Fig 1.
The workflow for inference of the IR- injury mediated regulatory loops.
Step I: IR-related miRNAs, TFs, and mRNAs were collected from the experimental mRNA- and miRNA-arrays produced in our laboratory. These represent the altered expression values of the three elements detected at five different time points during ischemia-reperfusion injury. TF-mRNA pairs, miRNA-mRNA pairs, and miRNA-TF pairs were constructed with the aid of external databases and/or software. Step II: The paired constructs were used to build three closed loop-motifs interconnected by three edges. Step III: The closed loops were subjected to mediation analysis resulting in three classes of mediated loops. Step IV: Mediated loops were subjected to motif detection analysis to identify significant regulatory motifs.
Fig 2.
The Pseudo code for inference of closed regulatory loops.
Three tables are given as inputs for the algorithm, a transcription factors table TF, a microRNA table miRNAs, and a mRNA table mRNA. If a gene in the mRNA table is a common target by an miRNA and a TF in the miRNA and the TF table respectively, and synchronously the TF is a target for the miRNA, then the triple of miRNA, TF, mRNA is marked as a potential loop and inserted in the Loops_Database repository. Otherwise another gene in the mRNA table should be considered. Previous steps continue until consuming all genes in mRNA table.
Fig 3.
The single variable mediator model.
A simple mediation model composed of two variables, X and Y, where Y is dependent on X. The upper diagram illustrates the effect c from X to variable Y in the absence of any additional variables. The lower diagram illustrates how c is split into a, b when a mediator variable is introduced between X, and Y. In this case, effect a is along the X-M path, and effect b is along M-Y path. The split effect will in turn change c into an updated effect cʹ along the X-Y path.
Fig 4.
The model-based approach of the causal mediation analysis.
At the beginning, two regression models were constructed and fitted separately: model.m and model.y, where model.m modeled the influence dictated by miRNA on TF and model.y modeld the influence dictated by both miRNA and TF on mRNA. The two models were then processed by the causal mediation function. A sensitivity analysis was followed to measure the significance of the model and to plot its summary results.
Fig 5.
Classification of the closed regulatory loops by mediation analysis.
Closed regulatory loops are classified into three main classes: A) The mediated loops by TFs, where all influence on mRNA originates from miRNA delegating its entire influence to the TFs and is represented by MT in the study; B) The mediated loops by miRNAs, where all influence on mRNA originates directly from miRNAs and is represented by MM in the study; C) The mediated loops by TFs and miRNAs together, where all influence on mRNA originates from both miRNAs and TFs and is represented by MTM in the study.
Table 1.
Number of mediated loops per time point per loop class.
Table 2.
Classification of mediated loops by TFs per time point.
Table 3.
Classification of mediated loops by miRNAs per time point.
Table 4.
Classification of mediated loops by both miRNAs and TFs MTM based on signs of ACME and ADME per time point.
Table 5.
Classification of mediated loops by both miRNAs and TFs based on target gene regulation per time point.
Table 6.
Classification of mediated loops by both miRNAs and TFs based on agreement of ACME, ADE, with target gene regulation per time point.
Table 7.
The highest and lowest ACME and ADE per time point per loop class.
Fig 6.
ACME and ADE graphical plots for some exemplary regulatory loops at 24h IR.
A dashboard showing graphical plots associated with two types of loops at 24h of IR, partial mediation and complete mediation loop respectively. Each row displays three plots. The left plot shows the average causal mediation effect ACME, average direct effect ADE, and total effect for the particular type of loop on right margin of the plots. The dashed horizontal line represents the estimated mediation effect under the sequential ignorability assumption. The middle and right plots are the sensitivity analysis plots as a function of the standard deviation of the ACME ρ and the mean square error R2 respectively. is the square of the correlation between independent variables(M→X), while
is the square of the correlation between dependent and independent variables(Y→X,M).
Fig 7.
Significant four-node motifs detected by FANMOD exact enumeration algorithm per time point.
Four-node significant motifs detected by FANMOD for each class of loops at 24h, and 7d IR. Significance of motifs is determined based on z score ≥ 2 and P-value ≤ 0.05. Unique motifs are surrounded with a red frame in each class.
Table 8.
Significant network motifs per time point per loop class.
Fig 8.
Construction of six-node significant motifs from-four node significant motifs.
Two four-node significant motifs at 24h, 7d -IR are assembled to form six-node significant motifs (far right) similar to the six-node significant motifs discovered by FANMOD sampling algorithm. All motifs have z score ≥ 2 and P-value ≤ 0.05.
Fig 9.
Six-node motifs per time point.
Possible six-node motifs arrangements obtained from mapping combined four-node significant motifs at 24h, 7d of IR-injury to the six-node significant motifs in Fig 8. All motifs have z score ≥ 2 and P-value ≤ 0.05.
Table 9.
ACME and ADE values for the loops: Rno-miR-207->Rnf138->Creld2 and Rnf138->Rno-miR-207->Creld2.