On the complexity of directed biological networks

Predicting Metabolic Reaction Networks with Perturbation-Theory Machine Learning (PTML) Models

BACKGROUND

Checking the connectivity (structure) of complex Metabolic Reaction Networks (MRNs) models proposed for new microorganisms with promising properties is an important goal for chemical biology.

OBJECTIVE

In principle, we can perform a hand-on checking (Manual Curation). However, this is a challenging task due to the high number of combinations of pairs of nodes (possible metabolic reactions).

RESULTS

The CPTML linear model obtained using the LDA algorithm is able to discriminate nodes (metabolites) with the correct assignation of reactions from incorrect nodes with values of accuracy, specificity, and sensitivity in the range of 85-100% in both training and external validation data series.

METHODS

In this work, we used Combinatorial Perturbation Theory and Machine Learning techniques to seek a CPTML model for MRNs >40 organisms compiled by Barabasis' group. First, we quantified the local structure of a very large set of nodes in each MRN using a new class of node index called Markov linear indices fk. Next, we calculated CPT operators for 150000 combinations of query and reference nodes of MRNs. Last, we used these CPT operators as inputs of different ML algorithms.

CONCLUSION

Meanwhile, PTML models based on Bayesian network, J48-Decision Tree and Random Forest algorithms were identified as the three best non-linear models with accuracy greater than 97.5%. The present work opens the door to the study of MRNs of multiple organisms using PTML models.

Which inorganic structures are the most complex?

The discovery of the diffraction of X-rays on crystals opened up a new era in our understanding of nature, leading to a multitude of striking discoveries about the structures and functions of matter on the atomic and molecular scales. Over the last hundred years, about 150,000 of inorganic crystal structures have been elucidated and visualized. The advent of new technologies, such as area detectors and synchrotron radiation, led to the solution of structures of unprecedented complexity. However, the very notion of structural complexity of crystals still lacks an unambiguous quantitative definition. In this Minireview we use information theory to characterize complexity of inorganic structures in terms of their information content.

Scoring function for DNA-drug docking of anticancer and antiparasitic compounds based on spectral moments of 2D lattice graphs for molecular dynamics trajectories

We introduce here a new class of invariants for MD trajectories based on the spectral moments pi(k)(L) of the Markov matrix associated to lattice network-like (LN) graph representations of Molecular Dynamics (MD) trajectories. The procedure embeds the MD energy profiles on a 2D Cartesian coordinates system using simple heuristic rules. At the same time, we associate the LN with a Markov matrix that describes the probabilities of passing from one state to other in the new 2D space. We construct this type of LNs for 422 MD trajectories obtained in DNA-drug docking experiments of 57 furocoumarins. The combined use of psoralens+ultraviolet light (UVA) radiation is known as PUVA therapy. PUVA is effective in the treatment of skin diseases such as psoriasis and mycosis fungoides. PUVA is also useful to treat human platelet (PTL) concentrates in order to eliminate Leishmania spp. and Trypanosoma cruzi. Both are parasites that cause Leishmaniosis (a dangerous skin and visceral disease) and Chagas disease, respectively; and may circulate in blood products collected from infected donors. We included in this study both lineal (psoralens) and angular (angelicins) furocoumarins. In the study, we grouped the LNs on two sets; set1: DNA-drug complex MD trajectories for active compounds and set2: MD trajectories of non-active compounds or no-optimal MD trajectories of active compounds. We calculated the respective pi(k)(L) values for all these LNs and used them as inputs to train a new classifier that discriminate set1 from set2 cases. In training series the model correctly classifies 79 out of 80 (specificity=98.75%) set1 and 226 out of 238 (Sensitivity=94.96%) set2 trajectories. In independent validation series the model correctly classifies 26 out of 26 (specificity=100%) set1 and 75 out of 78 (sensitivity=96.15%) set2 trajectories. We propose this new model as a scoring function to guide DNA-docking studies in the drug design of new coumarins for anticancer or antiparasitic PUVA therapy.

