A Monte Carlo Approach to Measure the Robustness of Boolean Networks

Emergence of robustness in biological networks is a paramount feature of evolving organisms, but a study of this property in vivo, for any level of representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard challenge. In the case of Genetic Networks, mathematical models have been used in this context to provide insights on their robustness, but even in relatively simple formulations, such as Boolean Networks (BN), it might not be feasible to compute some measures for large system sizes. We describe in this work a Monte Carlo approach to calculate the size of the largest basin of attraction of a BN, which is intrinsically associated with its robustness, that can be used regardless the network size. We show the stability of our method through finite-size analysis and validate it with a full search on small networks.Comment: on 1st International Workshop on Robustness and Stability of Biological Systems and Computational Solutions (WRSBS

Efficient component-hypertree construction based on hierarchy of partitions

The component-hypertree is a data structure that generalizes the concept of component-tree to multiple (increasing) neighborhoods. However, construction of a component-hypertree is costly because it needs to process a high number of neighbors. In this article, we review some choices of neighborhoods for efficient component-hypertree computation. We also explore a new strategy to obtain neighboring elements based on hierarchy of partitions, leading to a more efficient algorithm with the counterpart of a slight decrease of precision on the distance of merged nodes

Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes

Interactive image manipulation using morphological trees and spline-based skeletons

The ability to edit an image using intuitive commands and primitives is a desired feature for any image editing software. In this paper, we combine recent results in medial axes with the well-established morphological tree representations to develop an interactive image editing tool that provides global and local image manipulation using high-level primitives. We propose a new way to render interactive morphological trees using icicle plots and introduce different ways of manipulating spline-based medial axis transforms for grayscale and colored image editing. Different applications of the tool, such as watermark removal, image deformation, dataset augmentation for machine learning, artistic illumination manipulation, image rearrangement, and clothing design, are described and showcased on examples

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Abstract\ud \ud \ud \ud Background\ud \ud A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it.\ud \ud \ud \ud Results\ud \ud We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered.\ud \ud \ud \ud Conclusions\ud \ud The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.This work was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).This work was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).This article has been published as part of BMC Proceedings Volume 5 Supplement 2, 2011: Proceedings of the 6th International Symposium on Bioinformatics Research and Applications (ISBRA10). The full contents of the supplement are available online at http://www.biomedcentral.com/17536561/5?issue=S2.This article has been published as part of BMC Proceedings Volume 5 Supplement 2, 2011: Proceedings of the 6th International Symposium on Bioinformatics Research and Applications (ISBRA'10). The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/5?issue=S2

Assessing the gain of biological data integration in gene networks inference

Background: A current challenge in gene annotation is to define the gene function in the context of the network of relationships instead of using single genes. The inference of gene networks (GNs) has emerged as an approach to better understand the biology of the system and to study how several components of this network interact with each other and keep their functions stable. However, in general there is no sufficient data to accurately recover the GNs from their expression levels leading to the curse of dimensionality, in which the number of variables is higher than samples. One way to mitigate this problem is to integrate biological data instead of using only the expression profiles in the inference process. Nowadays, the use of several biological information in inference methods had a significant increase in order to better recover the connections between genes and reduce the false positives. What makes this strategy so interesting is the possibility of confirming the known connections through the included biological data, and the possibility of discovering new relationships between genes when observed the expression data. Although several works in data integration have increased the performance of the network inference methods, the real contribution of adding each type of biological information in the obtained improvement is not clear. Methods: We propose a methodology to include biological information into an inference algorithm in order to assess its prediction gain by using biological information and expression profile together. We also evaluated and compared the gain of adding four types of biological information: (a) protein-protein interaction, (b) Rosetta stone fusion proteins, (c) KEGG and (d) KEGG+GO. Results and conclusions: This work presents a first comparison of the gain in the use of prior biological information in the inference of GNs by considering the eukaryote (P. falciparum) organism. Our results indicates that information based on direct interaction can produce a higher improvement in the gain than data about a less specific relationship as GO or KEGG. Also, as expected, the results show that the use of biological information is a very important approach for the improvement of the inference. We also compared the gain in the inference of the global network and only the hubs. The results indicates that the use of biological information can improve the identification of the most connected proteins

