Modeling complex metabolic reactions, ecological systems, and financial and legal networks with MIANN models based on Markov-Wiener node descriptors.

The use of numerical parameters in Complex Network analysis is expanding to new fields of application. At a molecular level, we can use them to describe the molecular structure of chemical entities, protein interactions, or metabolic networks. However, the applications are not restricted to the world of molecules and can be extended to the study of macroscopic nonliving systems, organisms, or even legal or social networks. On the other hand, the development of the field of Artificial Intelligence has led to the formulation of computational algorithms whose design is based on the structure and functioning of networks of biological neurons. These algorithms, called Artificial Neural Networks (ANNs), can be useful for the study of complex networks, since the numerical parameters that encode information of the network (for example centralities/node descriptors) can be used as inputs for the ANNs. The Wiener index (W) is a graph invariant widely used in chemoinformatics to quantify the molecular structure of drugs and to study complex networks. In this work, we explore for the first time the possibility of using Markov chains to calculate analogues of node distance numbers/W to describe complex networks from the point of view of their nodes. These parameters are called Markov-Wiener node descriptors of order k(th) (W(k)). Please, note that these descriptors are not related to Markov-Wiener stochastic processes. Here, we calculated the W(k)(i) values for a very high number of nodes (>100,000) in more than 100 different complex networks using the software MI-NODES. These networks were grouped according to the field of application. Molecular networks include the Metabolic Reaction Networks (MRNs) of 40 different organisms. In addition, we analyzed other biological and legal and social networks. These include the Interaction Web Database Biological Networks (IWDBNs), with 75 food webs or ecological systems and the Spanish Financial Law Network (SFLN). The calculated W(k)(i) values were used as inputs for different ANNs in order to discriminate correct node connectivity patterns from incorrect random patterns. The MIANN models obtained present good values of Sensitivity/Specificity (%): MRNs (78/78), IWDBNs (90/88), and SFLN (86/84). These preliminary results are very promising from the point of view of a first exploratory study and suggest that the use of these models could be extended to the high-throughput re-evaluation of connectivity in known complex networks (collation).

New Markov-Shannon Entropy models to assess connectivity quality in complex networks: from molecular to cellular pathway, Parasite-Host, Neural, Industry, and Legal-Social networks.

Graph and Complex Network theory is expanding its application to different levels of matter organization such as molecular, biological, technological, and social networks. A network is a set of items, usually called nodes, with connections between them, which are called links or edges. There are many different experimental and/or theoretical methods to assign node-node links depending on the type of network we want to construct. Unfortunately, the use of a method for experimental reevaluation of the entire network is very expensive in terms of time and resources; thus the development of cheaper theoretical methods is of major importance. In addition, different methods to link nodes in the same type of network are not totally accurate in such a way that they do not always coincide. In this sense, the development of computational methods useful to evaluate connectivity quality in complex networks (a posteriori of network assemble) is a goal of major interest. In this work, we report for the first time a new method to calculate numerical quality scores S(L(ij)) for network links L(ij) (connectivity) based on the Markov-Shannon Entropy indices of order k-th (θ(k)) for network nodes. The algorithm may be summarized as follows: (i) first, the θ(k)(j) values are calculated for all j-th nodes in a complex network already constructed; (ii) A Linear Discriminant Analysis (LDA) is used to seek a linear equation that discriminates connected or linked (L(ij)=1) pairs of nodes experimentally confirmed from non-linked ones (L(ij)=0); (iii) the new model is validated with external series of pairs of nodes; (iv) the equation obtained is used to re-evaluate the connectivity quality of the network, connecting/disconnecting nodes based on the quality scores calculated with the new connectivity function. This method was used to study different types of large networks. The linear models obtained produced the following results in terms of overall accuracy for network reconstruction: Metabolic networks (72.3%), Parasite-Host networks (93.3%), CoCoMac brain cortex co-activation network (89.6%), NW Spain fasciolosis spreading network (97.2%), Spanish financial law network (89.9%) and World trade network for Intelligent & Active Food Packaging (92.8%). In order to seek these models, we studied an average of 55,388 pairs of nodes in each model and a total of 332,326 pairs of nodes in all models. Finally, this method was used to solve a more complicated problem. A model was developed to score the connectivity quality in the Drug-Target network of US FDA approved drugs. In this last model the θ(k) values were calculated for three types of molecular networks representing different levels of organization: drug molecular graphs (atom-atom bonds), protein residue networks (amino acid interactions), and drug-target network (compound-protein binding). The overall accuracy of this model was 76.3%. This work opens a new door to the computational reevaluation of network connectivity quality (collation) for complex systems in molecular, biomedical, technological, and legal-social sciences as well as in world trade and industry.