Alignment-free prediction of a drug-target complex network based on parameters of drug connectivity and protein sequence of receptors

There are many drugs described with very different affinity to a large number of receptors. In this work, we selected drug-receptor pairs (DRPs) of affinity/nonaffinity drugs to similar/dissimilar receptors and we represented them as a large network, which may be used to identify drugs that can act on a receptor. Computational chemistry prediction of the biological activity based on quantitative structure-activity relationships (QSAR) substantially increases the potentialities of this kind of networks avoiding time- and resource-consuming experiments. Unfortunately, most QSAR models are unspecific or predict activity against only one receptor. To solve this problem, we developed here a multitarget QSAR (mt-QSAR) classification model. Overall model classification accuracy was 72.25% (1390/1924 compounds) in training, 72.28% (459/635) in cross-validation. Outputs of this mt-QSAR model were used as inputs to construct a network. The observed network has 1735 nodes (DRPs), 1754 edges or pairs of DRPs with similar drug-target affinity (sPDRPs), and low coverage density d = 0.12%. The predicted network has 1735 DRPs, 1857 sPDRPs, and also low coverage density d = 0.12%. After an edge-to-edge comparison (chi-square = 9420.3; p < 0.005), we have demonstrated that the predicted network is significantly similar to the one observed and both have a distribution closer to exponential than to normal.

Study of peptide fingerprints of parasite proteins and drug-DNA interactions with Markov-Mean-Energy invariants of biopolymer molecular-dynamic lattice networks

Since the advent of Molecular Dynamics (MD) in biopolymers science with the study by Karplus et al. on protein dynamics, MD has become the by foremost well established, computational technique to investigate structure and function of biomolecules and their respective complexes and interactions. The analysis of the MD trajectories (MDTs) remains, however, the greatest challenge and requires a great deal of insight, experience, and effort. Here, we introduce a new class of invariants for MDTs based on the spatial distribution of Mean-Energy values ξk (L) on a 2D Euclidean space representation of the MDTs. The procedure forces one MD trajectory to fold into a 2D Cartesian coordinates system using a step-by-step procedure driven by simple rules. The ξk (L) values are invariants of a Markov matrix (1 Π), which describes the probabilities of transition between two states in the new 2D space; which is associated to a graph representation of MDTs similar to the lattice networks (LNs) of DNA and protein sequences. We also introduce a new algorithm to perform phylogenetic analysis of peptides based on MDTs instead of the sequence of the polypeptide. In a first experiment, we illustrate this algorithm for 35 peptides present on the Peptide Mass Fingerprint (PMF) of a new protein of Leishmania infantum studied in this work. We report, by the first time, 2D Electrophoresis isolation, MALDI TOF Mass Spectroscopy characterization, and MASCOT search results for this PMF. In a second experiment, we construct the LNs for 422 MDTs obtained in DNA-Drug Docking simulations of the interaction of 57 anticancer furocoumarins with a DNA oligonucleotide. We calculated the respective ξk (L) values for all these LNs and used them as inputs to train a new classifier with Accuracy = 85.44% and 84.91% in training and validation respectively. The new model can be used as scoring function to guide DNA-Drug Docking studies in drug design of new coumarins for PUVA therapy. The new phylogenetics analysis algorithms encode information different from sequence similarity and may be used to analyze MDTs obtained in Docking or modeling experiments for any classes of biopolymers. The work opens new perspective on the analysis and applications of MD in polymer sciences.

From Molecular to Biological Structure and Back

A comparative analysis of the topological structure of molecules and molecular biology networks revealed both similarity and differences in the methods used, as well as in the essential features of the two types of systems. Molecular graphs are static and, due to the limitations in atomic valence, show neither power distribution of vertex degrees nor "small-world" properties, which are typical for dynamic evolutionary networks. Areas of mutual benefits from an exchange of methods and ideas are outlined for the two fields. More specifically, chemical graph theory might make use of some new descriptors of network structure. Of interest for quantitative structure-property relationship/quantitative structure-activity relationship and drug design might be the conclusion that descriptors based on distributions of vertex degrees, distances, and subgraphs seem to be more relevant to biological information than the single-number descriptors. The network concepts of centrality, clustering, and cliques provide a basis for similar studies in theoretical chemistry. The need of dynamic theory of molecular topology is advocated.