Dynamical Analysis of a Boolean Network Model of the Oncogene Role of lncRNA ANRIL and lncRNA UFC1 in Non-Small Cell Lung Cancer

Long non-coding RNA (lncRNA) such as ANRIL and UFC1 have been verified as oncogenic genes in non-small cell lung cancer (NSCLC). It is well known that the tumor suppressor microRNA-34a (miR-34a) is downregulated in NSCLC. Furthermore, miR-34a induces senescence and apoptosis in breast, glioma, cervical cancer including NSCLC by targeting Myc. Recent evidence suggests that these two lncRNAs act as a miR-34a sponge in corresponding cancers. However, the biological functions between these two non-coding RNAs (ncRNAs) have not yet been studied in NSCLC. Therefore, we present a Boolean model to analyze the gene regulation between these two ncRNAs in NSCLC. We compared our model to several experimental studies involving gain- or loss-of-function genes in NSCLC cells and achieved an excellent agreement. Additionally, we predict three positive circuits involving miR-34a/E2F1/ANRIL, miR-34a/E2F1/UFC1, and miR-34a/Myc/ANRIL. Our circuit- perturbation analysis shows that these circuits are important for regulating cell-fate decisions such as senescence and apoptosis. Thus, our Boolean network permits an explicit cell-fate mechanism associated with NSCLC. Therefore, our results support that ANRIL and/or UFC1 is an attractive target for drug development in tumor growth and aggressive proliferation of NSCLC, and that a valuable outcome can be achieved through the miRNA-34a/Myc pathway

Finding Optimal Sequential Decompositions Of Erosions And Dilations

. A fundamental problem in the eld of automatic design of morphological operators is the transformation of standard morphological representations, that are adequate for operator learning, into other equivalent representations, that permit eÆcient implementations of the operators learned. In this paper, we study this problem restricted to the families of set translation invariant erosions and dilations. We present a general method for the decomposition of erosions (respec., dilations) by arbitrarily shaped structuring elements into a minimum number of compositions of erosions (respec. dilations) by subsets of the elementary square (i.e.,the 3 3 square centered at the origin). The fundamental idea of the method proposed is the application of Combinatorial Optimization techniques, supported by generic algebraic and geometrical properties of erosions and dilations. Key words: erosion, dilation, Minkowski addition, decomposition, structuring element. 1. Introduction The problem of desi..

The lncRNA DLX6-AS1/miR-16-5p axis regulates autophagy and apoptosis in non-small cell lung cancer: A Boolean model of cell death

Long non-coding RNA (lncRNA) distal-less homeobox 6 antisense RNA 1 (DLX6-AS1) is elevated in a variety of cancers, including non-small cell lung cancer (NSCLC) and cervical cancer. Although it was found that the microRNA-16-5p (miR-16), which is known to regulate autophagy and apoptosis, had been downregulated in similar cancers. Recent research has shown that in tumors with similar characteristics, DLX6-AS1 acts as a sponge for miR-16 expression. However, the cell death-related molecular mechanism of the DLX6-AS1/miR-16 axis has yet to be investigated. Therefore, we propose a dynamic Boolean model to investigate gene regulation in cell death processes via the DLX6-AS1/miR-16 axis. We found the finest concordance when we compared our model to many experimental investigations including gain-of-function genes in NSCLC and cervical cancer. A unique positive circuit involving BMI1/ATM/miR-16 is also something we predict. Our results suggest that this circuit is essential for regulating autophagy and apoptosis under stress signals. Thus, our Boolean network enables an evident cell-death process coupled with NSCLC and cervical cancer. Therefore, our results suggest that DLX6-AS1 targeting may boost miR-16 activity and thereby restrict tumor growth in these cancers by triggering autophagy and apoptosis