IDPs) with unstable structures can promote the promiscuity of hubs and also involve in many disease pathways, so they also could serve as potential drug targets. Moreover, proteins with similar functions measured by semantic similarity of gene ontology (GO) terms tend to interact with each other. Here, the relationship between hub proteins and drug targets based on GO terms and intrinsic disorder was explored. The semantic similarities of GO terms and genes between two proteins, and the rate of intrinsic disorder residues of each protein were extracted as features to characterize the functional similarity between two interacting proteins. Only using 8 feature variables, prediction models by support vector machine (SVM) were constructed to predict PPIs. The accuracy of the model on the PPI data from human hub proteins is as high as 83.72%, which is very promising compared with other PPI prediction models with hundreds or even thousands of features. Then, 118 of 142 PPIs between hubs are correctly predicted that the two interacting proteins are targets of the same drugs. The results indicate that only 8 functional features are fully efficient for representing PPIs. In order to identify new targets from IDP dataset, the PPIs between hubs and IDPs are predicted by the SVM model and the model yields a prediction accuracy of 75.84%. Further research proves that 3 of 5 PPIs between hubs and IDPs are correctly predicted that the two interacting proteins are targets of the same drugs. All results demonstrate that the model with only 8-dimensional features from GO terms and intrinsic disorder still gives a good performance in predicting PPIs and further identifying drug targets.     

Four new topological indices based on the molecular path code

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.     

Using pseudo amino acid composition to predict protein structural class: approached by incorporating 400 dipeptide components

The proteins structure can be mainly classified into four classes: all-alpha, all-beta, alpha/beta, and alpha + beta protein according to their chain fold topologies. For the purpose of predicting the protein structural class, a new predicting algorithm, in which the increment of diversity combines with Quadratic Discriminant analysis, is presented to study and predict protein structural class. On the basis of the concept of the pseudo amino acid composition (Chou, Proteins: Struct Funct Genet 2001, 43, 246; Erratum: Proteins Struct Funct Genet 2001, 44, 60), 400 dipeptide components and 20 amino acid composition are, respectively, selected as parameters of diversity source. Total of 204 nonhomologous proteins constructed by Chou (Chou, Biochem Biophys Res Commun 1999, 264, 216) are used for training and testing the predictive model. The predicted results by using the pseudo amino acids approach as proposed in this paper can remarkably improve the success rates, and hence the current method may play a complementary role to other existing methods for predicting protein structural classification.     

Comparative study of topological indices of macro/supramolecular RNA complex networks

RNA function annotation is often based on alignment to a previously studied template. In contrast to the study of proteins, there are not many alignment-free methods to predict RNA functions if alignment fails. The use of topological indices (TIs) of RNA complex networks (CNs) to find quantitative structure-activity relationships (QSAR) may be an alternative to incorporate secondary structure or sequence-to-sequence similarity. Here, we introduce new QSAR-like techniques using RNA macromolecular CNs (mmCNs), where nodes are nucleotides, or RNA supramolecular CNs (smCNs), where nodes are RNA sequences. We studied a data set of 198 sequences including 18S-rRNAs (important phylogenetic molecular biomarkers). We constructed three types of RNA mmCNs: sequence-linear (SL), Cartesian-lattice (CL), and sequence-folding CNs (SF-CNs) and two smCNs: sequence-sequence disagreement CN (SSD) and sequence-sequence similarity (SSS-smCN). We reported the first comparative QSAR study with all these CIs and CNs, which includes: (i) spectral moments ( ( i )micro d ( w)) of SL-mmCNs (accuracy = 75.3%), (ii) electrostatic CIs (xi d ) of CL-mmCNs (>90%), (iii) thermodynamic parameters (Delta G, Delta H, Delta S, and T m) of SF-mmCNs (64.7%), (iv) disagreement-distribution moments ( M k ) of the SSD-smCN (79.3%), and (v) node centralities of the SSD-smCN (78.0%). Furthermore, we reported the experimental isolation of a new RNA sequence from Psidum guajava leaf tissue and its QSAR and BLAST prediction to illustrate the practical use of these methods. We also investigated the use of these CNs to explore rRNA diversity on bacteria, plants, and parasites from the Dactylogyrus genus. The HPL-mmCNs model was the best of all found. All the CNs and TIs, except SF-mmCNs, were introduced here by the first time for the QSAR study of RNA, which allowed a comparative study for RNA classification.     