New Markov-autocorrelation indices for re-evaluation of links in chemical and biological complex networks used in metabolomics, parasitology, neurosciences, and epidemiology.

The development of new methods for the computational re-evaluation of links in chemical and biological complex networks is very important to save time and resources. The Moreau-Broto autocorrelation indices (MBis) are well-known topological indices (TIs) used in QSAR/QSPR studies to encode the structural information contained in molecular graphs. In addition, MBis and similar autocorrelation measures have been used to study other systems like, for example, proteins. In the present work, MBis are combined with Markov chains to develop a general class of stochastic MBis of order k (MB(k)) that is used to encode the structural information contained in different types of large complex networks. The MB(k) values obtained for the nodes (centralities) of these networks are used as input variables to seek QSPR-like equations (by means of linear discriminant analysis) in which the outputs are numerical scores S(L(ij)) that allow us to discriminate between connected and nonconnected nodes and therefore re-evaluate the connectivity of the whole network. The models developed in this work produced the following results in terms of overall accuracy for network reconstruction: metabolic networks (72.10%), parasite-host networks (88.70%), CoCoMac brain cortex coactivation network (81.89%), and fasciolosis spreading network (86.39%).

The Rücker-Markov invariants of complex Bio-Systems: applications in Parasitology and Neuroinformatics.

Rücker's walk count (WC) indices are well-known topological indices (TIs) used in Chemoinformatics to quantify the molecular structure of drugs represented by a graph in Quantitative structure-activity/property relationship (QSAR/QSPR) studies. In this work, we introduce for the first time the higher-order (kth order) analogues (WCk) of these indices using Markov chains. In addition, we report new QSPR models for large complex networks of different Bio-Systems useful in Parasitology and Neuroinformatics. The new type of QSPR models can be used for model checking to calculate numerical scores S(Lij) for links Lij (checking or re-evaluation of network connectivity) in large networks of all these fields. The method may be summarized as follows: (i) first, the WCk(j) values are calculated for all jth nodes in a complex network already created; (ii) A linear discriminant analysis (LDA) is used to seek a linear equation that discriminates connected or linked (Lij=1) pairs of nodes experimentally confirmed from non-linked ones (Lij=0); (iii) The new model is validated with external series of pairs of nodes; (iv) The equation obtained is used to re-evaluate the connectivity quality of the network, connecting/disconnecting nodes based on the quality scores calculated with the new connectivity function. The linear QSPR models obtained yielded the following results in terms of overall test accuracy for re-construction of complex networks of different Bio-Systems: parasite-host networks (93.14%), NW Spain fasciolosis spreading networks (71.42/70.18%) and CoCoMac Brain Cortex co-activation network (86.40%). Thus, this work can contribute to the computational re-evaluation or model checking of connectivity (collation) in complex systems of any science field.

From QSAR models of drugs to complex networks: state-of-art review and introduction of new Markov-spectral moments indices.

Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) models have been largely used for different kind of problems in Medicinal Chemistry and other Biosciences as well. Nevertheless, the applications of QSAR models have been restricted to the study of small molecules in the past. In this context, many authors use molecular graphs, atoms (nodes) connected by chemical bonds (links) to represent and numerically characterize the molecular structure. On the other hand, Complex Networks are useful in solving problems in drug research and industry, developing mathematical representations of different systems. These systems move in a wide range from relatively simple graph representations of drug molecular structures (molecular graphs used in classic QSAR) to large systems. We can cite for instance, drug-target interaction networks, protein structure networks, protein interaction networks (PINs), or drug treatment in large geographical disease spreading networks. In any case, all complex networks have essentially the same components: nodes (atoms, drugs, proteins, microorganisms and/or parasites, geographical areas, drug policy legislations, etc.) and links (chemical bonds, drug-target interactions, drug-parasite treatment, drug use, etc.). Consequently, we can use the same type of numeric parameters called Topological Indices (TIs) to describe the connectivity patterns in all these kinds of Complex Networks irrespective the nature of the object they represent and use these TIs to develop QSAR/QSPR models beyond the classic frontiers of drugs small-sized molecules. The goal of this work, in first instance, is to offer a common background to all the manuscripts presented in this special issue. In so doing, we make a review of the most used software and databases, common types of QSAR/QSPR models, and complex networks involving drugs or their targets. In addition, we review both classic TIs that have been used to describe the molecular structure of drugs and/or larger complex networks. In second instance, we use for the first time a Markov chain model to generalize Spectral moments to higher order analogues coined here as the Stochastic Spectral Moments TIs of order k (πk). Lastly, we report for the first time different QSAR/QSPR models for different classes of networks found in drug research, nature, technology, and social-legal sciences using πk values. This work updates our previous reviews Gonzalez-Diaz et al. Curr Top Med Chem. 2007; 7(10): 1015-29 and Gonzalez-Diaz et al. Curr Top Med Chem. 2008; 8(18):1676-90. It has been prepared in response to the kind invitation of the editor Prof. AB Reitz in commemoration of the 10th anniversary of this journal in 2010.

