Evolutionary approaches for the reverse-engineering of gene regulatory networks: a study on a biologically realistic dataset

Abstract

Background: Inferring gene regulatory networks from data requires the development of algorithms devoted to structure extraction. When only static data are available, gene interactions may be modelled by a Bayesian Network (BN) that represents the presence of direct interactions from regulators to regulees by conditional probability distributions. We used enhanced evolutionary algorithms to stochastically evolve a set of candidate BN structures and found the model that best fits data without prior knowledge.

Results: We proposed various evolutionary strategies suitable for the task and tested our choices using simulated data drawn from a given bio-realistic network of 35 nodes, the so-called insulin network, which has been used in the literature for benchmarking. We assessed the inferred models against this reference to obtain statistical performance results. We then compared performances of evolutionary algorithms using two kinds of recombination operators that operate at different scales in the graphs. We introduced a niching strategy that reinforces diversity through the population and avoided trapping of the algorithm in one local minimum in the early steps of learning. We show the limited effect of the mutation operator when niching is applied. Finally, we compared our best evolutionary approach with various well known learning algorithms (MCMC, K2, greedy search, TPDA, MMHC) devoted to BN structure learning.

Conclusion: We studied the behaviour of an evolutionary approach enhanced by niching for the learning of gene regulatory networks with BN. We show that this approach outperforms classical structure learning methods in elucidating the original model. These results were obtained for the learning of a bio-realistic network and, more importantly, on various small datasets. This is a suitable approach for learning transcriptional regulatory networks from real datasets without prior knowledge.

Figure 1

Evolution of the EA for a genetic algorithm with link-recombination. These figures show the evolution of the population distribution during the learning process using link-recombination with niching (A1-A4) and without niching (B1-B4). The populations were recorded every 2000 generations and after the algorithm's convergence. Each plot represents the graphs of two populations sampled consecutively. The graphs of both populations are represented as points on a 2D map using Kernel Principal Composant Analysis.

Figure 2

Evolution of the EA for a genetic algorithm with parental-recombination. These figures show the evolution of the distribution of the population during the learning process using parental-recombination with niching (A1-A4) and without niching (B1-B4). The populations were recorded every 2000 generations and after the algorithm's convergence. Each plot represents the graphs of two populations sampled consecutively. The graphs of both populations are represented as points on a 2D map using Kernel Principal Composant Analysis.

Figure 3

Comparison of the learning curves of parental-recombination and link-recombination. For each learning algorithm, the results of the comparison of the graph learnt for various sample sizes and the reference graph are expressed in terms of positive predictive value (A1 and A2) and sensitivity (B1 and B2). Figures A1 and B1 show the results obtained without niching, while Figures A2 and B2 show the results obtained with niching. The color coding is blue for parental-recombination and red for link-recombination. For each sample size, tests are performed on 10 different and independent datasets. The same datasets are used for every EA. Each point along the curves, which correspond to a given sample size, represents the mean value and the standard deviation of the quality measurement across the 10 runs of the algorithms.

Figure 4

Comparison of the learning curves of six different structure learning algorithms. For each learning algorithm, the results of the comparison of the graph learnt for various sample sizes and the reference graph are expressed in terms of positive predictive value (A) and sensitivity (B). The color coding is green for Greedy search, blue for MCMC, black for K2, dashed black for MMHC, magenta for TPDA, and red for EA. For each sample size, tests are performed on 10 different and independent datasets. The same datasets are used for every algorithm. Each point along the curves, which correspond to a given sample size, presents the mean value and the standard deviation of the quality measurement across the 10 runs of the algorithm.