RLowPC – evaluation and improvement of the regulatory inference for large co-expression networks with limited sample size

Co-expression has been widely used to identify novel regulatory relationships using high throughput measurements, such as microarray and RNA-seq data. Evaluation studies on co-expression network analysis methods mostly focus on networks of small or medium size of up to a few hundred nodes. For large networks, simulated expression data usually consist of hundreds or thousands of profiles with different perturbations or knock-outs, which is uncommon in real experiments due to their cost and the amount of work required. Thus, the performances of co-expression network analysis methods on large co-expression networks consisting of a few thousand nodes, with only a small number of profiles with a single perturbation, which more accurately reflect normal experimental conditions, are generally uncharacterized and unknown.

Researchers at the James Hutton Institute proposed a novel network inference methods based on Relevance Low order Partial Correlation (RLowPC). RLowPC method uses a two-step approach to select on the high-confidence edges first by reducing the search space by only picking the top ranked genes from an intial partial correlation analysis and, then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association.

 Indirect edge and RLowPC network

a An indirect association from X ₁ → X ₂ could arise from a regulatory structure of X ₁ → X ₃ → X ₂. b RLowPC network inference. In an RLowPC network, firstly only the top ranked edges are kept in a pre-inferred PC network and then for each pair of genes, only the immediate neighbours will be regressed for PC calculation. In this example only the top 6 of 10 edges with highest correlations are kept and PC between X ₁ and X ₂ is re-calculated by removing the effects from two immediate neighbouring nodes (X ₃, X ₅). The correlation values are represented by the thickness of the edges

The researchers selected six co-expression-based methods with good performance in evaluation studies from the literature: Partial correlation, PCIT, ARACNE, MRNET, MRNETB and CLR. The evaluation of these methods was carried out on simulated time-series data with various network sizes ranging from 100 to 3000 nodes. Simulation results show low precision and recall for all of the above methods for large networks with a small number of expression profiles. They improved the inference significantly by refinement of the top weighted edges in the pre-inferred partial correlation networks using RLowPC. They found improved performance by partitioning large networks into smaller co-expressed modules when assessing the method performance within these modules.

The evaluation results show that current methods suffer from low precision and recall for large co-expression networks where only a small number of profiles are available. The proposed RLowPC method effectively reduces the indirect edges predicted as regulatory relationships and increases the precision of top ranked predictions. Partitioning large networks into smaller highly co-expressed modules also helps to improve the performance of network inference methods.

Availability – The RLowPC R package for network construction, refinement and evaluation is available at GitHub: https://github.com/wyguo/RLowPC .