Inference of gene networks from gene expression time series using recurrent neural networks and sparse MAP estimation

BACKGROUND The inference of genetic regulatory networks (GRNs) provides insight into the cellular responses to signals. A class of recurrent neural networks (RNNs) capturing the dynamics of GRN has been used as a basis for inferring small-scale GRNs from gene expression time series. The Bayesian framework facilitates incorporating the hypothesis of GRN into the model estimation to improve the accuracy of GRN inference. RESULTS We present new methods for inferring small-scale GRNs based on RNNs. The weights of wires of RNN represent the strengths of gene-to-gene regulatory interactions. We use a class of automatic relevance determination (ARD) priors to enforce the sparsity in the maximum a posteriori (MAP) estimates of wire weights of RNN. A particle swarm optimization (PSO) is integrated as an optimization engine into the MAP estimation process. Likely networks of genes generated based on estimated wire weights are combined using the majority rule to determine a final estimated GRN. As an alternative, a class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -norm ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> ) priors is used for attaining the sparse MAP estimates of wire weights of RNN. We also infer the GRN using the maximum likelihood (ML) estimates of wire weights of RNN. The RNN-based GRN inference algorithms, ARD-RNN, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN, and ML-RNN are tested on simulated and experimental E. coli and yeast time series containing 6-11 genes and 7-19 data points. Published GRN inference algorithms based on regressions and mutual information networks are performed on the benchmark datasets to compare performances. CONCLUSION ARD and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -norm priors are used for the estimation of wire weights of RNN. Results of GRN inference experiments show that ARD-RNN, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN have similar best accuracies on the simulated time series. The ARD-RNN is more accurate than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> -RNN, ML-RNN, and mostly more accurate than the reference algorithms on the experimental time series. The effectiveness of ARD-RNN for inferring small-scale GRNs using gene expression time series of limited length is empirically verified.

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