From chemical graphs in computer-aided drug design to general Markov-Galvez indices of drug-target, proteome, drug-parasitic disease, technological, and social-legal networks.

Complex Networks are useful in solving problems in drug research and industry, developing mathematical representations of different systems. These systems move in a wide range from relatively simple graph representations of drug molecular structures to large systems. We can cite for instance, drug-target protein interaction networks, drug policy legislation networks, or drug treatment in large geographical disease spreading networks. In any case, all these networks have essentially the same components: nodes (atoms, drugs, proteins, microorganisms and/or parasites, geographical areas, drug policy legislations, etc.) and edges (chemical bonds, drug-target interactions, drug-parasite treatment, drug use, etc.). Consequently, we can use the same type of numeric parameters called Topological Indices (TIs) to describe the connectivity patterns in all these kinds of Complex Networks despite the nature of the object they represent. The main reason for this success of TIs is the high flexibility of this theory to solve in a fast but rigorous way many apparently unrelated problems in all these disciplines. Another important reason for the success of TIs is that using these parameters as inputs we can find Quantitative Structure-Property Relationships (QSPR) models for different kind of problems in Computer-Aided Drug Design (CADD). Taking into account all the above-mentioned aspects, the present work is aimed at offering a common background to all the manuscripts presented in this special issue. In so doing, we make a review of the most common types of complex networks involving drugs or their targets. In addition, we review both classic TIs that have been used to describe the molecular structure of drugs and/or larger complex networks. Next, we use for the first time a Markov chain model to generalize Galvez TIs to higher order analogues coined here as the Markov-Galvez TIs of order k (MGk). Lastly, we illustrate the calculation of MGk values for different classes of networks found in drug research, nature, technology, and social-legal sciences.

2D MI-DRAGON: a new predictor for protein-ligands interactions and theoretic-experimental studies of US FDA drug-target network, oxoisoaporphine inhibitors for MAO-A and human parasite proteins.

There are many pairs of possible Drug-Proteins Interactions that may take place or not (DPIs/nDPIs) between drugs with high affinity/non-affinity for different proteins. This fact makes expensive in terms of time and resources, for instance, the determination of all possible ligands-protein interactions for a single drug. In this sense, we can use Quantitative Structure-Activity Relationships (QSAR) models to carry out rational DPIs prediction. Unfortunately, almost all QSAR models predict activity against only one target. To solve this problem we can develop multi-target QSAR (mt-QSAR) models. In this work, we introduce the technique 2D MI-DRAGON a new predictor for DPIs based on two different well-known software. We use the software MARCH-INSIDE (MI) to calculate 3D structural parameters for targets and the software DRAGON was used to calculated 2D molecular descriptors all drugs showing known DPIs present in the Drug Bank (US FDA benchmark dataset). Both classes of parameters were used as input of different Artificial Neural Network (ANN) algorithms to seek an accurate non-linear mt-QSAR predictor. The best ANN model found is a Multi-Layer Perceptron (MLP) with profile MLP 21:21-31-1:1. This MLP classifies correctly 303 out of 339 DPIs (Sensitivity = 89.38%) and 480 out of 510 nDPIs (Specificity = 94.12%), corresponding to training Accuracy = 92.23%. The validation of the model was carried out by means of external predicting series with Sensitivity = 92.18% (625/678 DPIs; Specificity = 90.12% (730/780 nDPIs) and Accuracy = 91.06%. 2D MI-DRAGON offers a good opportunity for fast-track calculation of all possible DPIs of one drug enabling us to re-construct large drug-target or DPIs Complex Networks (CNs). For instance, we reconstructed the CN of the US FDA benchmark dataset with 855 nodes 519 drugs+336 targets). We predicted CN with similar topology (observed and predicted values of average distance are equal to 6.7 vs. 6.6). These CNs can be used to explore large DPIs databases in order to discover both new drugs and/or targets. Finally, we illustrated in one theoretic-experimental study the practical use of 2D MI-DRAGON. We reported the prediction, synthesis, and pharmacological assay of 10 different oxoisoaporphines with MAO-A inhibitory activity. The more active compound OXO5 presented IC(50) = 0.00083 µM, notably better than the control drug Clorgyline.