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

Abstract

BackgroundA 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.ResultsWe 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.ConclusionsThe 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.

Network Weight Estimation for Binary-Valued Observation Models

“…In [30], an estimation procedure for BNps from temporal data sequence was proposed based on a transition counting matrix and the optimal selection of input nodes. The authors studied the estimation problem of restricted BNs in [20], [36], but did not present a rigorous performance analysis. Additionally, [3], [32] investigated the inferring of Boolean threshold functions for probabilistic BNs, but data samples were assumed to be independent instead of taken from a time series.…”

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“…A more generalized and substantial approach to solving the problem is found in [12][13][14], the authors of which used the limited Boolean networks. In this case the regulatory relations are presented by the matrix A nń , where a ij = 1 at positive regulation of gene x i by gene x j ; a ij = -1 at negative regulation of gene x i by gene x j and a ij = 0 in other cases.…”

“…The known algorithms are backtracking, constraint propagation, and local search [12]. The processes of selecting variables and assigning some values to these variables depend on the order of selection, therefore, there are many heuristic methods to solve CSP [15] which has evident effect on the reconstruction accuracy.…”

Interações gênicas usando redes booleanas limiarizadas modeladas como um problema de satisfação de restrições

“…Construímos assim, partir do CSP e usando Programação de Restrições, um solver, que foi usado para encontrar redes consistentes com a série temporal usada como entrada. Este solver foi usado para inferir redes consistentes com séries temporais de entrada, e com isso publicamos o trabalho Higa et al (2011). O solver criado durante esse trabalho foi usado como base para outras ferramentas propostas por .…”

“…Usando então o arcabouço do CSP, durante a execução desse trabalho, criamos uma extensão deste algoritmo, convertendo cada um dos três passos em um conjunto de restrições. Tal extensão foi então usada no artigo Higa et al (2011). A seguir, descrevemos cada conjunto de restrição, que juntos representam parcialmente as relações entre os genes.…”