Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

Intrinsically Multivariate Predictive Genes

Canalizing genes possess such broad regulatory power, and their action sweeps across a such a wide swath of processes that the full set of affected genes are not highly correlated under normal conditions. When not active, the controlling gene will not be predictable to any significant degree by its subject genes, either alone or in groups, since their behavior will be highly varied relative to the inactive controlling gene. When the controlling gene is active, its behavior is not well predicted by any one of its targets, but can be very well predicted by groups of genes under its control. To investigate this question, we introduce in this paper the concept of intrinsically multivariate predictive (IMP) genes, and present a mathematical study of IMP in the context of binary genes with respect to the coefficient of determination (CoD), which measures the predictive power of a set of genes with respect to a target gene. A set of predictor genes is said to be IMP for a target gene if all properly contained subsets of the predictor set are bad predictors of the target but the full predictor set predicts the target with great accuracy. We show that logic of prediction, predictive power, covariance between predictors, and the entropy of the joint probability distribution of the predictors jointly affect the appearance of IMP genes. In particular, we show that high-predictive power, small covariance among predictors, a large entropy of the joint probability distribution of predictors, and certain logics, such as XOR in the 2-predictor case, are factors that favor the appearance of IMP. The IMP concept is applied to characterize the behavior of the gene DUSP1, which exhibits control over a central, process-integrating signaling pathway, thereby providing preliminary evidence that IMP can be used as a criterion for discovery of canalizing genes.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

A neural networks study of quinone compounds with trypanocidal activity

This work investigates neural network models for predicting the trypanocidal activity of 28 quinone compounds. Artificial neural networks (ANN), such as multilayer perceptrons (MLP) and Kohonen models, were employed with the aim of modeling the nonlinear relationship between quantum and molecular descriptors and trypanocidal activity. The calculated descriptors and the principal components were used as input to train neural network models to verify the behavior of the nets. The best model for both network models (MLP and Kohonen) was obtained with four descriptors as input. The descriptors were T(5) (torsion angle), QTS1 (sum of absolute values of the atomic charges), VOLS2 (volume of the substituent at region B) and HOMO-1 (energy of the molecular orbital below HOMO). These descriptors provide information on the kind of interaction that occurs between the compounds and the biological receptor. Both neural network models used here can predict the trypanocidal activity of the quinone compounds with good agreement, with low errors in the testing set and a high correctness rate. Thanks to the nonlinear model obtained from the neural network models, we can conclude that electronic and structural properties are important factors in the interaction between quinone compounds that exhibit trypanocidal activity and their biological receptors. The final ANN models should be useful in the design of novel trypanocidal quinones having improved potency.