Transmission analysis in ultrafiltration of ternary protein mixture through a hydrophilic membrane

One of the main reasons for the underutilization of ultrafiltration has been the lack of experimental data on transmission of proteins for complex systems and its corresponding theoretical analysis. Of course, the presence of fouling coupled with concentration polarization have had their share in making ultrafiltration operation a difficult one to understand. In the present study, the systematic ultrafiltration of 3-protein mixture, namely lysozyme, myoglobin and ovalbumin, has been carried out using a hydrophilic 30,000 molecular weight cut off membrane. The experimental data of individual protein transmission in ternary mixture showed a very low transmission (as low as 3% for ovalbumin) to a very high transmission (as high as 90% for lysozyme) of proteins for different operating conditions. This behaviour of each protein in the mixture was analyzed using combined concentration polarization and irreversible thermodynamics model. The parameters of the modeled values gave a very good fit with experimental data and the resulting analysis indicated some interesting findings, which are discussed in this paper. The comparison of parameters obtained for single protein solution and the ternary protein solution showed some unusual results that point to the presence of the protein–protein and protein–membrane interactions.     

QSAR model for alignment-free prediction of human breast cancer biomarkers based on electrostatic potentials of protein pseudofolding HP-lattice networks

Network theory allows relationships to be established between numerical parameters that describe the molecular structure of genes and proteins and their biological properties. These models can be considered as quantitative structure-activity relationships (QSAR) for biopolymers. The work described here concerns the first QSAR model for 122 proteins that are associated with human breast cancer (HBC), as identified experimentally by Sj?blom et al. (Science 2006, 314, 268) from over 10,000 human proteins. In this study, the 122 proteins related to HBC (HBCp) and a control group of 200 proteins that are not related to HBC (non-HBCp) were forced to fold in an HP lattice network. From these networks a series of electrostatic potential parameters (xi(k)) was calculated to describe each protein numerically. The use of xi(k) as an entry point to linear discriminant analysis led to a QSAR model to discriminate between HBCp and non-HBCp, and this model could help to predict the involvement of a certain gene and/or protein in HBC. In addition, validation procedures were carried out on the model and these included an external prediction series and evaluation of an additional series of 1000 non-HBCp. In all cases good levels of classification were obtained with values above 80%. This study represents the first example of a QSAR model for the computational chemistry inspired search of potential HBC protein biomarkers.     

Design of topological indices: computer-oriented approach

A novel method is suggested for constructing topological indices (TIs) of molecular graphs which models human logic. This method is described in terms of a block scheme, consisting of the mutually connected elementary blocks. In each block the simple transformations of a molecular graph are fulfilled. A variant of the transformation is selected from the list of possible variants. Every TI is obtained as a result of the sequential execution of a number of operations, corresponding to some ‘walk’ on the block scheme. This walk can be selected both randomly and by the investigator. The suggested method can serve as a basis for the development of the respective computer program which may be used for the automatic construction of any number of TIs of differing nature. By this process one can also obtain the TIs that are unlikely to be constructed manually, due to their complexity. The set of obtained TIs may be used for building the structure–property models. In the case of an unsatisfactory result the obtained set of TIs may be changed using the described generator of TIs. A number of examples of application of the suggested approach for the building QSAR/QSPR models is given.     

Ab initio protein structure prediction with force field parameters derived from water-phase quantum chemical calculation

Molecular dynamics (MD) simulations are extensively used in the study of the structures and functions of proteins. Ab initio protein structure prediction is one of the most important subjects in computational biology, and many trials have been performed using MD simulation so far. Since the results of MD simulations largely depend on the force field, reliable force field parameters are indispensable for the success of MD simulation. In this work, we have modified atom charges in a standard force field on the basis of water-phase quantum chemical calculations. The modified force field turned out appropriate for ab initio protein structure prediction by the MD simulation with the generalized Born method. Detailed analysis was performed in terms of the conformational stability of amino acid residues, the stability of secondary structure of proteins, and the accuracy for prediction of protein tertiary structure, comparing the modified force field with a standard one. The energy balance between alpha-helix and beta-sheet structures was significantly improved by the modification of charge parameters.     

On the Temperature–Pressure Free‐Energy Landscape of Proteins

We studied the thermodynamic stability of a small monomeric protein, staphylococcal nuclease (Snase), as a function of both temperature and pressure, and expressed it as a 3D free‐energy surface on the p,T‐plane using a second‐order Taylor expansion of the Gibbs free‐energy change ΔG upon unfolding. We took advantage of a series of different techniques (small‐angle Xray scattering, Fourier‐transform infrared spectroscopy, differential thermal analysis, pressure perturbation calorimetry and densitometry) in the evaluation of the conformation of the protein and in evaluating the changes in the thermodynamic parameters upon unfolding, such as the heat capacity, enthalpy, entropy, volume, isothermal compressibility and expansivity. The calculated results of the free‐energy landscape of the protein are in good agreement with experimental data of the p,T‐stability diagram of the protein over a temperature range from 200 to 400 K and at pressures from ambient pressure to 4000 bar. The results demonstrate that combined temperature–pressure‐dependent studies can help delineate the free‐energy landscape of proteins and hence help elucidate which features and thermodynamic parameters are essential in determining the stability of the native conformational state of proteins. The approach presented may also be used for studying other systems with so‐called re‐entrant or Tamman loop‐shaped phase diagrams.